United States Office of EPA 520/4-79-007D
Environmental Piotection Radiation Programs March 1980
Agency Washington DC 20460
Radiation
v>EPA Technical Support of
Standards for High-Level
Radioactive Waste
Management
t.
Volume D
Release Mechanisms
-------
TECHNICAL SUPPORT OF STANDARDS FOR
HIGH-LEVEL RADIOACTIVE WASTE MANAGEMENT
TASK D REPORT
ASSESSMENT OF RELEASE MECHANISMS
EPA Contract No. 68-01-4470
Prepared by
Arthur D. Little, Inc.
Cambridge, Massachusetts 02140
March 1980
-------
DISCLAIMER
This report was prepared as an account of work sponsored by the
Environmental Protection Agency of the United States Government
under Contract No. 68-01-4470. Neither the United States nor the
United States Environmental Protection Agency makes any warranty,
express or implied, or assumes any legal liability or responsibility
for the accuracy, completeness, or usefulness of any information,
apparatus, product, or process disclosed, or represents that its use
would not infringe privately owned rights.
ii
-------
ACKNOWLEDGMENTS
Many individuals contributed to the work done under the direction
of Arthur D. Little, Inc., for the U.S. Environmental Protection Agency
under Contract No. 68-01-4470. John L. Russell and Daniel Egan of the
Office of Radiation Programs at EPA served as constant guides in the
process of our work. Dr. Bruce S. Old, James I. Stevens, and David I.
Hellstrom of Arthur D. Little, Inc., were Program Director, Program
Manager, and Assistant Program Manager, respectively, of the overall
project. Key individuals involved in each of the reports prepared
under the four tasks were:
TASK A
Donald Korn
Arthur D. Little,
Task Director
Inc.
TASK B
Robert McWhorter,
Michael Raudenbush,
and Lester Goldstein
S.M. Stoller Corp.
_Edwin/ L. Field
Arthur D. Little,Inc.
Task Director
TASK C
Robert McWhorter and
Michael Raudenbush
S.M. Stoller Corp.
_Dr. P.J. O'Brien
Arthur D. Little,Inc.
Task Director
TASK D
Dr. Ronald B. Lantz
Intera Environmental
Consultants, Inc.
Dr. John Gormley
D'Appolonia Consulting
Engineers, Inc.
_Dr. Charles R. Hadlock
Arthur D. Little,Inc.
Task Director
Peter D. Mattison and
Dr. Ajit Bhattacharyya
Arthur D. Little, Inc.
iii
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FOREWORD
A major Federal effort is underway to develop methods for disposal
of high-level radioactive waste in deep geologic repositories. An impor-
tant element of this program is the development and promulgation by the
U.S. Environmental Protection Agency (EPA) of environmental standards
for the management of these wastes.
In anticipation of its efforts to develop these standards, EPA
recognized that it would be necessary to estimate the expected and
potential environmental impacts from potential geologic repositories
using modeling techniques based upon as thorough an understanding as
possible of the uncertainties involved in the quantities and charac-
teristics of the wastes to be managed, the effectiveness of engineering
controls, and the potential migration and accidental pathways that might
result in radioactive materials entering the biosphere. Consequently,
in March 1977, the EPA contracted with Arthur D. Little, Inc., for a study
to provide technical support for its development of environmental regula-
tions for high-level radioactive wastes. This study was divided into
the following four tasks:
Task A - Source Term Characterization/Definition
Task B - Effectiveness of Engineering Controls
Task C - Assessment of Migration Pathways
Task D - Assessment of Release Mechanisms
There are many national and international programs underway to
develop additional data, especially in the fields of waste forms, know-
ledge of geology and geohydrology, and risk assessment. The information
presented in these reports has been developed on conceptual bases and is
not intended to be specific to particular conditions at geologic reposi-
tories.
iv
-------
TABLE OF CONTENTS
Page
Acknowledgements iii
Foreword iv
List of Tables ix
List of Figures xvi
D-1.0 INTRODUCTION AND SUMMARY 1
1.1 BACKGROUND 1
1.2 OBJECTIVES AND SCOPE 1
1.3 SUMMARY OF RESULTS 2
1.4 GUIDE TO THIS REPORT 2
D-2.0 GUIDELINES AND METHOD OF APPROACH 21
2.1 GENERAL APPROACH 21
2.2 SPECIFIC GUIDELINES 23
2.3 SELECTION AND CHARACTERIZATION OF GENERIC GEOLOGIES 25
2.3.1 Bedded Salt 26
2.3.2 Granite 27
2.3.3 Basalt 30
2.3.4 Shale 34
2.3.5 Dome Salt 37
2.4 REPOSITORY ASSUMPTIONS 37
2.5 IDENTIFICATION OF FAILURE MECHANISMS 40
2.6 CONCEPTUAL FRAMEWORK FOR QUANTITATIVE ANALYSIS 40
2.6.1 Probabilities 42
2.6.2 Consequences 42
2.6.3 Uncertainty and Variability 44
D-3.0 TECHNOLOGICAL FAILURE ELEMENTS 47
3.1 FLOW THROUGH BULK ROCK 47
3.1.1 Summary 47
3.1.2 Background 49
3.1.3 Flow Through Bulk Rock Failure Model 51
3.1.4 Flow Through Bulk Rock Release Model 55
3.1.5 Literature Discussion 68
-------
TABLE OF CONTENTS (cont.)
Page
3.2 SHAFT SEAL FAILURE 68
70
3.2.1 Summary 68
3.2.2 Background
3.2.3 Shaft Seal Failure Model 80
3.2.4 Shaft Seal Release Model 87
3.2.5 Literature Discussion H6
D-3.3 BOREHOLE SEAL FAILURE 116
3.3.1 Summary 116
3.3.2 Background US
3.3.3 Borehole Seal Failure Model 126
3.3.4 Borehole Seal Release Model 129
3.3.5 Literature Discussion 154
D-3.4 UNDETECTED BOREHOLES 158
3.4.1 Summary 158
3.4.2 Background 158
3.4.3 Undetected Borehole Failure Model 169
3.4.4 Undetected Borehole Release Model 178
3.4.5 Literature Discussion 191
D-3.5 OTHER TECHNOLOGICAL EVENTS AND PROCESSES 192
3.5.1 Introduction 192
3.5.2 Waste-Rock Interactions 193
3.5.3 Brine Migration 194
3.5.4 Canister Migration 196
3.5.5 Criticality 197
D-4.0 HUMAN INTRUSION 199
D-4.1 FUTURE DRILLING ACTIVITIES 199
4.1.1 Summary 199
4.1.2 Background 202
4.1.3 Future Drilling Failure Model 208
4.1.4 Future Drilling Release Model 216
vi
-------
TABLE OF CONTENTS (cont.)
Page
D-4.2 OTHER HUMAN INTRUSION EVENTS AND PROCESSES 224
4.2.1 Introduction 224
4.2.2 Solution Mining 224
4.2.3 Interference with Hydrologic Conditions 225
4.2.4 Waste Recovery 228
4.2.5 Sabotage 228
4.2.6 Acts of War 229
4.2.7 Innocent Extraordinary Penetration 229
D-5.0 NATURAL EVENT FAILURE ELEMENTS 231
5.1 FAULT MOVEMENT 231
5.1.1 Summary 231
5.1.2 Background 233
5.1.3 Fault Movement Failure Model 250
5.1.4 Fault Movement Release Model 259
5.1.5 Literature Discussion 270
D-5.2 VOLCANOES 277
5.2.1 Summary 277
5.2.2 Background 278
5.2.3 Volcano Failure Model 284
5.2.4 Volcano Release Model 287
5.2.5 Literature Discussion 288
D-5.3 IGNEOUS INTRUSIVES 289
5.3.1 Summary 289
5.3.2 Background 289
5.3.3 Igneous Intrusive Failure Model 293
5.3.4 Igneous Intrusive Release Model 294
5.3.5 Literature Discussion 294
D-5.4 METEORITE IMPACT 295
5.4.1 Summary 295
5.4.2 Background 295
5.4.3 Meteorite Impact Failure Model 302
5.4.4 Meteorite Impact Release Model 304
5.4.5 Literature Discussion 307
vii
-------
TABLE OF CONTENTS (cont.)
Page
D-5.5 BRECCIA PIPES 308
5.5.1 Summary 308
5.5.2 Background 308
5.5.3 Breccia Pipe Failure Model 315
5.5.4 Breccia Pipe Release Model 317
5.5.5 Literature Discussion 319
D-5.6 OTHER NATURAL EVENTS AND PROCESSES 319
5.6.1 Introduction 319
5.6.2 Erosion 322
5.6.3 Sedimentation 327
5.6.4 Tectonism 327
5.6.5 Uplift and Downwatping 331
5.6.6 Sea Level Fluctuations 332
5.6.7 Climate 334
5.6.8 Salt Diapirism 337
5.6.9 Salt Dissolution 338
LIST OF REFERENCES 341
APPENDICES
Appendix D-I Glossary 1-1
Appendix D-II Repository Resaturation Times II-l
Appendix D-III Methodology for Dissolution Calcula-
tions III-l
Appendix D-IV Methodology for Diffusion Calcula-
tions IV-1
Appendix D-V Methodology for U-Tube Calculations V-l
Appendix D-VI Effect of Thermally Induced Buoyancy
on Vertical Flow VI-1
Appendix D-VII Salt Creep VII-1
Appendix D-VIII Canister Capabilities for Long-Term
Isolation VIII-1
Appendix D-IX Thermal Stress Cracking in Salt IX-1
viii
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LIST OF TABLES
Table No. Page
D-l Summary of Flow Through Bulk Rock Failure Element 3
D-2 Summary of Shaft Seal Failure Element 4
D-3 Summary of Borehole Seal Failure Element 6
D-4 Summary of Undetected Borehole Failure Element 8
D-5 Summary of Future Drilling Failure Element 10
D-6 Summary of Fault Movement Failure Element 12
D-7 Summary of Volcano Failure Element 13
D-8 Summary of Igneous Intrusive Failure Element 15
D-9 Summary of Meteorite Impact Failure Element 16
D-10 Summary of Breccia Pipe Failure Element 18
D-ll Explanation of Symbols and Terms in Tables D-l
Through D-10 19
D-12 Nominal Repository Parameters Used for Model Calculations 39
D-l3 Failure Element Chosen for Detailed Modeling 41
D-14 Summary of Flow Through Bulk Rock Failure Element 48
D-15 Model Permeabilities for Hard Rock Before and After
Thermal Cycle 54
D-16 Effective Vertical Hydraulic Gradient in Surrounding
Geologic Media from Thermally Induced Convection
(Granite Repository) 56
D-17 Volumetric Flow Rates Through Bulk Rock (Granite
Repository) - 57
D-18 Fluid Velocities Through Bulk Rock (Granite Repository) 58
D-19 Fluid Transit Time from Repository to Aquifer through
Bulk Rock (Granite Repository) 59
D-20 Effective Vertical Hydraulic Gradient in Surrounding
Geologic Media from Thermally Induced Convection and
Aquifer Interconnection (Basalt Repository) 61
ix
-------
LIST OF TABLES (cont.)
Table No.
D-21 Volumetric Flow Rates through Bulk Rock (Basalt
Repository) 62
D-22 Fluid Velocities through Bulk Rock (Basalt Repository) 63
D-23 Fluid Transit Times through Bulk Rock (Basalt
Repository) 64
D-24 Volumetric Flow Rates through Bulk Rock (Shale Repository) 65
D-25 Fluid Velocities through Bulk Rock (Shale Repository) 66
D-26 Fluid Transit Times through Bulk Rock (Shale Repository) 67
D-27 Summary of Shaft Seal Failure Element 71
D-28 Seal Material Characteristics 77
D-29 Properties of Possible Seal Materials 86
D-30 Permeability as a Function of Time for Shaft Seal
Degradation Model 88
D-31 Repository Resaturation Times (Bedded Salt Repository) 90
D-32 Approximate Fluid Velocities and Transit Times to
Aquifer Along Permeable Shafts During Period A (Bedded
Salt Repository) 94
D-33 Effective Vertical Hydraulic Gradient in Permeable Shafts
from U-Tube Effect During Period B (Bedded Salt Reposi-
tory) 95
D-34 Volumetric Flow Rates through Permeable Shafts During
Period B (Bedded Salt Repository) 96
D-35 Fluid Velocities through Permeable Shafts During
Period B (Bedded Salt Repository) 97
D-36 Effective Vertical Hydraulic Gradient in Permeable Shafts
from Thermally Induced Convection and U-Tube Effect
(Granite Repository) 99
D-37 Volumetric Flow Rates through Permeable Shafts (Granite
Repository) 101
-------
LIST OF TABLES (cont.)
Table No. Page
D-38 Fluid Velocities through Permeable Shafts (Granite
Repository) 102
D-39 Effective Vertical Hydraulic Gradient in Permeable Shafts
From Thermally Induced Convection and U-Tube Effect (Basalt
Repository) 104
D-40 Volumetric Flow Rate Through Permeable Shafts (Basalt
Repository) 105
D-41 Fluid Velocities Through Permeable Shafts (Basalt
Repository) 106
D-42 Volumetric Flow Rates Through Permeable Shafts (Shale
Repository) 108
D-43 Fluid Velocities Through Permeable Shafts (Shale Repository) 109
D-44 Repository Resaturation Times (Dome Salt Repository) 111
D-45 Approximate Fluid Velocities and Transit Times to Aquifer
Along Permeable Shafts During Period A (Dome Salt Repository) 112
D-46 Effective Vertical Hydraulic Gradient in Permeable Shafts
From U-Tube Effect During Period B (Dome Salt Repository) 113
D-47 Volumetric Flow Rate in Permeable Shafts During Period B
(Dome Salt Repository) 114
D-48 Fluid Velocities Through Permeable Shafts During Period B
(Dome Salt Repository) 115
D-49 Baseline Parameter Used by TASC in Fouled Shaft Seal
Calculations 117
D-50 Summary of Borehole Seal Failure Element 119
D-51 Permeability as a Function of Time for a Borehole Seal
Degradation Model 128
D-52 Approximate Fluid Velocities and Transit Times to Aquifer
Along Permeable Boreholes During Period A (Bedded Salt
Repository) 134
-------
LIST OF TABLES (cont.)
Table No.
D-53 Effective Vertical Hydraulic Gradient in Permeable Bore-
holes From Thermally Induced Convection and Aquifer
Interconnection (Bedded Salt Repository)
D-54 Volumetric Flow Rates and Fluid Velocities in Deep Permeable
Boreholes During Period B as Calculated Without Considering
Dissolution Effects (Bedded Salt Repository)
D-55 Volumetric Flow Rates in Deep Permeable Boreholes During
Period B Including Effects of Dissolution on Flow Rates
(Bedded Salt Repository)
D-56 Effective Vertical Hydraulic Gradient in Permeable Bore-
holes from Thermally Induced Convection and the U-Tube
Effect (Granite Repository)
D-57 Volumetric Flow Rates Through Permeable Boreholes (Granite
Repository)
D-58 Fluid Velocities Through Permeable Boreholes (Granite
Repository)
D-59 Effective Vertical Hydraulic Gradient in Permeable Boreholes
From Thermally Induced Convection U-Tube Effect and Aquifer
Interconnection (Basalt Repository)
D-60 Effective Vertical Hydraulic Gradients in Permeable Bore-
holes Connecting the Repository and the Lower Aquifer
(Basalt Repository)
D-61 Volumetric Flow Rates Through Permeable Boreholes (Basalt
Repository)
D-62 Fluid Velocities Through Permeable Boreholes (Basalt
Repository)
D-63 Volumetric Flow Rates Through Permeable Boreholes (Shale
Repository)
D-64 Fluid Velocities Through Permeable Boreholes (Shale
Repository)
D-65 Approximate Fluid Velocities and Transit Times to Aquifer
Along Permeable Boreholes During Period A (Dome Salt
Repository)
135
136
137
139
141
142
143
146
147
148
150
151
153
xii
-------
LIST OF TABLES (cont.)
Table No.
D-66
D-67
D-68
D-69
D-70
D-71
D-72
D-73
D-74
D-75
D-76
D-77
D-78
D-79
D-80
D-81
D-82
Effective Vertical Hydraulic Gradient in Permeable Bore-
holes From U-Tube Effect During Period B (Dome Salt
Repository)
Volumetric Flow Rates Through Permeable Boreholes During
Period B (Dome Salt Repository)
Fluid Velocities Through Permeable Boreholes During
Period B (Dome Salt Repository)
Summary of Undetected Borehole Failure Element
Probabilities of Undetected Boreholes in Buffer Zone Around
Page
155
156
157
159
171
Selected Values of a and ot (Bedded Salt Repository)
Bedded Salt Repository (First Estimate)
Effective Resistances a, through a^ (Bedded Salt Repository) 180
181
Volumetric Flow Rates Through Undetected Boreholes (Granite
Repository) 18A
Fluid Velocities Through Undetected Boreholes (Granite
Repository) 185
Volumetric Flow Rates Through Undetected Boreholes (Basalt
Repository) 187
Fluid Velocities Through Undetected Boreholes (Basalt
Repository) 188
Volumetric Flow Rates Through Undetected Boreholes (Shale
Repository) 189
Fluid Velocities Through Undetected Boreholes (Shale
Repository) 190
Summary of Future Drilling Activities Failure Element 200
Areal Borehole Densities From Past Drilling Activities 203
Future Drilling Rate Estimates for Bedded Salt 210
Future Drilling Rate Estimates for Granite 211
xiii
-------
LIST OF TABLES (cont.)
Table No.
D-83
D-84
D-85
D-86
D-87
D-88
D-89
I>-90
D-91
D-92
D-93
D-94
D-95
D-96
D-97
D-98
D-99
D-101
D-102
D-103
Page
Future Drilling Rate Estimates for Basalt 212
Future Drilling Rate Estimates for Shale 213
Future Drilling Rate Estimates for Dome Salt 214
Volumetric Flow Rates Through a Single Sealed Borehole 223
Summary of Fault Movement Failure Element 232
Fault Densities for Selected Areas of the United States 254
Volumetric Flow Rates Through a Fault (Bedded Salt
Repository) 261
Fluid Velocities Through a Fault (Bedded Salt Repository) 263
Volumetric Flow Rates Through a Fault (Granite Repository) 266
Fluid Velocities Through a Fault (Granite Repository) 267
Volumetric Flow Rates Through a Fault (Basalt Repository) 268
Fluid Velocities Through a Fault (Basalt Repository) 269
Volumetric Flow Rates Through a Fault (Shale Repository) 271
Fluid Velocities Through a Fault (Shale Repository) 272
Effective Vertical Hydraulic Gradient in a Fault From
Thermally Induced Convection and Aquifer Interconnection
(Salt Dome Repository) 273
Volumetric Flow Rates Through a Fault (Dome Salt Repository) 274
Fluid Velocities Through a Fault (Dome Salt Repository) 275
Summary of Volcano Failure Element 279
Volcanic Phenomena with Surface Manifestation 282
Summary of Igneous Intrusive Failure Element 290
Summary of Meteorite Impact Failure Element 296
-------
LIST OF TABLES (cont.)
Table No. Page
D-104 Proven or Probable Large Meteorite Impact Craters in
the United States 300
D-105 Effective Hydraulic Gradient in Extended Vertical Pathways 305
D-106 Volumetric Flow Rates Through Meteorite Induced Permeable
Zone 306
D-107 Summary of Breccia Pipe Failure Element 309
D-108 Effective Vertical Hydraulic Gradient in a Breccia Pipe
from Thermal Buoyancy and Aquifer Interconnection (Bedded
Salt Repository) 318
D-109 Volumetric Flow Rate Through a Breccia Pipe (Bedded Salt
Repository) 320
D-110 Fluid Velocities Through a Breccia Pipe (Bedded Salt
Repository) 321
D-lll Estimates of the Rate of Erosion Under Various Conditions
of Climate and Relief 333
xv
-------
LIST OF FIGURES
Figure No.
D-l Rock Salt Deposits in the United States
D-2 Repository in Bedded Salt
D-3 Crystalline Formations in the United States
D-4 Repository in Granite
D-5 Repository in Basalt
D-6 Argillaceous Formations in the United States
D-7 Repository in Shale
D-8 Repository in Salt Dome
D-9 Bedded Salt Repository Showing Vertical Shafts
D-10 Examples of Shaft Linings
D-ll Grouting Program for Shaft Stabilization
D-12 Example of Section of Multi-Layered Shaft Seal
D-13 Hydraulic Conductivity of Natural Materials
D-14 Typical Plugged Borehole
D-15 Electric Analog for Borehole Pathway Analysis in Basalt
D-16 Commercial Saline Deposits in the United States
D-17 Commercially Exploitable Organic Fuel Deposits
in the United States
D-18 Diagram of Salt Dome Showing Associated Oil Reservoirs,
Wells, and Deep Holes
D-19 Pathways Associated with the Analysis of Undetected
Boreholes
D-20 Migration of Brine Bubble in Thermal Gradient
D-21 Petroleum Wells Drilled in the Contiguous 48 States,
1976 and 1977
D-22 Region Within Which Canister and Drill Hole Overlap
Page
28
29
31
32
33
35
36
38
69
74
75
83
85
123
145
162
163
166
179
195
204
217
xvi
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LIST OF FIGURES (cont.)
Figure No. Page
D-23 Fluid Injection for Enhanced Well Production 227
D-24 Subparallel Faulting in Tertiary and Quaternary Periods 234
D-25 Basic Fault Types 236
D-26 Features Associated with Faulting 238
D-27 Dating of Non-tectonic Fault by Bed Displacements 239
D-28 Faulting in the Vicinity of a Salt Dome (Conceptual
Drawing) 241
D-29 Typical Paradox Basin Salt Anticline Structure Derived
from Seismic and Other Data 242
D-30 Age of Faults in the Gulf Coastal Region 243
D-31 Detection of Features by Seismic Reflection 245
D-32 Detection of Fault by Attenuation of Refracted Signals
Across Discontinuity 246
D-33 Processed Seismic Record of Section of Paradox Basin 247
D-34 Faulting Associated with Folding and Tilting 249
D-35 Waste Drift Before and After Faulting 264
D-36 Sketch of Plutonic and Volcanic Structures 281
D-37 Volcanic Hazards 283
D-38 Relative Crater Production Rate with Solar System Evolution 298
D-39 Distribution of Impact Craters 301
D-40 Simplified Crater Geometry 303
D-41 Conceptual Drawing of Breccia Pipe in Delaware Basin 311
D-42 Characteristics of Dissolution from Above and Below
Salt Formation 313
D-43 Average Rate of Denudation of Major Drainage Areas in the
U.S. 323
xvii
-------
LIST OF FIGURES (cont.)
Figure No. Page
D-44 Glaciated Areas of the Coterminous United States
Affected During Pleistocene Glaciation 326
D-45 Crustal Plates and Regions of the World in Which Major
Earthquakes and Volcanoes Occur 329
D-46 Isostasy 330
D-47 Fresh Water Overlying Dense Sea Water 335
D-48 Erosion Rates vs. Plant Cover 336
xviii
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D-1.0 INTRODUCTION AND SUMMARY
D-l.l BACKGROUND
The U.S. Environmental Protection Agency (EPA) is responsible for
the development of environmental standards for the disposal of
high-level radioactive wastes. As part of its development effort, EPA
contracted with Arthur D. Little, Inc., for a program of technical
support. This program consists of four principal tasks:
Task A — Source Term Characterization/Definition
Task B — Effectiveness of Engineering Controls
Task C — Assessment of Migration Pathways
Task D — Assessment of Release Mechanisms
This report represents the results of the work done under Task D.
D-1.2 OBJECTIVES AND SCOPE
The purpose of Task D is to analyze the potential for the release of
radionuclides from a deep mined repository for radioactive wastes. The
analysis is not intended to correspond to a particular site or
repository design, but rather it is to be generic in nature,
representing the synthesis of assumptions and data from many sources.
The EPA wishes to consider the potential performance of repositories in
its determination of appropriate standards.
Repositories in five different geologic media were considered in
this study. These media include bedded salt, dome salt, granite,
basalt, and shale. A wide range of potential containment failure
mechanisms have been proposed in the literature. These failure
mechanisms were evaluated and compared with each other to determine
their relative importance. As a result of this process, ten failure
mechanisms were selected for detailed modeling. They were chosen with a
view toward including those that appeared to be the most important, as
well as ones that would span a wide range of risk characteristics (e.g.,
high probability/low consequence, low probability/high consequence). The
list includes the following:
-------
9 flow through bulk rock;
• shaft seal failure;
e borehole seal failure;
• undetected boreholes;
• future drilling;
• fault movement;
0 volcanoes;
• igneous intrusives;
• meteorite impacts;
• breccia pipes.
A number of other failure mechanisms, or processes that might contribute
to failure, are discussed in this report, although detailed models have
not been developed.
The results of Task D can be combined with radionuclide transport
and dose calculations in order to assess the potential effects of a
repository on human health.
D-1.3 SUMMARY OF RESULTS
Each of the ten failure elements was modeled in terms of its
likelihood of occurrence and its physical characteristics. In six
cases, the likelihood of occurrence is estimated in terms of an annual
probability (events/year). However, some failure modes are considered
sufficiently likely that they are modeled as deterministic events.
Summaries of the model assumptions and parameters for each of the
failure elements are given in Tables D-l through D-10. A key to the
symbols that appear in these tables can be found in Table D-ll. The
remainder of this report can be regarded as an explanation of these
tables .
D-l.4 GUIDE TO THIS REPORT
Chapter D-2.0 contains a summary of the methods and guidelines
adopted for this study. Chapters D-3.0, D-A.O, and D-5.0 contain
detailed analyses of the ten failure elements that were modeled, as well
as discussions of other potential failure elements. The first appendix
-------
TABLE D-1
SUMMARY OF FLOW THROUGH BULK ROCK FAILURE ELEMENT
MEDIUM
Bedded Salt
Grenrte
Basalt
Shale
Dome Salt
o5
fc«
j Z
5 X
03 5
Is
p
D
D
D
P
NATURE
OF
MODEL
Cumulative occur-
rence probability
Change in permea-
bility after thermal
peak
Change in permea-
bility after thermal
peek
Change in permea-
bility after thermal
peek
Cumulative occur-
rence probability
RELEASE
MODE
Groundwater
Groundwater
Groundwater
Groundwater
Groundwater
DRIVING
FORCE
Pressure from salt
closure, thermally
induced convection.
and gradient from
aquifer interconnec-
tion
Thermally induced
convection
Thermally induced
convection and
gradient from aquifer
interconnection
Thermally induced
convection end
gradient from aquifer
interconnection
Pressure from salt
closure, thermally
induced convection.
and gradient from
lower aquifer at edge
of salt dome
SOURCE
TEAM
Uniform
concentration
Uniform
concentration
Uniform
concentration
Uniform
concentration
Uniform
PARAMETERS
1st ESTIMATE
p-0
K - 10'10 cm/sec for
t< 100 yrs
K - 10-9 cm/tec for
t > 100 yrs
17 - 10"4
A - 8xin6m2
K = 10"9 cm/sec for
t < 100 yn
K = 10"8 cm/sac for
t > 100 yn
T, = 10-4
A - BxlO^m2
K » 10"9 cm/sec for
t < 100 yrs
K - 10-8 cm/sec for
l > 100 yrs
A - s'T.oS m*
p - 0
2nd ESTIMATE
p-0
K - 10* cm/sac lot
t < 100 yn
K = 10"7 cm/sec for
1 > 100 yrs
D = 10-*
A • SxlO6*)2
K - 10"7 cm/jec for
t < 100 yn
K " 10-* cm/sec (or
t > 100 yrs
A - SxlO6!!!2
K - 10~7 cm/sec lor
t < 100 yrs
K * 10^ cm/sec for
t> 100 yrs
0 - 10-4
A - BxlO^rn2
p . 0
FLUID FLOW RATES FROM
REPOSITORY TO UPPER AQUIFER
lit ESTIMATE
No releases need to be
calculated.
t (yn) Oltl Im3/yr)
100 1.4 XlO2
1000 8.8 xlO1
10,000 3.8x10'
t Ivnl Qltl (m3/yrl
100 1.8x10*
1000 1.5 x 10*
10.000 6.3 x 103
t (yn Oil) (m3/vr)
100 Unto*
1000 1.5x10*
10400 6 3 x 103
No releases fiMd to be
calculated.
2nd ESTIMATE
No nrioasn need to be
calculated.
tlyn)
100
1000
10.000
Oltl (m3/yrl
1.4 x 104
8.8 x 103
3.8 x 103
tlynl
100
1000
10,000
0(1) (n>3/yr)
73 x 106
7.7 x 106
6.8 x 106
tlyn
100
1000
10.000
6(tt (it.3/»rl
7SX106
7.7 x 10s
6^ xlO6
No mean need to be
olculated.
COMMENTS
The probability that the
spatial variability in
rock strength could
lead to an extensive
pathway from the re-
pository that would
fracture under the
stresses experienced
was found to be neg-
ligible.
Permeability change
after thermal peak is due
to several factors:
movement of blocks
during thermal cycle.
incomplete rebound of
material in crack*.
alteration ol minerals
in cracks.
Permeability change
after thermal peak is due
to several factors:
movement of blocks
during thermal cycle.
Incomplete rebound of
materiel in cracks,
alteration of minerals
in cracks.
Permeability change
after thermal peek is due
to seveial factors:
movement ol blocks
during thermal cycle,
incomplete rebound of
material In cracks.
alteration of minerals
in cracks.
The probability that
the spatial variabilitv in
rock strength could leed
to an extensive pathway
from the repository that
would fracture under
the stresses experienced
was found to be nee-
See Table D-11 for explanation of symbols and terms.
-------
TABLE D-2
SUMMARY OF SHAFT SEAL FAILURE ELEMENT
MEDIUM
Bedded Salt
Granite
Basalt
re
o £>
£5
35
If
ss
SES
D
D
0
NATURE
OF
MODEL
Linearly increasing
Linearly increasing
permeability
Linaariy increasing
penTMebilitv
RELEASE
MODE
Groundwater
Groundwater
Groundwater
DRIVING
FORCE
Initially pressure
from salt creep.
Afterwards, U-tube
effect.
Thermally induced
convection and
U-tube effect.
Thermally induced
convection and
U-tube effect.
SOURCE
TERM
Uniform
concentration
Uniform
concentration
Uniform
concentration
PARAMETERS
1st ESTIMATE
KQ = 10 cm/sec at
time of sealing
K,- NT6 cm/sec
after 10.000 years
K increases linearly
from KQ to K, over
10,000 years '
r| - 0.1
A - 100m2, total
cross-sectional area
of shafts
KQ- ID'8 cm/sec at
time of sealing
K, • 10"* cm/sec
after 10,000 years
K increases linearly
from Kg to Kj over
10.000 years
n • 0.1
A • 100m2, total
cross-sectional area
"of shafts
KQ n 10~» cm/sec at
time of sealing
K," 10-6 cm/sec
after 10,000 years
K increases linearly
from KQ to K1 over
10,000 years
n » 0.1
A • 100m2, ton!
cross-sectional area
of shafts
2nd ESTIMATE
KQ B 10 cm/sec at
time of sealing
K,« 10"4 cm/sec
after 10,000 years
K increases linearly
from K0 to K1 over
10.000 years
n - 0.1
A - 100m2. total
cross-sectional area
of shafts
<0= 10"* cm/sec at
time of sealing
K,- 10"4 cm/sec
after 10,000 years
K increases linearly
from Kg to K j over
10,000 years
r, • 0.1
A - 100m2, total
cross-sectional aree
of shafts-
K0» 10* cm/sec at
time of sealing
K, • 10"4 cm/sec
after 10.000 veers
K increases linearly
from KQ to K j over
10,000 years
u - 0.1
A = 100m2, total
cross-sectional-area
of shafts
FLUID FLOW RATES FROM
REPOSITORY TO UPPER AQUIFER
1st ESTIMATE
tlyrsl
200
223"
223*
1000
10,000
Q It) Im3/yrl
40 I Period
40 f0'""
w 1 creep
0.08
0.17
0.32
tlyrsl
100
1000
10,000
0 It) Im3/yrl
0.3
1.0
1.E
tlyrsl
100
1000
10.000
0 It) Im3/vrl
0.4
; 1'7
3.2
2nd ESTIMATE
tlyrsl
720
1000"
1000*
10,000
Q Itl Im3/yrl
200o| Period
>of salt
awo) creep
3.15
3.15
tlyrsl
100
1000
10,000
O Itl Im3/yrl
153
94.6
236.3
tlyrsl
100
1000
10.000
0
-------
TABLE D-2
SUMMARY OF SHAFT SEAL FAILURE ELEMENT (CONTINUED)
MEDIUM
Shate
Duma SKI
£i
H|
if
£8
D
D
NATURE
OF
MODEL
Unanty Intiaaalna
parmaaMhv
Ltnaariy men—tag
RELEASE
MODE
GrounoVamr
GroundiMar
DRIVING
FORCE
Tharmatty Induced
eomactfon and
It-tuba affact.
IrdtiaHv praaBira
from alt craap.
Altannrdi. U-tuba
affact
SOURCE
TERM
Uniform
concantratkm
Uniform
PARAMETERS
la ESTIMATE
Kg » 10* cm/iac at
Ikna of Haling
K, • lO"6 cm/aac
aftar 10,000 ytari
K incraam Itnaarly
from Kg to K| ovar
10,000 vcart
r, - 0.1
A - 100m2. total
cron-sactional araa
Olfh.lt!
Kg- 10* cm/aac at
lima of aariina.
aftar 10.000 vaari
K incraaan llnaarly
from Kg 10 K, ovar
10.000 vaan
n • 0.1
A - 100m2, total
odh.lt!
2nd ESTIMATE
Kg - 10"8 cm/sac at
timaof araling
K, - 10"4 mime
ahar 1O.OOO vaari
Kmcraaanlinaarly
from KgtoK, ovar
10.000 vaari
n - 0.1
A - 100m3. total
ercts-iactional araa
of ihafn
Kg- 10* cm/aac at
tana of lading
K,- 10-* cm/a*
altar 10.000 vaari
K inuaaau linaarlv
from Kg to K| ovar
10,000 vaari
r, - 0.1
A - 100m2, total
olaS.lt,
FLUID FLOW RATES FROM
REPOSITORY TO UPPER AQUIFER
la ESTIMATE
tlvnl
100
1000
10,000
Q III Im3/vrl
0.4
1.7
3.2
tlvnl
200
260
260
1000
10.000
O III Im3/yrl
IS ) Parted
« sr
0.04
0.10
OJ4
. 2nd ESTIMATE
tlvnl
100
1000
10.000
Q III Im3/v)
28.6
157.6
472fi
tlvnl
748
1000"
1000*
10.000
6 It) Im3'vrl
2000f Pirfod
—t sr
3.1 S
3.15
COMMENTS
reutumion.
H it comcnoiivc to
•tsumc closure bv till
creep for ihn failure
reuluraiion time would
Closure aUo impliei
itrong driving force for
-------
TABLE D-3
SUMMARY OF BOREHOLE SEAL FAILURE ELEMENT
MEDIUM
bdfrdS,!,
~
Gmrin
Badt
11
_ —
fs
£S
D
D
D
NATURE
OF
MODEL
Linearly increasing
permeability
LJ nearly increasing
permeability
Linearly increasing
permeability
RELEASE
MODE
Ground water
Groundwater
Groundwater
DRIVING
FORCE
Initially pressure from
alt creep. Afterwards,
thermally induced
gradient from aquiler
interconnection for
boreholes extending
to lower aquifer.
Thermally induced
convection
Thermally induced
convection and
gradient from aquifer
interconnection for
boreholes extending
to lower aquifer.
SOURCE
TERM
Jniform
concentration
Uniform
concentration
Uniform
concentration
PARAMETERS
let ESTIMATE
C- « 10 cm/sec at
time of sealing
KI • 10"5 em/tec after
1 0,000 years
K increases linearly
from KQ to K. over
10,000 years
T; - 0.1
50 boreholes penetrate
to repository, 10 of
which continue to
lower aquifer
A - 0.1 m2/borehole
(Q » 10*3 cm/sec at
time of sealing
K, - ifl'5 cm/sec after
10.000 years
K increases linearly
from KQ« K1 over
10,000 years
n • o.i
50 boreholes penetrate
to repository
A • 0.1 m2/borehoJ*
KQ = 10 cm/sec at
lime of sealing
Kj-iO* cm/sec efter
10.000 veers
K increases linearly
from KQ to K1 over
10,000 years
F) - 0.1
SO boreholes penetrate
to repository, 10 of
which continue to
tower aquifer
A - 0.1 m2/borehoU
2nd ESTIMATE
KO- 10"8 cm/sec at
time of sealing
K . • 1 0"* cm/sec after
10,000 years
K increases linearly from
XQ to K j over
10,000 yean
r, • 0.1
50 boreholes penetrate
to repository. 10 of
which continue to
lower aquifer
A • 0.1 m2'borehole
time of sealing
Kf - 10"^ cm 'tec after
10,000 years
K increases linearly from
KQ to K| over
10.000 years
U - 0.1
SO boreholes penetrate
to repository
A • 0.1 m^/borehol*
KQ « 10"® cm/sec at
time of sealing
i<1 - 10T* cm/sec after
10.000 years
K increases linearly from
KQ to K | over
10,000 yean
r, • 0.1
50 boreholes penetrate
to repository, 10o<
which continue to
lower aquifer
A • 0.1 m2/borehole
FLUID FLOW RATES FROM
REPOSITORY TO UPPER AQUIFER
1st ESTIMATE
tlyn)
200
223-
223'
1000
10.000
100
1000
10.000
ttyrs)
100
1000
10.000
Q (tl Im3/yrl
M i Period
\ of »it
14 f creep
0.05
0.13
0.63
0.1
0.6
2.4
0 It) tm3/yr)
o.os
1 0.4
1.6
2nd ESTIMATE
lynl '- Q (tl Im /yr)
720 100 | Pt"°°
Vof salt
1000" 100 (creep
lOOO" 19
0.000 167
|
100 . 0.9
1000 5.S
0.000 t 31.5
t (yrs) Q (t) (m3/yr)
100 2.0
1000 19.2
10.000 170.1
r-nftM4EU
e.ease o-vy t>ej<-
fter repository
on m u
-------
TABLE D-3
SUMMARY OF BOREHOLE SEAL FAILURE ELEMENT (CONTINUED)
MEDIUM
SM«
CHmSM
el
if
si
o *-
D
D
NATURE
OF
MODEL
LmMriv incranmg
pvmMbility
RELEASE
Ground«Mttr
DRIVING
•wfitnt from •quit*
tanrcomwction lor
bortfcota extending
to loiwr >quif tr.
InitMly prwur* from
MhcTMp. Afttnjwnh,
ttw U-tubt «ff tct.
SOURCE
unifom,
PARAM
in ESTIMATE
K,- lOrGon/MClfnr
10.000 yon
K 1 •• liniHlv 'rom
KQlO K^ OMT
10.000 V^l
n - 0.1
tomxxitofv. 10 oi
«hid.eootinu«
to IOVMT iquifir
A - 0.1 fnzftnnhol«
Kg -104 cm/Hen
limxrfMriing
C, - lO^antocatw
loxnovMr*
KgtoK) OMT
IQ^lOOvMrs
1 - 0.1
tonpotitory
* - 0.1 m'/bor*
100 \ P"iod
00 } ofBlt
100 I cra*>
IB
IB
I^MMllUfy (MMUIllion.
r\t\tmm only b»gJn
*lUi t^pi^ilAtr
raMturatfon. Ineon-
mn to undMKMd
m«Tt.ho(«inthiicaH
rapoiHorv and so can-
•quHvitidgiafmt
dom.
See Table O-11 for explanation of symbols and terms.
-------
TABLE D-4
SUMMARY OF UNDETECTED BOREHOLE FAILURE ELEMENT
MEDIUM
BofctadSalt
Granita
Bolt
ES
n. Negligible flow in
most cases deduced
from consideration of
relative resistance of
alternative pathway*
'or
-------
TABLE D-4
SUMMARY OF UNDETECTED BOREHOLE FAILURE ELEMENT (CONTINUED)
MEDIUM
Shale
Dome Salt
It
z
_ —
Si
• w
IB
p
p
NATURE
OF
MODEL
Past drilling density
and detection re-
liability yield
probability of one
or more pertially
filled holes.
Past drilling density
and detection re-
liability yield
probability of one
or more partially
filled holes.
RELEASE
MODE
Groundwater
Groundwater
DRIVING
FORCE
Thermally induced
convection and
gradient from aquifer
interconnection.
Second estimete
Period B flows
derive from equifer
interconnection
gradient. Other flows
negligible.
SOURCE
TERM
Uniform
concentration
Uniform
concentration
PARAMETERS
1st ESTIMATE
prob (1 hole on site)
- 0.05
("site" " repos. <•
300 m buffer zone)
prob (failure to detect)
= .01
prob (undet. hole)
= S x 10-*
K - 10-* cm/sec
1 • 0.2
A • 0.1 m
Distance from drift
n 5m but flows
assume hole through
repository. Holes
extend to lower
equifer.
exp. no. holes on site
• 3
("site" • 300 m
buffer zone only)
prob (failure to detect
indiv. hole)
- 0.001
prob (3 undet. holes)
• 0.003 (Assumes
partial dependence)
K • 10-* em/sec
n - 0.2
A - 0.1 m2
Distance from drift
• lOOm.
Holes extend to lower
aquifer.
2nd ESTIMATE
exp. no holes on site
• 9
prob (failure to detect)
• 0.01
prob (3 undet. holes)
= 0.09 (Assumes
partial dependence)
K - 10-3 cm/sec
1 = 0-2
A • 0.1 m2
Distance from drift
• 5m but flows
assume hole through
repository. Holes
extend to lower
aquifer.
exp. no holes on site
- 30
prob (failure to detect
indiv. hole)
- 0.001
prob 15 undet. holes)
= Oj03 (assumes
partial dependence)
K - 10-3 cm/sec
n - 0.2
A - 0.3 of (total)
Distance from drift
=• 100m.
Holes extend to lower
aquifer.
FLUID FLOW RATES FROM
REPOSITORY TO UPPER AQUIFER
1st ESTIMATE
tlyrs)
100
1000
10.000
0 (m3/yrl
4.4
3.8
1.6
Negligible with respect
to other failure elements.
2nd ESTIMATE
Hyn)
100
1000
10,000
tlyrs)
1000
10.000
Q Im3/vrl
594
576
510
Q (m3/yrl
630
630
COMMENTS
Repository rasaturatlon
neoMary for releases
to begin.
Distance from drift
precludes significant
connection with re-
pository except In case
ol significant dissolu-
tion. Negligible flow in
most cases deduced
from consideration of
nrtatrv* resistance of
alter native pathway*
for water to enter and
leave repository. Re-
pository reenuratton
necessary for releases.
VO
See Table D-11 for explanation of symbols and terms.
-------
TABLE D-5
SUMMARY OF FUTURE DRILLING FAILURE ELEMENT
MEDIUM
B«dd«lSalt
Gmtita
ta.lt
SB
g|
j Z
a 5
< E
O t-
£ 0
P, O
P,D
P,D
NATURE
OF
MODEL
Postulated determin-
istic drilling rate.
probabilistic for
hitting canister.
Postulated determin-
istic drilling rate,
probabilistic for
hitting canister.
Postulated determin-
istic drilling rate.
probabilistic for
hitting canister.
RELEASE
MODE
A. Land surface
B. Groundwater
A. Land surface
B. Groundwater
A. Land surface
B. Groundwater
DRIVING
FORCE
A, Materials raised
with drilling mud.
B. Thermally induced
convection and
gradient from
aquifer inter-
connection.
A. Material! raised
with drilling mud.
B. Thermally induced
convection.
A. Material) raised
with drilling mud.
B. Thermally induced
convection and
gradient from
aquifer inter-'
connection
SOURCE
TERM
A, Part of canister
and fluid from
waste drift.
B. Uniform
concentration.
A. Part of canister
and fluid from
wast* drift.
B. Uniform
concentration.
A. Part of canister
and fluid from
waste drift.
B. Uniform
concentration.
PARAMETERS
lat ESTIMATE
No holes fart century;
5 holes next century;
2 holes each subsequent
century. All holes to
lower aquifer.
Holes sealed with
permeability
K = 10-4 cm/sec
rj •= 0.2, and
A - 0.1 m2.
Probability of hitting a
canister = 10*3 per hole.
with expected removal
of 1 5% contents.
No holes first century;
1 hole next century;
1 hole every four sub-
sequent centuries.
Holes sealed with
permeability
K - 10"4 cm/sec,
T) - 0.2, and
A - 0.1 m2.
Probability of hitting a
canister - 10*3 per
hole, with expected
removal of 15%
conteno.
No holes first century;
3 holes next century;
1 hole each subsequent
century. All holes to
lower aquifer.
Holes sealed with
permeability
K - 10"* cm/sec,
T) = 02, and
A - 0.1 m2.
Probability of hitting a
canister = 10*3 per hole
with expected removal
of 15% contents.
2re5 ESTIMATE
No holes first century;
50 holes next century;
5 holes each subsequent
century. All holes to
lower aquifer.
Holes sealed with
permeability
K •= 10-3 cm/sec.
T) - 0.2, and
A - 0.1 m2.
Probability of hitting a
canister = 10*3 per hole.
with expected removal
of 15% contents.
No holes first century;
10 holes next century;
2 holes every subse-
quent century.
Hota sealed with
permeability
K « ID"3 cm/sec.
TI o 0.2, and
A - 0.1 m2.
Probability of hitting a
canister - 10'3 par
hole, with expected
removal of 15%
contents.
No holes first century;
20 holes next century;
5 holes each subsequent
century. All holes to
lower aquifer.
Holes sealed with
permeability
K = 10-3 cm/sec.
TJ n 0 3.. and
A - 0.1 m2.
Probability of hitting a
canister = 10"3 per hole
with expected removal
of 15% contents.
FLUID TRANSPORTED
TO SURFACE
1st ESTIMATE
0.07 m3 /drill hole
200 m3 /drill hole
2OQ m3/drill hole
2nd ESTIMATE
1400 m3 /drill hole
5OOO m3 /drill hole
5OOO m3 /drill hole
COMMENTS
Analysis assumes no
knowledge of reposi-
tory before, during, or
after drilling. Ground-
water releases from
post-sealing leakage are
calculated in the text
Hit are, in general, less
significant than releases
to the surface.
Analysis assumes no
knowledge of reposi-
tory before, during, or
after drilling. Ground-
water releases from
post-Mating leakage are
calculated in the text
but are. in general, (ess
significant than releases
to the surface.
Analysis assumes no
knowledge of reposi-
tory before, during, or
after drilling. Groun-
watar releases from
post-sealing leakage are
calculated in the text
but are, in general, less
significant than releases
to the surface.
See Table D-11 for explanation of symbols and terms.
-------
TABLE D-5
SUMMARY OF FUTURE DRILLING FAILURE ELEMENT (CONTINUED)
MEDIUM
Shita
DoimSilt
Si
II
|i
II
P.D
P, D
NATURE
OF
MODEL
. Postulated determin-
istic drilling rate.
probabilistic for
hitting canister.
Postulated determin-
istic drilling rate,
probabilistic for
hitting canister.
RELEASE
MODE
A. Land surface
B. Groundwater
A. Land surface
B. Groundwater
DRIVING
FORCE
A. Materials raised
with drilling mud.
B. Thermally induced
convection and
gradient from
aquifer inter-
connection.
A. Materials railed
wim drilling mud.
B. Thermally induced
convection.
SOURCE
TERM
A. Part of canister
and fluid from
waste drift.
B. Uniform
concentration.
ft. Part of caniiter
and fluid from
waste drift.
1. Uniform
concentration.
PARAMETERS
1st ESTIMATE
No holes first century;
5 holes next century;
2 holes each subsequent
century. All holes to
ower aquifer.
Holes sealed with
permeability
K • lO^4 cm/sec.
u - 0.2. and
A - 0.1 m2.
Probability of hitting a
canister = 10~3 per hole.
with expected removal
of 15% contents.
Jo holes first century;
» holes next century;
2 holes every
subsequent century.
Holes sealed with
permeability
K - 10-4 cm/sec.
TI * 0.2, and
A - 0.1 m2.
Probability of hitting a
canister - 10-3 per hole.
with expected removal
of 15% contents.
2nd ESTIMATE
No holes first century:
50 holes next century;
5 holes each subsequent
century. All holes to
lower aquifer.
Holes sealed with
permeability
K = 10-3 cm/sec.
rj B 03. and
A = 0.1 m2.
Probability of hitting a
canister = 10"3 per hole.
with expected removal
of 15% contents.
No holes first century;
30 holes next century;
5 holes every
subsequent century.
Holes sealed with
permeability
K - 10-3 cm/sec.
n « 0.2. and
A - 0.1 m2.
Probability of hitting a
canister = 10~3 per hole.
with expected removal
of 15% contents.
FLUID TRANSPORTED
TO SURFACE
1st ESTIMATE
200 m3 /drill hole
0.04 m3 /drill hole
2nd ESTIMATE
5000 m3/drill hole
1300 m3/drill hole
COMMENTS
Analysis assumes no
knowledge of reposi-
tory before, during, or
attet drilling. Ground-
water releases from
post-sealing leakage are
calculated in the text
but are, in general, less
significant then releases
to the surface.
Analysis assumes no
knowledge of reposi-
tory before, during, or
after drilling. Ground-
water releases from
post-sealing leakage are
calculated in the text
but are, in general, less
significant then releases
to the surface.
See Table 0-11 for explanation of symbols and terms.
-------
TABLE D-6
SUMMARY OF FAULT MOVEMENT FAILURE ELEMENT
MFDIUM
Beritlrci Sad
Gran Ke
Basalt
Shale
Dome Salt
i 9
«j y
£ £
3 z
at 5
2 *
0 K
Ix O
r
p
P
9
)
MATURF
OF
MOOEI
Aft , rohabtl
nt ncruTenre ol r^rw
fault 01 rrwvemer-i
alonq olrt fj»un
Annual probability
of occurrence ol new
fauh or movement
alonq old fault.
Annual probability
of occurrence of new
fault or movement
along old fault.
Annual probability
of occurrence of new
autt or movement
along old fault.
Annual probability
of occurrence of new
ault or movement
along old fault.
RELEASE
MODE
Grnu'Vlwaf*-
Groundwatet
! round water
round water
roundwater
DRIVING
FORCE
Thermally induced
convection effect
added to gradient
from aquife' intei
connection.
Thermally induced
convection.
Thermally induced
convection effect
added to gradient
from aquifer inter-
connection.
Thermally induced
convection effect
added to gradient
from aquifer inter-
connection.
Thermally induced
convection effect
added to gradient
from aquifer inter-
connection.
SOURCE
TERM
Canine* i in fault zone
broken and subteci to
leaching. Aceumu
lated dissolved radio-
nudtdes by time ol
faulting assumed
released through fault
'roin 100-m wde zone
around fault.
^anuteri tn fault /one
broken and subject to
each ing. Accumu-
ated dissolved radio
nuclides by time of
suiting assumed
released through fault
rom 100-m wide zone
around fault.
Caniners in fault zone
broken and subject to
leaching. Accumu-
ated dissolved radio-
udtdes by time of
aurting assumed
released through fault
rom lOOm wide zone
.wound fault.
Canisters in fault zone
broken and subject to
•aching. Accumu-
ated dissolved radio-
nuclides by time of
suiting assumed
treated through fault
rom 100-m wide tone
round fault.
Canisters in fault zone
broken and subject to
eaching. Accumu-
lated dissolved radio-
nuclkits by time of
aulting assumed
released through fault
rom 100-m wide zone
wound fault.
PARAMETERS
let ESTIMATE
H * 2 « 1 0"** events/vr
Flow path 1 m wide
WOO m long
K - 10'4cmAec
i) - 0.1
tOO canisters in fault
zone. 5% repository
in affected surrounding
zone.
X = 2 x lO^eventi/yr
Flow path 1 m wide
•000m long
K - 10-2cmfc.sc
T) - 0.1
100 caniners in fault
zone. 5% repository
n affected surrounding
zone.
X • 5 x 10~7 eveno/yi
Flow path 1 m wide
4000m long
K - 10'2 cm/sac
T) ~ 0.1
100 canisters in fault
zone. 5% repository
n affected surrounding
zone.
X = 2 K lO^evants/V'
Flow oath 1 m wide
4000m long
K - 10-4cnW*ec
n - 0.1
00 canisters in fault
zone. 5% repository
n affected surrounding
zone.
X • 3 K 10*7 events/yr
Plow path 1 m wide
4000m long
K - 10"4 cm/sac
it - 0.1
100 canisters in fault
zone. 5% repository
n affected surrounding
zone.
2nd ESTIMATE
\ = 4 « 10'7 events/y
Flow path 1 m wide
4000m long
K - 10* cm/sec
n ' 0.1
100 canisters in fault
zone. 5% repository
in affected surrounding
zone.
X = IO"5 events/yr
Flow path 1 m wide
4000m long
K - 10'2 cm/sec
T) •= 0.1
1OO canisters in fault
zone- 5% repository
in affected surrounding
X - 10'5events/yr
Flow path 1 m wide
4OOOmlong
K " lO^cmfcec
T) •= 0.1
100 caniners in fault
zone. 5% repository
in affected surrounding
zone.
A - 4 x IO*7 evena/yt
Flow path 1 m wide
4000m long
K - lO^cmAec
n • 0.1
100 canisters in fault
zone. 5% repository
in affected surrounding
_
X • 10"5aveira/yr
Flow path 1 m wkto
4000m long
K - 10-*anAec
i) • 0.1
100 caniitars in fault
zona. 5% repository
in affected surrounding
zone.
FLUID FLOM RATES FROM
REPOSITORY TO UPPER AQUIFER
In ESTIMATE
1 (yr«)
100
1000
10.000
Q (tl Im3/yrl
8.2 x 10
S3 x 10*
2.5 x IO4
t lyrtl
100
1000
10,000
6 (tl (m3/yrl
6.9 x 10°
4.4 x IO6
13. IO6
tlyrd
100
1000
10.000
6 (tl (m3/yrl
8.8 x IO6
7.6 X 106
3.2 x IO6
tlynl
100
1000
10,000
6 (tl (m3/yrl
8.8 x 10*
7.6 x 10*
3.2 x 10*
t(vnl
1100
1000
10,000
0 M (m3/yil
as x io4
6.0 x 104
23 x IO4
2nd ESTIMATE
tlynl
100
1000
10.000
6 III (m3/yrl
3.9 « IO5
3.8 x 10b
3.3 x 10b
llyr.)
100
1000
10,000
6 (tl (m3/yrl
6.9 x 10°
4.4 x IO6
1.9x IO6
t(ynl
100
1000
10,000
6 (tl
-------
TABLE D-7
SUMMARY OF VOLCANO FAILURE ELEMENT
MEDIUM
bddidSelt
Granite
""•"
|i
\\
11
Is
p
P
p
NATURE
OF
MODEL
Annual occurrence
probability.
Annual occurrence
probability.
Annual occurrence
probabHity.
RELEASE
MODE
Air and land
surface.
Air end land
surface.
Air and land
surface.
DRIVING
FORCE
Direct transport by
moving gates and
molten rock.
Direct transport by
moving gases and
molten rock.
Direct transport by
moving gases and
molten roc .
SOURCE
TERM
Fraction of repository
brought to surface.
Fraction of repository
brought to surface.
Fraction of repository
vought to surface.
PARAMETERS
let ESTIMATE
X = 1 x 10-10/yr
Fraction of repository
brought to surface is
0.4%, of which 1% is
in rcapirable form. 9%
consists of fine particles
which can be easily
dbpenad, and 90% is
reburred near the
surface.
X •= 1 x 10-lo/yr
Fraction of repository
brought to surface is
0.4%, of which 1% is
in rttpirabt* form, 9%
consists of fine particles
which can be easily
dispersed, and 90% i>
nburied near the
surface.
X » 6 x 10-10/yr
Fraction of repository
brought to surface is
Dj4%, of which 1% is
in rexpirabJe form, 9%
wnsitts of fine particles
which can be easily
cnspaned, and 90% is
eburied near the
urface.
2nd ESTIMATE
X •> 1 x 10-8/yr
Fraction of repository
brought to surface is
0.4%, of which 1%is
inr*aj>irabl«formc9%
consists of fine particles
which can be easily
dispersed, and 90% is
reburied near the
surface.
X - 1 x 10-«/vr
Fraction of repository
brought to surface is
0.4%, of which 1% is
in reqiirabte form, 9%
consists of fine panidas
which can be easily
dispersed, and 90% is
roburMd naar the
surface.
X • 1 x 10-8/yr
Fraction of repository
brought to surface is
0.4%. of which 1% is
in reapirablt form, 9%
consists of fine particles
which can be easily
dispersed, and 90% is
reburied near the
surface.
RELEASE MODELING STEPS
1st ESTIMATE
Direct release
Direct release
Direct release
2nd ESTIMATE
Direchretease
Deract release
Direct release
COMMENTS
First estimate based on
national average. Lower
rates could probably be
derived from additional
siting assumption, such
as location in East or
Midwest.
First estimate baaed on
national average. Lower
ram court probably be
derived from additional
siting assumption, such
as location in East or
Midwest.
Based on Columbia
Plateau basalts.
See Table D-11 for explanation of symbols and terms.
-------
TABLE D-7
SUMMARY OF VOLCANO FAILURE ELEMENT (CONTINUED)
MEDIUM
9*.
Dem Sri!
El
55
J Z
< «
£8
p
p
NATURE
OF
MODEL
Annuxl occurrence
."""•WHY.
Annual occurrence
probability.
RELEASE
MODE
Air and (and
surface.
Air and tend
surface.
DRIVING
FORCE
Direct transport by
moving gases and
Direct transport by
moving gases anrj
SOURCE
TERM
Fraction of repository
brought to surface.
Fraction of repository
brought to surface.
PARAMETERS
lit ESTIMATE
X - 1 x iO-10/yr
Fraction of repository
brought to eurfaca is
0.4%. of which 1%is
inresptrablaform.9%
consists of fine particles
which can be easily
dispersed, and 30% Is
reburied near the
surface.
X - 1 x 10-10/yr
Fraction of repository
brought to surface is
0.4%, of which 1% is
in respiratote form, 9%
consists of fine particles
which can be eastty
disparted, and 90% Et
reburied near the
surface.
2nd ESTIMATE
A » 1 x 1Cr*/yr
Fraction of repository
brought to surface is
0.4%, of which 1%is
in respirable form. 9%
consists of fine particles
which can be easily
dispareed, and 9O% is
reburied near the
surface.
X *> 1 x 1C-10/yr
Fraction of repository
brought to surface is
0.4%. of which 1% is
in rvspirable form, 9%
consists of fine particles
which can be easily
reburied near the
surface.
RELEASE MODELING STEPS
1st ESTIMATE
Direct release
Direct release
2nd ESTIMATE
Direct release
Direct release
COMMENTS
First estimate bawd on
national avtrage. Lowei
rates could probably be
siting assumption, such
as location in East or
Estimates based on
national average. Could
be refined to e lower
value for salt dome
region. First and
second estimate* are the
standpoint of volcantsm,
the Gulf region shows
no variation.
See Table D-11 for explanation of symbols and terms.
-------
TABLE D-8
SUMMARY OF IGNEOUS INTRUSIVE FAILURE ELEMENT
MEDIUM
Bedded Salt
Granite
Basalt
Shale
Dome Salt
||
j|
• I
< c
*£
p
p
f
P
p
NATURE
OF
MODEL
Annual probability
of occurrence.
Annual probability
of occurrence.
Annual probability
of occurrence.
Annual probability
of occurrence.
Annual probability
of occurrence.
RELEASE
MODE
Groundwater
Groundwater
Groundwater
Groundwater
Groundwater
DRIVING
FORCE
Physical traneport of
wastes by magma to
upper aquifer.
Physical transport of
wastes by magma to
upper aquifer.
Physical transport of
wettes by magma to
upper aquifer.
Physical transport of
wastes fay magma to
upper aquifer.
Physical transport of
we net by neigma to
upper aquifer.
SOURCE
TERM
Waste material inter-
sected by magma.
Waste material inter-
sccted by magma.
Wane material inter-
sected by magma.
Waste material inter-
sected by magma.
Waste materiel inter-
sected by magma.
PARAMETERS
let ESTIMATE
X •* 2 x 10*10
Dimensions of dike:
1 mn4 km.
intenecting 0.05%
waste inventory.
x-2,10-'0
Dimensions of dike:
Imx4km.
Intersecting OJK%
w-teirr-mory.
X-Sx10~9
Dimensions of dike:
1 m x4 km.
intersecting 0.05%
WM""WMt°'Y-
Dimensions of dike:
1 m x4 km.
intersecting 0.05%
waste inventory.
V • 3 X 10*
Dimensions of dike:
1 mx4km.
intenecting 0.06%
«m««n,ory.
2nd ESTIMATE
. H « 4 x 10*
Dimensions of dike:
1 m>4 km.
intersecting 0.05%
waste inventory.
x-to-7
Dimensions of dike:
1 mx4 km.
intersecting OjDS%
wane inventory.
X - 10'7
Dimensions of dike:
1 m x4 km.
intersecting 0.05%
waste inventory.
X - 4 x 10'9
Dimensions of dike:
1 mx4 km.
intersecting 0.05%
waste inventory.
k • 5 x 10"7
Dimensions of dike:
1 m it 4 km.
intenecting 0.05%
waste inventory.
RELEASE MODELING STEPS
Material moved to aquifer and subject to leaching.
Leech characteristics of weste (uim assumed
unchanged, elthough canisters would be removed.
Material moved to aquifer and subject to leaching.
Leach characteristics of wane form assumed
unchanged, although canisters would be removed.
Material moved to aquifer and subject to leaching.
Leach characteristics of waste form assumed
unchanged, although canisters would be removed.
Material moved to aquifer and subject to leaching.
Leach characteristics of wasu form assumed
unchanged, although canisters would be removed.
Materiel moved to aquifer and subject to leaching.
Leach characteristics of waste form assumed
unchanged, although canisters would be removed.
COMMENTS
Probabilities deter-
mined as 1% of values
for faulting.
Probabilities deter-
mined es1% of values
for faulting.
Probabilities deter-
mined as 1% of values
for faulting.
Probabilities denr-
minad as 1% of values
for faulting.
Probabilities deter-
mined as t% of values
for faulting.
See Table D-11 for explanation of symbols and terms.
-------
TABLE D-9
SUMMARY OF METEORITE IMPACT FAILURE ELEMENT
MEDIUM
B«*fedSalt
Graniu
Basalt
£9
ii
J Z
SI
B UJ
Is
p
p
F
NATURE
OF
MODEL
Annual occurrence
probability.
Annual occurrence
probability.
Annual occurrence
probability.
RELEASE
MODE
A. Land surface
B. Groundwater
A. Land surface
B. Groundwater
A. Land surface
B. Groundwaler
DRIVING
FORCE
A. Impact
B. Thermal convection
added to aquifer
interconnection
gradient.
A. Impact
B. Thermal convec-
tion.
A. Impact
B. Thermal convec-
tion added to
aquifer inter-
connection
gradient.
SOURCE
TERM
A, 0,1% repository
inventory to
surface.
B. 20% cumulative
teached nu elides
released to ground-
water. Continued
leaching of broken
canisters in fracture
or breccia zone
U0%) and sur-
rounding caniners
(10%).
A. 0,1% repository
inventory to
surface.
B. 20% cumulative
leached nudides
released to ground-
water. Continued
leaching of broken
canisters in fracture
or breccia zone
(10%) and sur-
rounding canisters
M0°0),
A. 0.1% repository
inventory to
urface.
B. 2O°D cumulative
leached nuclides
released 10 ground-
water. Continued
leaching of broken
canister; in Iracture
or breccia zone
(10%l and sur-
rounding canisters
(10%).
PARAMETERS
In ESTIMATE
\ c 4 ,10-1 1/ r
A = 0.8 km2
K = 10-4 cm/see
i) = 0-2
A " Q£ km2
K - 10-4 cm/sec
TJ = 0.2
X = 4 k 10"1 Vyr
A - 0.8 km?
K - 10-4 cm/sec
1 - 0.2
2nd ESTIMATE
X •= 4n I0'11'vr
A « 0.8 km2
K - 10"4 cm/sec
ij - 0.2
X - 4x 10'11 >T
A - 0.8 km2
K n 10*4 cm 'sec
1 • 0.2
A = 4x 10'n/vr
A = 0 £ km2
K = 10-4 cm/sec
n r 0.2
FLUID FLOW RATES FROM
REPOSITORY TO UPPER AQUIFER
1st ESTIMATE
t fyri) Q (tt (m3/yrl
100 1.6x10
7
1000 , 1.4 x 10
10,000 5.0 x 106
t (yn) 6 (t) (m3/vr)
10O 1.4 x 10'
1000 8.8 x 106
10,000 3.8 x 106
t (yre) Q (t) (m3/yr)
100 13x10
1000 1.5x10
10.000 6.3 x 106
2nd ESTIMATE
fyrs) ! 6 It) (m3/yr)
100 7^*10
7
10OO 7.6 xlO7
0,000 ; 6.7 x 107
1
t(yrj) j Q U) Im3/yrl
100 1.4 x 107
:
1000 ) 8.8 v 106
0,000 i 3£ v 106
i
1
t IVTJ) 6)0 (m3/yr)
7
100 7.9x10
7
1000 7.7 * 10
10,000 6.8 x 107
COMMENTS
Water availability may
ttverely limit flows
below levels calculated.
Water availability may
tevefely limit flows
below levels calculated.
Water availability may
«verely limit flows
below levels calculated.
See Table D-11 for explanation of symbols and terms.
-------
TABLE D-9
SUMMARY OF METEORITE IMPACT FAILURE ELEMENT (CONTINUED)
MEDIUM
Sruto
Dorm Silt
0 Si
C Jj
5z
0 *
ES
p
p
MATURE
OF
MODEL
Anmjri oecurranei
probability.
Annuol oecurranc*
problbilltv.
RELEASE
MODE
A. Landmrhoi
B. GroundMOr
A. Undiurrtc.
B. Groundwvtw
DRIVING
FORCE
A. Impact
B. Ttumul convvc-
tloniddidto
•quite Innr-
comwclion
gradton.
A. ImpKt
B. Tlmiinl comae i
HonKfcMto
•qurhv inur-
conmctlon
SOURCE
TERM
A. 0.1% npoBtorv
inmniury to
mirtac*.
laiahid nudidis
ratavMd to ground-
wittr. Continued
(•Khingolbralun
anlaun in Iractur*
orbracctezoM
IIOKIandoir-
<10W.
A. 0.1% rapoiUorv
invomorv to
lurlira.
' taodHdnudMii
ralMMd to ground-
MUr. CormiMd
teen ing olbrokm
onlmrt Hi franuni
orbnediioni
<10%l md «ur-
110%).
PARAMETERS
in ESTIMATE
X • 4>10-"/yr
A • o£ krn^
C • 1O-4 cm/we
* ' "
X • 4« 10-"/yr
A • OJkmJ
K - tO^cm/HC
2nd ESTIMATE
X - 4«10-"/yr
A • OJkm2
K • lO^ern/HC
n • OJ
X « 4 » 10-' '/»r
A « OJkmJ
«• O^
™ w^
FLUID FLOW RATES FROM
REPOSITORY TO UPPER AQUIFER
IB ESTIMATE
tlynl
100
1000
10.000
Q (t) (m'/yrl
1 J « 107
1i « 10J
SJ . 10S
llyn)
100
1000
lOjDOO
6 It) Im'/ytl
,*,107
141 > Id7
5.0 . 10E
2nd ESTIMATE
tlynl
100
1000
10.000
6 It) Im3/vr)
T3 K 107
7.7 x 107
SJBxIO7
tlynl
100
1000
ioxno
6 It) In3/Vrl
4JIH107
3^.107
13 * 107
COMMENTS
Wmr vrailability mty
•Mraly HmH flows
biton towli afcubnd.
•mnly limit Itom
btloo Inrii akulrad
•mMhtMlbvfnctura
zontntdgtolMlt
domt.
See Table D-11 for explanation of symbols and terms.
-------
TABLE D-10
SUMMARY OF BRECCIA PIPE FAILURE ELEMENT
MEDIUM
Bedded Salt
Granite
Basalt
State
Dome Salt
PROBABILISTIC (PI
DETERMINISTIC ID)
P
NATURE
OF
MODEL
Annual occurrence
probability.
ItA.
MA.
N.A.
NJk.
RELEASE
MODE
Upper aquifer
DRIVING
FORCE
Thermally induced
convection and
aquifer interconnec-
tion.
SOURCE
Canisters in breccia
pipe assumed to be
broken and subject
10 leaching.
PARAMETERS
IB ESTIMATE
* - Ofort<500yn
X « lO-S/yr lor
t>500yrs
K - 10-2 cm/sec
n - 0.2
A » 3* lff»mZ
2nd ESTIMATE
» Ofort<500yrs
X lO-fyyr lor
tS*SOOyrs
K - 10-2 cm/see
1 - 0.2
A - 3 « I04 n>2
FLUID FLOW RATES FROM
REPOSITORY TO UPPER AQUIFER
IX ESTIMATE
tlyrs)
BOO
1000
10.000
Q (m'/yrl
6.107
5,107
2x107
2nd ESTIMATE
tlynl
500
1000
10.000
0 (m3/yr)
3,108
3x108
3»108
COMMENTS
Limited availability of
water from lower
aquifer expected to
significantly restrict
flows beknv levels
calculated.
00
Sae Table D-11 for explanation of symbols and terms.
-------
TABLE D-ll
EXPLANATION OF SYMBOLS AND TERMS IN TABLES D-l THROUGH D-10
K "hydraulic conductivity, also referred to throughout as the
permeability
t = time from repository closure
n = effective porosity of flow pathway
A. = cross-sectional area of flow pathway
p « cumulative probability of occurrence
^ - annual probability of occurrence
Q » volumetric flow rate
n » n , where n is a value of time, t, refers to a jump in the value of
a dependent variable (such as Q) at t = n. The value associated
with n is the limiting value as t approaches n through smaller
values (t v n); the value associated with n is the limiting value
as t approaches n through larger values (t > n).
Groundwater — Aquifer overlying the repository formation.
Salt closure or creep — Tendency of salt to flow plastically under
pressure.
Thermally induced convection — Water heated by wastes has lower density
and is forced upward by buoyancy effect.
Aquifer interconnection — A pathway connecting aquifer above and below
repository can lead to hydraulic imbalance (gradient) and
corresponding flow. This flow has been modeled upward.
U-tube effect — When at least two points in upper aquifer, at different
hydraulic potentials, are connected to repository and to each other
through backfilled tunnels, flow can result. The new pathway acts
as a high resistance in parallel to the pathway through the aquifer
connecting the two points.
Uniform concentration — Average concentration in water in backfilled
repository as a result of gradual leaching from waste package. May
be limited either by leach rates or by solubility limits.
First estimate — A parameter estimate assuming that the site exhibits
favorable characteristics with respect to the particular breach
mechanism in question (i.e., tending to reduce the risk).
Second estimate — A parameter estimate assuming that the site exhibits
somewhat less favorable characteristics (than first estimate) with
respect to the particular breach mechanism in question, although it
may be highly favorable with respect to other factors.
19
-------
is a glossary of terms that are used in the main text, not just
specialized geologic or engineering terms, but also terms that are used
in the introductory chapters before they can be discussed at length.
The remaining appendices generally discuss processes that take place in
or near the repository and that affect the quantity of radlonuclides
that might be released in the event of a breach of containment.
20
-------
D-2.0 GUIDELINES AND METHOD OF APPROACH
D-2.1 GENERAL APPROACH
There is wide current interest in the problem of estimating how well
deep geologic repositories would be able to contain radioactive wastes.
Research on this problem is being carried out by and for various
government agencies and other institutions in the United States and
abroad. The principal government programs in the United States are the
following:
1. Environmental Protection Agency. The Agency is responsible for
setting environmental standards governing the disposal of
radioactive wastes. Tn this connection, it wants to take into
account, among other factors, the estimated performance
capabilities of geologic repositories, considered conceptually
rather than on a design- or site-specific basis.
2. Nuclear Regulatory Commission. The Commission is responsible for
licensing a geologic repository for high-level radioactive
wastes. Therefore, it is developing its own modeling capabilities
in order both to determine appropriate regulatory guidelines and
to evaluate license applications.
3. Department of Energy. The Department is responsible for siting,
constructing, obtaining a license for, and operating a system for
high-level radioactive waste disposal; and the disposal option of
a deep geologic repository is being pursued as its favored
approach. Therefore, it is developing modeling capabilities
to use both in decisions regarding design and siting and in
making application for a license.
Because of these and other programs, there is an extensive literature
base on the potential performance of geologic repositories for nuclear
wastes. Much of this literature is cited throughout this report.
There are two important aspects to the performance evaluation:
1. The identification of scenarios or failure modes that would
result in or contribute to a breach of the repository
containment.
21
-------
2. The modeling of identified scenarios and failure modes in order
to assess their impact on the environment or on human health.
Various approaches to the first aspect have been vigorously pursued,
examples of which include:
1. The development of fault trees and, from them, event chains.
This approach has received impetus from the Reactor Safety
Study(2) and from the wide application of similar techniques in
other safety analyses.
2. The convening of panels of experts to list every failure element
or scenario they could reasonably imagine, and then to refine and
combine such lists.
3. The Identification of scenarios that would be extreme and whose
consequences would be expected to bound those of any other
scenarios, the latter of which would then not need to be defined
in detail.
The present study drew extensively on this earlier work in failure mode
(3—12}
identification, rather than developing sets of potential failure
elements independently.
With respect to the modeling of failure modes, it was not possible
to rely heavily on earlier work. There were two principal reasons for
this:
1. Other modeling efforts have generally been carried out for
different purposes than those of the present study. In
particular, models have been developed with specific sites in
mind, or at least with a view to eventual application to specific
sites. Therefore, these models can require detailed
site-specific data that may not even be available at present.
This study had to be more general in perspective and less
demanding in data requirements.
2. High priority was attached to developing models that would be as
simple as possible. Not only would these be more informative and
understandable to the users of this report, but they would enable
the easier identification of important assumptions and
uncertainties.
In spite of the limited applicability of the results of other modeling
efforts to the requirements of Task D, it has been possible to
22
-------
incorporate some of the modeling parameters derived elsewhere into
models developed in this study. Whenever possible, the results of the
Task D analysis have been compared or contrasted with results obtained
el se where.
It is important to emphasize at the outset that it is not the intent
of this study to draw any conclusions about the safety of the disposal
of radioactive wastes in geologic repositories. Such responsibilities
fall to the regulatory agencies and, more generally, to the public
through their elected government officials. The purpose of this study,
and in particular Task D, is to provide modeling techniques and
calculational results that have been requested as input for the
regulatory decision-making process. It should be noted that
uncertainties enter the analysis at every phase, from specific input
data, to the validity of modeling techniques, to the overall question of
whether something important might have been left out. Tt is not
possible to prove rigorously the correctness or completeness of the
results. However, it would be unusual to find any serious decision
process founded on complete and totally certain information. Therefore,
in this report the intention has been simply to explain the analytical
methods by which the results were obtained, to provide the rationale for
the choice of models and parameters, and to relate these, as far as
possible, to similar work being carried out by other groups. It is
largely through the peer review process that studies such as this
receive valuable feedback that can enhance the accuracy and precision of
the results. An early draft report on Task D received a wide review,
which has been very valuable in the preparation of this report.
D-2.2 SPECIFIC GUIDELINES
In developing a modeling strategy for nuclear waste repositories, it
is necessary to determine initially the time period for which the models
should apply. Various time periods have occasionally been suggested,
ranging from relatively short ones, such as 300 years, to rather long
ones, such as 10 million years. Part of the determination of time
frames depends on the nature of the wastes that would be placed in a
repository. Active and predominant fission products, such as cesium-137
23
-------
and strontium-90, have half-lives on the order of 30 years, so that
after a few hundred years they will have decayed to relatively l°w
levels. Transuranic elements, as well as some fission products, such as
technetium-99, have much longer half-lives. Tf spent reactor fuel is
placed in a repository, there would be a higher proportion of the
long-lived elements. The Task A Report discusses in greater detail how
these activity levels vary with time.
The regulatory philosophy in evidence in the United States today on
the subject of hazardous waste disposal is in a state of flux, largely
because of increased quantities of wastes and a greater awareness of the
pitfalls of past practice. Nevertheless, even new regulations make no
attempt to guarantee the complete integrity of the containment system in
perpetuity. Time periods of 30 to 100 years are generally the longest
under consideration even though many hazardous materials do not decay or
degrade with time. In the case of nuclear waste repositories, it was
decided Jointly by Arthur D. Little, Inc., and EPA to develop
performance models for a period of 10,000 years. This was thought to be
a conservatively long time period for repository evaluation, in the
sense that even a shorter period might be sufficient and consistent with
regulatory philosophy utilized in other areas. The 10,000-year period
allows for the modeling not only of direct releases to the biosphere,
but also of releases through groundwater pathways, which can require
very long times before harmful effects might occur. If the modeling
effort were carried even further into the future, the significance of
the results would decrease accordingly because so many factors
(available technology, population characteristics, future medical
capabilities, dominant health concerns, etc.) might be changed. In
fact, the past 10,000 years span the development of all important human
civilizations, and it does not seem necessary to carry future
projections into longer periods than this.
A second guideline for this study was that the performance
evaluation period should begin at the time the repository is sealed.
During the operational stage of the repository, there may exist some
risk of the release of radionuclides. For example, an accident could
24
-------
occur in transporting or emplacing a waste canister. Risks of this type
would be addressed by other regulations governing fuel cycle facilities,
but they are not addressed here.
A third guideline relates to the degree of future institutional
control or human knowledge of the repository. Consistent with EPA
direction, no control of the site after 100 years from repository
sealing has been assumed. In this study, this has been taken to imply
even the loss of knowledge that a repository exists on the site. Up
until this 100-year period has elapsed, however, full institutional
control of the site has been assumed to be capable of preventing
intrusions that could breach the containment system.
The last specific guideline has been referred to earlier, namely,
that this study is directed to the concept of geologic repositories
rather than to repositories at specific sites or with specific designs.
Thus it has been necessary to abstract from the literature a set of
engineering and geologic assumptions that represent so-called "generic"
repositories. Because the question of the estimation and importance of
uncertainties inevitably enters modeling efforts such as this, it is
important to note that in the case of generic repositories this question
takes an unusual form. Tt is not meaningful to assess the degree of
certainty one attaches to a parameter for a generic repository, since by
definition a generic repository is hypothetical and is defined by
whatever parameters have been specified. Rather, the uncertainty
question is transformed into the question of the variability of real
sites vis-a-vis the parameter values used in the generic model. In the
case of expected significant variability among real sites, two estimates
for parameters have been given in the generic description, one
correspond ing to rather favorable conditions (i.e., supportive of
containment) and another that would not appear to be so favorable.
These are referred to as the "first" and "second" estimates,
respectively. They are discussed in Section D-2.6.3.
D-2.3 SELECTION AND CHARACTERIZATION OF GENERIC GEOLOGIES
Based on the site selection programs of the Department of Energy and
the supporting research work reported in the literature, the following
25
-------
five geologic host media were chosen for detailed treatment in this
study:
• bedded salt
• granite
• basalt
• shale
• dome salt
There are other rock types that have been or are being seriously
considered for repositories, among which are welded volcanic tuff,
desert alluvium, anhydrite, and seabed sediments. Nevertheless,
the media chosen span a wide range of geologic structure and rock
properties, and an analysis based on them is believed to be
representative of the performance capabilities of geologic repositories
in general. The subsequent paragraphs contain discussions of the chosen
rock types and descriptions of the associated geologies assumed in this
study. Naturally, there can be wide variability in the geologic
parameters associated with a given type of rock.
D-2.3.1 Bedded Salt
Bedded salt has been prominently mentioned as a possible nuclear
waste repository host rock ever since a committee of the National
Academy of Sciences proposed that waste be buried in deep, stable
geologic media. Perhaps more research has gone into determining the
suitability of salt for this purpose than for any other
lithology. > > » »- jn Germany, some low-level radioactive waste
(21)
has already been deposited in unused salt mines. This interest in
salt is the result of some of its unique properties, in addition to its
common occurrence in stable formations at depths being considered for
repositories (200 ra to 1000 m) .
Salt is very soluble. However, it behaves plastically under
pressure, thereby tending to creep back into voids and cracks and seal
itself against the movement of water. This accounts for the lack of
water in most salt mines. Salt is also a relatively good thermal
conductor and thus has the ability to dissipate the heat generated by
26
-------
the wastes. The sedimentary sequences containing salt beds generally
contain aquifers both above and below the salt.
Salt itself is frequently mined, and there may be associated
deposits of other minerals or oil and gas. However, because massive
salt deposits are numerous, locations can probably be found with minimal
economic value and with a range of other desirable characteristics.
A map of prominent salt deposits in the United States is shown in
Figure D-i. The generic bedded salt stratigraphy adopted for modeling
purposes is shown in Figure D-2. It is implicit that the salt formation
is in a stable basin, and that the strata are relatively uniform and
continuous beyond the repository. For hydrologic modeling, both
aquifers are assumed to have identical horizontal gradients of 0.002 and
0.02 for first and second estimates, respectively. An average upward
vertical gradient for any connection between aquifers is assumed to
exist and to have the values 0.01 and 0.5 for first and second
estimates, respectively. (Note that a downward gradient may exist and
would, in general, represent a more favorable condition since any
leakage would then be to strata at greater depths. However, for
conservatism, an upward gradient has been assumed even in the first
estimate case.) The salt itself is assumed to be essentially
(22 23 24)
impermeable to the flow of water. ' '
D-2.3.2 Granite
Granite, or some similar monolithic crystalline rock, is another
important host rock. Canadian and Swedish studies of granitic rock as a
storage medium have provided some insight and details into the nature of
O S 76 ^
this candidate material. ' Excavations in granite have been used
for storage and military purposes.
Granite is an assemblage of minerals forming a rigid and essentially
insoluble rock. It is relatively strong and does not flow plastically;
thus, cracks can remain open to migrating fluids although some become
filled with clay or other materials. It does not conduct heat well, but
it does have a high heat capacity. In addition, the water passing
through granite is generally less corrosive than the brines and bitterns
associated with salt. Because it is an Intrusive, and therefore not
27
-------
oo
ARKO BASIN
I
PALO DURO BASIN
Source: Adapted from U.S. Department of Energy, Draft Environmental Impact Statement: Management of
Commercially Generated Radioactive Waste, Volume I, April 1979.
FIGURE D-1 ROCK SALT DEPOSITS IN THE UNITED STATES
-------
Surface
Surface
Deposits
Salt
-Repository
^-_-_- Shale
~// ^-*.~t ^*- -
x// Basement
/// Complex
330 Meters
360 Meters
410 Meters
460 Meters
510 Meters
560 Meters
590 Meters
FIGURE D-2 REPOSITORY IN BEDDED SALT
29
-------
stratified, granite is modeled without an underlying aquifer. This
limits the mechanisms for water flow through the repository.
Many areas of the country have granite or similar rocks at suitable
depths for a repository. Occasionally, vein minerals, pegmatites, or
quarry stone make granite economically important, but the vast expanse
of crystalline rocks suggests that many potential site locations remain.
A map of prominent granitic formations is shown in Figure D-3a. The
generic granite geology adopted for modeling purposes is shown in Figure
D-4. The aquifer is assumed to have horizontal gradients of 0.002 and
0.02 for first and second estimates, respectively. Reported
permeability values for granite vary over a wide range of test
conditions and may be as low as 4 x 10 cm/sec. ' Fluid flow
is governed by fracture systems.
D-2.3,3 Basalt
Basalt is another igneous rock that is being considered as a
(19 31)
repository medium. ' It shares with granite many properties common
to igneous rocks. It is strong, rigid, insoluble, and has a complex
mineralogy.
The extensive flow basalts being investigated are unlike other
igneous rocks in a number of important ways. Because these basalts have
formed as a series of layers over a long period of time, there are
sedimentary interbeds and other permeable zones that can serve as
aquifers, and these aquifers would be expected to exist both above and
below any basalt flow in which the repository would be located. Basalt
characteristically breaks into slender columns as it cools, producing
vertical joints. However, weathering products of the rock often fill
these cracks. Basalt is rarely associated with mineral resources, and
its most common economic use is as fill material.
The principal flow basalts that are being investigated for possible
repository siting are limited to the northwestern United States, in the
states of Washington, Oregon, and Idaho. (See Figure D-3.) The generic
basalt stratigraphy assumed in this study is shown in Figure D-5. The
hydraulic gradients within and between aquifers are assumed to be the
same as those specified earlier for bedded salt. Reported permeability
30
-------
PRECAMBRIAN
SHIELDGRANITES NORTHERN
(MARITIME)
APPALACHIAN.,
CENTRAL
APPALACHIANS
SOUTHERN
APPALACHIANS
a. Granitic Rock
COLUMBIA RIVER BASALT
KEWEENAWAN LAVAS
TRIASSIC LAVAS
b. Potential Repository Basalts
Source: U.S. Department of Energy, Draft Environmental Impact Statement: Management of
Commercially Generated Radioactive Watte, Volume 1, April 1979.
FIGURE D-3 CRYSTALLINE FORMATIONS IN THE UNITED STATES
31
-------
Surface
Surface
Deposits
.,..,..--•. -.-'j-....U-.-I.T- .-i..u 200 Meters
y^ Aquifer fyi^&®$3W$^^ ^Z&X M •>-^ 230 Meters
460 Meters
FIGURE D-4 REPOSITORY IN GRANITE
32
-------
-Surface
Surface
Deposits
-.7 - •-. . .. •.-..y..---,-.T*-VTBS»-v-^>f !*•.•'. .ragr'n-p- •„.-.. ...TT7~-.T-T..-;-?a-W--T.TT^T,;-...^ www mCtCrS
fotf:*y^ y^y r^^^^jtyiy yy^^ 360 meter$
/£.?<*?'?^ ^K'';^^'^^r/;"v • -'^\
C^~^' ~'^-~, v'\- ' '' 7«i^^^^^^^»'Rep_p^itoryi\ .,X-^\^_X460 meters
\'f i7^ ^r^ ,V^'"1 feW •:';! l^^iv, '^
A-^i^-/->;:; ^'-'':'-^-^;'>vi7-'''r^l' .'-^'••>rn
^pj^ Aquifer ^^ja^^'^^l^T^W^^g^M^BI ^ m6terS
V^Vr^;^-r^ v- :l/^J^'^'^'^^ meter$
\^ — D.e.if.' --v/^"^\.'\-' / "'-y x s~\-x ~"~^\'— r/1 ^ — ~~ t''•t1'
','1 J^^JvV '_' ,,\- -, ^ ', \ -x / \/_\''_v^x_-x«'-/NI.'>/_V x '
' •> \ "". s"| ^~/. ^ " \" S ^ \' I - \~ ^ ' v-~/ N~l ' ""/ N J" I I X ~ t x' " •' - ' .
i <^ N— 'iv ix ~xi/\~/^/-x\7-\"''' ^s r \ ^i"_"\ ~ /" ' -^ i —
FIGURE 0-5 REPOSITORY IN BASALT
33
-------
values for basalt range as low as 10 cm/sec, but there is a wide
(19,31,32,33)
range due to variable rock properties and test conditions.
D-2.3.4 Shale
Argillites, siltstones, and shales are the most common find extensive
sedimentary rocks. ^34^ These clay-rich rocks are often found in thick
deposits, and they are often nearly impermeable. Some shales exhibit a
plastic behavior similar to that of salt, but clay minerals have the
advantage over salt that they are essentially insoluble. There is a
very wide range in the properties of shales.
Clay minerals have a number of properties that may be important to
waste containment. Several clays will absorb water into their
structures, swelling in the process and sealing the water
passageways. ' Similarly, clays can adsorb chemicals, including
(36)
radionuclides, restricting or essentially stopping their movement.
However, as they can hydrate, many clay minerals can be dehydrated by
heating. This process may change both their chemical and mechanical
properties.
Argillaceous (clay-containing) deposits have a variety of economic
uses. Their abundance, however, suggests that many potential sites are
available where economic and other social impacts would be minimal.
A map of shales and related argillaceous deposits in the United
States is given in Figure D-6. The generic shale stratigraphy adopted
for modeling purposes is shown in Figure D-7. It is assumed that the
shale being modeled is highly indurated, which would aid the stability
of a mine while perhaps increasing the potential for fluid flow through
fractures. While some shales are nearly impermeable to the flow of
water, the hard shale in the model is assumed to have hydrologic
properties similar to those of basalt. Assumptions about the aquifer
hydraulic potentials are taken to be the same as in the case of bedded
salt and basalt. Reported shale permeabilities cover a very wide
range.(12,19,22,29,37,38,39)
34
-------
MICHIGAN
BASIN >
OJ
WEST
COAST
CLAYS
BASINS CONTAINING
ARGILLACEOUS FORMATIONS
TRIASSIC
BASINS
Source: U.S. Department of Energy, Draft Environmental Impact Statement: Management
of Commercially Generated Radioactive Waste, Volume 1, April 1979.
FIGURE D-6 ARGILLACEOUS FORMATIONS IN THE UNITED STATES
-------
Surface
Surface
Deposits
________ ..... . .... ..... ______ .,..•.. ...... ...... - - i.. ji. i j.-i i: • ij- 330 meters
36Q meter$
Repository '-iHH?: 460 meters
^^Pgfe^P^l?^^:^i^^^
FIGURE 0-7 REPOSITORY IN SHALE
36
-------
D-2.3.5 T)0me Salt
Many salt deposits are not bedded, but are formations that have been
forced up through overlying rocks from original beds at considerable
depths. These domes or stacks of salt are cbmposed of fairly
homogeneous halite and are generally devoid of interbeds or similar
features found in bedded salt. Typically, a salt dome will be roughly a
kilometer in diameter and capped with a blanket of less soluble
, (40,41)
evaporites.
Because a dome is injected into the overlying rock, the latter is
often shattered and disrupted with prevalent joints and fractures. The
salt itself may come very near to, or even reach, the surface; but the
(42)
source of the salt column may extend to depths near 10 kilometers.
The geometry of a dome implies that an aquifer directly below the
repository will not exist. However, the fracturing of the adjacent rock
indicates that the salt will be in contact with groundwater in adjacent
aquifers. These and other differences between bedded and dome salt
deposits indicate that each deserves a separate analysis. As with
bedded salt deposits, domes are frequently associated with oil, gas, and
various mineral resources.
Salt domes are found in several states in the South, as shown in
Figure D-l. The generic dome salt stratigraphy adopted for modeling
purposes is shown in Figure D-8. The hydraulic conditions in the upper
aquifer are assumed to be the same as in all the other cases. For
certain failure elements, the lower aquifer, while not directly below
the repository, is relevant. The vertical hydraulic gradients upward
between it and the upper aquifer have the values 0.01 and 0.2 for first
and second estimates respectively. The salt itself is assumed to be
/ »j o *)i O/ \
essentially impermeable to the flow of water. ' '
D-2.4 REPOSITORY ASSUMPTIONS
Conceptual repository designs have been discussed in the Task A and
B Reports and continue to be modified and refined in studies for the
(19 43)
Department of Energy. ' Based on this work, the parameters given
in Table D-12 have been used in this report. It should be noted that
37
-------
Surface
Surface
Deposits
Country /"\
Rock .TV. N ,
/ /l*x Caprock
* Six
x^\ \
;-/\\ x
Repository „ "I • . 460 Meters
,*f ' \N.
l\\
560 meters
590 meters
FIGURE D-8 REPOSITORY IN SALT DOME
38
-------
TABLE D-12
NOMINAL REPOSITORY PARAMETERS USED FOR MODEL CALCULATIONS
Depth of repository 460 m
Areal dimensions 2 km x 4 km
Number of canisters 35,000
Number of waste drifts 350
Canisters per waste drift 100
Length of waste drift 500 m
Canister spacing 5 m
Total mined volume 10 m
Percent of total volume used
for waste drifts 90%
39
-------
actual designs might vary considerably from the values given. For
example, a repository in an average-size salt dome could not occupy the
horizontal area specified in the table. Such differences are not
important for the purposes of the present performance model. Other
parameters specific to individual model calculations will be introduced
as necessary in later sections of this report.
D-2.5 IDENTIFICATION OF FAILURE MECHANISMS
The principal purpose of Task D is to identify potential
breach-of-containment mechanisms for geologic repositories and to
characterize them quantitatively. A review of the literature indicated
a wide range of potential failure mechanisms that have been identified.
These were evaluated and compared to determine their relative
importance; and, as a result, ten were selected for detailed modeling.
These are shown in Table D-13. It is believed that a repository
performance assessment based on these mechanisms includes the dominant
contributors to risk and covers the range from likely events with small
consequences to very unlikely events with large consequences. A number
of events and processes not chosen for detailed modeling are also
discussed later in this report. Many of these are relatively slow
geologic processes that would not be expected to have significant
effects over the 10,000-year time frame chosen for this study.
D-2.6 CONCEPTUAL FRAMEWORK FOR QUANTITATIVE ANALYSIS
The quantitative evaluation of potential breach-of-containment
mechanisms includes two principal aspects:
1. Estimates of the likelihood or probability of occurrence of
various mechanisms.
2. Estimates of the consequences of such mechanisms.
Naturally, it is important to take into account interactions between
various mechanisms when these appear to be capable of increasing either
their likelihood or their consequences.
40
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TABLE D-13
FAILURE ELEMENTS CHOSEN FOR DETAILED MODELING
TECHNOLOGICAL
HUMAN INTRUSION
NATURAL
Flow through bulk rock with altered permeability
Shaft seal failure
Borehole seal failure
Undetected boreholes
Future drilling
Fault movement
Volcanoes
Igneous intrusives
Meteorites
Breccia pipes
-------
D-2.6.1 Probabilities
It is inevitable that probabilistic considerations enter into any
performance assessment program for repositories, even if they do not
enter explicitly. This is true even for the approach using so-called
"worst case scenarios", since the judgment is made therein that cases
worse than those treated have negligible probabilities of occurrence.
Despite the ubiquitous necessity of at least qualitative judgments on
likelihoods and probabilities,•efforts to systematize and quantify such
judgments are difficult to carry out and often lacking in precedent.
Probabilities may be interpreted in different senses, according to
various schools of thought. They may, for example, be used to refer
to the long-term frequency of occurrence of certain events. On the
other hand, they may be taken as subjective measures of belief that a
certain event will occur. Statistical analyses usually derive
probabilities from data on frequency of occurrence; decision analysis
and strategic planning often deal more with probabilities as measures of
belief. In these and other interpretations of probabilities, the same
mathematical formulations apply, and in areas where the different
interpretations overlap, the results will ordinarily be consistent. The
approach of the present study was strictly pragmatic. It was desired to
use the best information available to clarify and improve otherwise
qualitative judgments, even though the result might fall somewhat short
of a mathematically axiomatized probability theory. Thus the
probabilities assigned to various breach-of-containment mechanisms had
to be derived on an ad hoc basis. Some result from crude statistical
analyses, some from simple models with statistical components, and some
primarily from the judgment of the authors, based on personal experience
and a review of the literature. In each case the derivation of the
probabilities has been explained.
D-2.6.2 Consequences
The ultimate consequences of concern in evaluating repository
performance capabilities are adverse effects on the health of present
42
-------
and future generations. The estimation of such consequences requires
several steps:
1. The physical characterization of a breach of containment
mechanism.
2. The characterization of a source term, I.e., the radionucllde
inventory affected by the breach.
3. The identification and quantification of driving forces that
would tend to move the radionuclides out of the repository.
4. The modeling of the actual leaching of radionuclides and their
transport through groundwater systems or through surface
pathways.
5. The calculation of doses to individuals and populations.
6. The estimation of the health effects of the calculated doses.
The scope of Task T) only pertains to the first three of these steps.
The last three are being modeled by the EPA, based on methods described
in Task C and elsewhere.
The physical characterization of breach mechanisms generally
involves considerations such as size, depth, location, permeability, and
porosity of the resulting pathway. Not all of these apply to all cases
since the mechanisms vary widely. The characterization of the source
term generally refers to the extent of the repository subject to the
effects of the breach. For example, one waste drift might be subject to
leaching as the result of a borehole passing through it. The term
"uniform concentration" is frequently used in the sequel to refer to the
average concentration of radionuclides in the waste drifts as a result
of canister degradation and leaching of the waste form. Parameters and
models relating to corrosion and leaching have been discussed in the
reports of Tasks B and C. (Appendix D-VIII of this report also discusses
some aspects of canister performance.)
Driving forces that enter into various release calculations include
direct physical transport and transport in groundwater. Groundwater
flows can be driven by a number of factors that affect hydraulic
potentials, such as artesian conditions in confined aquifers, buoyancy
forces resulting from density differences, and others. Several of these
are discussed in the appendices, the principal results being employed in
the main text.
43
-------
A prerequisite for a number of the release mechanisms is that the
repository and the surrounding rock return to a saturated condition
after the perturbation caused by the operational stage, during which any
water in the surrounding rock would tend to flow into the cavity and
then be pumped out. Resaturation times for all cases have been
estimated in Appendix D-II. For all but the two repositories in salt,
these times are not judged to be significant enough to warrant further
consideration. However, since salt tends to flow plastically and close
up void spaces, the time to establish resaturation is closely related to
the total quantity of water present under that condition. For this
reason, resaturation is considered in connection with a number of
release mechanisms in the salt repositories.
D-2.6.3 Uncertainty.and Variability,
The subject of uncertainty analysis has been briefly referred to
earlier (Section D-2.1), where it was pointed out that the basic
question is one of variability, namely, to what extent might the
properties of real sites vary from those used in the generic
description. When significant variability is identified, it is
incorporated into the analysis by the use of so-called "first" and
"second" estimates, defined as follows:
First Estimate - a parameter estimate assuming that the site exhibits
favorable characteristics with respect to the
particular breach mechanism in question (i.e., tending
to reduce the risk) .
Second Estimate - a parameter estimate assuming that the site exhibits
somewhat less favorable characteristics with respect
to the particular breach mechanism in question,
although it may be highly favorable with respect to
other factors.
In both cases, models and approximations have been chosen to err on the
conservative side, i.e., tending to overestimate the likelihood or the
consequences of the events. It is believed that, for each first
estimate, sites will be able to be identified where the corresponding
property is at least as good as the estimate. Many more sites can
44
-------
probably be found where the property is better than the second estimate.
The use of relatively simple models in the report, rather than complex
computerized ones, facilitates the determination of the sensitivities of
results to the various input parameters and assumptions.
It is important to emphasize that the primary emphasis in this study
has been on rough order-of-magnitude estimates. Therefore specific
details that could only slightly perturb the results are often ignored.
At the same time, a number of the calculations are reported with greater
precision than the input data or the goals justify. This has been done
simply to aid readers who wish to retrace the calculations in order to
test their understanding of the methods employed.
45
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D-3.0 TECHNOLOGICAL FAILURE ELEMENTS
The failure elements considered in this chapter correspond either to
the degradation or failure of engineered systems or to the effect of the
repository on the host geologic formation. Those elements chosen for
detailed modeling are all capable of providing pathways for the movement
of radionuclides from the repository to the aquifer system. Failures in
some individual components, such as waste forms, are briefly discussed
in Section D-3.5.
D-3.1 FLOW THROUGH BULK ROCK
D-3.1.1 Summary
A major consideration in both the design and the performance
assessment of a repository is the fact that high-level radioactive
wastes generate considerable quantities of heat. This heat can affect
both engineered barriers to waste migration, such as waste forms and
canisters, and the surrounding rock. The present model deals with the
latter aspect.
In particular, temperature changes cause stress changes in the rock,
which can alter its hydraulic conductivity. Examples of mechanisms for
this alteration include additional fracturing, movement along fractures,
or changes in the dimens'ions of fractures or pores. For repositories in
salt, either bedded or domed, probabilistic calculations were carried
out, based on a statistical characterization of spatially varying
materials properties, to determine the probability of a fracture pathway
developing through the salt. For the non-salt repositories — granite,
basalt, and shale — a simple deterministic model was used for the
variation of the hydraulic conductivity as a function of time.
A summary of the analysis is given in Table D-14, and the details
follow in subsequent sections.
47
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TABLE D-14
SUMMARY OF FLOW THROUGH BULK ROCK FAILURE ELEMENT
MEDIUM
BaddodS.lt
Granite
Baeatt
State
Dora Silt
PROBABILISTIC (PI
DETERMINISTIC IOI
P
D
0
0
P
NATURE
OF
MOD€L
Cumulative occur-
rence probability
Change in permea-
peek
Clung* in permea-
bility after thermal
pee*
Change In painiM
Witty after thermal
P-k
Cumulative occur-
rence probability
RELEASE
MODE
Groundnater
GroundMrater
Groundiwter
Groundwater
Groundwater
DRIVING
FORCE
Pressure from silt
closure, thermally
induced convtction,
and gradient from
aquifer imereonnec-
tion
Thermally induosd
Tharmalry Induced
convtctton end
gradient from aquifer
Thermalry i*iducad
gradient tram aquiftr
interconnection
Pressure from silt
etosura. rharmalry
lower aquifer at edge
ofsaHdoma
SOURCE
TERM
concentration
Uniform
Uniform
concentration
Uniform
concentration
Uniform
concentration
PARAMETERS
in ESTIMATE
p-0
K • 10'10 cm/sac for
KlOOyn
K • 10-*cm/iacfor
t> 100 yn
n • 10-*
A - 8»!0*m2
K > 10* cm/sac for
KlOOyn
K - 10* cm/sec tor
t > 100 yn
" ' 1a*-« 1
A - BxlO^m2
K - 10* em/sac for
KtOOvrs
K - 10* cm/sac for
»100yn
" ' 1 100 yrs
D - 10-*
A - BilO6"2
K - 10"' cm/we for
K 100 yrs
K ' 10"* cm/sec for
t > 100 yn
n • 10-*
A - S'lO^m3
K • 10"7 cm/tac for
t< 100 yrs
K - 10* cm/sac for
t> 100 yrs
n • 10-*
A • B»10*m2
P-0
FLUID FLOW RATES FROM
REPOSITORY TO UPPER AQUIFER
1«t ESTIMATE
No releases need to be
calculated.
1 (yn) 6(0 Im3/yrl
100 1.4 KlO2
1000 8.8 « 10*
10.000 3.8x10'
t (ynl Qdl Im3/yrl
100 1.8x10*
1000 1.5 » 10*
10.000 6.3 x 103
t (yn CMO (m3rVI
100 UxlO*
1000 1£«10*
10JOOO 6J > 10?
No rslsaiai n«ad to be
calculated.
2ml ESTIMATE
No rslesm need to be
calculated.
t Ivn) Oh) iro'/yr)
100 1.4x10*
1000 en > to3
0.000 3.8 x 103
< (ml Olll (m3/VT)
100 73x10*
1000 7.7 x Id6
10.000 6B x 106
t (y» 6(t! 10*
10.000 68. 106
No nlaam need to be
calculated.
COMMENTS
The probability that the
spatial variability in
rock strength could
lead to an extensive
patfmiay from the ra-
portoryrhat~Hild
fracture under tha
msaas axperiancad
mas found to be neg-
ligibla.
Permaabtlitv change
after thermal oaak » dus
to savaral factors:
moMnvjnt of blocks
during thermal cycle.
material in cradu.
alteration of minerals
in cracks.
Parrnaabilrtv change
after thermal peak is dm
to savaral factors:
during thermal cycle,
incomplete rebound of
malarial In cradu.
in cracks.
Pairnaabmty change
after thermal peak is due
to savaral factors:
movamant of blocks
during thermal cycle.
material in cracks,
in cracks.
Tha probability that
rock strength could laad
to an extensive pathway
from the repository that
would fracture under
was found to be nag-
ligalla.
00
-------
D-3.1.2 Background
Heat generation j)v_.high-level wastes. High-level radioactive wastes
generate heat, on the order of up to several kW per canister according
to present packaging concepts. Depending on the average planar heat
density at which the wastes are placed in a repository (ranging from 60
to 200 kW/acre in conceptual designs) and on the proportions of short-
and long-lived radionuclides in the wastes, the temperature of the rock
surrounding the repository can rise considerably. In the immediate
vicinity of the wastes, this rise might be as great as 100-200 C,
depending on the age of the waste, the quantity per canister, and the
spacing between canisters. Representative temperature profiles were
calculated and reported in the Task B Report (Engineering Controls), and
simplified approximations to these are discussed in Appendix D-VT of
this report.
Effects of heat. Heat can affect both engineered and natural
barriers to waste migration. The focus of this failure element is on
changes in the rock characteristics that control the movement of fluids.
In particular, heat can:
• modify basic rock properties, such as brittleness, ductility, and
strength;
• alter mineralogical structure (e.g., by dehydrating clays),
thereby also affecting rock properties;
• cause stress buildups and movement from thermal expansion. New
stresses may cause fracturing.
These effects all contribute to modifications in the ability of rock to
serve as a barrier to fluid migration.
In fact, there is not a simple heating effect, but rather a
heating-cooling cycle, because the heat-generating wastes gradually
decay to low levels. This factor will be considered further in Section
D-3.1.3 on the failure model.
Fluid flow model. The Task C Report (Migration Pathways) contains a
discussion of Darcy's law and its application to fluid flow calculations
in both porous and fractured rock; further discussion may be found In
Appendices D-V and D-VI of this report. A summary of the principal
points follows.
49
-------
The flow of groundwater in saturated porous rock dan be described by
Darcy's law, in the form of the equation:
Q - KiAc(u)
where
Q = volumetric flow rate (volume/time);
K « hydraulic conductivity (length/time);
i = hydraulic gradient (dimensionless);
A = cross-sectional area of the flow path being considered;
c(p) = viscosity correction factor (dimensionless) that accounts for
increased flow at lower viscosities.
K is frequently given in cm/sec, which is also the basic unit used here.
However, because of the magnitude of the flows that result in the
present situation, for calculational purposes K will be transformed to
units of m/yr and Q will be given in m /yr. Although Darcy's law is
generally applied only to relatively homogeneous porous media, it has
been found suitable for application to fractured media to describe the
hydrologic system on a macro scale. Although the law may not be
sufficiently accurate to model the yield of a single well, for example,
which depends on the local distribution of fractures, it can be applied
(28)
to describe gross water movement over large areas or regions. In
fact, the hydraulic conductivity, K, corresponding to fracture flow can
be modeled analytically, using fracture parameters and the principles of
fluid mechanics, ' although research continues into improving these
models.
The expression Kic(u) has the units of velocity and is sometimes
called the Darcy velocity. It is not a true fluid velocity at all, but
rather a measure of the volumetric flow rate per unit of cross-sectional
area of the flow path. By dividing by the effective porosity, n, of
the rock, the actual average fluid movement rate is obtained. This
velocity,
Kic(y)
n
is useful for estimating how long it would take for noninteracting
solute to be carried along the flow pathway with the groundwater. Of
50
-------
course, It is only an average value and therefore an approximation to
the actual rates in different fracture paths. For porous rock like
sandstone, the value of n may be in the range of 0.1 to 0.5 . For
fractured but tightly squeezed rock, as in deep granitic stocks, n may
-4
be in the vicinity of 10 . Such low values of n mean that transit
times may be fast, even when the hydraulic conductivity and volumetric
flow rates are low.
Ranges of parameter values have been given in the Task C Report
(Migration Pathways) and in Chapter D-2.0 of this report. They will be
cited as appropriate in the next section, where the present failure
element is characterized in terms of changes in K. The parameter K is
often loosely referred to as the permeability, especially when the fluid
under consideration is known and fixed. In fluid mechanics, there is
also an "intrinsic" permeability, k (in units of area), which permits
the separation of fluid properties from those of the rock itself ; but
this latter permeability will not be used here. Therefore, in keeping
with common practice, K will often be referred to as the permeability.
Permeability measurements. Specific permeability values are applied
in subsequent sections to characterize rocks or other materials. It is
not easy to measure values in the ranges given, especially by in-situ
techniques, which would be expected to represent more accurately the
fluid flow properties of the bulk rock mass. Thus, the actual
verification that a specific rock mass has an approximate permeability
in some of the ranges referred to may be quite difficult. However,
because of this relatively new need for measuring very low
permeabilities, techniques are being actively developed for this
purpose.
D-3.1.3 Flow Through Bulk Rock Failure Model
The breach-of-containment mechanism under discussion here refers to
fluid movement through the bulk rock itself, independent of the
development of additional permeable pathways, such as faults, leaky
shafts, and borehole seals. As long as two conditions hold, namely,
• the rock has a permeability greater than zero, and
• a hydraulic gradient is present,
51
-------
there will be fluid flow through the rock. If the permeability
is sufficiently small, then the flow volume can be considered
negligible. Some of the calculations reported in the next section do
lead to such negligible flows.
The purpose of this section is to characterize the permeability and
porosity of the rock surrounding the repository for use in the flow
calculations of Section D-3.1.4.
D-3.1.3.1 Bedded Salt and Dome Salt
Relatively pure salt at the depths considered in this study has a
permeability that is so low that it is nearly impossible to
(22 23 24)
measure. ' ' For the purposes of this study, intact salt may be
regarded as impermeable. The heat generated by the wastes is not
expected to change the value, except perhaps to decrease it by
compression of pores, unless sufficient stresses are generated to cause
fracturing. Rock mechanics calculations based on uniform rock salt
characteristics do not predict such fracturing because the stresses do
not exceed the rock strength and, in addition, they can be relieved by
salt deformation. Additional calculations were carried out with a
stochastic model that accounts for local spatial variation of rock
properties. The question was whether there might be a combination of
weaker zones in the salt through which a long fracture pathway might
develop. These probabilistic calculations, reported in detail in
Appendix D-IX, show that this probability is negligible. Thus the
permeability value of the salt is assumed not to increase with time.
Because of this and because there is negligible flow with the baseline
salt permeability value, no detailed flow calculations are necessary.
D-3.1.3.2 Granite, Basalt, and Shale
Granite and basalt are igneous rocks in which fluid flow is almost
entirely within fracture systems. Shale is a sedimentary rock whose
characteristics are extremely variable, ranging from relatively soft,
plastic material to highly indurated rock similar in many properties to
igneous rocks. The latter type of shale has been assumed for modeling
52
-------
purposes, so that fracture flow also dominates in this case.
The following processes will, in general, occur during the period of
temperature rise:
• expansion of rock, thereby decreasing the size of openings such as
pore spaces, fractures, and other discontinuities;
• compaction of fill material, (such as clays) In fractures;
• slippage and movement along fractures; and
• alteration of mineral content, such as by dehydration of clays.
In addition, new fractures may develop, but this Is not considered
likely to occur to a significant degree from the temperature changes
expected In the rock surrounding the repository. Some of the above
processes can contribute to a decrease In bulk permeability during this
(48 49)
period. ' However, no attempt has been made in this report to
model this effect quantitatively.
More important is the fact that after the temperatures peak and then
begin to decrease, several effects can contribute to a new higher bulk
rock permeability. For example, the surfaces of fractures may not
return to their original position, and asperities may keep them apart.
Clay fill that has been compacted may not rebound completely, leading to
open channels. Clays that have been altered may crumble and fail to
fill their original volume. Mechanistic models are not available to
predict the net effect of these processes, either generically or in
specific instances. Nevertheless, by considering the range of
permeability values for the types of rock formations in question,
modified permeabilities may be estimated. The values chosen for
modeling purposes are summarized in Table D-15. For purposes of
conservatism, the increase in permeability is modeled at the 100-year
point after repository closure, even though the increase is expected to
be gradual and may actually occur later. Note that it is difficult to
estimate the level of assurance with which a given specific site can be
determined to have the kind of low permeabilities assumed here. This
problem must be addressed in the detailed characterization of specific
sites.
53
-------
TABLE D-
MODEL PERMEABILITIES FOR TUB".
BEFORE AMP AFTER THERMAL CYCLE
Bulk Rock Permeability (K)
(cm/sec)
Basalt
Shale
First Estimate
Granite t < 100 yrs**
t > 100 yrs
t < 100 yrs
t > 100 yrs
t < 100 yrs
10
-10
10
-9
10
-9
.-8
10
-9
t > 100 yrs 10
-8
Second Estimate
10
-7
10
10
-7
10
-7
10
-6
Note: Permeabilities of these rocks can be much higher than the values
given in this column. The second estimate corresponds in this
case to suboptimal values, but ones that might reasonably still
be in the range of consideration for repository siting.
**Years after repository closure.
54
-------
D-3.1.4 Flow Through Bulk Rock Release Model
D-3.1.4.1 Bedded Salt
Because thermal effects do not alter the permeability of the
surrounding salt and because salt is essentially an impermeable medium,
all flows in the bulk rock are negligible in comparison with other
release mechanisms. Consequently, no calculations are presented for
this case.
D-3.1.4*2 Granite
Of the driving forces discussed in the appendices, only thermal
convection is relevant for this release mechanism. This driving force
depends on time because the temperature profile varies over time. The
methodology for evaluating this driving force is presented in Appendix
D-VI and the resulting effective gradients are shown in Table D-16. As
pointed out in the appendix, these values represent upper bounds on the
possible buoyancy forces.
The volumetric flow rate can be calculated from Darcy's law. The
2
values of K have been given in Section 0-3.1.3; A is 8 km ; and c(y) is
5, in accordance with Appendix D-VI. The results are presented in Table
D-17.
As discussed in Appendix D-VI, the average vertical fluid velocity
is obtained from the equation
Ki
lOOun
The resulting velocities and transit times are presented in Tables D-18
and D-19. As discussed in Appendix VI, because water may be more
readily available near the edge of the repository, the vertical velocity
may be as much as ten times higher in some locations, leading to shorter
transit times to the aquifer.
The source term for this failure element consists of the
concentration of radionuclldes that have leached into the water in the
55
-------
TABLE D-16
EFFECTIVE VERTICAL HYDRAULIC GRADIENT IN SURROUNDING
GEOLOGIC MEDIA FROM THERMALLY INDUCED CONVECTION
(GRANITE REPOSITORY)
Hydraulic Gradient (i)
100 years 1000 years 10,000 years
First Estimate 0.011 0.007 0.003
Second Estimate 0.011 0.007 0.003
*
Years after repository closure.
Source: Appendix D-VT, taking into account a ten-fold reduction because
of the resistance of the recharge pathway, as discussed in the
last section of that appendix.
56
-------
TABLE 0-17
VOLUMETRIC FLOW IUTES THROUGH BULK ROCK
(GRANITE REPOSITORY)
Volumetric Flow (Q)
(m3/yr)
100 years 1000 years 10.000 years
2 1
First Estimate 1.4 x in 8.8 x in
3.S x 10
Second Estimate 1.4 x 10 4 8.8 x in3 3.8 x 103
Years after repository closure.
57
-------
TABLE D-1B
FLUID VELOCITIES THROUGH BULK ROCK
(GRANITE REPOSITORY)
Velocity (v)
(m/yr)
100 years 1000 years 10.000 years
First Estimate
0.20
0.11
0.05
Second Estimate
18.0
11.0
4.7
Years after repository closure.
58
-------
TABLE T5-1Q
FLUID TRANSIT TIME FROM REPOSITORY TO AQUIFER THROUGH BULK ROCK
(GR\NTTE REPOSITORY)
Time
(yrs)
IPO years 1000 years 10.om years
First Estimate
1150
2100
4*00
Second Estimate
20
Years after repository closure.
59
-------
repository during the time frame of interest. This is the uniform
concentration situation described earlier.
D-3.1.4.3 Basalt
The two possible driving forces for this case are thermally induced
convection and an aquifer interconnection. Because the temperature
profile varies with time, the magnitude of the combined effect also
varies with time. The methodology used to evaluate thermally induced
convection is developed in Appendix D-VI, and estimates for the
effective vertical hydraulic gradient are presented in Table D-20.
These values represent upper bounds on the possible gradients. Using
these hydraulic gradients, the volumetric flows can be calculated from
Darcy's law. Table D-21 presents the results of the calculation. As
discussed earlier, the vertical fluid velocity is obtained by dividing
the volumetric flow rates by n. This leads to the velocity and transit
time estimates in Tables D-22 and D-23.
The source term for this failure element consists of the
concentration of radionuclides that have leached into the water in the
repository during the time frame of interest. This is the uniform
concentration situation discussed earlier.
D-3.1.4.3 Shale
All modeling parameters relevant to this release mechanism are
identical for the shale and basalt repositories. Therefore the
discussion and calculations for the two repositories are identical. The
results are summarized in Tables D-24, D-25 and D-26.
D-3.1.4.4 Dome Salt
As in the case of bedded salt, all flows in the bulk rock are
negligible in comparison with the other release mechanisms.
Consequently, no detailed calculations are required for this case.
60
-------
TABLE D-20
EFFECTIVE VERTICAL HYDRAULIC GRADIENT IN SURROUNDING GEOLOGIC
MEDIA FROM THERMALLY INDUCED CONVECTION AND AQUIFER INTERCONNECTION
(BASALT REPOSITORY)
Hydraulic Gradient (i)
100 years
1000 years
10.000 years
Thermally Induced
**
Convection
First Estimate
Second Estimate
Aquifer Interconnection
First Estimate
Second Estimate
First Estimate
Second Estimate
***
0.13
0.13
0.01
0.5
0.14
0.63
0.11
0.11
0.01
0.5
0.12
0.61
0.04
0.04
0.01
0.5
0.05
0.54
**
***
Years after repository closure.
t
These values are from Table D-VI-4, Appendix D-VI,
These values are from Section D-2.3.3.
61
-------
TABLE D-21
VOLUMETRIC FLOW RATES THROUGH BULK ROCK
(BASALT REPOSITORY)
Volumetric Flow (Q)
(m /yr)
100 years* 1000 years IQ.flno years
First Estimate
l.R x 104 1.5 x 104 6.3 x 103
Second Estimate 7.9 x
7.7 x 106 6.8 x 1C6
Years after repository closure.
62
-------
TABLE D-22
FLUID VELOCITIES THROUGH BULK ROCK
(BASALT REPOSITORY)
Velocity (y)
(m/yr)
100 years 1000 years 10.000 years
First Estimate 23 19 7.9
Second Estimate Q.9 x 10 9.6 x 10 P.5 x 10'
*
Years after repository closure.
63
-------
TABLE D-23
FLUID TRANSIT TIMES THROUGH BULK ROCK
(BASALT REPOSITORY)
Time
(yrs)
100 years 1000 years 10.0^0 years
First Estimate
4.3
5.3
Second Estimate
0.01
0.01
0.01
Years after repository closure.
64
-------
TABLE D-24
VOLUMETRIC FLOW RATES THROUGH BULK ROCK
(SHALE REPOSITORY)
•
Volumetric Flow (Q)
(m3/yr)
*
100 years 1000 years 10.000 years
First Estimate 1.8 x 104 1.5 x 104 6.3 x 103
Second Estimate 7.9 x 106 7.7 x 106 6.R x 1Q6
Years after repository closure.
65
-------
TABLE D-25
FLUID VELOCITIES THROUGH BULK ROCK
(SHALE REPOSITORY)
Velocity (v)
(m/yr)
*
100 years 1000 years in.QQO years
First Estimate 23 19 7.9
Second Estimate Q.9 x lV 9.6 x ]V «.5 x 10
Years after repository closure.
66
-------
TABLE D-26
FLUID TRANSIT TIMES THROUGH BULK ROCK
(SHALE REPOSITORY)
Time
(yrs)
100 years 1000 years 10.000 years
First Estimate
4.3
5.3
Second Estimate 0.01
0.01
0.01
Years after repository closure.
67
-------
D-3.1.5 Literature Discussion
Flow through bulk rock has been considered in a number of studies
(11)29) as well as in the Task C Report for this project. In addition,
some researchers have discussed waste- induced permeability changes.
(
The NRC/Sandia risk program proposes a model for stress- induced
fracturing in terms of "reference cracks." A reference crack is a
vertical planar crack whose horizontal cross-section has dimensions 1 mm
x 3 km. The effect of stress buildups on the rock is measured in terms
of a number of new reference cracks. This number is obtained from the
expression 5h , where h is the vertical displacement in centimeters.
Since the vertical displacement is expected to be on the order of one or
several meters, somewhat over 500 reference cracks might be expected.
The authors do note large sources of error in this approximate model.
The BNWL/ONW1/DOE WISAP program has also noted this failure
element, although quantitative estimates of permeability changes have
not been reported .
D-3.2 SHAFT SEAL FAILURE
D-3.2.1 Summary
During the operational stage of the repository, several vertical
shafts will be required for ventilation and for the transport of
personnel and materials between the underground workings and the
surface. (See Figure D-9). Part of the process of sealing the
repository for long-term isolation of the radioactive wastes requires
that these shafts be filled with appropriate materials in order to
prevent them from serving as pathways for fluid flow or radionuclide
migration.
The sealing materials will need to be chosen with a specific
environment in mind so that they may approach, as nearly as possible,
chemical and mechanical equilibrium with the surrounding rock. The seal
may consist of several layers of completely distinct types to provide a
multi-barrier line of defense against expected or unexpected forces.
68
-------
Shaft »
Surface
deposits
^pfi,Aquif^^|l^
Shale
Salt
-« .Shaft
i;CW^&^';^v#M^!i#fe^
®.'&*a!jit.si!!'>-> •'#*"•&. Sl'.-iWfv/::!-:.'-!
Surface
330 Meters
360 Meters
410 Meters
460 Meters
510 Meters
£HHH?^!'L~I^-I^:£HI-~1^~^-~^^
/////"/,
Basement
FIGURE D-9 BEDDED SALT REPOSITORY
SHOWING VERTICAL SHAFTS
69
-------
Nevertheless, it is reasonable to expect that over a long period of
time, such as 10,000 years, the combination of processes such as
settling, leaching, expansion and contraction due to fluctuations in
water content or temperature, earth movements, weathering, and fatigue
may lead to some degradation in the integrity of the seal.
The shaft seal performance model considered here is not derived from
a particular design. It is intended to be generic in nature and
conservative; that is, it is believed that the performance
characteristics described here can be equalled or exceeded by actual
designs for specific circumstances.
The generic model used in this report characterizes the shaft seal
integrity by a spatially uniform hydraulic conductivity K. One
hydraulic conductivity value (KQ) is estimated for the time of seal
emplacement, and another value (K.) is estimated for the time 10,000
years later. It is assumed that K increases linearly from Kg to K. over
this period. A summary of the analysis is given in Table D-27.
D-3.2.2 Background
The excavation and operation of an underground repository require
the sinking of a number of shafts to provide access, ventilation,
removal of rock, etc. These shafts will vary in size and construction
depending upon their function and the rock through which they pass.
Even in relatively simple geologic settings, such as those represented
by the generic models in this report, a variety of construction and
maintenance techniques may be required for the shafts to remain usable
during the operational life of the repository. It is important to
review these technologies in order to set the framework for discussion
of the shaft sealing problem.
Much of the focus of mine shaft engineering is on the problems of
hole stability and water inflow. These problems are often interrelated,
and even when they are not, some of the same engineering techniques may
be effective for both. For example, the portion of a shaft penetrating
either incompetent or water-bearing rock, or occasionally an entire
shaft, may be lined with a tubular structure, and the annular space
between this liner and the rock then filled with a sealer or grout. The
70
-------
TABLE D-27
SUMMARY OF SHAFT SEAL FAILURE ELEMENT
MEDIUM
Bedded Sett
Granite
Basalt
It;
Si
S I
Is
E8
0
D
D
NATURE
OF
MODEL
Lbiaarly Increasing
permeeMlity
Linearly increasing
permeability
Linearly increasing
peimaabahy
RELEASE
MODE
Grounrhvater
Groundvwater
Grourahvatar
DRIVING
FORCE
Initially pressure
from art craap.
Aftanoards. U-tube
effect.
Thermally induced
convection and
U-lube effect.
Thermal ly induced
U-tutae effect.
SOURCE
TERM
Uniform
Uniform
Concentration
Uniform
concentration
PARAMETERS
1st ESTIMATE
Kg- 10* cm/sec at
time of seeling
K, - 10* cm/sac
after 10.000 year.
K increase* linaariy
from Kg to Kj over
10,000 years
n - 0.1
A - 100m2, total
cross seuioiial area
of shafts
Kg- 10* cm/sec at
time of sealing
K, - 1CT6 cm/sac
attar 10.000 years
K increessi linearly
from Kg to Kj over
10.000 yean
1 • 0.1
A - 100m2, total
ofshafts
Kg- 10*cm/sacat
time of seeling
K,- 10* cm/sac
aftar 10JOOO yean
K lnitsa.ii linaariy
from Kg to K, ovar
10.000 yean
T, * 0.1
A - 100m2. total
o< shafts
2nd ESTIMATE
Kg- 10"8 cm/tec »t
lima of easting
K, - 10-* cm/sec
after 10X100 years
from Kg to K^ over
10.000 year.
1-0.1
A • 100m2.total
cross-factional aree
ofshafts
Kg- 10"8 cm/sec at
time of seeling
K,- 10-4 cm/sec
alter 10.000 years
•K increases linearly
from Kg to Kj over
10,000 yean
1 - 0.1
A - 100m2. total
ofshafts
Kg- 10*cm/eacat
time of sealing
K,- ID"4 cm/sec
after 10.000 yean
Killiiessei linearly
from Kg to K, over
10.000 yean
n - 0.1
A - 100m2. total
of shafts
FLUID FLOW RATES FROM
REPOSITORY TO UPPER AQUIFER
Itt ESTIMATE
tlyn)
200
223"
223*
1000
10.000
O It) Im3/Vrl
40 ) Parted
40 I0*""
40 ) craap
OJ08
0.17
0.32
tlyn)
100
1000
10.000
Q It) Im3/yrl
0.3
1.0
1.6
tlynl
100
1000
10.000
dlt)lm3/yr>
0.4
1.7
3.2
2nd ESTIMATE
tlynl
720
1000'
1000*
10,000
d It) Im3/yrl
^H.?
3.15
3.15
tlynl
100
1000
10^100
d 111 Im3/yrl
153
94.6
236.3
tlyn)
100
1000
10.000
0 It) Ini3/yrl
28j>
1S7i
472.6
COMMENTS
It is conservative to
assume dceure bysart
creep for this failure
laaaluiaUmi time would
be enremel Viang.
Oosurealsoinipllaa
ill oily driving fores for
release.
RriMW only DBBMI
•ftvr npository
tmnuntian.
R--.»oo*yb.^
•flaw raparitory
-------
TABLE D-27
SUGARY OF SHAFT SEAL FAILURE ELEMENT (CONTINUED)
MEDIUM
Stole
Dome Salt
SB
Si
32
< GC
is
D
O
NATURE
OF
MODEL
Ltntsriy mcrtatins
parrn*8biJltv
Limarlv Iner-Ming
paffsTMSblliry
RELEASE
MODE
Ground water
Groundwater
DRIVING
FORCE
Thermally induced
convection and
U tube effect.
Inilisllv pressure
from »ll creep.
Afterwards. U-uibe
effect.
SOURCE
TERM
Uniform
concentration
Uniform
concentration
PARAMETERS
1st ESTIMATE
Kg - 10 8 cm/sec at
time of sealing
K, - 10* cm/sec
after 10,000 years
K increases .inearry
from Kg to K* over
10,000 years
n = 0.1
A - 100m2. total
cron-secitonal area
of shaft i
Kg » 10"8 cm/sec at
tkne of scaling
K, - 10"6 cm/tac
after 10,000 years
K increases li newly
from Kg to KI over
10.000 years
-1 - 0.1
A - 100m2. total
crosf-tccttonaJ area
of (hafu
2nd ESTIMATE
K0= tO^em/iecat
lima of sealing
K|- lO^cm/wc
alter 10,000 years
K increases linearly
from Kg to K 4j over
10,000 years
U - 0.1
A <• 100m2, total
cross-sectional area
of shafts
Kg = 10 cm/sec at
lime of seating
K,- 10"4 cm/sec
after 10.000 years
K increases linearly
from Kg to K | over
10,000 years
n - 0.1
A - 100m2, total
cross-sectional area
of shafts
FLUID FLOW RATES FROM
REPOSITORY TO UPPER AQUIFER
1st ESTIMATE
ttvrsl
100
1000
10.000
Q (tl .m3/yr)
0.4
1.7
3.2
Uyrs)
200
260
260
1000
10,000
6 (t) )m3/yr»
IS } Period
} of salt
15 ( creep
0.04
0.10
0.24
2nd ESTIMATE
t of salt
2000^ CTWp
3.15
3.15
COMMENTS
Releases only begin
after repository
resaturation.
It « conservative to
assume closure by salt
creep for this failure
mechanism; otherwise
resaturation time would
be extremety long.
Closure also implies
strong driving force for
release.
-------
liner may consist of a single layer, such as steel, cast iron, or
reinforced concrete, or a multi-layered system. Examples are shown in
Figure D-10. Other methods of stabilization, discussed below, include
freezing the ground around the shaft or filling the rock column with
grout before excavation.
Freezing requires the installation of refrigerant tubes in the
section requiring stabilization. These may be placed from the surface,
through an array of drilled holes, from within the shaft as a ring
against the shaft walls, or In holes drilled from the shaft.
Refrigerant is then forced through the tubes, cooling the ground and
freezing the interstitial water. Since it is the water in the rock that
freezes, this method of stabilization is suitable only for saturated or
nearly saturated rock. Furthermore, if the rock is kept frozen during
the operational life of the repository, the distance or depth of
freezing can continue to expand. The permanent effects on the rock
would depend, In part, on the extent of freezing, and hence on the time
span of the operation.
Grouting to stabilize soil and rock involves drilling a series of
closely spaced holes and injecting grout under pressure. The injection
pressure must be carefully controlled to ensure that grout is forced a
sufficient distance into the rock without causing additional fracturing.
The grout is designed to fill voids in the rock before it sets and forms
a rigid bonding agent. The spacing of the holes must be close enough to
permit grout from one hole to spread to the next and coalesce. When
grout has been injected into all the holes, a continuous curtain or
column of rock and soil, cemented by the grout, remains in the ground.
Excavation of the shaft can then proceed within the curtain wall or
along the column. Figure D-ll shows a typical grouting program. Neat
cement (cement without aggregate) or cement with fine fillers are the
most common grout materials. Chemicals, such as sodium silicate gel and
epoxy and polyester resins, are used in some instances; the limited
availability of these specialized products and their expense have
restricted their general use.
Methods used to sink shafts are affected by the stability and water
content of the ground, and they affect stability and water content in
return. In the fairly competent rock expected near a repository, rotary
73
-------
(a) Schematic of drop shaft
Concrete liner
is lowered as
excavation
proceeds
Ground level
.// "
Floor of excavation
Source: Arthur D. Little,Inc.
(b) Shaft lining used in Asse Salt Mine
Repository, Federal Republic of
West Germany.
/ Rock
ff ^ Concrete backfilling
Cast iron segments
Asphalt joint
Steel cylinder
Reinforced
concrete shell
Source: On the Safety of Disposing of Radioactive Wastes in the Asse Salt Mine.Gesellschaft fUr Strahlen
und Umweltforschung mbH, Munich, Germany, undated.
FIGURE D-10 EXAMPLES OF SHAFT LININGS
74
-------
Shaft location
Holes for
injection
of grout
„.- .. I- v, . .
•• ••* I •"
• •' f '!'-^-
• "-••' "\:\'
••'•••' \.'
•••^~-
1-.-J
Zone to be stabilized
before excavation
Source: Arthur D. Little, Inc.
Grout is injected in
holes around shaft location.
Sufficient grout is injected
to form continuous curtain
around shaft.
FIGURE D-11 GROUTING PROGRAM FOR SHAFT STABILIZATION
75
-------
boring or percussion drilling and explosives may be most practical.
Each technique differs somewhat in its effect on the rock surrounding
the shaft. Typically, some fracturing of the wall rock is expected as
the stress field changes when rock is removed from the shaft.
Explosives and percussion drilling shatter rock around the shaft
opening, with the degree of shattering depending upon the forces
generated, rock type, and in-situ stresses. Rotary boring, in which
rock is more or less continuously removed, generally has less effect on
wall rock. For each rock formation, the relative advantages of
different excavation techniques must be weighed against the
stabilization problems introduced by excavation in order to estimate the
most economical and safest combination for sinking and stabilizing a
shaft.
Upon closing a repository, the several shafts from the surface must
be sealed to prevent or retard the vertical movement of fluids to or
from the repository level. Sealing abandoned or inactive mines is a
common practice, but the seals are usually intended more to prevent
humans and livestock from falling into a shaft, to permit later
reopening of a mine, or, to a lesser extent, to reduce flooding of or
outflow from a mine. The special requirement of long-term isolation of
a repository, demands that shaft seals be placed with exceptional care
and thoroughness.
Careful preparation for sealing will be important to ensure that the
shaft seal performs to its full potential. These preparations will
entail removal from the shafts of operational equipment, pipes, cables,
guide tracks, and other hardware. Contaminants, such as oils and loose
earth, must be removed from the walls if these substances might
interfere with the bonding properties of the sealing agents. Also,
liners will probably have to be stripped from the shafts.
Sealing the shaft, including the possibly altered or fractured rock
immediately surrounding it, is likely to require a combination of
materials and techniques if the desired impermeability and longevity are
to be achieved. A number of studies have examined individual aspects of
repository shaft or borehole sealing.(11'50~55) Some have suggested the
use of specific materials, equipment, and procedures, as summarized in
Table D-2R.
76
-------
Material
TABLE D-2R
SEAL MATERIAL CHARACTERISTICS
Emp1acement Requ iremen t s
and Practices
Comments
Concrete
(Cement with aggregate
added)
Chemical Grouts
(Both organics: epoxy,
etc., and inorganics:
sulfur, silica gel)
Bitumens
(Tar, asphalt)
Pumped or placed
continuously or In
batches. Equipment
and techniques are in
common use.
Pumped or injected as
liquid. May require
catalyst or subsequent
treatment, e.g.,
heating. Use is
limited to specific
problem areas.
Pumped or injected.
Often heated to
facilitate
emplacement.
Technology existent
but seldom applied.
Forms rigid mass.
Sulfate-res1stant
cements available.
Additives are possible
for specific problems
or rock/cement
interaction. Cannot
fill fine cracks or
pores. Strength and
permeability worsen at
high temperature.
Good longevity
expected. Some
ability to "heal" if
fractured.
Forms rigid or
semi-rigid seal. May
be sensitive to
rock/water chemistry.
Bond to wet rock may
be weak. Range of
viscosities permit
filling of fine
cracks, etc.
Long-term stability
uncertain.
Temperature
sensitivities range
from very low to
extreme. Plastic
materials can
generally deform
without fracture.
Forms plastic or
viscous seal.
Insensitive to
rock/water chemistry.
Sensitive to
hydrocarbons in rock
formations.
77
-------
TABLE D~2ft (continued)
Material
Bitumens (continued)
Emplacement Requirements
and Practice
Compacted Formation
Rock
Compacted Earthen
Materials
(Clays, sands, etc.
Mixed with or distinct
from formation rock)
Batch or continuous
feed down shaft.
Continuous or
intermittent
compaction by
machinery. Equipment
and procedures require
development. Crushing
of rock may be
necessary for
handling.
(Same as above)
Comments
Adhesion to rock often
greater than cohesion
of bitumen. Viscosity
is temperature
sensitive.
Contraction during
cooling may cause
cracks or separation
from rock. Long
stability expected.
Can deform viscously
or "heal" fractures.
Forms rigid plug.
Insensitive to rock
chemistry; may be
water sensitive. Poor
bond in to rock.
Difficulty in filling
fine cracks, etc.
Sensitive to feed
rate, compaction
process, particle
size, moisture
content. Temperature
sensitivity is similar
to in-sltu rock.
Unless supported or
mixed with binder,
strength is low.
Compaction may improve
with time and
overburden.
Forms rigid plug.
Reaction with
rock/water expected to
be slight. Poor bond
to in-situ rock.
Sensitivity to water
somewhat controllable.
Difficulty in filling
fine cracks.
Sensitive to feed
rate, compaction, etc.
78
-------
Material
Compacted Earthen
Materials (continued)
Melted Rock
Rock Mineral Solution
(Calcite, silica)
TABLE D-2R (continued)
Emplacement Requirements
and Practice
Rock delivered to work
face either molten or
solid, melted in
place, and sprayed or
pooled. Feed,
melting, and applying
equipment and
techniques are
experimental.
Same as above except
that the rock is
dissolved in solution,
not molten.
Application and
equipment are
experimental•
Comments
Temperature
sensitivity may differ
from in-situ rock.
Low unsupported
strength. Long
stability expected.
Some plastic
deformation possible
without fracturing.
Compaction may improve
with time.
Forms solid mass.
Chemistry similar to
in—situ rock. Most
suitable material is
low-melting-point rock
with few and
single-phase minerals
(e.g., salt) .
Cracking and
separation expected on
cooling. May fuse or
fill small fissures in
in-situ rock. If
properly emplaced,
good stability
expected.
Forms solid mass.
Insensitive to in-situ
rock chemistry. May
be sensitive to water
chemistry. Implies a
single mineral phase.
Good adhesion
expected. Low
sensitivity to
temperature.
Solubility of solid
seal in question.
Good stability,
expected. Does not
heal.
Sources: References 52, 54, 55, 62.
79
-------
In general, the sealing operation will probably attempt to fill the
shaft in such a way that it has mechanical, hydraulic, and chemical
properties as near as possible to those of the virgin rock. Some
concepts may approach this ideal in specific rocks; for example, the
melting and fusing of salts has been suggested as a possibility for
shafts through evaporites. ' Other methods are applicable to a wider
range of rock types, e.g., using compacted earth as a seal, or filling
the shaft with concrete and using the excavated rock for aggregate. An
important factor in sealing a shaft is the fact that the rock
surrounding a shaft is likely to differ in certain characteristics from
the virgin rock. This is true not only for the very short distance (say
one or two meters) from the shaft, where grouting is possible to seal
excavation-induced fractures, but also for distances on the order of up
to tens of meters. The following are examples of changes in
characteristics that must be considered in designing and emplacing
seals:
• MDisture content may change because of drainage into the shaft.
• Hydraulic conductivity may change because of leaching,
fracturing, and stress changes.
• Rock chemistry may change because of exposure to atmospheric
conditions, leaching, and interaction with grouts and lining
materials.
• Volume changes may result from pore water pressure changes,
temperature changes, and freezing.
After the shaft is sealed, the entire system will move toward chemical,
mechanical, and hydrologic equilibrium, and how the system will adjust
must be carefully considered in the design. The effects of various
processes on shaft seal integrity are discussed in the next section.
D-3.2.3 Shaft Seal Failure Model
Scope of Model. For this analysis, the performance of a shaft seal
is characterized by the seal's ability to restrict fluid movement along
the shaft. The principal parameter affecting such movement Is the
hydraulic conductivity of the filled shaft, including the immediately
surrounding rock. While the fill material may vary from one point to
80
-------
another, for simplicity and in the absence of a definitive proposed
design, an effective uniform hydraulic conductivity has been assumed to
characterize the sealed shaft or any portions thereof. Auxiliary
parameters, such as cross-sectional area and porosity, are also
necessary to determine fluid flow rates.
The model's emphasis on fluid flow is not meant to imply that there
may not be other potentially important purposes for the shaft seal.
Naturally, one of the prime purposes of the seal is to prevent or
discourage accidental entry into an abandoned shaft; however, this is
rather easy to accomplish and does not affect design. Tn addition, it
is possible that a seal may be sought with favorable
radionuclide-retention properties, in which case its chemical and
mineralogical composition would be important. This factor is not
included in the present model.
The present model hypothesizes a linear increase in shaft seal
permeability over a period of 10,000 years. Specific parameters are
presented after the following discussion of degradation mechanisms.
Mechanisms for Shaft Seal Degradation. Degradation of the shaft
seal over a long period of time, such as 10,000 years, is the likely
result of a combination of processes, examples of which are discussed in
the following paragraphs .
Leaching, which involves the removal of material by dissolution in
groundwater, has occasionally caused rapid deterioration of sealants.
Examples have recently been collected and documented in which cemented
borehole plugs have disintegrated and disappeared because of leaching of
the cementitious material, usually by sulfate-rich or acidic water (see
Section D-3.3). In response, a number of cements that are resistant to
sulfate attack have been developed. " ' ' With the proper
characterization of the local groundwater, carefully chosen rock and
seal materials would be expected to have very low solubilities;
nevertheless, increases in temperature and changes in water pH or
chemical composition may increase the rate of leaching.
Pressure and volume changes in the seal material can cause the
development of fractures and void spaces. For example, thermal expansion
will result from the heat generated by the wastes, but this heating
effect will eventually decrease because of radioactive decay, giving the
81
-------
effect of a thermal cycle. The corresponding stress changes can result
in fractures or voids. Changes in moisture content can also lead to
similar effects; certain clays exhibit considerable swelling as water is
absorbed, then crack upon drying. Some synthetic grouts and sealers are
formed in place by polymerization of their components. Corresponding
volume changes often involve shrinkage, so that if the polymerization is
not complete at the time shaft filling is resumed, or if the stresses in
the material are excessive, cracks or voids may develop.
Degradation from tectonic stresses and earth movements is a most
difficult engineering problem. Because it is highly unlikely that a
site will be free of differential stresses, gradual ground deformation
over time may be expected even if no ground movement is felt. For
example, pipes in oil fields have been knoxm to be distorted, crushed,
/COS
closed, and inclined from the vertical by such forces. Although
some of these movements occur along faults, they may also occur
independently. While such deformation is expected to be
relatively slow in the stable areas being considered for repositories,
the 10,000-year time frame is sufficiently long that the cumulative
effect could be substantial.
Other forces and processes that may have an impact on the integrity
of the shaft seal include settling within the fill material, changes in
overburden pressure from natural processes (e.g., erosion, glaciation),
chemical interaction between fill material and surrounding rock, changes
in physical properties caused by variations in water content, and
chemical changes within the fill material itself (such as reactions
between aggregate and cement in a concrete) .
Specific Model Assumptions. The previous discussion suggests a
picture of a shaft seal with somewhat different appearance and
properties after 10,000 years than immediately after emplacement. This
concept is sketched in Figure D-12. The development of the
corresponding model is described in the paragraphs below. It is
important to keep in mind that the intention here is to present a
generic characterization of shaft seal performance and that this has
been done by selecting performance characteristics that are believed to
be achievable without technological breakthroughs. With specific
82
-------
00
Grout
^;. Grout
Breccia from
collapsed
walls
Voids
Fractures
from settling
Loss of adhesion
with walls
Aggregate residue
where cement leached
Breccia from
slumping after
grout leached
(a) At Time of Emplacement
(b) After 10,000 Years
(Degradation may be exaggerated)
Source: Arthur D. Little, Inc.
FIGURE D-12 EXAMPLE OF SECTION OF MULTI-LAYERED SHAFT SEAL
-------
designs and thorough experimental evaluation even better shaft seal
performance may be found to be possible.
As stated earlier, an effective, spatially uniform hydraulic
conductivity has been used to characterize the performance of shaft
seals. Consideration of seal degradation mechanisms indicates that the
conductivity value will increase in time. Therefore, the essential step
in characterizing shaft seal performance is to determine a function K(t)
which for each time t is an estimate of the hydraulic conductivity of
the filled shaft. This determination involves three steps: the
estimation of the initial value KO for the time of seal emplacement, the
estimation of the deteriorated (i.e., larger) value K, at time 10,000
years, and the estimation of a rule governing the transition from KQ to
V
Initial permeabilities K^ for both first and second estimates are
taken as 10 cm/sec. It appears that this value can be met or bettered
by a number of materials and designs, as suggested by the data in Table
D-29. The performance measure is independent of the host rock, although
the specific design to achieve it may well depend closely on the host
rock. (For example, various additives may be used in concrete in order
to aid bonding with the surrounding rock.)
Estimates of the final permeability K- can be expected to vary from
site to site, depending on the harshness of the environment for the
seal, so it is appropriate that first and second estimates be different.
The first estimate value is taken to be t^ = 10~ cm/sec, which is in
the range of permeabilities expected of sandy or silty clays or clayey
sands. That is, it is envisioned that, the design of the shaft seal can
be so chosen that even with moderate deterioration it would be expected
to behave equivalently to such natural soils after 10,000 years.
Similarly, the second estimate value is taken to be K.. = 10~ cm/sec,
which lies, for example, within the range for silty sand or silty sand
and gravel. The permeabilities of specific soil types vary greatly
depending on conditions of compaction, but the data in Figure D-13
provide a context within which to interpret the numbers chosen.
Values of KQ and ^ having been specified, it is next necessary to
estimate the function K(t) that describes the changes from K to K...
In the absence of detailed seal designs and models for degradation
84
-------
00
10"
Hydraulic Conductivity (cm/ssc)
fl-4 inB ,n-6
10'7 10R 10 9
,-10
1 1 1 1 1 I 1 1
1 1 1 1 1 1 1 1
Oa/
Silt
Cl»ar. Fi-ie S*"d
Coarse Sa-"1
Si'ty ?3"'1 »n'1 G'a.'-1
SiH.y Sa"H
Compacted Cl.iy *
Sources: Stockton, S.L. and A.M. Batch. The Utility of Petroleum Seismic Exploration Data in Delineating Structural Features within Salt
Anticlines. USGS Open File Report 78-591. 1978.
Karoi, R.H. Soils and Engineering. Prentice-Hall, Inc., Englewood Cliffs, N.J. 1960.
Lambe, T.W. and R.V. Whitman. Soil Mechanics, John Wiley & Sons, Inc., New York.1969.
Terzaghi, K. and R.P. Peck. Soil Mechanics in Engineering Practice, 2nd Edition. John Wiley & Sons, Inc., New York.1969.
Charles Stark Draper Labs., Inc. (McGowan, C. et al.). Borehole Plugging by Compaction Process, Final Report. For Office
of Waste Isolation. Y-OWI-Sub 7087-1. August 1976.
FIGURE D-13 HYDRAULIC CONDUCTIVITY OF NATURAL MATERIALS
-------
TABLE n-29
PROPERTIES OF POSSIBLE SEAL MATERIALS
Seal Material Permeability
(cm/sec)
Porosity
(%)
References
Concrete
10~6 - 10~12
Compacted Earth 10~6 - 10~10
1-5
1-15
51,56,61,62
51,54,63,64
Sand/
Montmorrillonite
Bentonite 10~8 - 10~10
Fused Salt
10
~10
p in
Chemical Grout 10-10
Bitumens
10
~*10
1-15
0-0.5
30,51,64
52
51,65
51,62
These values cover the ranges reported in the references cited.
Testing procedures are not uniform. Larger variations are possible as
materials and conditions are varied.
86
-------
mechanisms, the simplest model, namely a linear increase from Kn to K. ,
has been adopted. This results in the equation
K .
0 10 4
A summary of the corresponding numerical formulas in two sets of units
is given in Table D-30.
A constant porosity value,
n = 0.1,
is assumed in conjunction with the above permeability values in order to
calculate actual fluid velocities. This parameter is alsd subject to
variation depending on the design of the shaft seal.
D-3.2.4 Shaft Seal Release Model
A permeable shaft seal represents a possible pathway for fluid
migration from the repository level to the groundwater system and to the
surface. If radionuclides have been leached from the waste package as
well, they may be transported to the geosphere or biosphere along with
the fluid. Releases to the groundwater system would be expected to
dominate over those to the surface for several reasons. For example,
the hydrologic assumptions for the generic repositories admit the
possibility of fluid flow from the repository to the upper aquifer,
whereas there is no mechanism or sufficient driving potential to force
water all the way to the surface. Transport of radionuclides to the
surface could only be by diffusion in any water that might be seeping
downward to the water table; diffusion calculations (see Appendix D-IV)
show that mass transport by this process is exceedingly small.
Furthermore, radionuclides migrating as far up as the aquifer would be
largely washed into it by the groundwater flow. Therefore, only
releases to groundwater, and in particular to the upper aquifer, have
been modeled. Because certain parameter values and the dominant driving
87
-------
TABLE D-30
PERMEABILITY AS A FUNCTION OF TIME
FOR SHAFT SEAL DEGRADATION MODEL
Permeability (K)
(cm/sec)
(m/yr)
First Estimate
Second Estimate
10 8 + 9.9 x 10""11 t
10 8 + 9.9 x 10~9 t
3.15 x 10~3 + 3.12 x 10~5 t
3.15 x 10~3 + 3.15 x 10 3 t
88
-------
forces vary from one host rock to another, the release models are
discussed here for each of the five geologic settings separately.
D-3.2.4.1 Bedded Salt
Repository resaturation times for a bedded salt repository are shown
in Table D-31 based on calculations presented in Appendix D-TI. Since
the pore volume tends to decrease because of salt creep at the same time
that water seeps into the repository, these resaturation times represent
a balance point at which the remaining pore volume is exactly equal to
the volume of water that has seeped in. Naturally there will be some
non-uniformities in water distribution as well as in salt closure, but
these factors are not included in the model.
Since the shafts extend down only to the repository level, they do
not provide a connection between the upper and lower aquifers. It is
possible that they may be coupled with other pathways from the
repository to the lower aquifer, but this possibility will be discussed
in connection with these other pathways (e.g., deep degrading
boreholes). The hydraulic gradients generated in the cases of thermally
induced convection or the U-tube effect are at most on the order 1=0.1
or 0.2 . Furthermore, mass transport by diffusion is much less. The
effective hydraulic gradient generated by salt creep may be estimated as
follows. The pressure exerted by the salt on the pore water is roughly
equal to (and certainly bounded by) lithostatic pressure, which can be
approximated by twice the hydrostatic pressure of a column of water
extending to the surface. For a repository whose depth is 460 meters
(recall Figure D-9), this corresponds to a pressure head of 920 meters
of water. The permeable shafts cover a distance of 100 meters from the
repository to the bottom of the aquifer, at which point the hydrostatic
pressure is roughly 30 meters of water- Therefore, a net pressure head
of 920-100-30 = 790 meters of water acts over a path length of 100
meters, corresponding to a hydraulic gradient i = 7.9. This number is
slightly conservative in the sense of overestimating the driving force,
and hence appropriate to the approach of the present report, because as
long as there is a permeable pathway from the repository, full
lithostatic pressure on the pore water will never quite be achieved.
89
-------
TABLE 0-T!
REPOSITORY RF.SATURATION TIMES
(BEDDED SALT REPOSITORY)
Fluid Volume at
Time to Resaturation Resaturation
(yrs) (nf )
First Estimate 200 1.2 x 101
Second Estimate 720 5.6 x 10
Source: Appendix D-II.
90
-------
It is clear from this calculation that salt creep provides the dominant
driving force until the salt reaches a state of approximate mechanical
equilibrium. The period between resaturation and arrival at this
equilibrated state will be called Period A.
The effective hydraulic gradient just calculated can be used in
Darcy's law to calculate volumetric fluid flow and fluid vplocity. Tn
particular
Q = KiAc(w),
where
•
Q = volumetric fluid flow rate through permeable shafts;
K = hydraulic conductivity;
i = hydraulic gradient;
A = total cross-sectional area of the shafts;
c(P) = viscosity correction factor, given by .01/U, where V is
the viscosity in poise. (Note that 0.01 represents the
viscosity of water at 20°C, so that c(u) is
dimensionless .)
Values of the function K(t) have been given in Section D-3.2.3 and are
summarized there in Table D-30. The total cross-sectional shaft area
2
was also specified in that section as A = 100 m . While the viscosity u
varies with temperature and hence with depth, the value y = 0.002 poise,
which corresponds to a temperature of 125 C, will be used throughout, so
that c(vO = 5. (For further details on temperature and viscosity
distributions, see Appendix D-VI.)
It is important to keep in mind that releases via this pathway
continue to occur for a limited time only, determined by the time
necessary for essentially all the water that has seeped into the
91
-------
repository to be squeezed back out. Using the first estimate parameter
values, the cumulative outflow by time T is given by
T .
Q(T) = / Qdt
200
T -3 -5
/ 3950(3.15 x 10 + 3.12 x 10 t)dt
200
0.062 T2 + 12.4 T - 4953
Complete depletion of the volume V of water in the repository would be
achieved by this single pathway at the time T when Q(T) = V; that is
Q(T)
0.062 T2 + 12.4 T - 4953 = 1.2 x 103
T =231 years.
However, permeable boreholes are additional pathways. Since these
account for some of the outflow, the water will be depleted slightly
sooner. Calculations in Section D-3.3.4 show that this time is the
•
period from 200 to 223 years; thus the volumetric flow rate Q through
the shafts is almost 40 m /yr- Note that this is only an approximate
release period, not only because of variability and uncertainty in
parameter values but also because the fluid volume will change somewhat
because of the dissolution of some of the salt. Corresponding
calculations for second estimate parameter values require some
modification in the method. These calculations yield a total water
release by a time that is earlier than the hypothesized time of complete
repository closure, given as 1000 years. This implies that the rate of
closure is the controlling factor in this case, the permeability of the
shafts being sufficiently high so that the water moves out relatively
easily. The release rate will therefore be modeled simply as the
92
-------
constant rate of void space volump change assumed in the closure model
ATT 1 "\
of Appendix D-VTI, namely 2 x 10 in /10 years or 2 x ]0 m /year.
Vertical fluid velocities may be obtained by dividing the "Darcy
velocity,"
Kic(u),
by the effective porosity n, which was given in Section D-3.2.3 as n =
0.1 . Therefore, the velocity v is given by the formula:
Kic(u)
v = —
n
nA
where the units are m/yr. It follows that the approximate average fluid
velocities and the corresponding transit times from repository to
aquifer are as given in Table D-32.
All the calculations performed so far in this section have been for
Period A, which represents the period of non-negligible salt creep.
During this period, the dominant driving mechanism is the pressure
produced by this process. By the end of this period, the salt has
reached a state of approximate mechanical equilibrium.. The water that
seeped in during the resaturation period has been forced back out, and
the repository is still saturated but the fluid volume is relatively
small. The tunnel backfill has been compacted, probably to near
equilibrium, but it still has some permeability to fluid flow.
During the ensuing period of time, called Period B, the U-tube
effect is the dominant driving force. The effective gradients have been
calculated in Appendix D-V and are summarized in Table T)-33. These
gradients may be applied with Darcy's law to calculate the volumetric
flow rates shown in Table D-34. (The cross-sectional area is A = 50
2
m .) Corresponding fluid velocities are given in Table D-35. The
source term for this failure element consists of the concentration of
93
-------
TABLE D-32
APPROXIMATE FLUID VELOCITIES AND TRANSIT TIMES TO AQUIFER
ALONG PERMEABLE SHAFTS DURING PERIOD A
(BEDDED SALT REPOSITORY)
Fluid Velocity Transit Times
(m/yr) (yr)
First Estimate 4 25
Second Estimate 200 0.5
94
-------
TABLE D-33
EFFECTIVE VERTICAL HYDRAULIC GRADIENT TN PERMEABLE SHAFTS
FROM U-TUBE EFFECT DURING PERIOT) B
(BEDDED SALT REPOSITORY)
Hydraulic Gradient (i)
223 years*
1000 years
10.000 years
First Estimate
Second Estimate
0.03
0.02
**
Not applicable 0.004
0.004
0.0004
Years after repository closure.
**
Ptriod B only begins at 1000 years after repository closure in the
cast: of second estimates.
95
-------
TABLF. 0-34
VOLUMETRIC FLOW RATES THROUGH PERMEABLE SHAFTS
DURING PERIOD B
(BEDDED SALT REPOSITORY)
Volume trie Flow (Q)
(m /yr)
223 years
1000 years
10.000 years
First Estimate
0.08
0.17
0.32
Second Estimate
Not applicable 3.15
3.15
Years after repository closure.
96
-------
TABLE D-35
FLUID VELOCITIES THROUGH PERMEABLE SHAFTS
DURING PERIOD B
(BEDDED SALT REPOSITORY)
Velocity (v)
(m/yr)
223 years
1000 years
10.000 years
First Estimate
0.02
0.03
0.06
Second Estimate Not applicable 0.63
0.63
Years after repository closure.
97
-------
radionuclides that have leached into the water in the repository during
the time frame of interest.
Dissolution along the flow pathway is expected to be minimal because
of the limited volume of fluid that would come into contact with the
actual boundary of the shaft. In addition, half of the shaft length
between repository and aquifer is through a shale layer. Even if the
entire portion of the shaft through the salt were to be "short
circuited" by dissolution pathways along the edfges, the resulting flow
would increase at most by a factor of two (since the driving potential
would be dissipated over half the length, thereby doubling the
gradient). The coupling of this pathway with others, such as degrading
deep boreholes, is possible during the period before salt creep closes
the repository, but the corresponding hydraulic potential would be
sufficiently small that this effect would neither persist nor be
significant compared with the release model presented above.
D-3.2.4.2 Granite
Assuming that repository resaturation has taken place, two driving
forces need to be evaluated for their potential contribution to fluid
flow from the repository to the aquifer. These forces are thermally
induced convection and the U-tube effect. (Note that molecular
diffusion is always negligible compared with mechanisms that move
radionuclides by fluid flow, and that there is no lower aquifer in the
generic granite repository.) Both of these forces are functions of
time. Thermally induced convection depends on time because the
temperature profile changes with time. The U-tube effect depends on
time because of the gradual change in the hydraulic conductivity of the
shaft seals. The values of the corresponding gradients, if calculated
independently, are shown in Table D-36. These values are based on
Appendices D-V and D-VI. These effects interact, tending to move water
in opposite directions in those shafts where the U-tube effect would
lead to a downward flow. For the present calculations, flow rates are
based on the larger of the two effects. Since the flow pathway for the
U-tube effect is half that for thermally induced convection, the
98
-------
TABLE D-36
EFFECTIVE VERTICAL HYDRAULIC GRADIENT IN PERMEABLE SHAFTS
FROM THERMALLY INDUCED CONVECTION AND U-TUBE EFFECT
(GRANITE REPOSITORY)
Hydraulic Gradient (i)
*
100 years 1000 years 10.000 years
Thermally Induced
Convection
First Estimate 0.10 0.06 0.01
Second Estimate 0.10 0.06 0.01
U-Tube Effect
First Estimate 0.02 0.02 0.02
Second Estimate 0.17 0.12 0.03
*
Years after repository closure.
Source: Appendices D-V and D-VI.
99
-------
effective gradients for the former need to be more than twice as large
for that effect to dominate.
The volumetric flow rate is calculated from the equation:
Q = KiAc(p)
where
Kl - K0 t
K = K + ~ ~
u 10
50 or 100
c(u)
and i is given as a function of time in Table D-36. The value of
permeability K as a function of time has been given previously in Table
2
D-30. Note that A = 50 m in the U-tube cases because only half the
total cross-sectional shaft area is used for transport upwards. The
results of the calculation are given in Table D-37. By a modification
of these results one obtains the fluid velocity from the formula
v = Kic(u)/n
= Q/nA
in m/yr, where the porosity n = 0.1, given earlier, has been employed.
The corresponding velocities are given in Table D-38.
The source term for this failure element consists of the
concentration of radionuclides that have leached into the water in the
repository during the time frame of interest.
No significant coupling is expected between this failure element and
others. In addition, the flows evaluated here are much smaller than
those through the bulk rock, and therefore this failure element is not
very significant for the granite repository.
100
-------
TABLE D-37
VOLUMETRIC FLOW RATES THROUGH PERMEABLE SHAFTS
(GRANITE REPOSITORY)
Volumetric Flow (Q)
(m /yr)
100 years
1000 years
10.000 years
First Estimate
0.3
1.0
1.6
Second Estimate
15.9
94.6
236.3
Years after repository closure.
101
-------
TABLE D-38
FLUID VELOCITIES THROUGH PERMEABLE SHAFTS
(GRANITE REPOSITORY)
Velocity (v)
(m/yr)
100 years
1000 years
10.000 years
First Estimate
O.CP
0.1
0.3
Second Estimate
3.2
18.9
47.3
Years after repository closure.
102
-------
D-3.2.4.3 Basalt
Assuming that repository resaturation has taken place, two driving
forces need to be evaluated for their potential contribution to fluid
flow from the repository to the aquifer. These forces are thermally
induced convection and the U-tube effect. With respect to other
potential driving forces, note first that molecular diffusion is always
negligible compared with mechanisms that move radionuclides by fluid
flow. Second, the other potential driving mechanism—the hydraulic
gradient resulting from the connection between the lower and upper
aquifer—cannot result from shaft seal degradation alone because this
does not provide a pathway to the lower aquifer. It is possible that
the shaft seal failure may interact with other pathways to the aquifer,
such as degrading deep boreholes, and this possibility will be evaluated
later in this section. Both thermally induced convection and the U-tube
effect are functions of time, and the analysis for basalt closely
parallels that presented in the previous section for granite.
Therefore, this section will concentrate on a summary of the
corresponding results for the basalt repository.
The values of the effective hydraulic gradients corresponding to
thermally induced convection and the U-tube effect, if calculated
independently, are shown in Table D-39. As discussed earlier, it
follows that for the purposes of calculating the joint effect the
maximum of the individual effects may be utilized. The volumetric flow
rate calculations are summarized in Table D-40, and the actual fluid
velocities are shown in Table D-41. As in the case of granite it turns
out that these quantities are negligible with respect to those
calculated earlier for flow through the bulk rock, and therefore they
are relatively unimportant. The source term for this failure element
consists of the concentration of radionuclides that have leached into
the water in the repository during the time frame of interest.
A certain degree of coupling between this failure element, and
others, such as permeable boreholes, is possible. In the case of
first-estimate calculations, the assumed hydraulic potential between the
upper and lower aquifers (see Chapter D-2.0) is sufficiently small so
that even if this factor were added to the gradient operative from the
103
-------
TABLE D-39
EFFECTIVE VERTICAL HYDRAULIC GRADIENT IN PERMEABLE SHAFTS
FROM THERMALLY INDUCED CONVECTION AND TJ-TUBE EFFECT
(BASALT REPOSITORY)
Hydraulic Gradient (i)
*
100 years 1000 years 10.000 years
Thermally Induced
Convection
First Estimate 0.12 0.10 0.03
Second Estimate 0.12 0.10 0.03
U-Tube Effect
First Estimate 0.04 0.04 0.04
Second Estimate 0.36 0.20 0.04
*
Years after repository closure.
Source: Appendices D-V and D-VI,
104
-------
TABLE D-40
VOLUMETRIC FLOW RATES THROUGH PERMEABLE SHAFTS
(BASALT REPOSITORY)
Volumetric Flowx(Qj
(m3/yr)
100 years
1000 years
10.000 years
First Estimate
0.4
1.7
Second Estimate
28.6
157.6
472.6
Years after repository closure.
105
-------
TABLE D-41
FLUID VELOCITIES THROUGH PERMEABLE SHAFTS
(BASALT REPOSITORY)
Velocity (v)
(m/yr)
First Estimate
100 years
0.04
1000 years
0.2
10.000 years
0.6
**
Second Estimate
5.7
31.5
63
**
**
Years after repository closure.
k
Although the maximum volumetric flow rate in this case would result
from thermally induced convection, the maximum velocity corresponds to
the U-tube effect.
106
-------
U-tube or thermal convection cases the result would not be significantly
modified. The value of the second estimate for the average hydraulic
gradient for the upper and lower aquifers is considerably larger,
however, namely, 0.5. This corresponds to a hydraulic potential
equivalent to 100 meters of water acting over the 200-meter distance
between the upper and lower aquifers. The corresponding flow would be
in the upward direction. If a significant portion of this driving force
is dissipated over the upper half of the flow pathway, namely, from the
repository to the upper aquifer, then it is possible that the
corresponding gradient over this pathway is greater than that from
either thermally induced convection or the U-tube effect. Calculations
(see Section D-3.3) show that this is not the case, however. In the
case of second estimates, the permeability function describing the
performance of the shaft seals is identical to the permeability function
describing the performance of the boreholes. Therefore the drop in
hydraulic potential over the shaft seal pathway from the repository to
the upper aquifer compares with that over the 10 boreholes from the
repository to the lower aquifer in inverse proportion to the
corresponding cross-sectional areas. Since these cross-sectional areas
have been assumed to be in the ratio 100 to 1, it is clear that the
overwhelming fraction of the hydraulic potential drop is dissipated over
the lower half of the pathway and the contribution to flow in permeable
shafts is negligible. Therefore this interactive effect does not need
to be considered further. Even beyond considerations such as this,
however, is the fact that the flows through the shafts are themselves
small in terms of both volumetric rates and fluid velocities with
respect to those through the bulk rock.
D-3.2.4.4 Shale
With respect to all the modeling parameters relevant to the present
release mechanisms, the basalt and shale repositories appear identical.
Therefore the discussion and the numerical computations for basalt carry
over the shale. Tables D-42 and D-43 summarize these results for shale.
107
-------
TABLE D-42
VOLUMETRIC FLOW RATES THROUGH PERMEABLE SHAFTS
(SHALE REPOSITORY)
Volumetric Flow (Q)
(m3/yr)
100 years
1000 years
30.000 years
First Estimate
0.4
1.7
3.2
Second Estimate
28.6
157.6
472.6
Years after repository closure,
108
-------
TABLE D-43
FLUID VELOCITIES THROUGH PERMEABLE SHAFTS
(SHALS REPOSITORY)
Velocity (v)
(m/yr)
First Estimate
100 years
0.04
1000 years
0.2
10.000 years
0.6
**
Second Estimate
31.5
63.0
**
**
Years after repository closure.
*
Although the maximum volumetric flow rate in this case would result
from thermally induced convection, the maximum velocity corresponds to
the U-tube effect.
109
-------
D-3.2.4.5 Dome Salt
Repository resaturation times for a repository in a salt dome are
shown in Table 0-44, based on calculations presented in Appendix D-II.
Since the pore volume tends to decrease because of salt creep at the
same time that water seeps into the repository, these resaturation times
represent a balance point at which the remaining pore volume is exactly
equal to the volume of water that has seeped in. Naturally there will
be some non-uniformities both in water distribution and in salt closure,
but these factors are not included in the model.
The analysis of the dominant driving forces to cause water to move
from a salt dome repository to the groundwater is analogous to that for
bedded salt. Therefore this section will simply summarize differences
in the parameter values and in the numerical results.
First, for the period of extensive salt creep (Period A), the
effective hydraulic gradient tending to force water along permeable
shafts needs to be recalculated because the distance from the repository
to the upper aquifer is different in this case. In particular there is
a net pressure head of 920-230-30 = 660 meters of water acting over a
path length of 230 meters (cf. earlier calculations for bedded salt).
This yields an effective hydraulic gradient of i - 2.9. Calculations
proceed analogously to the case of bedded salt. For the first estimate
case, Period A extends from 200 to about 260 years after repository
closure, with an average volumetric flow rate Q equal to about 15 m /yr-
For the second estimate case, Period A extends from 748 to 1000 years
after repository closure, with an average volumetric flow rate Q equal
o o
to about 2 x 10 m /yr. The corresponding fluid velocities and transit
times are shown in Table D-45. Fluid flows during Period B result from
the U-tube effect. Effective gradients are given in Table D-46,
volumetric flow rates in Table D-47, and fluid velocities in Table D-48.
The source term for this failure element consists of the concentration
of radionuclides which have leached into the water in the repository
during the time frame of interest.
Dissolution along the flpw pathway is expected to be minimal because
of the limited volume of fluid which would come into contact with the
actual boundary of the shaft. In addition, half of the shaft length
110
-------
TABLE D-44
REPOSITORY RESATURATION TIMES
(DOME SALT REPOSITORY)
Time to Resaturation
(yrs)
Fluid Volume at
Resaturation
(m3)
First Estimate
200
865
Second Estimate
748
5 x 10'
Source: Appendix D-II.
Ill
-------
TABLE D-45
APPROXIMATE FLUID VELOCITIES AND TRANSIT TIMES TO AQUIFER
ALONG PERMEABLE SHAFTS DURING PERIOD A
(DOME SALT REPOSITORY)
Fluid Velocity Transit Times
(m/yr) (yr)
First Estimate 1.5 150
Second Estimate 200
112
-------
TABLE D-46
EFFECTIVE VERTICAL HYDRAULIC GRADIENT IN PERMEABLE SHAFTS
FROM U-TUBE EFFECT DURING PERIOD B
(DOME SALT REPOSITORY)
Hydraulic Gradient (1)
260 years
1000 years
10 .000 years
First Estimate
0.014
0.012
0.003
Second Estimate Not applicable
0.004
0.0004
Years after repository closure.
113
-------
TABLE D-47
VOLUMETRIC FLOW RATES IN PERMEABLE SHAFTS DURING PERIOD B
(DOME SALT REPOSITORY)
Volumetric Flow (Q/
(m /yr)
260 years
1000 years
10.000 years
First Estimate
0.04
0.10
0.24
Second Estimate Not applicable
3.15
3.15
Years after repository closure.
114
-------
TABLE D-48
FLUID VELOCITIES THROUGH PERMEABLE SHAFTS DURING PERIOD B
(DOME SALT REPOSITORY)
Velocity (v)
(m/yr)
First Estimate
260 years
0.01
Second Estimate Not applicable
1000 years
0.02
0.63
10.000 years
0.05
0.63
Years after repository closure.
115
-------
between repository and aquifer is through a shale layer. Even if the
entire portion of the shaft through the salt were to be
"short-circuited" by dissolution pathways along the edges, the resulting
flow would increase at most by a factor of two (since the driving
potential would be dissipated over half the length, thereby doubling the
gradient) .
D-3.2.5 Literature Discussion
The shaft seal failure model has also been discussed by TASC. '
While recognizing that the condition of a sealed shaft is both
temporally and spatially dependent, they do not try to quantify this
dependence. Instead they perform a number of flow calculations based on
the assumption of a shaft with "failed backfill." The parameters used
for the analyses are summarized in Table D-49. For purposes of
sensitivity analysis, permeabilities were varied by up to three orders
of magnitude, and porosities by one order of magnitude. These
parameters were not based on specific designs or site characteristics.
D-3.3 BOREHOLE SEAL FAILURE
D-3.3.1 Summary
During both the preliminary and the detailed site evaluation for a
repository, a number of boreholes will be drilled to various depths at
the site. These will be used for geologic and hydrologic
characterization of the site as well as to determine the potential for
mineral and energy resources that may be sought on the site by future
generations. In addition to these boreholes, which will be drilled
specifically for repository site investigations, there may be old
boreholes on the site representing previous water, mineral, or energy
resource exploration or exploitation. In some cases, it may be
difficult or impossible to find these older boreholes; the risks
associated with those that remain undetected are discussed as a separate
failure event in Section D-3.4. All old boreholes that are found,
116
-------
TABLE D-49
BASELINE PARAMETERS USED BY TASC IN FAILED SHAFT
SEAL CALCULATIONS
Permeability Porosity Area
(cm/sec) (%) (m2)
-4 -3
Fracture zone around 10 10 10
shaft through shale
— _
Fracture zone around 10 10 60
shaft through salt
/ *")
Shaft with failed 10 10 64
backfill
Sources: The Analytic Sciences Corporation (Berman, L.E., et al.)«
Analysis of Some Nuclear Waste Management Options. For
Lawrence Livermore Laboratory. UCRL/13917; TR-1100-1-1.
October 10,1978.
The Analytic Sciences Corporation (Koplik, C.M. et al-).
Information Base for Waste Repository Design. Vol. I.
Borehole and Shaft Sealing. For U.S. Nuclear Regulatory
Commission. NUREG/CR-0495, TR - 1210-1. March 1979.
117
-------
however, are expected to be redrilled and replugged according to the
same specifications as the new boreholes drilled during the repository
site evaluation. The purpose of this section is to present a model of
the performance of borehole plugs emplaced as part of the repository
sealing process. Both the general considerations and the specific model
approach parallel to a considerable extent the discussion on shaft seal
failure presented in the previous section, to which reference will
frequently be made.
The borehole sealing materials will need to be chosen with a
specific environment in mind, so that they may approach, as nearly as
possible, chemical and mechanical equilibrium with the surrounding rock.
The seal may consist of several layers of completely distinct types that
provide a multi-barrier line of defense against expected or unexpected
forces. Nevertheless, it is reasonable to expect that over a long
period of time, say, 10,000 years, the combination of processes such as
settling, leaching, expansion or contraction from fluctuations in water
content or temperature, earth movements, weathering, and fatigue may
lead to some degradation in the integrity of the seal.
The borehole seal performance model in this report is not based upon
a particular design. It is intended to be "generic" in nature and
conservative; that is, it is believed that the performance
characteristics described here can be equalled or exceeded by actual
designs for specific circumstances.
The specific model in this report characterizes the borehole seal
integrity in terms of a spatially uniform hydraulic conductivity K. One
hydraulic conductivity value (KQ) is estimated for the time of seal
emplacement, and another value (K-) is estimated for the time 10,000
years later. It is assumed that K increases linearly from KQ to K, over
this period. The specific values of the parameters used as well as a
summary of the corresponding release models are given in Table D-50.
D-3.3.2 Background
Site exploration and repository monitoring will involve the drilling
of a number of small diameter (less than 0.5 meter) boreholes into the
host rock and surrounding formations. These borings will provide
118
-------
TABLE D-50
SUMMARY OF BOREHOLE SEAL FAILURE ELEMENT
MEDIUM
BMa.lt
= 1
_l Z
i§
C O
0
NATURE
OF
MODEL
• -
* .
(Jneerty mcreesina
pameeUllitv
RELEASE
GlUUIUWetef
nrfiM
GlUUflUlMlaf
Groui.tl*.lter
DRIVING
th.Hn...4lv.ndue.>d
osadMrnftm aquifer
borahoto emending
to tower equifer.
convection
TtwrneUy indue-
•radiem from equifer
to lower equifer.
SOURCE
Unif Drift
Uniform
PARAM
let ESTIMATE
.g
K,- 10* cm/sac after
10.000 years
K increases linearly
10.000 years
D - 0.1
to repository. 10 of
which continue to
A - 0.1 m2/borehale
r»*
KQ" 10 uii/sat al
10.000 years
K increases lineerty
from Kg to K, over
10.000 year.
i, - O.I
to repository
A - 0.1 m2/bonmole
KO- 10*cnuascet
Kj-io6 cm/asc after
10.000 yeses
from KO to Kf over
10JMO years
7 • 0.1
to repository. 10 of
which continue to
lower aquifer
A - 0.1 m2/borehale
ETERS
2nd ESTIMATE
K.- 10-4 cm/sec after
10.000 yam
K increases linearly from
KQ 10 K*! over
lO^fOOyearv
q - 0.1
to repository, 10 of
which continue to
lower aquifer
A • 0.1 m2/botehole
K,- 10"* cm/sac after
10.000 years
K inn sales linearly from
K0tO K| OMT
10.000 years
n - 0.1
A - 0.1 n>2/borehole
Kg- 10-8 cm/sec et
K,- «r4 cm/sac after
10.000 years
K0toK1oMr
q - 0.1
to repository. 10 of
which continue to
lower aquifer
A - 0.1 m2/bonhote
R
1st
200
223-
223+
1000
10.000
too
1000
10.000
tlyfal
100
1000
lOjOOO
FLUID FLOW 1
EPOSITORV TO
ESTIMATE
3
.4) Period
> of salt
"jcrasp
0.05
0.18
0£3
0.1
0£
2.4
O It) Im'/yrl
O.OS
0.4
1.6
tATESFI
UPPER t
2n
720
1000'
1000*
10400
100
1000
10.000
tlyrs)
100
1000
ROM
OUIFER
d ESTIMATE
3
100 psS;
100 (creep
19
167
03
B.S
31 .5
0 It) Im3/yrl
2.0
19J
170.1
•fttr rapontorv
reMtur.rt.on. Diwolu-
tioo in salt tav.w b
included in woond
for period after exten-
tivtialt creep.
after iepotL*UM~y letat*
RriM»onlybNm
uratton
-------
TABLE D-50
SUMMARY OF BOREHOLE SEAL FAILURE ELEMENT (CONTINUED)
MEDIUM
Shale
Dome Salt
£9
- P
j 5
S £
4 orehole
FLUID FLOW RATES FROM
REPOSITORY TO UPPER AQUIFER
In ESTIMATE
tlyra)
100
1000
10,000
Q (t) tm3/yrl
0.05
0.4
1.6
t(yrc)
200
260"
260+
1000
10,000
Q (t) (m3/yr)
5 law
S | crap
0.01
0.03
0.16
2nd ESTIMATE
.(vn)
100
1000
10,000
Q (t) Im3/vrl
2.0
19.2
170.1
tlynl
748
1000"
1000*
10,000
Q It) Im3/vr)
100 1 creep
1,6
2.8
COMMENTS
Releens only begin after
rvpofftory maturation.
Releani only begin
after repository
resaturation. In con-
trast to undetected
borehole failure ele-
ment, holes in this case
are near or through
repository and so can-
not intersect lower
aquifer at edge of salt
dome.
N3
O
-------
information on the depth, thickness, lithology, geohydrology, and
structure of the geologic formations at the site. Core samples taken
from the drill holes can be used for laboratory studies of mineralogy,
chemistry, porosity, permeability, strength, etc., and the collective
data can be used in the evaluation of the site's suitability for a
repository. Major factors of interest include the effectiveness of the
geology in providing a barrier to radionuclide escape and the possible
presence of natural resources that might be sought by future
generations.
In addition to holes that are related to the repository, a number of
boreholes may have been drilled previously for unrelated purposes, for
example, to explore or to exploit water, mineral, and energy resources
at the site. Drilling records from such holes might also serve to
enhance the information obtained from the repository-related borings,
particularly in assessing the economic potential of a site and the
effects of its loss to future generations. Of course, it is possible
that one or more pre-existing holes may fail to be identified. The
problem of undiscovered boreholes is discussed in Section D-3.4; this
section is concerned only with those that are identified.
The technology for plugging boreholes for abandonment has been well
developed, especially in response to legal requirements by the petroleum
producing states. These requirements are primarily intended to prevent
the contamination of water supplies or the escape of fluids to the
surface. Plugging or replugging has also been carried out in order to
seal off depleted gas fields so that they might be used for storage of
injected gas. In addition to sealing for abandonment, plugging
techniques have been developed for a number of other purposes, such as
separating productive horizons, diverting drill strings from a blocked
. , , . . (51,56,62,66,67)
hole, and preventing blowouts.
The most common sealing materials for abandoned boreholes are cement
and heavy mud. They are usually used in combination, with the cement
being placed against permeable or soluble formations and the dense mud
providing support for the cement. The cement is formulated to withstand
chemical attack and to provide adhesion with the rock. For example,
salt is typically added to the cement if the plug is placed in a salt
formation, in circulating brines, or in water sensitive shales.
121
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Sulfate-resistant cements are used near evaporites or where groundwater
contains sulfate ions, and other formulations are available for
different adverse conditions. Typical muds consist of starches and
clays suspended in water and brine, and barite or other dense minerals
may be added to adjust the mud's density. A cement-mud plug is
shown schematically in Figure D-14.
Studies examining the suitability of concrete plugs for boreholes
into a nuclear repository have noted some of the problems that can arise
(53)
in connection with plug emplacement and long-term stability-
Furthermore, because a cement slurry has a high viscosity compared with
water, it is questionable whether cement could successfully seal the
fine fissures or permeable zones in the rock immediately surrounding the
borehole.
If injection pressure were to be high enough to force the cement
deeply enough into the rock to seal fine fissures, the fissures might be
extended by induced fracturing.
The problems involved in designing cement seals and in emplacing
them properly are emphasized by some failures that have been noted in
the past. For example, in one study, the quality of plugs in abandoned
(fiT. ^
holes was checked about 40 years after emplacement. Twenty holes
were rebored and the findings compared with plugging records.
Forty-nine plugs had been set in these twenty wells. The findings were:
• 11 plugs (22%) were missing,
• 6 plugs (12%) were soft,
• 5 wells (25%) had all plugs soft or missing,
• 10 wells (50%) had soft or missing bottom plugs, and
• 2 wells (10%) had no top plugs.
Naturally, one expects significant improvements after the many
intervening years of development of materials and engineering practices.
But it is also true that the degradation referred to took place over 40
years, and the repository model is concerned with a period of 10,000
years. In any case, uncertainties remain about the long-term
performance capabilities of cement plugs.
Along with continuing investigations into cement's behavior as a
borehole plug material, work has also been conducted on the properties
of other sealants and fillers, and on other plugging methods. Among the
122
-------
Ground
Steel pipe with marker or
r~Ti ^-^" pipe cut off below plow depth
« . 1
Cement ' ^ ;
<*
Cement pluy
Mud-Tilled hole
x*
**
Cenieni pluy
Casing stub
(may or may •"
not be in hole)
Cement pluy
'&//'
yy///;
x-v^-w
-**\*ST~'
v\
ffi/'
7///<
Xt-1x^
*-H-^
^^
0
lUJI
^
^P
^
^
s. r» ^
H " outface casing
*
"~~~~~" * Fresh water strata
below surface casinq
Mud-filled hole
x-
w
Murl fillrrl hnln
Production horizon -May
have perforated casiny
Source: Adapted from Herndon, J. and O.K. Smith. Plugging Wells for Abandonment: A State of the
Art Study. For Office of Waste Isolation. Y/OWI/Sub-76/99068, 1976.
FIGURE D-14 TYPICAL PLUGGED BOREHOLE
123
-------
other materials examined are a variety of chemical sealants, natural
sealants, original formation rock, and earthen fills. Emplacement
techniques include injection, catalyzation, high-temperature melting,
(47,52,54,55,58)
and compaction.
Some of the chemical sealants have properties that enable them to be
used in conjunction with cement to overcome the limitations of the
latter alone. For example, plasticizing resins with viscosities as low
as that of water can fill small fractures and permeable zones more
effectively than can cement. ' ' They also are frequently more
flexible than cement and can adjust to minor rock movements. On the
other hand, many chemical sealants have unproven stability over long
periods. Some are moisture sensitive or may have differing physical
properties in different rock types. Also, since most synthetic sealants
contain organic compounds, there arise questions about possible chemical
breakdown from bacterial action.
Natural sealants, such as asphalt, tar, and similar bituminous
materials, may have long life expectancies under a variety of
conditions. ' However, emplacement of these materials may require
heating, which could result in contraction of the sealant upon cooling.
The contraction could pull the sealant from the borehole walls and
negate its effectiveness. Alternatively, a plastic or viscous sealant
may seep out of the borehole into fractures or into the rock pores.
This volume loss could initiate additional movement in other sections of
the seal column. The organic components of natural sealants may also be
subject to some of the same bacterial breakdown mechanisms as are the
synthetic compounds.
The use of rock or earthen materials has also been
suggested. ' ' Plugging with molten rock represents one approach,
the intent being to provide a plug that is chemically and physically
(52)
identical to the in-situ rock. To do this, rock taken from the
formation to be plugged would be crushed and introduced into the
borehole. There, heaters would melt the crushed rock and either spray
it on the walls or allow it to pool at the bottom of the open hole.
Alternatively, the rock could first be melted at the surface. Although
a promising concept, this method has not yet been successfully
demonstrated in practice, and it has potential problems. Cracking of
124
-------
the plug and wall rock during cooling is likely. Also, the method is
essentially limited to rocks with low melting points and
temperature-insensitive mineralogies, such as rock salt. The compaction
of earthen materials represents another approach to create a plug with a
long probable life. In this case, clays, clay-sand mixes, or excavated
formation rock would be introduced into a borehole and compacted at the
bottom of the hole. A number of methods of compaction are possible.
Impact compaction could be accomplished by dropping a cable tool
manipulated from the surface or by pneumatic or electric hammers within
the hole. Static compaction might require hydraulic or pneumatic rams
affixed to the sides of the hole. Kneading of the fill could be carried
out using rotary drill equipment at the surface to operate a roller
(54\
compactor at the end of a drill string. Since the compacted earth
would consist of materials with chemical and physical properties similar
to those of the formation rock, interaction with the rock may be very
minor. However, as with the molten rock concept, other problems can
arise. For example, compacted-earth plugging requires the development
of new equipment. Adhesion between the plug and the native rock may be
poorer than for other seal materials, and initial permeabilities may be
higher than expected and difficult to control. *
Both the initial quality of a plug and its longevity are affected by
the care with which the borehole is prepared and the plug emplaced.
Several stages of preparation are involved regardless of the plugging
material or emplacement methods. In general, anything that might
interfere with the plug, the rock, or the bond between the plug and the
rock must be remedied. All foreign matter should be removed. This
entails stripping from the hole any remaining casing, equipment, or
debris. If such materials cannot be extracted, it is sometimes
necessary to overbore the hole or to cut windows in the casings or
obstructions so that sealants may be forced past. Residual drilling
fluid, mud, oil, or other contaminants must be removed. Both mechanical
scrubbers and specialized solvents are available, but their use requires
care and judgment in order to avoid substituting one contamination
problem for another. Next, the walls of the borehole should be logged
so that the position and characteristics of the rock along its length
are well known. This step is essential in order to match sealants with
125
-------
the rock, to determine quantities of plugging material to be used, and
to select the best emplacement method.
At present, no plugging method appears assured of providing both low
initial hydraulic conductivity and long-term stability. The purpose of
the previous paragraphs has been to highlight possible techniques and
indicate potential problem areas.
D-3.3.3 Borehole Seal Failure Model
For this analysis, the performance of a borehole plug is defined by
its ability to restrict fluid movement along the borehole. The
hydraulic conductivity of the plug is the principal parameter
controlling fluid movement. Although the fill material and its
properties may vary from point to point, for the purpose of this model
it is sufficient to assume an effective uniform hydraulic conductivity
for the entire length of the filled hole. Auxiliary parameters, such as
number and size of boreholes and the porosity of the fill, must also be
specified in order to compute total volumetric fluid flows and fluid
velocities.
Many of the same degradation mechanisms that we discussed in the
section on shaft seals also apply to borehole seals, and so a gradual
increase in hydraulic conductivity is expected over time. Therefore,
modeling plug performance requires the determination of a function K(t)
that expresses the hydraulic conductivity of the plug as a function of
time. Determination of this function involves the specification of
three items: the initial value KQ for the time of plug emplacement, the
deteriorated (greater) value K. for 10,000 years, and a rule governing
the transition from KQ to K, .
Initial permeabilities, KQ, for both first and second estimates are
taken as 10 cm/sec. It appears that this value can be met or bettered
by a number of materials and designs, as suggested by the data in Table
D-29. (See Section D-3.2) This performance measure is independent of
the host rock, although the specific design to achieve it may well
depend on the host rock. It is further assumed that all known boreholes
are sealed to this degree of impermeability. Previously plugged holes
must be reamed out, all junk, old casings, and loose materials must be
126
-------
stripped from them, and mud, oil, or other contaminants must be cleaned
from the walls.
Estimates of final permeabilities, K, , follow the rationale set
forth for shaft seal performance. For borehole plugs, however, the
first estimate permeabilities are taken to be 10 cm/sec rather than
10 cm/sec, as was assumed for the shaft seals. This difference
reflects perceived difficulties in placing and testing a borehole plug.
Unlike a shaft seal, a borehole plug must be inspected or tested
remotely. The quality of plugs is therefore more suspect, and a more
rapid degradation is assumed.
The second estimate for the final permeability, K- , is taken to be
y J-
10 cm/sec, as it was for the shaft seal. This condition also
corresponds to a borehole filled with silty sand, or silty sand and
gravel. The permeabilities of specific soil types vary greatly
depending on conditions of compaction, but the data given earlier in
Figure D-13 (see Section D-3.2) provide a context within which to
interpret these numbers.
Values of K_ and K, having been specified, it is next necessary to
estimate a function K(t) that describes the change from K to K... In
the absence of detailed plug designs and models for degradation
mechanisms, the simplest model, namely a linear increase from KO to K.. ,
has been adopted. This results in the equation
*1 -KQ
K -K°+^7" "
A summary of the corresponding numerical formulas in two sets of units
is given in Table D-51.
Flow volume along a filled borehole is proportional to its
cross-sectional area, other factors being fixed. Therefore, in order to
calculate quantities of water moving through a borehole, a value for its
cross-sectional area is required. For the present model, each hole has
2
been assigned a conservatively large cross section of 0.1 m • For this
analysis, 50 holes have been assumed to reach the repository. Where the
generic medium is modeled with a lower aquifer, 10 of these 50 holes
have been assumed to reach the lower aquifer. A constant porosity
value, n • 0.1, Is used in conjunction with the other parameter values
127
-------
TABLE D-51
PERMEABILITY AS A. FUNCTION OF TIME FOR BOREHOLE
SEAL DEGRADATION MDDEL
Permeability (K)
(cm/sec) (m/yr)
First Estimate 10~8 + 9.9 x 10~10 t 3.15 x 10~3 + 3.15 x 10~4 t
Second Estimate 10~8 + 9.9 x 10~9 t 3.15 x 10~3 + 3.15 x 10~3 t
128
-------
in order to calculate actual fluid velocities. This parameter is also
subject to variation, depending on the design of the borehole plug.
It is likely that a repository will be planned so that the rock
surrounding the boreholes will not be excavated. The intention would be
to contain the boreholes in such pillars as an additional barrier to
fluid flow. Nevertheless, at a depth of 500 meters there is likely to
be some uncertainty over the exact location of a borehole, and so it is
possible that the excavation may actually intersect it. Furthermore,
previously undetected boreholes may be discovered by the excavation
process itself. Because of these uncertainties, it has been
conservatively assumed for this analysis that all the boreholes actually
intersect mine drifts.
D-3.3.4 Borehole Seal Release Model
A permeable borehole seal represents a possible pathway for fluid
migration from the repository level to the groundwater system and to the
surface. If radionuclides have been leached from the waste package as
well, they may be transported to the geosphere or biosphere with the
fluid. Releases to the groundwater system would be expected to dominate
over those to the surface for the same reasons discussed earlier for
shaft seals. Therefore, only releases to groundwater, and in particular
to the upper aquifer, have been modeled. Because both the parameter
values and the dominant driving forces vary from one rock to another,
the release models are discussed here for each of the five geological
settings separately.
D-3.3.4.1 Bedded Salt
Repository resaturation times for a bedded salt repository have been
given in Table D-31 (see Section D-3.2) based on calculations presented
in Appendix D-II. Since the pore volume tends to decrease because of
salt creep at the same time that water seeps into the repository, these
resaturation times represent a balance point at which the remaining pore
volume is exactly equal to the volume of water that has seeped in.
Naturally, there will be some non-uniformities in water distribution as
129
-------
well as in salt closure, but these factors have not been included in the
model.
All of the driving forces discussed in Chapter D-3.0 are present to
a certain extent in the case of borehole seal degradation, and different
ones dominate at different points in time. The period of possible fluid
migration may be divided into two basic parts:
Period A—From resaturation time until effective closure of cavities
and void spaces by extensive salt creep; and
Period B—Following Period A.
During Period A, the hydraulic pressure generated by salt creep can
result in substantial gradients along permeable boreholes. The analysis
for the corresponding situation with permeable shafts (Section D-3.2.4)
also applies here, yielding a gradient on the order i = 7.9 in the
portion of a borehole connecting the repository and the upper aquifer.
According to the model assumptions discussed in Section D-3.3.3, there
are 50 borehole pathways to the upper aquifer, 10 of which also connect
to the lower aquifer. The 10 boreholes that penetrate to the lower
aquifer also provide a small flow pathway downward, but the lower
section of these boreholes has not been included in the calculations.
The effect of omitting them from consideration for Period A releases is
conservative in the sense of assuming that the fixed amount of fluid in
the repository will all be forced into the upper aquifer, where the
consequences of radionuclide concentrations would be expected to be more
significant (albeit at the expense of a slight increase in the duration
of the release).
Period A fluid flows were first calculated without consideration of
the interactive effect with the permeable shafts (Section D-3.2). That
is, all the water that entered the repository during the resaturation
period was assumed to be forced out through the boreholes. The result
of this calculation is therefore an upper bound on flow through the
boreholes; in addition it enables a comparison between the effects of
shafts and boreholes.
The calculations for first estimate parameter values proceed as
•
follows. The volumetric fluid flow rate Q is given by
Q = KiAc(u)
130
-------
at 20°c, so that c(u) is dimensionless.)
; parameters are
« /
K = 3.15 x 10"" + 3.15 x 10 t m/yr (from Table D-51)
where
K = hydraulic conductivity, or permeability;
i = hydraulic gradient;
A = total cross section of all boreholes;
c(P) = viscosity correction factor, given by 0.01/P, where V is the
viscosity in poise. (Note that 0.01 represents the viscosity of water
at 20°C, so that c(U) is dimension]
The values of these parameters are
K - 3.1^
i = 7.9
2
A = 50 x 0.1 = 5 m (from Section D-3.2.3)
c(p) - 5 (from Section D-3.2.4)
It follows that the cumulative outflow from resaturation time (200
years) to an arbitrary time T is given by
T
Q(T) = f TQdt
200
T 3 A
= f 197.5(3.15 x 10" + 3.15 x 10 t)dt
200
2 ,T
= (0.62t + 0.031t )|
200
= 0.031 T2 + 0.62 T - 1364.
If this flow pathway were to account for the complete depletion of the
water in the repository at resaturation time, namely a volume
V = 1.2 x 103, m3 (from Table D-31)
then the flow would continue at the increasing rate Q until Q(T) = V.
This would enable the determination of T as follows:
0.031 T2 + 0.62 T - 1364 = 1.2 x 103
T = 278 years.
However, it is more accurate to take into account the fact that the
outflow pathway consists of both shafts and boreholes, so that the
131
-------
volumetric flow rate is actually the sum of the individual functions
Q(T) obtained here and in Section D-3.2.4. This approach yields the
function:
Q(T) = 0.093 T2 + 13 T - 6317.
The water available will then be depleted when Q(T) - V, which implies:
that
0.093 T2 + 13 T - 6317 = 1.2 x 103
T =223 years.
The flow through the boreholes during this period (220-223 years) is
o
approximately 14 m /yr.
As in the case of shaft seals, the analysis with second estimate
parameters is somewhat different. Since the shaft seal analysis showed
that in this case the limiting factor is the rate of salt creep rather
than the conductivity of the flow path, the consideration of borehole
pathways ought not affect the flow rates. In addition, the permeability
functions for both shaft and borehole seals are identical, so that their
relative importance is in the same proportion as their total
cross-sectional areas, namely, 100:5. Therefore, the borehole pathway
is quite insignificant by comparison. The volumetric flow rate is about
3
100 m /yr through this pathway.
Vertical fluid velocities within the boreholes may be obtained by
dividing the Darcy velocity, Kic(vi), by the effective porosity n, which
was given in Section D-3.2.3 as n = 0.1. Therefore, the velocity v is
given by the formula:
v = Kic(U)/n
= Q/nA
- 2Q,
where the units are m/yr. It follows that the approximate average fluid
132
-------
velocities and the corresponding transit times from the repository to
the aquifer within each borehole are as given in Table D-52.
All the calculations performed so far in this section have been for
Period A, which represents the period of non-negligible salt creep.
During this period, the dominant driving mechanism is the pressure
produced by this process. At the end of this period the salt has
reached a state of approximate mechanical equilibrium. The water that
seeped in during the resaturation period has been forced back out; and
the repository is still saturated, but the fluid volume is relatively
small. The tunnel backfill has been compacted, probably to near
equilibrium, but it still has some permeability to fluid flow.
The boreholes that descend only to the repository horizon cease to
be important at this point compared with those that extend through to
the lower aquifer and that can still serve as release pathways. In this
case, the driving force consists of the combination of the difference in
hydraulic potentials of the two aquifers and the thermally induced
convection effect. These effects are essentially additive, so the
effective hydraulic gradient in these boreholes may be obtained as given
in Table D-53. By means of Darcy's law, these gradients yield the
volumetric flow rates (for the 10 boreholes) and fluid velocities shown
in Table D-54. The first estimate value for T = 223 years (the
approximate starting point for Period B) has been obtained by
interpolation. The values shown in Table D-54 do not account for
possible dissolution around the borehole, which could lead to
development of a wider channel and hence to greater flows. Detailed
calculations in Appendix D-III indicate that the flow rates
corresponding to first estimate parameter values are sufficiently small
that salt creep is capable of preventing the development of an open
channel. For the case of second estimate parameter values, however,
dissolution does have the capability to develop an open channel through
the salt. As a result, only that portion of the borehole through the
upper and lower shale levels should be assumed to act as a partial
barrier to fluid flow. Since this comprises one-half of the total
length of the borehole between the aquifers, the flow rates are roughly
doubled. Table D-55 incorporates these dissolution considerations into
the calculation of flow rates.
133
-------
TABLE D-52
APPROXIMATE FLUID VELOCITIES AND TRANSIT TIMES TO AQUIFER
ALONG PERMEABLE BOREHOLES DURING PERIOD A
(BEDDED SALT REPOSITORY)
Fluid Velocities (v) Transit Time
(m/yr) (yrs)
First Estimate 29 4
Second Estimate 200 0.5
134
-------
TABLE D-53
EFFECTIVE VERTICAL HYDRAULIC GRADIENT IN PERMEABLE BOREHOLES
FROM THERMALLY INDUCED CONVECTION AND AQUIFER INTERCONNECTION
(BEDDED SALT REPOSITORY)
Hydraulic Gradient (1)
100 years
1000 years
10.000 years
Thermally Induced
Convection
First Estimate
Second Estimate
Aquifer
Interconnection
First Estimate
Second Estimate
Effective Total
Gradient
First Estimate
Second Estimate
0.12
0.12
0.13
0.62
0.10
0.10
0.01
0.50
0.01
0.50
0.11
0.60
0.03
0.03
0.01
0.50
0.04
0.53
*Y.ears after repository closure.
Source: First column from Appendix D-VT ; second column from
Chapter D-2.0.
135
-------
TABLE D-54
VOLUMETRIC FLOW RATES AND FLUID VELOCITIES IN DEEP PERMEABLE
BOREHOLES DURING PERIOD B AS CALCULATED WITHOUT
CONSIDERING DISSOLUTION EFFECTS
(BEDDED SALT REPOSITORY)
Volumetric Jlow Fluid Velocity
(m/yr)
(m3/yr)
T = 223 years
First Estimate
0.05
0.5
* *
Second Estimate Not applicable Not applicable
T = 1000 years First Estimate
0.18
1.8
Second Estimate
9.5
95
T = 10,000 years First Estimate
0.63
6.3
Second Estimate
83.5
835
Note: T = 223 is not included in Period B for second estimate
assumptions, since Period A extends to T = 1000.
136
-------
TABLE D-55
VOLUMETRIC FLOW RATES IN PEEP PERMEABLE BOREHOLES
DURING PERIOD B INCLUDING EFFECTS OF
DISSOLUTION ON FLOW RATES
(BEDDED SALT REPOSITORY)
Volumetric Flow (Q)
(m3/yr)
T = 223 years First Estimate 0.05
*
Second Estimate Not applicable
T - 1000 years First Estimate 0.18
Second Estimate 19.0
T * 10,000 years First Estimate 0.63
Second Estimate 1^7.0
*
Note: T = 223 is not included in Period B for second estimate
assumptions, since Period A extends to T « 1000.
137
-------
The source term for this failure element consists of the
concentration of radionuclides that have leached into the water in the
repository during the time frame of interest. Wastes would not be
expected to be placed in or near the path of a borehole, and so none
would be expected to be directly in the path of the flows calculated
above.
D-3.3.4.2 Granite
Once repository resaturation has taken place, two driving forces
need to be evaluated for their potential contribution to fluid flow from
the repository to the aquifer. These forces are thermally induced
convection and the U-tube effect. (Note that molecular diffusion is
always negligible compared with mechanisms that move radionuclides by
fluid flow, and there is no lower aquifer in the generic granite
repository.) Both of these forces are functions of time. Thermally
induced convection depends on time because the temperture profile
changes with time. The U-tube effect depends on time because of the
gradual change in the hydraulic conductivity of the borehole plug. The
values of the corresponding gradients, if calculated independently, are
shown in Table D-56. These values are based on Appendices D-V and D-VI.
In particular, in the calculation of the gradients resulting from
thermally induced convection, the minimal average density of a water
column from the upper aquifer to an unspecified point below the
repository has been used, rather than that of a water column simply from
the upper aquifer to the repository itself. It is pointed out in
Appendix D-VI that the corresponding numerical values represent upper
bounds on the buoyancy force. It is believed that this approach is both
conservative and particularly appropriate here because at least some of
the boreholes may extend below the repository. By the reasoning
presented earlier, it follows that, for the purpose of calculating the
joint effect, the maximum of the individual effects may be utilized.
Therefore, the gradient resulting from the thermally induced buoyancy
effect dominates in most cases.
138
-------
TABLE D-56
EFFECTIVE VERTICAL HYDRAULIC GRADIENT IN PERMEABLE BOREHOLES FROM
THERMALLY INDUCED CONVECTION AND THE U-TUBE EFFECT
(GRANITE REPOSITORY)
Hydraulic Gradient (1)
100 years*
1000 years
10.000 years
Thermally Induced
Convection
First Estimate
0.11
0.07
0.03
Second Estimate
0.11
0.07
0.03
U-Tube Effect
First Estimate 0.01
Second Estimate 0.09
0.01
0.09
0.01
0.08
*Years after repository closure
Source: Appendices D-V and D-VI
139
-------
The volumetric flow rate can be calculated from the equation
Q - KiAc(U)
where
K is given in Table D-51,
i is obtained from Table D-56,
A equals 50 x 0.1 - 5, or 2.5 for the U-tube case, and
c(y) equals 5.
The results of this calculation are given in Table D-57. The
corresponding fluid velocities are given in Table D-58.
The source term for this failure element consists of the
concentration of radionuclides that have leached into the water in the
repository during the time frame of interest. This is the uniform
concentration situation referred to earlier. Because a number of flow
pathways may exist through the bulk rock in the neighborhood of the
repository, there is expected to be sufficient convective movement so
that transport to the borehole is not limited by very slow diffusion
rates.
D-3.3.4.3 Basalt
Once repository resaturation has taken place, there are three
driving forces that need to be evaluated for their potential
contribution to fluid flow from the repository to the aquifer. These
forces are thermally induced convection, the U-tube effect, and the
gradient from an aquifer interconnection. The gradients from these
three forces, if calculated independently, are shown in Table D-59. The
gradient values shown for the thermally induced convection effect
correspond to Table D-VI-4 in Appendix D-VI. They represent bounds on
this effect for boreholes that penetrate only to the repository layer as
well as for those that penetrate all the way to the lower aquifer. In
the case of first-estimate parameter values, the U-tube effect is always
dominated by thermally induced convection, and so the former will not be
considered in the flow calculations. In the case of second estimates
for boreholes extending all the way to the lower aquifer, the aquifer
140
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TABLE D-57
VOLUMETRIC FLOW RATES THROUGH PERMEABLE BOREHOLES
(GRANITE REPOSITORY)
Years after repository closure.
Volumetric Flow (Q)
(m /yr)
100 years
1000 years
10.000 years
First Estimate
0.1
0.6
2.4
Second Estimate
0.9
5.5
31.5
141
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TABLE D-58
FLUID VELOCITIES THROUGH PERMEABLE BOREHOLES
(GRANITE REPOSITORY)
Years after repository closure.
Velocity (v)
(m/yr)
100 years
1000 years
10.000 years
First Estimate
0.2
1.2
4.8
Second Estimate
1.8
11.0
125.9
142
-------
TABLE D-59
EFFECTIVE VERTICAL HYDRAULIC GRADIENT IN PERMEABLE BOREHOLES
FROM THERMALLY INDUCED CONVECTION. U-TUBE EFFECT.
AND AQUIFER INTERCONNECTION
(BASALT REPOSITORY)
Hydraulic Gradient (1)
100 years*
1000 years
10.000 years
Thermally Induced
Convection
First Estimate
Second Estimate
U-Tube Effect
First Estimate
Second Estimate
Aquifer
Interconnection**
First Estimate
Second Estimate
0.13
0.13
0.02
0.20
0.01
0.50
0.11
0.11
0.02
0.19
0.01
0.50
0.04
0.04
0.02
0.16
0.01
0.50
*Years after repository closure.
**0nly applies to the 10 of the 50 boreholes that are assumed to
penetrate to the lower aquifer.
Source: Appendices D-V and D-VI.
143
-------
interconnection gradient dominates the U-tube effect. In the case of
second estimates for the boreholes that do not extend to the lower
aquifer, it is possible that some U-tube flows might occur.
Nevertheless, these would not be significant compared to the other flows
calculated.
In calculating fluid flow rate through the boreholes, it is
necessary to consider the interconnection between the deep boreholes
(those extending to the lower aquifer) and the others, since this
interconnection can have the effect of increasing the flow rates. In
particular, the system may be analyzed with the aid of its electrical
analog, shown in Figure D-15. (The use of electrical analogs is
discussed in Appendix D-V.) Since the relatively large permeability and
cross-sectional area of the repository tunnels imply a relatively low
resistance, compared with boreholes, the system shown in Figure D-15 has
been adopted as the basis for the analysis. All the resistances have
the same value. The driving potential between points A and B is not
dissipated uniformly in the vertical direction, but in inverse
proportion to the resistance of each of the two parts of the pathway.
Therefore, the lower part experiences five-sixths of the potential drop.
If more resistances were added in parallel to the upper part (for
example, by considering additional pathways, such as degrading shaft
seals) , then the fraction of the potential drop over the lower half
would be even larger. Therefore it is both conservative and yet not a
significant overestimate to assume for the purpose of calculation that
the entire potential drop is experienced over the lower half. The
resulting flow in this half also represents the flow in the upper half
because the two halves are connected in series. To effect these
assumptions in the actual calculations, the gradients for thermally
induced convection and aquifer interconnection, as given in Table D-59,
should be doubled and then added to represent the combined effect. The
resulting values are given in Table D-60. Using these gradients in
Darcy's law yields the flow rates shown in Table D-61. Assuming that
these flows all move from the repository to the upper aquifer within
boreholes (rather than through shafts or other breach pathways), the
actual fluid velocities can be estimated as shown in Table D-62.
144
-------
(a) Basic System
• B
(b) Simplified System Ignoring Resistance of Tunnel Backfill
-•A
(50)
-0-
(10)
J.L.
-•B
Note: Vertical resistances represent boreholes. Horizontal
resistances represent segments of backfilled tunnels.
FIGURE 0-16 ELECTRICAL ANALOG FOR BOREHOLE PATHWAY ANALYSIS IN BASALT
145
-------
TABLE D-60
EFFECTIVE VERTICAL HYDRAULIC GRADIENT IN PERMEABLE BOREHOLES
CONNECTING THE REPOSITORY AND THE LOWER AQUIFER
(BASALT REPOSITORY)
Hydraulic Gradient (i)
First Estimate
Second Estimate
100 years
0.28
1.26
1000 years
0.24
1.22
10.000 years
0.10
1.08
Years from repository closure.
146
-------
TABLE D-61
VOLUMETRIC FLOW RATES THROUGH PERMEABLE BOREHOLES
(BASALT REPOSITORY)
Volumetric Flow (Q)
~
/yr)
100 years
1000 years
10.000 years
First Estimate
0.05
0.4
1.6
Second Estimate
2.0
19.2
170.1
Years after repository closure,
147
-------
TABLE D-62
FLUID VELOCITIES THROUGH PERMEABLE BOREHOLES
(BASALT REPOSITORY)
Velocity (v)
(tn/yr)
First Estimate
Second Estimate
100 years
0.1
4.0
1000 years
0.8
38.4
10.000 years
3.2
340.2
Years after repository closure.
148
-------
Consideration of additional flow pathways for the same flow rates would
decrease the fluid velocities calculated.
The source term for this failure element consists of the
concentration of radionuclides that have leached into the water in the
repository during the time frame of interest. This is the uniform
concentration situation described earlier.
D-3.3.4.4 Shale
For all the modeling parameters relevant to the present release
mechanism, the basalt and shale repositories appear identical.
Therefore the discusion and the numerical computations for basalt are
identical for shale. The results for shale are shown in Tables D-63 and
D-64.
D-3.3.4.5 Dome Salt
Repository resaturation times for a dome salt repository are
calculated in Appendix D-II. As indicated there, these resaturation
times represent a balance point at which the remaining pore volume is
exactly equal to the volume of seepage water. Non-uniformities in water
distribution and in salt creep rates are not included in the model.
The analysis of releases from a salt dome repository through leaky
boreholes during the initial period of extensive salt creep parallels
very closely that for a bedded salt repository. Reference will also be
made to the analysis of releases through permeable shafts in the case of
a salt dome repository, which were discussed in Section D-3.2.4. The
period of possible fluid migration may be divided into two basic parts:
Period A—From resaturation time until effective closure of cavities
and void spaces by extensive salt creep.
Period B—Following Period A.
During Period A the hydraulic pressure generated by salt creep can
result in substantial gradients along plugged but permeable boreholes.
The analysis for the corresponding situation with shafts (Section
D-3.2.4) also applies here, yielding a gradient on the order of i - 2 in
the portion of the borehole connecting the repository and the upper
149
-------
TABLE D-63
VOLUMETRIC FLOW RATES THROUGH PERMEABLE BOREHOLES
(SHALE REPOSITORY)
Volumetric Flow (Q)
(m3/yr)
100 years
1000 years
10.000 years
First Estimate
Second Estimate
0.05
2.0
0.4
19.2
1.6
170.1
Years after repository closure.
150
-------
TABLE D-64
FLUID VELOCITIES THROUGH PERMEABLE BOREHOLES
(SHALE REPOSITORY)
Years after repository closure.
Velocity (v)
(m/yr)
100 years
1000 years
10.000 years
First Estimate
0.1
0.8
3.2
Second Estimate
4.0
38.4
340.2
151
-------
aquifer- According to the model assumptions specified in Section
D-3.3.3, there are 50 borehole pathways to the upper aquifer. The
hydraulic gradient resulting from salt creep tends to force water from
the repository through these boreholes to the upper aquifer. At the
same time, this gradient is also forcing water out through the filled
shafts. The combined outflow along these two pathways continues until
the total amount of water that has entered the repository during the
resaturation period has been forced out. (This is an approximation;
there will always be some residual water that is not squeezed out.) The
corresponding flow rates and time periods can be calculated in the same
way as they were for bedded salt.
For the first estimate case, the volumetric flow rate during Period
A (200-260 years) is approximately 5 m /yr. In the second estimate
case, the flow rate during Period A (748-1000 years) is approximately
100 m /yr. It follows from these results that the approximate average
fluid velocities and the corresponding transit times from repository to
aquifer within each borehole are as given in Table D-65. All these
calculations are for Period A, which represents the period of extensive
salt creep when the dominant driving mechanism is the pressure produced
by this process. By the end of this period the salt has reached a state
of approximate mechanical equilibrium. The water that seeped in during
the resaturation period has been forced back out and the repository is
still saturated, but the fluid volume is relatively small. The tunnel
backfill has been compacted, probably to near equilibrium, but it still
has some permeability to fluid flow.
The period following Period A has been called Period B. In the case
of bedded salt, 10 of the boreholes were assumed to penetrate to the
lower aquifer and during Period B movement of fluid along these
boreholes could lead to releases to the upper aquifer. In the case of
the salt dome repository, however, there is no lower aquifer in the
generic model. As a result there is no gradient present in these
boreholes from an aquifer interconnection and there is no recharge
pathway available for the thermally induced convection effect. The only
driving force expected to be present, therefore, is the U-tube effect.
This is the driving force used to calculate releases during Period B.
152
-------
TABLE D-65
APPROXIMATE FLUID VELOCITIES AND TRANSIT TIMES TO AQUIFER
ALONG PERMEABLE BOREHOLES DURING PERIOD A
(DOME SALT REPOSITORY)
Fluid Velocity (v) Transit Time
(m/yr) (yr)
First Estimate 11 21
Second Estimate 200 1.1
153
-------
The gradients in the boreholes which represent the vertical parts of
the U-tube, have been calculated by methods outlined in Appendix D-V and
are shown in Table D-66. Although the gradients decrease with time,
because of a decrease in the resistance of the borehole segments
relative to that of the tunnel, the flow rates will increase because the
total U-tube resistance is still decreasing as the borehole plugs
degrade. Utilizing these gradients in Darcy's law, the volumetric flow
rates and fluid velocities may be calculated as shown in Tables D-67 and
D-68, respectively.
The source term for this failure element consists of the
concentration of radionuclides that have leached into the water in the
repository during the time frame of interest.
D-3.3.5 Literature Discussion
Borehole plug failure has also been discussed by Claiborne and
Gera(3) and by TASC.(11»53)
Claiborne and Gera were concerned with a specific area in
southeastern New Mexico. On the basis of their analyses of site
hydrologic data, they concluded that if a connection were to be
established between upper and lower aquifer by failure of a borehole
plug, then flow would be in a downward direction and very slow. In the
case of a borehole which extended only to the repository level, they
argue that water in it would simply stagnate and not exhibit a flow that
could carry radionuclides.
TASC addressed borehole failure in the framework of a threshold
definition. In particular, a failed borehole was defined as one with a
permeability of 10 cm/sec. They postulated that 10% were in this
failed condition initially, 30% after 500 years, and 50% after 5000
years. They also assumed that each failed borehole plug had a porosity
value of 0.01 and that 0.5% of the repository was affected by each
failed plug.
154
-------
TABLE D-66
EFFECTIVE VERTICAL HYDRAULIC GRADIENT IN PERMEABLE BOREHOLES FROM
U-TUBE EFFECT DURING PERIOD B
(DOME SALT REPOSITORY)
Hydraulic Gradient (i)
260 years 1000 years 10.000 years
First Estimate 0.009 0.008 0.004
Second Estimate Not applicable 0.04 0.007
Years after repository closure.
155
-------
TABLE D-67
VOLUMETRIC FLOW RATES THROUGH PERMEABLE BOREHOLES
DURING PERIOD B
(DOME SALT REPOSITORY)
Volumetric Flow (Q)
(m /yr)
260 years
1000 years
10.000 years
First Estimate
0.01
0.03
0.16
Second Estimate Not applicable
1.6
2.8
Years after repository closure.
156
-------
TABLE D-68
FLUID VELOCITIES THROUGH PERMEABLE BOREHOLES
DURING PERIOD B
(DOME SALT REPOSITORY)
Velocity (v)
(m/yr)
260 years 1000 years 10.000 years
First Estimate 0.04 0.12 0.64
Second Estimate Not applicable 6.4 11.2
Years after repository closure.
Source: Appendices D-V and D-VI.
157
-------
D-3.4 UNDETECTED BOREHOLES
D-3.4.1 Introduction
The repository site selection process is expected to favor sites on
which there has been little or no known deep drilling activity in the
past. * Nevertheless, past drilling is frequently not well
documented and therefore it is possible that a given site may contain
old boreholes about which the site selection group is unaware. Because
of this possibility, thorough searches for old boreholes can be expected
before and during repository construction. Boreholes that are found on
the site are expected to be replugged according to the best available
technology; the effect of these on repository integrity has been
discussed in Section D-3.2. Nevertheless, even after thorough searches,
one or more undetected boreholes may remain.
This section analyzes the effect of undetected boreholes on
repository integrity by considering the following aspects:
• the probability of boreholes on a hypothetical site;
• the probability of detection of a borehole, given that it is
present; and
• the physical characteristics of a borehole that might elude a
comprehensive detection program.
A summary of this analysis is shown in Table D-69. A detailed
explanation of the model parameters is found in Sections D-3.4.3 and
D-3.4.4. Section D-3..4.2 provides background information on drilling
and detection activities.
D-3.4.2 Background
A potential repository site may contain old boreholes that were
drilled for any of several purposes, such as
• oil and gas exploration or recovery,
e water exploration or recovery,
• geothermal resource evaluation,
• brine injection or disposal of other wastes,
• mineral exploration,
158
-------
TABLE D-69
SUMMARY OF UNDETECTED BOREHOLE FAILURE ELEMENT
Bedded Salt
Granite
Basalt
si
52
j Z
11
It
p
p
p
NATURE
OF
MODEL
Past drilling density
and detection re-
liability yield
probability of one
or more partially
tilled holes.
Pan drilling density
and detection re-
liability yield
probability of one
or more partially
filled holes.
Past drilling density
and detection re-
liability yield
probability of one
or more partially
filled holes.
RELEASE
MODE
Groundwater
Groundwater
Groundwater
DRIVING
FORCE
Second estimate
Period B flows
derive from aquifer
interconnection
gradient. Other
flows negligible.
Thermally induced
convection.
Thermally induced
convection and
gradient from aquifer
interconnection.
SOURCE
TERM
Uniform
concentration
Uniform
concentration
Uniform
PARAMETERS
1st ESTIMATE
prob (1 hole on site)
- O016
("site" - 300 m buffer
zone only)
prob (failure to detect)
- 0.001
prob (under hole)
= 1j6 X 10"®
K - MT4 cm/sec
17 ° O.2
A - 0.1 m2
Distance from drift
- 100m
Holes extend to tower
aquifer.
prob (1 hole on site)
• 0.005
("site" • repos. +
300 m buffer zone.)
prob (failure to detect)
- 0.01
prob (undet. hole)
* 5 x 10~^
K •» 10~* cm/sec
n - 0.2
A - 0.1m2
Distance from drift
11 5m but flows
assume hole through
repository.
protod hole on site)
<• 0.07S
("site" - repos. +
300m buffer zone)
prob (failure to detect)
- 0.001
prob (undet. hole)
= 7.5x10
K • 10-* em/sec
n • 02
A = 0.1 m2
Distance from drift
• 5 m but flows
assume hole. through
repository. Holes
extend to lower
aquifer.
2nd ESTIMATE
exp. no. holes on site
- 3
prob (failure to detect
indiv. hole) - 0.001
prob (3 undet. holes)
- 0.003 (assumes
partial dependence)
K • 10"3 cm/sec
i) - 0.2
A • 0.3 ffl (total)
Distance from drift
- 100m
Holes extend to tower
aquifer.
prob (1 hole on site)
- 0.05
prob (feilure to detect)
- 0.01
prob (undet. hole)
- Sx10~*
K - 1(T3 cm/sec
ri - 0.2
A - 0.1 m2
Distance from drift
- 5 m but flows
aasume hole through
repository.
prob (1 hole on she)
prob (feilure to detect)
- 0.01
prob (undet. hole)
- 2 x 10"3
K - 10"3 cm/sec
u - 02
A - 0.1 m2
Distance from drift
- 5 m but flows
assume hole through
repository. Holes
extend to lower
aquifer.
FLUID FLOW RATES FROM
REPOSITORY TO UPPER AQUIFER
1st ESTIMATE
NegtigAle with respect
to other failure elements
tlyrs)
100
1000
10.000
tlyrs)
too
1000
10.000
6 (m3/yr)
1.7
1.1
0.5
0 (m3/yr)
4.4
3S
1.6
2nd ESTIMATE
tlytil Q(tllm3/yr)
1000 945
10,000 945
t lyrs) Q Im3,yr)
100 17
1000 11
10.000 5
t (yrs) 6 (m3/yr)
100 19B
1000 192
10,000 170
COMMENTS
Distance from drift
precludes significant
connection with re-
pository except in case
of significant dissolu-
tion. Negligible flow in
most cases deduced
from consideration of
relative resistance of
alternative pathways
for water to enter end
leave repository.
Repository resatura-
tion necessary for
releases.
Repository resaturation
nil slimy for releases
to begin.
Repository resaturation
"•! "iri'y for releases
to begin.
01
SO
-------
TABLE D-69
SUMMARY OF UNDETECTED BOREHOLE FAILURE ELEMENT (CONTINUED)
MEDIUM
State
Dorm Ml
£l
II
I*
o P
fZ
p
'
MATURE
or
MODCL
PM drifting dmitv
vddmcitonn>
HAHHrvWd
proMbilitvolOM
orfimptrtMy
MM hotel.
PM drill it* dm.tr
•nddmtiOfiro.
UobUtv vMd
probcMity en OM
or more ptrliilry
lilted hotel
•ELCAH
MODE
Grounrtarar .
Gfoundmmr
DRIVIM6
FORCE
Thtrrratrr inducad
conMction and
•radtem Iram miter
hmrionnonton.
Socondwinm
PvtadBflom
inwrcoMHction
•radim. OHMrllom
imiiiafcii-
SOUHCC
TEMM
Uniform
concommion
UnDorm
conanmnion
•AMAMCTCm
M ESTIMATE
arabdhoteonilnl
- aos
I" •*»- • r«K». »
300m barter ton*)
prob IbHuraio dmetl
• .01
prab lundn. hate)
• S«W*
n • OJ
A - aim'
Otrano from drift
• SmbMtMM
•gvitor.
•xp. no. hotel on sit*
- 3
btrfftr zorMonly)
prab IMkn to dract
Indta. hotel
• aooi
prob (3 undn. hotel)
' OJ)OJ(A«um«
K - 10-«cnW«K
1 • 03
A • 01 m^
DfcBnatramdrtti
- 100m.
HotamnridiotoMr
•quHtr.
hd ESTIMATE
ap.nohotaoniiu
- 9
prablteikirandmctl
• aoi
prab 13 undn. hated
pinill datttndinct)
K - 10-3on/M.
<> • 0.2
A • 0.1m2
OilSMet from drift
- SmbvlflOM
•Mrmhoklkrougk
'•pmllory. Hotet
•ttundtolowir
agurttr.
tw.no hotel an ult
- 30
prabllcikinndMoa
indh. hotel
• OM1
prob IS undtt. hotel)
- O.O3 Imunoi
UnteldlpindinLlI
K - 10"3 cm/He
A - O3mzltonll
DJ.UIH. Irom drift
• 100 m.
Hotel ntmd to toMr
•qutter.
FLUID FLOW RATES FROM
rUrOUTCWY TO UPPf R AQUIFER
Hi ESTIMATE
ilml
too
1000
10.000
NoHtejM
tOOtfMT
b(-3/rrl
4.4
18
1.6
.mthrw.1
1^ ESTIMATE
tlynl
too
1000
10.000
tlvn)
1000
10JOO
0 l-3/»r)
SH
sn
sn>
ab»3/>T>
S30
S30
COMMENTS
Hopoilio*Y (•Hiitriiion
nKBH(ly f Qf rdfjiMjij
•otMffin.
Dtanca from drift
^^^^
paotory CBCiVM in CM*
of tiinHtaMt divolit-
tton. NofUflfeto How kn
most MM dnfciMd
homcon..t.w.«tkinof
tor«iMr«o«MiVMid
IMM npMitofv. R»-
flKMwv fo> Mlmn.
-------
• scientific investigation, or
• fluid storage.
Holes may have also been drilled for other purposes, but these have been
excluded from the above list either because they are too shallow (e.g.,
soil borings for planning foundations of structures) or too localized
(e.g., borings related to nuclear testing). Although the current site
selection process would generally attempt to avoid locations with
previous deep drilling (i.e., to the formation that would contain the
repository), documentation of such drilling may be incomplete, records
may be lost or undiscovered, and physical evidence may be difficult to
find.(71)
This section treats the following topics:
• nature of past drilling activities in the five generic geologic
settings,
• methods of detection, and
• experience in applying these detection methods in the past.
Subsequent sections will provide actual data from which to estimate the
parameters that characterize this failure element.
D-3.4.2.1 Nature of Past Drilling Activities
Bedded Salt. Bedded salt formations are particularly attractive for
a variety of drilling activities. Salt is a valuable commodity itself,
and it is also frequently associated with other mineral resources such
as gypsum, anhydrite, and potassium salts. The range of commercial
deposits of these minerals is indicated in Figure D-16. The sedimentary
sequences containing salt beds frequently contain deposits of oil and
gas, the ranges of which are shown approximately in Figure D-17. While
salt deposits are generally shunned in the development of water
resources, permeable strata close to salt layers may be penetrated by
injection wells for brine disposal. Such wells are usually abandoned
petroleum production wells and, therefore, do not represent additional
drilling. Nevertheless, possible dissolution and fracturing around them
require that they be considered. Storage of oil or compressed gas in
abandoned excavations in salt is a relatively recent development.
Access to the excavation horizon is usually obtained through old
161
-------
10
Potash
A Mines
9 Wells
--- Limit in Evaporite Basin
Major Mining Area
Salt
fl Mines
, Wells
• Domes
~~ Limit in Evaporite Basin
Limit of Brine Basin
Gypsum
A Mines & Pits
Plants
Outcrops
Limit in Evaporite Basin
Indefinite Limit
Commercial Magnesite & Brucite
Commercial Borates
Source: The National Atlas of the United States of America. U.S. Geological Survey, 197O.
FIGURE D—16 COMMERCIAL SALINE DEPOSITS IN THE UNITED STATES
-------
Source: The National Atlas of the United States of America, U.S. Geological Survey, 1970.
FIGURE D-17 COMMERCIALLY EXPLOITABLE ORGANIC FUEL DEPOSITS IN THE UNITED STATES
-------
boreholes and, therefore, this process does not require the drilling of
new holes.
Granite. Mineral and water exploration are the principal reasons
for past drilling into granitic rocks. Precious and heavy metals,
including gold, silver, tin, copper, tungsten, and lead, may be
concentrated in enriched zones (veins) in felsic rocks. Mica, lithium
minerals, and other ore minerals may be generally distributed throughout
a granitic stock. Because it is difficult and expensive to mine in such
rock, especially at considerable depths, only granitic ores with a high
economic value have been sought in the past. Searches for gold and
copper, in particular, have been carried to considerable depths.
However, this has occurred only after surface exploration suggested the
existence of deep deposits. Many of the minerals associated with
igneous rocks are found in veins at the contacts between igneous rocks
and the surrounding formations or in zones of hydrothermal alteration.
Therefore, deep penetration into a granitic mass devoid of signs of
minerals is likely to be fruitless.
Important crystalline rock aquifers exist in various parts of the
country, especially in the Appalachians of North Carolina, Virginia,
Vermont, and New Hampshire. These aquifers are highly fractured zones
and, if present at depths near those considered for repositories, would
tend to discourage interest in an area as a potential repository site.
There are a small number of cases where granitic rocks have been drilled
for petroleum exploration and extraction, when the petroleum has been
trapped against the flank of the intrusive or in its fractures. There
has also been more recent interest in geothermal resource evaluation in
granitic intrusions, but this interest is sufficiently new and well
documented that undetected boreholes in this connection are extremely
unlikely.
Basalt. Flood basalts, assumed for the generic basalt geology in
this report, often contain alluvial or other permeable interbeds, and
these may be drilled as important sources of water. In addition,
sedimentary deposits underlying basalt flows may also contain oil and
gas. Nevertheless, because basalt is difficult and costly to drill
through and because geophysical techniques for identifying petroleum
reservoirs are difficult to assess in basalt, petroleum exploration and
164
-------
exploitation have been limited. Valuable metals such as platinum,
nickel, chromium, and iron ore are occasionally found in basalt, though
less frequently in flood basalts, and some enrichment can be noted where
leaching and rock alteration have taken place. However, because of the
general lack of ore-forming fluids in these rocks, concentrated deposits
(72)
are unlikely. (Copper associated with basalt in Michigan may be an
exception.) Geothermal exploration is sufficiently recent not to be of
concern for undetected boreholes; furthermore, source areas rather than
the basalt flows themselves would be the principal source of heat.
Shale. Shales are the most common sedimentary rocks and may be
associated with almost any assemblage of other sedimentary rocks. They
generally have little or no economic value in themselves, except for oil
shales and building stone, but they may be extensively drilled during
the exploration or recovery of associated resources. Oil and gas wells
may penetrate shale formations, since the relatively low permeability of
the shale often causes the accumulation of exploitable reservoirs
underneath these formations. Coal may also be associated with shales,
and previous coal exploration could be the source of old boreholes.
Uranium, vanadium, and phosphates are among the mineral resources
commonly found in shale or its associated rocks. Exploration for
uranium has intensified over the last 30 years. Shales can also act as
aquicludes, leading to artesian heads in underlying aquifers. One of
the most outstanding examples of this geology involves the Dakota
sandstone aquifer, which is overlaid by thick sections of Cretaceous
shales. Since this aquifer is one of the principal sources of water in
the Great Plains, the shales there have frequently been penetrated in
the development of water resources.
Salt Domes. Salt domes, including the rock surrounding them, have
been of considerable interest for drilling. The salt itself can be of
commercial value, as can the associated minerals, which are similar to
those found with bedded salt. Concentrated mineral deposits, such as
sulfur, may be found above or on the flanks of a salt dome, since
discontinuities and upturned strata, which tend to collect oil and gas,
often result from the intrusion of the dome through the overlying
sediments. (See Figure D-18.) Deep borings directly through the salt
are uncommon, although borings through overhanging portions that may
165
-------
Surface
Source: Adapted from Bateman, M. The Formation of Mineral Deposits, John
Wiley & Sons, New York, 1951.
FIGURE D-18 DIAGRAM OF SALT DOME SHOWING ASSOCIATED
OIL RESERVOIRS, WELLS, AND DEEP HOLES
166
-------
serve to trap petroleum below are frequently carried out. While
geothermal resources may be associated with salt domes, there has not
been sufficient investigation to add to the risk of undetected
boreholes.
D-3.4.2.2 Methods for Detection of Old Boreholes
The first step in a program of identifying old boreholes is to
review mineral claims, drilling permits, and leases recorded by various
government agencies for information on locations, depths, and plugs.
These records may also indicate unusual situations, such as multiple
shafts from a single surface hole, offshoot holes, obstructions, etc.
Unfortunately, regulations governing such documentation are relatively
recent, so that while records may be an aid in locating old holes, they
are not completely reliable. Documentation of unsuccessful water or
mineral exploration holes, particularly in states where regulations have
not been motivated by extensive petroleum or mineral industries, is
often lacking.
Documentation may be supplemented by aerial photographs and
interviews with local residents. Aerial photographs often reveal access
roads, ground damage from drill machinery, pits for drill mud, and other
scars. Interviews are particularly useful where obvious traces are
obliterated by vegetation or construction, or where records are
incomplete or in error.
After the general location of a borehole has been determined, the
hole itself must be found. Sometimes the uppermost pipe extends above
the ground or some other marker has been left. Metal detectors can be
used to find casings and debris close to the surface. Hydrocarbon
detectors can be used to locate gas escaping from leaking holes as well
as traces of oil or gas that may have permeated the ground during
drilling or pumping operations. Even the location of scars or traces
from guy cables from the drill derrick may be useful in finding the
approximate location of an old borehole. Once a possible boresite has
been located, it may be necessary to remove the top layers of earth in
order to find the actual hole.
167
-------
Underground methods, such as sonar and radar, are also used to
detect boreholes from other boreholes or from excavations. In these
cases, interpretation of reflected signals by skilled personnel may
indicate underground structures. Radar uses electromagnetic signals to
detect fractures with anomalous electrical properties, such as empty or
brine-filled holes, cracks or voids, or metals (such as casings).
However, the cracks and voids of fractured rock scatter radar signals,
and wet rock, with high electrical conductivity, can severely attenuate
the signal and thereby limit the range. In salt or other dry rock it is
possible to detect an open, caved, or brine-filled borehole at a
(73-75)
distance of many meters.
Sonar, which uses sound waves, is not affected by moisture in the
rock to the same degree as radar. Sonar's range through dry, fractured
rock may be limited, however, since energy is lost at each rock/air
interface. Also, a filled borehole may have acoustic properties very
similar to those of the surrounding rock.
Radar and sonar use short wavelength signals; the shorter the
wavelength, the more limited the range but the better the resolution.
Experience suggests that in fractured or wet rock it may be possible to
detect a borehole at distances of 10 to 100 meters away. In salt, the
detection capability is over 100 meters. Because of the water bound-up
in shale minerals, even uniform and apparently dry shales limit the
detection capabilities to about the same level as for crystalline
, (74)
rocks.
D-3.4.2.3 Experience in Borehole Detection
The petroleum and mining industries have devoted considerable effort
to the technology of detecting (and replugging) abandoned boreholes.
The motivation for this includes legal requirements (concerning gas
leakage from old fields) , the desire to limit oil and gas loss into
barren strata, protection of miners against flooding or dangerous gas
accumulations, and the use of depleted gas fields as 1535 storage
reservoirs. Several examples of this last case have recently been
(62 ^
documented and are summarized below.
168
-------
The Webb storage field in Oklahoma had 25 old wells, which were
found primarily through a search of records. The Lyons, Kansas field,
however, contained many wells that could not be found from records.
Aerial photographs proved useful in locating drilling sites, and then
metal detectors and excavating equipment were used to locate the
wellbores. The Jackson, Mississippi storage field proved even more
difficult. About 80 boreholes had to be located and replugged, but the
few existing records were often inaccurate. Houses and other buildings
had even been built over some of the old wells. Eventually, however,
the abandoned wells were found and the field was successfully put into
service.
D-3.4.3 Undetected Borehole Failure Model
The quantitative characterization of the undetected borehole failure
element consists of three elements:
• the probability of a borehole or the expected number of boreholes
present on the repository site;
• the probability of failure to detect any such boreholes; and
• physical parameters to describe the nature of an undetected
borehole so that consequence calculations may be carried out.
The first two factors vary considerably from one geologic medium to
another, but the third has been modeled independently of the medium,
except for the location'and length of the borehole.
D-3.4.3.1 Bedded Salt
Number of boreholes. First estimate values are based on the
assumption of a site where the major productive oil and gas horizons, if
any, lie above the formation containing the repository; mineral
resource recovery has also been generally limited to considerably
shallower depths; and sufficient water is available near or at the
surface so that deep water wells would not have been necessary. Much of
the Sallna and Appalachian basins, for example, meet these criteria. In
the case of the Salina basin, it has been estimated that holes extending
into the deep Silurian salt deposits that might be considered for a
169
-------
repository occur with a spatial density of about one hole per 100 square
miles (256 km )« Because of the capabilities of radar and other
detection techniques in salt deposits, boreholes within the actual
repository boundary have been assumed to have a negligible probability
of failing to be detected. (Because of the network of drifts and
tunnels, any such borehole would be within a few meters of the mine
opening).
The calculations here concentrate on a 300-meter-wide buffer zone
2
around the repository; the area of this zone is about 4 km . Boreholes
beyond 300 meters are assumed to be too far away to contribute
significantly to any risk. Thus, the boreholes referred to in this
subsection on bedded salt are assumed to be in this zone. The
probability of such a borehole existing is thus 4 x (1/256) = 0.016 if
the site is randomly chosen. In particular, the Poisson distribution
describes the probabilities of various numbers of holes on the site, the
probability of N holes being given by e ~°'016 (0.016)N/N!. The values
of this function for small values of N are given in Table D-70.
Multiple holes are seen to have negligible probabilities compared
with a single hole, and thus the event of a single hole is the one that
has been modeled in the first estimate case. Since site selection is
expected to favor sites with lower than average past drilling rates, it
is conservative to use the average rates as the basis for the
probabilities.
Second estimate values correspond to regions with extensive mineral
and energy resource recovery activities. Typical of such regions is the
Carlsbad, New Mexico mining district, where approximately 125 holes to a
2 (20)
candidate repository formation are known in an area of 166 km .
(Approximately 60% of these are potash exploration holes, which
generally terminate above the actual strata that have been proposed for
the Waste Isolation Pilot Plant. However, the total number has been
used as an estimate for the generic calculations in this report.) For
2
an area of 4 km , this leads to an expected number of about three holes
per repository.
Failure to detect boreholes. Statistical analyses of the
effectiveness of borehole detection techniques are not available, and
the estimates adopted here are based on very limited data. Conventional
170
-------
TABLE n-70
PROBABILITIES OF UNDETECTED BOREHOLES TN BUFFER 7.0MR
AROUND BEDDED SALT REPOSITORY (FIRST ESTIMATE)
N(number of holes) Probability (e~°;016)(0.016)N/N!
0 0.9841
1 0.0157
2 1.26 x n~4
3 6.72 x ]0~7
4 2.69 x 10~9
171
-------
surface methods have been totally effective in several cases, but
failures are sometimes unknown and often not documr-nted. One
significant failure involved the interception of an unknown abandoned
borehole by an advancing mine excavation. Tn that case, the unknown
hole represented one out of about 100 boreholes in the area, yielding a
detection failure rate of 1%.
When conventional surface techniques are augmented by techniques
such as radar, the detection probability can be expected to improve.
For example, with skilled operators working in dry, homogeneous salt, it
may be possible to find all boreholes out to a distance of 100 meters or
more. However, since operators can make errors and geologic conditions
vary, finding all abandoned holes is not an absolute certainty.
Instead, it has been assumed for the case of both first and second
estimates that radar can reduce the failure rate to 0.1% per hole. This
detection failure probability has been combined with the expected number
of boreholes as follows.
For the first estimate case, the event being modeled is the
existence of one undetected borehole, whose probability is the product
of the probabilities that a hole is present (0.016) and the probability
of detection failure (0.001). The resulting probability is 1.6 x 10~ .
For the second estimate case, where more than one borehole is expected
on the site, the probability of at least one undetected borehole out of
three is 1 - (0.999)3 = 0.003. Note: 0.999 is the probability of
o
detecting each individual hole, so (0.999) is the probability of
detecting all three, assuming independence. While the case of exactly
one undetected borehole is the largest contributor to this probability,
to allow for some dependence among detection failures, the event
corresponding to this probability has been modified to be the existence
of three undetected boreholes on the site. (It is appropriate to make
some allowance for dependence because the causes for detection failures,
such as faulty equipment operation, inadequate coverage of the area, or
interfering geologic features, may encourage multiple detection
failures.) This is a rough approximation to a more detailed analysis
based on hypotheses of dependencies in borehole detection; however, it
is believed to be adequate for the purposes of this study.
172
-------
Nature of undetected boreholes. It is reasonable to assume that
boreholes that escape detection do so because, in terms of density and
water content, they are not very different from the surrounding rock.
Thus they can be assumed to be filled or plugged. Their hydraulic
conductivity has been modeled to be uniform over time and spatial
extent, and to have the values of 10 cm/sec as a first estimate and
10 cm/sec as a second estimate. These values are in the range
corresponding to silty sand and gravel, as well as other materials, as
shown previously in Figure D-13 (see Section D-3.2). They represent
relatively permeable fill material such as might be expected from
material falling from the sides of the hole in loose upper levels or
from a poor concrete-drill mud plug. Their cross-sectional area has
2
been taken as 0.1 m , their porosity as 0.2, and their distance from the
nearest point of the repository as 100 m. For conservatism, all such
holes have been assumed to penetrate to the lower aquifer.
D-3.4.3.2 Granite
Number of boreholes. Deep drilling in granite is much less common
than in bedded salt. Granite rarely contains reserves such as gas or
oil that can be exploited through boreholes. In general, it is
penetrated only when some surface indications suggest that deep mining
may be profitable, or when fractures in the rock are extensive
enough that the granite can be tapped for water. Indeed, there may be
locations where it can be assumed that no drilling has taken place, such
as a National Park. However, such locations are also likely to be
unavailable or undesirable for a repository.
The first estimate assumes a location that shows no surface
indications of ore minerals deep in the granite, and where water is
either readily available at the surface or else past land use suggests
that deep water exploration has not been carried out. Detailed drilling
data for such regions are often lacking. For example, local statutes
may not require reporting of drilling, or the mineral companies
performing the drilling may be reluctant to release their information.
In the absence of adequate data, it has been conservatively assumed that
granite is penetrated to the depth of a potential repository one tenth
173
-------
as often as in the first estimate bedded salt situation. This results
in a deep borehole density of one hole per thousand square miles (2560
«
km )• Since the area of the repository plus a 300-meter-wide parameter
is about 12 km2, this implies a probability of about 0.005 that there is
a borehole at the site. The second estimate for granite is based on a
drilling rate ten times as high as in the first estimate, resulting in a
probability of 0.05 that there is a borehole on the site.
Failure to detect boreholes. Conventional borehole-locating
techniques are expected to be as reliable for granite as for bedded
salt, although specific data to prove this assumption are not available.
The use of radar for detection of features in granite has not been
demonstrated, and it is not assumed to contribute to the probability of
finding abandoned holes. For both first and second estimates, the
detection failure rate has been assumed to be 1%, equivalent to that for
bedded salt without the advantage of radar. This failure rate is
combined with the expected number of boreholes as follows. For both
cases, the event being modeled is the existence of one undetected
borehole, for which the probability is the product of the probability
that a hole is present and the probability of detection failure. For
the first estimate the resulting probability is 5 x 10 that an
undetected borehole is present. For the second estimate, the
probability is 5 x 10 for an undetected borehole.
Nature of undetected boreholes. As in the case of bedded salt, it
has been assumed that a borehole escaping detection does so because, in
terms of density and water content, it is not too different from the
surrounding rock. Thus, it has been assumed to be filled or plugged.
The hydraulic conductivity has been modeled to be uniform over time and
-4
spatial extent, and to have the values 10 cm/sec as a first estimate
^o
and 10 cm/sec as a second estimate. Its cross-sectional area has been
2
taken as 0.1 m , its porosity as 0.2, and its distance from the nearest
point of the repository as five meters. (Five meters is intended to be
a conservative estimate. Boreholes closer than five meters are highly
likely to be found during excavation, either by leakage or through
detection techniques.)
174
-------
D-3.4.3.3 Basalt
Number of boreholes. Borehole densities in the basalt regions of
the Pacific Northwest have been used in estimating the probability of a
borehole at the repository site. In that region deep drilling has been
dominated by water wells, and reported numbers of wells are used to
derive borehole density estimates. The first estimate is based on a
(78)
study of wells in the Pasco Basin, where 34 wells were reported
reaching or exceeding depths of 1000 feet (300 m). The area covered in
o
that study included approximately 5400 km , and so for a repository and
2
perimeter of 12 km , there is a probability of approximately 0.075 that
an old borehole exists on a randomly chosen site. The second estimate
2
is based on well populations for a larger area (30,000 km ) of
southeastern Washington state, where an estimated 500 wells may reach
(79)
depths of 1500 feet (400 m). For a randomly chosen site with an
2
area of 12 km , this implies a probability of about 0.2 that an old
borehole will be present. (Multiple occurrences have sufficiently small
probabilities that they need not be considered.)
Failure to detect boreholes. Much of the Pasco Basin area has been
under close government control, and most of the deep drilling has been
supervised by the Federal government. The location of these holes Is
well known and well documented. Although special techniques, such as
tadar, are not expected to be adaptable to borehole detection in basalt,
the exceptional quality of records kept for this particular area should
improve the chances of finding holes to the degree that the probability
of detection failure is reduced to the level achievable in bedded salt,
i.e., 0.001. Combining this probability with the probability that a
borehole is present (0.075)results in a first estimate probability of an
undetected borehole of 7.5 x 10
The second estimate probability of detedtion failure is taken to be
the same as for other areas where surface detection techniques alone are
relied upon (0.01) since much of the area defined above for the second
estimate is not under tight control and the location of wells may not be
accurately known. The probability of an undetected borehole is again
the probability of a hole (0.2) multiplied by the probability of failing
_3
to detect it (0.01), with a resulting probability of 2.0 x 10 .
175
-------
Nature of undetected boreholes. Boreholes In basalt are assumed to
have the same characteristics as those in granite. For conservatism, it
is further assumed that all holes penetrate to the lower aquifer.
D-3.4.3.4 Shale
Number of boreholes. First-estimate values are based on assumptions
of a site where productive gas, oil, coal, and water lie above the
shale. Such a site is analogous to that assumed for bedded salt and so
the same borehole density applies. However, because of poorer detection
2
capabilities in shale, the entire area of site and buffer zone (12 km )
has been used. Therefore, the probability of a borehole on the site is
0.05. Second estimate values are also based on the case of bedded salt,
2
leading to nine expected boreholes on a 12-km site.
Failure to detect boreholes. For shale areas, conventional
detection techniques cannot be augmented by radar since the fractures
and moisture in shale severely limit the range of radar and similar
techniques. Therefore, the first and second estimates for the
probability of failure to detect boreholes are the same as for
conventional detection methods (0.01). As before, the probability of an
undetected borehole is calculated as the product of the probability that
a borehole is present and the probability of failing to detect it. For
a first estimate, the resulting probability is 5 x 10~ . For the second
estimate, the probability of failure to detect at least one borehole in
the expected nine is about 0.09. To allow for dependence among
failures, the event with which this probability has been associated is
that of three undetected boreholes, as in the case of bedded salt.
Nature of undetected boreholes. The boreholes that escape detection
are assumed to be similar to the surrounding rock. Their hydraulic
conductivity has been modeled as uniform over time and space, and to
have the values of 10 cm/sec as a first estimate and 10~" cm/sec as a
2
second estimate. Their cross-sectional area has been taken as 0.1 m ,
their porosity as 0.2, and their distance to the nearest point of the
repository as 5 m. For conservatism, all holes are assumed to penetrate
to the lower aquifer-
176
-------
D-3.4.3.5 Dome Salt
Number of Boreholes. The cross-sectional area of a salt dome is
generally of the same order of magnitude as the area required for a
repository. As explained in the section on bedded salt, boreholes
located within the actual repository boundary are most unlikely to go
undetected because of the effectiveness of detection techniques in salt.
Therefore, the area that has been modeled for undetected boreholes is
that of a 300 meter wide buffer zone around the repository. Since this
zone is expected to be close to the flanks of the salt dome, where
drilling activities are concentrated, the total number of holes reported
as penetrating the dome will be used as the number of holes penetrating
the buffer zone. Surveys of records for a number of interior domes in
Texas, Louisiana, and Mississippi place this number in the range 0 to
30. For the first-estimate value, three boreholes have been assumed;
for the second estimate, 30 have been assumed.
Failure to detect boreholes. As in the case of bedded salt, failure
to detect a given borehole has been assumed to have a probability of
0.001 for both first and second estimates. Thus, in the first estimate
case, the probability of failure to detect at least one borehole,
assuming independence, is 1 - (0.999) - 0.003. A simple and
conservative way to allow for the possibility of dependence among
detection failures is to use this probability for the event of failing
to detect three boreholes, which has been done here.. A similar approach
has been taken for the second estimate. Assuming independence, the
probability of failure to detect at least one of 30 boreholes is 1 -
(0.999) = 0.03. Some dependence is roughly introduced by using this
same probability to correspond to a different event, namely the failure
to detect five boreholes.
Nature of undetected boreholes. It is reasonable to assume that
boreholes that escape detection do so because, in terms of density and
water content, they are not too different from the surrounding rock.
Thus, they have been assumed to be filled or plugged. Their hydraulic
conductivity has been modeled as uniform over time and spatial extent,
• o
and to have the values of 10~ cm/sec as a first estimate and 10
cm/sec as a second estimate. Their cross-sectional area has been taken
177
-------
2
as 0.1 m , their porosity as 0.2, and their distance from the nearest
point of the repository as 100 m. For conservatism, all such holes have
been assumed to penetrate to a lower aquifer or pressurized brine
reservoir along the flank of the dome.
D-3.4.4 Undetected Borehole Release Model
The purpose of this section is to analyze how undetected boreholes
may constitute or contribute to a breach of the repository. As
discussed in the previous section, undetected boreholes do not intersect
repository drifts. Furthermore, because of the assumed reliability of
detection techniques carried out from the repository itself,
conservative estimates of minimum distances between repository drifts
and such undetected boreholes were given in the previous section as 100
meters for salt and 5 meters for the other rock types. Consequently,
for such boreholes to serve as pathways for the release of
radionuclides, communication must exist between them and the backfilled
repository drifts. An electrical resistance analog is useful in
representing this situation and in identifying cases in which
significant levels of flow may take place. The general situation is
represented in Figure D-19a. The quantitative analysis for each of the
two salt formation repositories will be presented in the following
sections in terms of the diagram in Figure D-19b. Effective resistance
will be calculated as in earlier sections and as explained in Appendix
D-III, according to the formula a = L/KA, where L is the pathway length,
K is its permeability, and A is its cross-sectional area. (The
unlabeled resistances along the aquifers are relatively low and do not
enter into the calculations.)
D-3.4.4.1 Bedded Salt
The values of the effective resistances »1 through a.^, based on
parameter values presented earlier, are shown in Table D-71. Since o^
and a^ are functions of time, selected values are tabulated in Table
D-72. The values of a.^ and a, ignore the possibility of dissolution
178
-------
(a) Physical Pathways
II
11
Ji-
I I
I I
Permeable
shafts and
boreholes,
fracture systems
Upper aquifer
Repository
Permeable
deep boreholes,
fracture systems
Permeable
interbeds
or fractures
Undetected
borehole
Lower aquifer *
(b) Electrical Analog
Upper aquifer
Shafts,
boreholes,
fractures
Upper section
undetected borehole
Interbeds or fractures
Deep
boreholes,
fractures
Lower section,
undetected borehole
Lower aquifer*
Lower aquifer not present for certain rock types.
FIGURE D-19 PATHWAYS ASSOCIATED WITH THE ANALYSIS OF UNDETECTED BOREHOLES
179
-------
TABLE D-71
EFFECTIVE RESISTANCES ct THROUGH u
(BEDDED SALT REPOSITORY)
? 2
First Estimate (y/m ) Second Estimate (v/m J_
a * (3.31 x 10~3 + 4.70 x 10~3 t)'1 (3.31 x 10~3 + 3.31 x 10~3 t)'1
a (1.58 x 10~5 -f 1.58 x ](T6 t)"1 (1.58 x 10~5 + 1.58 x 10~5 t)'1
31.75 105.8
31.75 105.8
a5** 3.2 x 106 317.5
*
The calculation of a has been carried out by considering the
situation of two parallel resistances, one representing shafts and one
representing boreholes, t is time from repository closure.
**
The values are based on the assumption of communication through one or
more interbeds with a total effective pathway cross-sectional area of
1 m , permeabilities 10~ cm/sec, and 10~ cm/sec for first and
second estimates, respectively, and a length of 100 m. (Cf. Figure
D-13).
180
-------
TABLE D-72
SELECTED VALUES OF a AND a
First Estimate
10*
100
500
1000
5000
10,000
Second Estimate
10
100
500
1000
5000
10,000
(BEDDED SALT REPOSITORY)
2
Resistance (v/m )
1.
2.
4.
2.
4.
2.
3.
3.
6.
3.
6.
3.
99
11
25
13
25
13
02
02
04
02
04
02
!i
X
X
X
X
X
X
X
X
X
X
X
X
10
10
10
10
10
10
10
10
10
10
10
10
!i
i
j.
o
\J
-1
-1
-2
£,
-2
1
n
\J
-1
-1
-2
-2
3
5
1
6
1
6
5
6
1
6
1
6
.16
.75
.24
.27
.26
.32
.75
.27
.26
.32
.27
.33
x
X
X
X
X
X
X
X
X
X
X
X
10
10
10
10
10
10
10
10
10
10
10
10
A
*T
1
J
3
2
2
1
3
2
£>
2
1
1
0
*Years after repository closure.
181
-------
along the portion of the borehole with the salt strata; the case of
dissolutioning will be discussed later.
Without performing detailed network calculations, it is possible to
dismiss the importance of the undetected borehole pathway, in most
cases, by the following reasoning. Because a,, is much greater than o^,
flows out of the repository via the undetected borehole-interbed
pathway would be expected to be insignificant compared with flows
through shafts and boreholes to the upper aquifer. Because a- is much
greater than a., at least for t > 1000 years in the case of second
estimates, flows into the repository through the interbed are small
compared with those through the degrading deep borehole seals. (For t<
1000 years, releases are dominated by salt creep, and other driving
forces are not important.) In either case, consideration of this
pathway would lead to flows that are insignificant compared with those
calculated in the previous two sections.
The one additional possibility that needs to be considered is that
of dissolution around an undetected borehole and the resulting
consequences, if any, for repository integrity- Dissolution
calculations in Appendix D-IIT show that in the case of second
_^
estimates, where borehole permeability is high (K • 10 cm/sec) and
there is a significant aquifer interconnection gradient (i = 0.5), the
potential for dissolution is great. After the period of extensive salt
creep (Period A), releases through an undetected borehole connected to
the repository as a result of dissolution can be estimated simply by
assuming that the flow passes through the repository and encounters
resistance only in the part of the borehole extending from the lower
aquifer to the bottom of the salt stratum (since a dissolution pathway
extends through the salt and the part above may crumble and fall into
that void). Darcy's equation,
Q = KiAc(M),
182
-------
with parameters given earlier, leads to the volumetric flow rate
Q - 945 m3/yr
during Period B. (See Section D-3.2.4 for the definition of Period B.)
The source term for this failure element consists of the
concentration of radionuclides that have leached into the water in the
repository during the time frame of interest. This is the uniform
concentration situation described earlier.
D-3.4.4.2 Granite
An undetected borehole has been modeled at a distance of five meters
from a repository drift in the case of granite. Over this short
distance the flow between the repository and the borehole cannot be
adequately modeled by Darcy's law for flow through porous media, since
this law can only be applied to fracture flow on a larger scale. Direct
communication through a single open fracture could eliminate any
significant resistance along this part of the pathway. Therefore, the
borehole has been modeled as passing directly through the repository,
and volumetric flow rates have been calculated as they were in Section
D-3.3.4. Using the driving forces summarized in that section in
combination with the pathway parameters given in Section D-3.4.3, the
volumetric flow rates and fluid velocities shown in Tables D-73 and D-74
result.
The source term for this failure element consists of the
concentration of radionuclides that have leached into the water in the
repository during the time frame of interest. This is the usual uniform
concentration situation.
D-3.4.4.3 Basalt
As in the case of granite, flows through an undetected borehole in
the generic basalt repository have been calculated as though the
borehole passed through the repository Itself. The flow calculations in
Section D-3.3.4 Indicated that, because of multiple pathways from the
183
-------
TABLE D-73
VOLUMETRIC FLOW RATES THROUGH UNDETECTED BOREHOLES
(GRANITE REPOSITORY)
Volumetric Flow (0)
(m3/yr)
100 years 1000 years 10.000 years
First Estimate
1.7
1.1
0.5
Second Estimate
17
11
Years after repository closure.
184
-------
TABLE D-74
FLUID VELOCITIES THROUGH UNDETECTED BOREHOLES
(GRANITE REPOSITORY)
Velocity (v)
(m/yr)
100 years
1000 years 10.000 years
First Estimate
85
55
25
Second Estimate
850
550
250
Years after repository closure.
185
-------
repository to the upper aquifer (e.g., permeable shafts and boreholes),
the limiting factor in flows through deep boreholes is the resistance
over their lower sections (from lower aquifer to repository). It
follows that the driving hydraulic potential is almost entirely
dissipated over this part of the pathway. This reasoning was used in
the earlier section to derive the hydraulic gradients given there in
Table D-60. By using these gradients in Darcy's law, the marginal
increase in fluid flows caused by an undetected borehole through the
repository can be calculated; these are given in Table D-75.
Corresponding fluid velocities, assuming that the flow continues to the
upper aquifer through the same borehole (a conservative assumption in
that it tends to overestimate the velocity) are given in Table D-76.
The source term for this failure element consists of the
concentration of radionuclides that have leached into the water in the
repository during the time frame of interest.
D-3.4.4.4 Shale
Although the probability of an undetected borehole differs in the
case of shale from that calculated for basalt, the flow calculations for
each such borehole are identical. Therefore, Tables D-75 and D-76 carry
over to this case, except that on the second estimate for shale three
boreholes are used. The results for shale are given in Tables D-77
and D-78. The source term is also the same as in the case of basalt.
D-3.4.4.5 Dome Salt
The analysis for a salt dome repository closely parallels that for
bedded salt. Since an undetected borehole will be close to the
periphery of the dome, there is a significant possibility that it will
pass through an overhanging flank and make contact with an aquifer (or
pressurized brine reservoir) below. This has been assumed in the model
for all undetected boreholes in dome salt. As in the case of bedded
salt, the only significant flows can occur during Period B and under
second estimate model assumptions. In this case, there are five such
boreholes and the original hydraulic gradient of 0.2 (from the aquifer
186
-------
TABLE D-75
VOLUMETRIC FLOW RATES THROUGH UNDETECTED BOREHOLES
(BASALT REPOSITORY)
Volumetric Flow (0)
(m /yr)
100 years
1000 years 10.000 years
First Estimate
4.4
3.8
1.6
Second Estimate
198
192
170
Years after repository closure.
187
-------
TABLE 0-76
FLUID VELOCITIES THROUGH UNDETECTED BOREHOLES
(BASALT REPOSITORY)
Velocity (v)
(m/yr)
100 years 1000 years 10.000 years
First Estimate
220
190
80
Second Estimate
9900
9600
8500
Years after repository closure.
188
-------
TABLE D-77
VOLUMETRIC FLOW RATES THROUGH UNDETECTED BOREHOLES
(SHALE REPOSITORY)
Volumetric Flow (0,)
(m3/yr)
100 years 1000 years 10.006 years
First Estimate
4.4
3.8
1.6
Second Estimate
594
576
510
Years after repository closure.
189
-------
TABLE D-78
FLUID VELOCITIES THROUGH UNDETECTED BOREHOLES
(SHALE REPOSITORY)
Velocity (v)
(m/yr)
100 years
1000 years 10.000 years
First Estimate
220
190
80
Second Estimate
9900
9600
8500
Years after repository closure.
190
-------
interconnection) leads to a concentration of the driving force over the
undissolved and unbrecciated section of the borehole between the lower
aquifer and the point where it enters the salt. If this distance is one
quarter the distance between the aquifers, the effective gradient is
four times the original value of 0.2. The corresponding volumetric
flow rate is given by
Q = KiAc(u)
= (10~3 cm/sec)(3.15 x 105 cm/sec/m/yr)(.8)(.5 m2)(5)
- 630 m3/yr
which applies to Period B.
The source term for this failure element consists of the
concentration of radionuclides that have leached into the water in the
repository during the time frame of interest.
D-3.4.5 Literature Discussion
Undetected boreholes have also been discussed by an NRC-Sandia
group ^ ' and by Battelle Pacific Northwest Laboratory (BNWL)^ under
the WISA.P Program.
In the NRC Sandia report, a general methodology is proposed for
modeling this phenomenon. Input requirements are the following:
3 = mean areal density of undetected boreholes
f - fraction of the undetected holes that are unsealed
S • a random variable representing the shortest distance from an
undetected borehole to a waste drift, whose distribution
would be calculated from the repository geometry
o(s) • a function describing the time required for solutioning
along a borehole to extend the radius to value s
-------
V - rate of salt removal from a cavity formed by flow through an
unsealed borehole
W - rate of salt removal from a cavity formed by the failure of
a sealed borehole.
* 3 * 3 /
The report suggests values V - 1.5 m /yr, W - 0.15 m /yr, and the range
27 to 113 meters for the distances between an undetected borehole and a
waste drift. (These parameters apply to the generic bedded salt
reference repository defined in detail in the same report.)
In the BNWL project, it has been asserted that for the Columbia
Plateau (basalt) the identification of all old boreholes to the
repository depth should be a relatively simple task. In addition, it is
argued that two additional factors would need to be present in order for
such a borehole to lead to a breach of the repository containment: a
connection with the repository and a hydraulic driving force.
D-3.5 OTHER TECHNOLOGICAL EVENTS AND PROCESSES
D-3.5.1 Introduction
Mechanisms and processes that fall into the "technological" category
are those related to the presence of the wastes or the repository, or
those related to the site exploration process. In other projects on
disposal of high-level radioactive wastes, the term "near field" effects
has been used to include most of these processes. The analysis of
such effects is difficult with a generic repository because detailed
engineering assumptions are necessary for a complete analysis, and the
repository systems treated here are not defined to such a level of
detail. For example, questions have been raised concerning the
stability of borosllicate glass as a waste form when placed in a salt
(81)
environment. ' Since stability is related to both waste form and
temperature, it Would be necessary to specify a waste form and a level
of thermal loading for the repository, calculate estimated temperature
profiles, and then determine what laboratory data and
thermodynamic/kinetic analysis could contribute to a quantitative
assessment of the magnitude of the potential problem. A different
192
-------
approach has been adopted here, one more suitable for a generic study.
Potential problem areas have been reviewed and, except in the case of
those identified as particular failure elements in previous sections, it
has been assumed that they represent engineering problems amenable to
analysis and solution.
D-3.5.2 Waste-Rock Interactions
Interaction between the radioactive wastes and the surrounding rock
can affect both the waste package and the rock. Examples of particular
effects are discussed in the following paragraphs.
Waste form degradation. The waste forms under consideration in this
study range from spent fuel to special solid matrices (e.g., cement,
glass, synthetic minerals) for processing or reprocessing wastes. In
each case and in each geologic environment, the effects of the host rock
and groundwater on the waste forms must be addressed. A particular case
that has received considerable recent attention is the effect of hot
brines on borosilicate glass. A straightforward engineering solution
to such a problem might be to decrease the level of waste loading so
that the temperature remains at a level where such a reaction would
occur at a negligible rate, if at all. Other questions would be whether
the altered waste form is significantly more leachable than the
original, whether the canister (i.e., the package) might be able to
Insulate the waste form from the environment until the critical thermal
period has passed, whether brines or otherwise active groundwater can
ever reach the waste form, etc. Current research on waste forms should
provide the information necessary to deal with these questions
effectively.
Canister degradation. Canister research and development work in the
United States and abroad reflects several different philosophies about
this component of the waste containment system. These range from the
view that the canister is important only through the handling and
emplacement stage, to the view that the canister can be one of the most
important barriers to radionuclide release, perhaps for periods up to
hundreds of thousands or millions of years. More details on canister
capabilities may be found in Appendix D-VIII of this report and in the
193
-------
Task B Report. In any case, the geochemical, thermal, and mechanical
parameters of the emplacement environment can certainly affect the
integrity of the canisters, and therefore these factors must be
considered carefully in the engineering design of the system.
Rock alteration. Rock in the immediate vicinity of the waste
canisters will be subjected to heat and radiation, which can affect it
in a variety of ways. For example, heat can lead to spelling, cracking,
or decrepitation through differential expansion or high vapor pressure
of fluids in the rock. Such fracturing would be expected to increase
the hydraulic conductivity, but probably only within a few meters of the
wastes. (This increase is different from the bulk rock failure element
discussed in Chapter 3.0, wherein large scale movement along existing
joints was considered.) In the special case of shales and some other
rocks composed of certain hydrous clay minerals and metastable minerals,
more extensive changes are possible. Some clays, such as
montmorillonite, contain loosely bonded water in the crystal structure,
and this can be liberated at temperatures in the range of 100-200 C.
As a result of dehydration, the clay contracts, cracks, and loses
strength; in addition, water is provided to the repository. Other modes
of alteration are also possible but are not discussed here since it is
believed that they are likely to be less significant.
D-3.5.3 Brine Migration
Salt deposits frequently contain fluid inclusions, which are
(generally very small) bubbles or pockets of fluid within the salt
matrix. These inclusions occasionally have both a liquid and a vapor
phase. Some of these inclusions may represent connate water contained
in the salt since its deposition, although other mechanisms may also
account for such inclusions. Geochemical studies now under way may
provide a greater understanding of this phenomenon. '
Fluid inclusions can migrate in a thermal gradient as a result of
(83)
several possible mechanisms, one of which is sketched in Figure
D-20. In the situation represented, salt dissolves on the left side of
the bubble and reprecipitates on the right side because of the variation
194
-------
Diffusional transport
of solute, driven by
concentration gradient.
Dissolution \
Precipitation
Decreasing temperature
Bubble migration
FIGURE D-20 MIGRATION OF BRINE BUBBLE IN THERMAL GRADIENT
195
-------
of solubility with temperature. This has the effect of moving the fluid
inclusion' to the left, toward the heat source.
The rate of brine migration and the total amount that might
accumulate near the hot waste canisters depends on a number of factors,
such as the magnitude of the thermal gradient and the amount of water
present in the salt. The results of modeling efforts and laboratory
experimental programs now in progress may provide further illumination
on the relationships among the parameters and indicate the extent to
which this mechanism should be considered in site selection (e.g., fluid
content of salt may vary from site to site) and in the choice of
engineered barriers. The potential for migration of brine will be an
important factor in determining the requirements a the waste package in
a salt repository.
D-3.5.4 Canister Migration
Various mechanisms have been proposed by which canisters emplaced in
a salt environment might physically migrate either upward or
downward. ' Representative mechanisms are briefly described
below.
Sinking because of canister density. Because the canister is denser
than the salt and because the salt is plastic, the canister might sink
right through it. (Movement might be slow because of the high viscosity
of the salt.)
Sinking because of formation of a brine bubble. If the canister is
enveloped by fluid (through brine migration, discussed in the previous
section), it would sink to the bottom of the surrounding bubble. The
higher temperatures at the bottom, where the canister would rest on the
salt, could lead to preferential dissolution there, and thus continue
the sinking process.
Rising caused by thermal buoyancy (induced salt diapirism). The
salt surrounding one or more waste canisters or the entire repository
would be expected to expand upon heating. The resulting decreased
density might cause this entire mass to rise, carrying the canisters
with it.
196
-------
A number of scientists at different laboratories using different
analytical and experimental tools have investigated possible waste
(53 87—92}
migration in salt. ' ' A substantial effort to characterize
behavior of the salt of the Delaware Basin has been carried out and is
continuing at Sandia Laboratories. This effort includes laboratory
measurements of salt creep, constitutive modeling of salt response, and
the application of numerical stress analysis procedures for predicting
canister movement.
Analysis of the steady-state and transient response of a single 3-m
long, 30-cm diameter canister were performed using lower bound (worst
(87)
case) viscosity estimates. The predicted velocities are in the
order of 1 cm/1000 years. The long-term total movement predicted from
convective cell movement is 5-10 meters per 10 years. The Sandia
effort has also examined various canister and repository configurations
and emplacement schemes with a view toward determining the effects of
those factors on both individual canister motion and repository motion.
The studies indicate that movement of the salt mass would not cause a
salt dome to form.
In the present study of generic repository designs and geologic
formations, canister or repository movement is not modeled as a failure
element since most recent investigations agree that such motions are not
a serious concern. The mechanisms described are amenable to engineering
analysis, based on the parameters appropriate to a specific situation
(salt viscosity, temperature profiles, etc.). If such movement is
predicted to be a problem in a particular case, the design (e.g., shape
or thermal loading of canisters), can be modified or a repository
considered elsewhere.
D-3.5.5 Criticalitv
Concentration of certain radioactive material can result in
self-sustaining nuclear reactions. This condition of high concentration
is referred to as criticality. To avoid the possibility of reaching
critical levels, waste forms, concentrations of fissionable material,
and canister spacing can be planned with this factor in mind.
Criticality calculations are straightforward and well understood.
197
-------
Naturally, allowance must be made for the movement of canisters and for
the introduction of water, as discussed in the previous sections. The
concentration of fissionable material by chemical means (i.e., by
dissolving out of the waste form matrix and reconcentrating elsewhere)
is also a theoretical possibility, but no reasonable mechanism has been
postulated by which this might occur in a repository.
198
-------
D-4.0 HUMAN INTRUSION
One failure element, future drilling, is modeled in detail in this
chapter, and several additional possible failure mechanisms are
discussed. Some repository risk assessments have avoided quantitative
models for future human intrusion events, but it appears that this
approach is unrealistic. There are large uncertainties associated with
the prediction of future natural events or technological failures as
well, and to neglect one important class of events may cause too much
emphasis or importance to be placed on others. While the estimates
given here must obviously be speculative, they would appear to be useful
not only for rough estimates of repository performance, but also to
clarify the importance of key assumptions in the assessment process.
D-4.1 FUTURE DRILLING ACTIVITIES
D-4.1.1 _Summar_Y
Future deep drilling on the repository site could lead to the direct
transport of radioactive material to the surface or to the establishment
of an additional groundwater pathway. Estimates of the possible extent
of such drilling depend on assumptions made about future knowledge and
control of the repository site. EPA guidelines for this study require
the assumption that after a period of 100 years from repository closure,
control of the site is lost and it reverts to prevailing land use
patterns of the area in which it is located. Based on this assumption,
estimates were made of the frequency of future deep drilling. Three
modes of release were modeled: transport of pieces of canister to the
surface with the drilling fluid in the case of a direct hit; transport
of fluids, from the repository to the surface during drilling; and the
establishment of a groundwater pathway from the repository to the upper
aquifer by means of an imperfectly plugged hole. A summary of
assumptions, parameters, and calculational results is given in Table
D-79.
199
-------
TABLE O-79
SUMMARY OF FUTURE DRILLING FAILURE ELEMENT
ro
o
o
M50IUM
8^sa|i
Grwh.
Saoil
§S
p P
Si
II
§!?
K
£ 3
P, D
P, O
P, D
MATURE
OF
MOOS!,
Postulated determin-
istic drilling rate.
probabilistic for
hitting canister.
Postulatad determin-
istic drilling raw.
probabilistic for
hitting canister.
Postulated determin-
istic drilling rate.
probabilistic for
hitting canister.
RELEASE
MODE
A. Land surface
B. Groundwater
A. Land surface
B. Groundwater
A. Land surface
B. Groundwater
DRIVING
FORCE
A. Materials raised
with drilling mud.
B. Thermally induced
convection and
gradient from
aquifer inter-
connection.
A. Materials raised
with drilling mud.
B. Thermally induced
convection.
A. Materials raised
with drilling mud.
3. Thermally induced
convection and
gradient from
aquifer inter-
connection
SOURCE
TERM
A. Part of canister
and fluid from
waste drift.
B. Uniform
concentration.
A. Part of canister
and fluid from
waste drift.
B, Uniform
concentration.
A. Part of canister
and fluid from
waste drift.
B. Uniform
concentration.
PARAMETERS
1st ESTIMATE
No holes first century;
5 holes next century:
2 holes each subsequent
century. All holes to
lower aquifer.
Holes seated with
permeability
K = 10-* cm/sec
TJ = 0.2, and
A => 0.1 m2.
Probability of hitting a
canister = 10*3 pef hole.
with expected removal
of 15% contents.
No holes first century;
1 hole next century;
1 hole every four sub-
sequent centuries.
Holes seated with
permeability
K - 10"4 cm/see.
11 - 0.2, and
A - 0.1 m2.
Probability of hitting a
canister - 10"3 per
hole, with expected
removal of 15%
contents.
No holes first century;
3 holes next century;
1 hole each subsequent
century. All holes to
lower aquifer.
Holes sealed with
permeability
K • 10" cm /sec.
n - 0.2. end
A « 0.1 m2.
Probability of hitting a
canisier = 10"3 per hole.
with expected removal
of 15% contents.
2nd ESTIMATE
No holes first century;
50 holes next century;
5 holes each subsequent
century. All holes to
lower aquifer.
Hales sealed with
permeability
K = 10-3 cm/sec.
ij =• 0,2. and
A = 0.1 m2.
Probability of hitting a
canister =• 10*3 per hote.
with expected removal
of 15% contents.
No holes first century;
10 holes next century;
2 holes every subse-
quent century.
Holes sealed with
permeability
K - 10"3 cm/sec.
n - 0.2, and
A - 0.1 m2.
Probability of hitting a
canister - 10""* per
hole, with expected
removal of 15%
contents.
No holes first century;
20 holes next century;
5 holes each subsequent
century. All holes to
lower aquifer.
Holes sealed with
permeability
K =• 10-3 cm/sac.
T) *> 0.2, and
A - 0.1 m2.
Probability of hitting a
canister « 1Q-3 per hole.
with expected removal
of 15% contents.
FLUID TRANSPORTED
TO SURFACE
1st ESTIMATE
0.07 m3 /drill hole
200 m3/drill hole
200 m3/dnll hole
2nd ESTIMATE
1400 m3 /drill hole
5OOO m3 /drill hole
5000 m3/drill hole
COMMENTS
Analysts assumes no
knowledge of reposi-
tory before, during, or
after drilling. Ground-
water releases from
post-sealing leakage are
calculated in the text
but are, in general, less
significant than releases
to the surface.
Analysis assumes no
knowledge of reposi-
tory before, during, or
after drilling. Ground-
water releases from
post-sealing leakage are
calculated in the text
but are, in general, less
significant than releases
to the surface.
Analysis assumes no
knowledge of reposi-
tory before, during, or
after drilling. Groun-
water releases from
post-sealing leakage are
calculated in the text
but are, in general, less
significant than releases
to the surface.
-------
TABLE D-79
SUMMARY OF FUTURE DRILLING FAILURE ELEMENT (CONTINUED)
MEDIUM
Shale
Dome Salt
§1
I!
o ™
P.D
P. 0
MATURE
OF
MODEL
Postulated determin-
istic drilling rate.
probabilistic for
hitting canister.
PCM 1 y^J J^
istic drilling rate,
probabiliflic for
Mining canistar.
RELEASE
MODE
A. Lend surface
B. Groundweter
A. Lsndsurface
B. GroundMStar
DRIVING
FORCE
A. Materials raised
with drilling mud.
B. Thermally induced
convection end
gradient from
aquifer intar-
eonnactlon.
A. Msteriels raised
with drilling mud.
B Thermally induced
SOURCE
TERM
A. Part of canister
and fluid from
varo drift.
B. Uniform
concentration.
A. Pan of canistar
and fluid from
1. Uniform
concentration.
PARAMETERS
1st ESTIMATE
No holes first century;
5 holes next century;
2 holes each subsequent
century. All holes to
tower equifer.
permeability
K - 10"4 cm/mac.
1 " 0.2. and
A - 0.1 m2.
Probability of hitting a
canister- 10-3 per hole.
of 15% contents.
No holes first century:
> hates next century:
2 hales every
mosaquent century.
Hoses sealed with
permeability
K - If)"4 em/iec.
i) • 0.2, and
A - 0.1 m2.
'robetaiNty of hitting a
anister- 10-3 par hole.
of 15* contents.
2nd ESTIMATE
No holes first century;
50 holes next century;
5 holes each subsequent
century. All holes to
lower aquifer.
Holes sealed with
permeability
K * 10-3 cm/sec.
il - 0.2, and
A - 0.1 m2.
Probability of hitting a
centner -10-3 per hole.
of 15% contents.
No holes first century;
30 holes next century;
Sholes every
subsequent century.
Holas sealed with
fMrmeBbdity
K - 10-3 cm/sec.
-------
D-4.1.2 Background
Estimates of the likelihood of future penetration of a repository by
drilling activities must be made in the context of past and present
drilling rates as well as the. extent to which the rates, purposes, and
characteristics of drilling activity vary with time. These topics are
discussed in this section. In addition, there are subsections on
various activities associated with drilling, since these activities may
affect whether an unknown repository is detected before or during
drilling. They may also affect the consequences of drilling into a
repository.
Past drilling activity. The reasons for and extent of past drilling
into potential repository formations are relevant to estimating the
potential for future drilling. Data on historical drilling activity
were presented in Section D-3.4 and will only be summarized here. The
scope of drilling activities discussed in that section includes:
• oil and gas exploration and recovery,
• water exploration and recovery,
e geothermal resources evaluation,
« brine injection or disposal of other wastes,
• mineral exploration,
« scientific investigation,
• fluid storage, and
• other special and localized drilling.
The areal densities that were estimated for old boreholes are summarized
in Table D-80. They were determined on the basis of the expected
dominant types of activity in the past: oil and gas, water, and mineral
exploration and/or recovery.
Present drilling rates. The present drilling rate appears to be
well documented only for the petroleum industry- Figure D-21 shows
numbers of oil and gas holes drilled by state (or groups of states) in
1976 and 1977. Of these, about 37,000 holes drilled in 1977 exceeded
(93)
1250 feet (385 m). This represents an average rate of 0.04 hole per
2
year per repository area, using 8 km for the area of the repository and
r 9
7.8 x 10 km for the area of the 48 contiguous states. Since this
drilling was generally confined to potential oil- and gas-bearing
202
-------
TABLE D-80
AREAL BOREHOLE DENSITIES FROM PAST DRILLING ACTIVITIES
*
Holes per Repository Area
First Estimate Second Estimate
Bedded Salt 0.08 6.0
Granite 0.003 0.0?
Basalt 0.05 0.13
Shale 0.03 6.0
**
Dome Salt 2.0 20.0
These estimates are based on Section D-3.4 of this report and refer to
holes at least 300-500 m deep. Depending on the rock type, the areal
densities were given earlier for either the buffer zone around the
2 2
repository (4 km ) or the repository plus buffer zone (12 km ). The
numbers in this table have all been normalized to the repository area
(8 km2).
**
The holes in salt domes tend to be concentrated near th« flanks of the
dome. Since the repository would be in the interior of the dome, the
average density of holes is a bound on the expected number penetrating
the repository area itself. Thus, it is a conservative estimate.
203
-------
KJ
O
1977 over 381 meters deep
11/7 K.isl
^---i \ «?/
(---- i
Scale in Kilometers \
I H
Sources- 1977 Joint Association Survey on Drilling Costs, sponsored by: American Petroleum Institute, Independent Petroleum
Association of America, and Mid-Continent Oil and Gas Association, February 1979.
1976 Joint Association Survey on Drilling Costs, The American Petroleum Institute , Dec., 1977 Edition.
FIGURE D-21 PETROLEUM WELLS DRILLED IN THE CONTIGUOUS 48 STATES, 1976 AND 1977
-------
sedimentary basins, the areal density is far from uniform and, In fact,
is much higher for such basins.
Non-uniformity of drilling rates with time. Tt is important to note
that extreme changes in drilling rates may occur with time. Reasons for
this include the following:
• Scarcity of oil, gas, water, or certain minerals may
encourage more extensive exploration.
• New recovery methods may make deposits attractive that
were previously partially depleted or not worth
exploiting at all.
• New drilling techniques may make it feasible to exploit
additional formations.
• New resource recognition may initiate entirely distinct
drilling programs.
• Demographic changes may encourage extensive drilling for water or
other resources in new areas.
• Other purposes for drilling may assume prominence.
Examples of these factors can be seen in the evolution of the petroleum
industry. A little over 100 years ago there was no such industry, and
the drilling of more than two million petroleum holes in the United
(94)
States over the period of a century was presumably not foreseen.
Several thousand holes are drilled annually in search for uranium, and
the recognition of this resource is only about forty years old.
Geothermal energy is in its commercial infancy, and it is impossible to
predict to what extent this industry will grow. Population movement to
the southwest has encouraged deep drilling for water in recent years,
and with the gradual depletion of water stored in certain formations,
additional resources will have to be sought in the future. Furthermore,
the development of extensive drilling programs for new purposes, such as
monitoring or control of tectonic events, waste disposal, or scientific
research, may well occur-
Activities prior to drilling. Tn assessing the possibility of
future drilling through a nuclear waste repository, it is relevant to
consider whether the repository might be detected prior to drilling.
The extent of such exploration depends on the nature of the resource
being sought. In the case of petroleum, which is generally found in
205
-------
specific structural traps, extensive geologic and geophysical
exploration usually precedes the drilling. In the case of water wells,
drilling may start with little or no geophysical work, although the
types of geologic formations being drilled would be known on a regional
basis. Geothertnal drilling may be preceded by detailed area heat flow
analyses, although it is not yet clear what practices will be followed
when and if this resource becomes heavily exploited in the future.
Activities during drilling. The ways in which the presence of a
repository might be recognized during drilling are relevant to the
consequences that could follow from such a breach. As above, this
depends on the purpose for which the hole is being drilled. Activities
associated with petroleum well drilling are reviewed in the following
paragraphs.
Drilling boreholes involves a continuous process of investigation
and examination of the drill progress and the geology of the rocks being
penetrated. Typically, drilling to any considerable depth into
consolidated rock involves the use of rotary equipment cooled and
lubricated with any of a number of fluids (muds). In the process, chips
of rock are broken at the bottom of the hole and carried to the surface
with the fluid. A regular inspection of the rock chips is made to
determine their nature and composition, as a guide for estimating the
formation being drilled. Thus, the drill crew is constantly aware of
the nature of the rock being penetrated. A written log of rock type, as
determined from the cuttings, is retained, at least within the depth
range of interest to the exploration program.
Other factors and conditions noted during drilling with common
rotary equipment are fluid used, gases and other contaminants, drilling
rate, and depth of drill string. From this information, a drill crew
can interpret the down-hole conditions and rock formation with
occasional reference to the material brought up by the drill and by
correlation with other holes in the vicinity.
Periodically, particularly when some unusual formation is reached,
when the drill stem has been pulled for some reason, or when it is
suspected that a productive horizon is being penetrated, the hole is
logged. This procedure involves a number of processes and different
equipments. Logging may simply measure the diameter and depth of the
206
-------
hole, or it may entail use of more sophisticated and sensitive equipment
to measure certain rock properties. Specialized logging devices include
electric resistance sondes, gamma radiation logs, sonic logs, neutron
logs, and magnetic and temperature sensors. These assist in determining
the rock type at depth, its physical properties, and its economic
potential. In some cases, the drill mud and cuttings are continuously
monitored by automatic equipment to indicate to the drill crew when
petroleum, radioactive minerals, or rock with specific properties (such
as high density) have been reached.
When circumstances permit and dictate (when drilling into competent
rock with important properties or characteristics such as distinctive
structure or minerals) a core of the rock may be taken. This procedure
requires a special drill bit, typically diamond faced. The core sample
is then examined and the results recorded. Important information
obtained from cores includes not only rock type, but porosity, strength,
permeability, structure, and mineral composition. Some of this
information is found through laboratory tests performed on the recovered
cores.
Much of the continuous investigation during drilling depends upon
the experience and expectations of the drill crew. In locations where
other boreholes have penetrated a considerable depth of unproductive
rock in reaching a readily identified horizon, logging and mud checking
may not be as conscientiously applied as in situations where the
sub-surface geology is less well known. This on-site subjectivity is
augmented by thorough preliminary geologic and geophysical surveys of
the area. Seldom, if ever, is a borehole started without a substantial
commitment of time and energy to determine the suitability of the drill
site. The occasional exception is when limited finances encourage a
private landowner to accept the risk of a blindly drilled hole for water
or mineral exploration. However, in such situations, the drill crew can
usually supplement the lack of knowledge with their own experience in
drilling other holes within the same geologic domain.
207
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D-4.1.3 FutureJ)rilling Failure Model
In accordance with EPA. guidelines on assumptions about future
institutional control of a radioactive waste repository site, the
following have been assumed for purposes of this study:
0 Institutional control of the site can prevent drilling for 100
years after repository closure.
• After the 100-year period of institutional control, the site
returns to the ordinary land use patterns of the area in which it
is located.
It should be emphasized that these are model assumptions, not assertions
about future events. Indeed, one can easily imagine conditions under
which one or both of these would be violated. For example, the
increasing scarcity of energy and perhaps other resources over the first
100-year period could result in strong pressures on the government to
permit exploration for and recovery of such resources on the sits.
These resources might today be completely unrecognized or undiscovered,
or be regarded as commercially worthless. The government might yield to
such pressures and permit drilling under controlled conditions. Because
such a decision would be made in full knowledge of the presence of the
repository, however, responsibility for any adverse consequences would
seem to rest with those future decision-makers. If such drilling were
undertaken, it is likely that assurances of its safety would also be
required. Therefore, conditions under which the first assumption is
violated have not been pursued here.
The second assumption may also not accurately represent the true
situation. It is highly probable that knowledge of the repository will
be preserved beyond 100 years and that this will influence activities on
the site even if the level of institutional control decreases or
disappears. In the absence of institutional control, however, knowledge
of the existence of the repository may still not be sufficient to
preclude activities that threaten the repository's integrity.
Obviously, one cannot predict the future or extrapolate
scientifically from past data to estimate future drilling rates at a
repository site. Nevertheless, it is believed that the probability is
sufficiently high of future deep drilling at the site that the question
208
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is not "whether" but "how often." That is, a rate of future drilling
should be a model parameter and various values should be used for
sensitivity analyses. The purpose of this section of the report is to
provide nominal values for this and associated parameters under first
and second estimate assumptions for each of the five geologic host media
being evaluated.
Estimated future drilling rates are presented in Tables D-R1 through
D-85. The drilling rates given in the tables are not the result of
scientific or statistical observation. They are rough estimates by
members of the Arthur D. Little, Inc. staff who have experience in
resource exploration and recovery. Tn the case of exploration, they are
generally based on the time interval over 'which factors may change
sufficiently to justify another exploratory drill hole.
The drilling rates are given in terms of holes per century. For
exploratory holes they might be spread out rather evenly in time, and
for holes for petroleum production they might be closely grouped in
time. The choice of a single more heavily drilled century was the
result of a two-step process. First, it appears likely that a valuable
resource on the site will be exploited over a limited period of time.
This period of time could fall during any century within the 10,000
years over which the repository is being evaluated. Thus, one century
is hypothesized to have a higher drilling rate. The choice of the first
century after the end of institutional control as this period of heavier
drilling was based on several factors:
1. Having been withdrawn from use for an entire century or more, the
site is more attractive for exploration since less is known about
it.
2. The commercial viability of mineral or energy resources will have
changed over that first 100 years, so that the new availability
of this site may open the door to new commercial recovery
operations.
3. The thermal anomaly represented by the repository itself may
encourage drilling.
Furthermore, it is in keeping with the conservative approach of this
modeling effort to assume drilling at the earliest possible moment,
since the radioactivity levels are highest then. A counterbalancing
209
-------
TABLE D-81
FUTURE PRILLING RATE ESTIMATES FOR BEDDED SALT
First Estimate Second Estimate
Characteristics of
Resources at Site
Hydrocarbons
Water
Minerals
Essentially none
in the entire
sedimentary
sequence.
Geothermal
Abundant water
at or near
surface.
No minerals at or
below repository
formation ever
expected to become
commercially valuable,
No thermal anomaly.
Present but not of
current commercial
interest, or "depleted"
formations, or unexplored
horizons with hydrocarbon
potential (possibly very
deep).
Limited water available
at or near surface. Deep
aquifer(s) below reposi-
tory formations even if
not potable.
No commercially
attractive reserves
in present terms.
No thermal anomaly.
Peep Holes Drilled
per Century
First century
after institu-
tional control
ends .
Subsequent
centuries.
50
Bases for Rate
Estimates
Unsuccessful petroleum
or mineral exploration.
210
One period of commercial
resource exploitation,
followed by occasional
exploration or water
wells.
-------
TABLE D-82
FUTURE DRILLING RATE ESTIMATES FOR GRANITE
First Estimate
Second Estimate
Characteristics of
Resources at Site
Hydrocarbons
Water
Minerals
Geothermal
None in or on flanks of
pluton.
Abundant water at or near
surface. No large
fracture system aquifers
expected at depth .
Fractures generally
closed at depth.
No expectation of signi-
ficantly valuable
mineral deposits, based
on detailed understanding
of regional geology.
No thermal anomaly.
None in or on flanks of
pluton.
Water supplies generally
from fracture systems.
None known at depth.
Limited surface water.
Mineral potential
uncertain.
Higher than average
regional heat flux.
Deep Holes Drilled
per Century
First century
after institu-
tional control
ends .
Subsequent
centuries.
10
0.25 (i.e., one hole
every four centuries)
Bases for Rate
Estimates
Undetermined purpose,
perhaps geothermal
exploration.
211
Water, geothermal, and
mineral exploration.
Possible geotherraal
wells.
-------
TABLE D-83
FUTURE DRILLING RATE ESTIMATES FOR BASALT
Characteristics of
Resources at Site
Hydrocarbons
Water
Minerals
Geothermal
Deep Holes Drilled
per Century
First Estimate
Essentially no petroleum
in any sedimentary strata
below basalt flow.
Abundant water at or near
surface.
No expectation of signi-
ficantly valuable mineral
deposits, based on de-
tailed understanding of
regional geology.
No thermal anomaly.
Second Estimate
Unexplored horizons with
hydrocarbon potential,
even if not presently
commercially attractive.
Limited water at or near
surface. Deep aquifer(s)
below repository forma-
tion even if not potable.
Mineral potential
uncertain.
Higher than average
regional heat flux.
First century
after institu-
tional control
ends .
Subsequent
Centuries
20
Basis for Rate
Estimates
Petroleum or mineral
exploration.
212
Commercial exploitation
of petroleum resources,
with hole economy due to
difficulty in drilling
basalt. Followed by
occasional exploration
and water wells.
-------
TABLE 0-R4
FUTURE DRILLING RATE ESTIMATES FOR SHALE
First Estimate Second Estimate
Characteristics of
Resources at Site
Hydrocarbons
Water
Minerals
Essentially none in the
entire sedimentary
sequence.
Abundant water at or
near surface.
Geothermal
No minerals at or below
repository formation
ever expected to become
commercially valuable.
No good indications of
valuable minerals.
No thermal anomaly.
Present but not of
current commercial
interest, or "depleted"
formation, or un-
explored horizons with
hydrocarbon potential
(possibly very deep) .
•Limited water avalable
at or near surface.
Deep aquifer(s) below
repository formations
even if not potable.
No commercially
attractive reserves
in present terms.
No thermal anomaly.
Peep Holes Prilled
per Century
First century
after institu-
tional control
ends .
Subsequent
centuries
50
Basis for Rate
Estimates
Unsuccessful petroleum
or mineral exploration.
213
One period of commercial
resource exploitation,
followed by occasional
exploration or water
wells.
-------
TABLE D-85
FUTURE DRILLING RATE ESTIMATES FOR DOME SALT
Characteristics of
Resources at Site
First Estimate
Second Estimate
Hydrocarbons
Water
Minerals
Geothermal
No oil- or gas-bearing
formations in contact
with dome at any depth.
No oil or gas of
promise in sedimentary
strata below deep under-
lying salt beds.
Abundant water at or
near surface.
No minerals associated
with dome ever expected
to be of commercial
interest.
No resource potential,
even very deep.
Present but not of
current commercial
interest, or "depleted"
formations or reserves
along flanks of dome.
Unexplored horizons
below deep underlying
salt beds .
Limited water at or
near surface.
Deep aquifers with
significant potential,
even if not potable.
Limited dome explora-
tion, or minerals
present but not
valuable in current
commercial terms.
Undetermined potential.
Deep Holes Drilled
per Century
First century
after institu-
tional control
ends .
Subsequent
centuries.
30
Basis for Rate
Estimates
Petroleum or mineral
exploration.
214
Petroleum, water, and
mineral exploration
and/or recovery.
-------
possibility, that during the first few hundred years the canisters
remain intact and thus the wastes are not leached into the surrounding
repository, should be omitted from the consequence analysis of this
failure element as long as the simplifying assumption of early maximum
drilling is retained.
In drawing the distinction between first and second estimates on the
subject of water resources, a paradoxical situation occurs. From the
point of view of future drilling, it is indeed preferable for abundant
water to be available at the surface or in aquifers overlying the
repository, since this eliminates or decreases the need to drill deep
for future water supplies. This distinction between first and second
estimates does not mean that from the total perspective of repository
evaluation it is better to have a productive aquifer above the
repository. The answer to this latter question depends on a number of
considerations, centering on the nature of all the pathways that could
allow radionuclides to enter the aquifer system. The literature of
nuclear waste management frequently exhibits the assumption that
(95 96}
productive aquifers should not overlie the repository, ' but the
present authors are unaware of conclusive evidence that this Is, in
general, a necessary or desirable criterion. With respect to water
potability, prospects for efficient desalination appear to make
potability an unreliable factor in evaluating the usefulness of aquifer
systems to future generations.
Consistent with previous sections of this report, the boreholes here
2
are assumed to have a cross-sectional area of 0.1 tn at the time they
are sealed, and they are assumed to penetrate at least as far down as to
the lower aquifer. After use they are assumed to be sealed to the same
standards as assumed for the case of presently undetected boreholes.
This assumption entails hydraulic conductivities of 10~ cm/sec and 10~
cm/sec for first and second estimates, respectively, and a porosity of
0.2. The holes are randomly distributed over the repository site.
Assuming that a future drill hole passes through the repository.
there is some probability that it will actually directly hit a waste
canister. This probability depends on the cross-sectional area of the
canister as well as on that of the drill bit and hole. The assumed
dimensions are as follows:
215
-------
Radius Area
?
Drill hole 0.1 m 0.03 m"
2
Canister 0.15 m 0.07 m
Note that the cross-sectional area of the borehole, when considered as a
7
fluid pathway, is somewhat larger (i.e., O.I m") than the area of the
drill bit and initial hole. This is because some enlargement may take
place over the period during which the hole is used and cleaned for
sealing. Moreover, the rock immediately surrounding the hole may also be
fractured and therefore augment the fluid flow. The dark ring in Figure
D-22 indicates a region where, if the center of the drill hole lies
within it, the drill will intersect part of the waste canister. The
area of this region is
A = (0.10 + 0.15)2
= 0.2 m2.
2
Since the area of the repository is 8 km , the probability that a drill
will actually hit one of the 35,000 canisters is given by
35000 x 0.2
8 x 106
- 0.0009
= 0.001.
The value p = 0.001 has been adopted in this model.
D-4.1.4 Future Drilling Release Model
Drilling into the repository may lead to the release of radionuclides
by several mechanisms, the principal ones being:
1. Direct transport of parts of the waste package to the surface in
the case of a direct hit.
2. Transport of radionuclide-contaminated water from the repository to
the surface. In the case of repositories in salt formations, this
water may be encountered under pressure.
216
-------
Note: Drill hole intersects canister if and only if its center
is within outer circle, which has radius of 25 cm.
FIGURE D-22 REGION WITHIN WHICH CANISTER AND DRILL HOLE OVERLAP
217
-------
3. Transport with groundwater to the upper aquifer through the filled
but permeable borehole pathway.
The extent of releases via any of these mechanisms depends on the degree to
which the drillers recognize the repository and its associated hazards when
they intercept it. If the drill bit passes directly into a waste drift
backfilled with densely packed yet porous and unconsolidated material, an
anomaly will in all likelihood be detected by any of several signs, among
them:
• rapid downward movement of the drill stem,
• loss of drill fluid,
• drill stem wandering and chatter,
• down-hole temperature changes caused by increased cooling of the
drill by water in repository. (This would only be detected in
the case of constant thermal monitoring, as presently practiced
in some geotherraal exploration work.)
The unconsolidated zone identified by these anomalies might be
interpreted as an extensive shear zone or, if there is some idea of a
repository in the area, it might be identified as such. If it is
identified as part of the repository, caution would presumably be
exercised in either sealing the hole or continuing to drill. For
example, samples of rock and water could be taken, down-hole logging and
geophysical techniques could be employed, and the repository section of
the hole could be grouted or cased to seal it off during subsequent use
of the hole.
Even if the repository were not recognized as such, it is likely
that the hole would be cased through the backfilled level at least
during the active life of the well. In case the drill passes through a
rock pillar rather than a mined opening, recognition of the repository
is much less likely. Pre-existing fractures or fractures induced by
drilling could establish sufficient interconnection with a nearby drift
to lead to fluid changes or loss of drill mud.
Despite the foregoing discussion, model calculations have not
assumed recognition of the repository by future drillers, although
alternative assumptions could be used to modify parameters in a
sensitivity analysis. This approach is based on three considerations:
218
-------
1. Although the mined portion of the repository occupies only 25% of
the total cross-sectional area, inclusion of portions of the
pillars in close proximity to the drifts significantly increases
this fraction.
2. The earlier assumption about loss of control and knowledge of the
repository site makes it likely that the repository would simply
be interpreted as a zone of incompetent rock.
3. Ignoring considerations about recognition leads to a simple and
conservative model.
Specific parameter values to model fluid or radionuclide releases are
given in the following paragraphs.
D-4.1.4.1 Direct Hit
In case a drill bit hits a waste canister, some fraction of the
canister's contents will be transported to the surface. Based on the
geometry presented in Figure D-22, the expected fraction of the canister
intersected by a drill hole whose center is randomly located within the
dark ring is approximately 0.15, which can be derived by a lengthy but
elementary geometric analysis. It is possible that the drillers will
notice that they have hit a strange object, either by examination of
chips at the surface, deflection of the drill stem, or clogging of the
cutters on lead or other materials that may form part of the waste
package. However, this observation by the drillers is not assured, and
so it has not been assumed in the model. Consequently, the drill has
been assumed to pass right through the portion of the canister it
intersects, which implies that the fraction 0.15 also corresponds to the
expected volumetric fraction of the canister that is raised to the
surface.
D-4.1.4.2 No Direct Hit — Fluid Released During Drilling
The analysis of this situation depends on the nature of the
repository host rock.
Bedded Salt. As discussed in Appendix D-II, water is expected to
seep gradually into the backfilled repository through slightly permeable
219
-------
shaft and borehole seals. (There may also be seepage along some natural
pathways, such as interbeds.) In addition, fluid inclusions in the
seemingly intact rock may migrate because of thermal gradients, thereby
increasing the water content of the backfill close to the canisters.
Therefore, whenever the repository is penetrated by a drill hole, the
accumulated fluid may leak out, taking with it any radionuclides that
may have leached out of the waste package. The amount of fluid present
at any moment is a function of time. There is an increase in this
amount during resaturation and then a decrease as salt creep tends to
squeeze some of it back out. For simplicity of calculations, the
maximum amount, which is the amount present just as the resaturation
condition is reached, has been assumed to be present whenever a drill
hole intersects the repository. This simplifying assumption tends to
overestimate the level of release. These volumes are calculated in
Appendix D-II and are as follows:
3 3
First estimate: 1.2 x 10 m
5 3
Second estimate: 5.6 x 10 m .
By means of the parameters given in Table D-12 (Chapter D-2.0), the
fluid volume per canister and per waste drift can be calculated. While
such volumes only represent averages and do not account for
inhomogeneities in fluid distribution, they are believed to be adequate
for modeling purposes.
The first estimate for fluid volume released during drilling is
3
0.07 m per drill hole. This is based on the low porosity and fluid
availability in the first estimate case, because of rapid salt creep,
and the assumption that at most the fluid associated with the two
nearest canisters would leak out. For simplicity, this value is also
applied to the case where a drill hole does not pass through a waste
drift, but rather through another backfilled room (other than a waste
drift) or a pillar. Possible fracturing or dissolution during drilling
do not permit adequate assurance that a drill hole through a pillar will
not communicate with a waste drift. The second estimate for fluid
3
volume released during drilling is 1400 m per drill hole, based on the
total fluid volume of one waste drift.
Granite. The fluid volumes per canister and per waste drift remain
constant after repository resaturation, with the approximate values
220
-------
3 3
50 m and 5000 m respectively. The first estimate for fluid volume
released during drilling is based on the assumption of backfill material
that is cohesive and will not easily wash into the drill hole. In this
case, the integrity of the backfill is expected to prevent more than
3
200 m from flowing into the drill hole. (This is, for example, the
quantity of water contained in a 20-m long section of the waste drift,
centered at the drill hole.) The second estimate value is based on less
cohesive backfill, the possibility that the hole is being drilled for
water, and the possibility that the drilling crew pump the repository
horizon to test it as a source of water. It would not prove to be a
desirable water supply, but the test might well empty most of the
contents of one waste drift, or 5000 m .
Basalt. The assumptions for basalt are identical to those for
3 3
granite, resulting in fluid flows to the surface of 200 m and 5000 m
as the first and second estimates, respectively.
Shale. The assumptions for shale are identical to those for granite
3
and basalt, resulting in fluid flows to the surface of 200 m and
3
5000 m as the first and second estimates, respectively.
Dome Salt. The analysis for the case of dome salt is analogous to
that for bedded salt, except that the available fluid volumes are
slightly different. Total fluid volumes for the resaturated repository
are calculated in Appendix D-II to be:
2 3
First estimate: 8.7 x 10 m
Second estimate: 5 x 10 m
3
The first estimate for the fluid released per drill hole is 0.04 m ,
based on the fluid associated with two canisters. The second estimate
3
is 1300 m , based on the fluid in one waste drift.
D-4.1.4.3 Fluid Flows After Plugging of Borehole
If the hole drilled is an unsuccessful exploratory hole, then it
would be expected to be plugged soon after being drilled. If it is
suitable for some resource recovery operation, it will probably be cased
where it passes the repository (interpreted as a horizon of incompetent
or soluble rock). The casing will prevent leakage during the production
stage. After this stage, sealing will take place. In either case
221
-------
(initial plugging or plugging after production), there may be subsequent
fluid migration along the sealed borehole up to the overlying aquifer.
This pathway is analogous to borehole pathways discussed in Sections
D-3.3 and D-3.4. First and second estimates of hydraulic conductivities
have been taken to be the same as for present undetected boreholes
A —3
(Section D-3.4), i.e., 10~ cm/sec and 10~ cm/sec, respectively. By
adopting the methods and results of Sections D-3.3 and D-3.4, the
volumetric flow rates shown in Table D-86 have been obtained. The
radionuclide source term for risk calculations! based on these flows is
the average concentration in the fluid in the backfilled repository.
D-4.1.5 Literature Discussion
Quantitative estimates of the likelihood and consequences of future
drilling activity do not seem to appear in other repository risk
assessments, although there is the realization that this may be an
important failure element.
(12)
The NRC/Sandia risk assessment does not treat this problem
quantitatively, although it does argue that the associated hazards are
small. The reason given is that the first exploratory hole would
probably lead to recognition of the repository and reeStablishment of
administrative control. Local contamination by material brought to the
surface would be recognized and decontamination would be carried out.
Claiborne and Gera argue that even if a future drilling crew were
too unsophisticated to detect radioactive material brought to the
surface, the resulting contamination would only be local and limited in
consequence.
( 7 fi ^
The Swedish KBS study argues that their proposed repository is
in one of their most common types of rock (granite) and "does not
contain any valuable minerals which could conceivably be considered for
profitable extraction." The depth and low water content also make water
exploration unlikely. They also argue that future drilling would
probably be preceded by exploration work that would detect the
repository.
222
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TABLE D-86
VOLUMETRIC FLOW RATES THROUGH A SINGLE SEALED BOREHOLE
Volumetric Flow
(m3/yr)
Rock Type
Bedded Salt
(1)
Granite
(2)
Basalt
(3)
Shale
(4)
Dome Salt
(5)
Time
(yrs)
250
1000
10,000
100
1000
10,000
100
1000
10,000
100
1000
10,000
Firs
2.0
1.7
.6
1.7
1.1
0.5
4.4
3.8
1.6
4.4
3.8
1.6
Second Estimate
Not applicable
189
167
17
11
5
198
192
170
198
192
170
(6)
Negligible at all times
(1)
(2)
(3)
(4)
Based on gradients in Table D-53, Section D-3.3., and corresponding
discussion of dissolution.
Based on Table 0-73, Section D-3.4.
Based on Table D-75, Section D-3.4.
Based on Table D-77, Section D-3.4, dividing by 3 since only
one hole is modeled here.
Cf. Table D-67, Section D-3.3, and corresponding discussion.
(6)For this case, Period B only begins at 1000 years after closure. See
Appendix D-TI.
223
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D-4.2 OTHER HUMAN INTRUSION EVENTS AND PROCESSES
D-4.2.1 Introduction
The most common and widespread human activity that could affect a
deep geologic repository is drilling for oil, water, and other
resources. This has already been examined as a specific failure element.
It is natural to consider whether future human endeavors other than
drilling programs may add substantially to the risk of releases from a
repository. Since future incentives, technologies, and opportunities to
intrude into a repository can be only imagined now, the discussion must
be speculative. It is believed that detailed modeling of these other
phenomena would not contribute significantly to the assessments made in
this generic study.
D-4.2.2 Solution Mining
Because of its high solubility, salt is often extracted from
underground formations by solution mining. In this process, water,
usually heated, is forced through wells into the salt. The water
dissolves the salt and the solution is pumped to the surface, where the
salt is removed and the water reinjected. This technique can also be
used for certain other minerals, such as sulfur. Solution mining is
applicable to both dome and bedded salt deposits. Some abandoned
solution cavities are used for the storage of hydrocarbons, and other
cavities have been developed exclusively for this purpose. It is
possible that in the future solution cavities will be developed and used
for additional purposes, such as the disposal of chemical wastes or
energy storage in the form of compressed air.
The potential hazard associated with solution mining is apparent. An
extraction well passing near or through a repository would circulate
large volumes of water that could accelerate leaching and transport of
the stored waste. The brine, with any waste material dissolved in it,
would be brought directly to the surface and distributed to any of a
number of users, such as the food and chemical industries. Although
224
-------
quality controls and purity requirements of the consumers may detect the
unusual radioactive constituents before they are dispersed, it is
questionable whether such measures can be relied upon. Furthermore,
when solutioning is carried out for the primary purpose of creating a
cavity, as for example for hydrocarbon storage, little or no attention
is paid to the composition of the waste brines.
The cavity developed in solution mining operations is typically
"carrot" shaped if a single well is used for water injection and
extraction. The usual dimensions of a single well cavity are about 15
meters (diameter) and 76 meters (height), although diameters twice this
(97)
size have been reported. Paired well mining, where water is
introduced through one well and brine is extracted from another nearby,
produces tunnels or lateral cavities. Wells are spaced from 100 to 400
meters apart and are connected by hydrofracturing the rock between.
Tunnel dimensions range from a few to perhaps 100 meters in cross
(97)
section. Crude oil storage cavities constructed in salt domes have
diameters of more than 70 meters and heights of more than 200 meters. If
future solution mining were carried out at a repository site, canisters
located in the dissolution zone could collect near the bottom of the
cavity, possibly generating more concentrated heat and radiation. These
effects would depend largely upon canister size, spacing, original
source term, and age.
Solution mining has not been analyzed as a separate failure element
because the exploratory drilling and testing usually performed before
mining facilities are installed are likely to detect a repository.
Furthermore, since salt is such a common mineral, the likelihood of this
activity at a repository site appears to be extremely low.
D-4.2.3 Interference with Hvdrqlqe;ic Conditions
Recovery or injection of fluids in the rocks bounding the repository
can alter hydraulic conditions, possibly changing flow characteristics
and apparent rock strength. The risk to a repository from interference
with groundwater is distinct from direct drilling risks.
Active control of hydraulic conditions is practiced in both water
and petroleum production. This technique is used to increase secondary
225
-------
recovery of oil, for example, where water or brine is injected into a
production zone through a nonproductive well. The water, under pressure,
displaces the petroleum and forces it toward production wells, as
illustrated by Figure T)-23. In a similar manner, recharge wells in arid
regions provide conduits for surface water to replenish depleted
aquifers.
Changes in the hydraulic regime in aquifers bounding a repository
are not, strictly speaking, failure elements, but they do affect
modeling parameters. The degree to which changes could occur depends
upon several indeterminate factors such as amount and pressure of fluid
injected or discharged and the duration of interference. In general,
pumping of aquifers adjacent to a repository would have only a local
effect, perhaps to a range of hundreds of meters. The effect would be to
change flow rates and direction for a brief period compared with the
total life of the repository. Since wells affecting a repository would
have to be very near or directly over the site, their probability of
occurrence has already been considered in Section D-4.1, and the
additional risk from changes in flow rates is insignificant.
Variations in rock strength due to water content are difficult to
quantify. To produce meaningful estimates, such factors as pore water
pressure and contact area between rock particles must be known. A
repository would be essentially unaffected, however, by strength
variations in the rock of the overlying aquifer. Lowering the strength
of the aquifer would, at worst, increase fracturing in this rock.
Fractures would increase the permeability of the aquifer somewhat, but
would not lead directly to water flow to or from the repository.
Changing rock strength and volume in the underlying aquifer by pumping
would be preceded by drilling through the repository level, a failure
which has already been examined. Nevertheless, the potential for
inducing fractures between the repository and the underlying aquifer may
exist for a given site and should be considered in the site selection
process.
226
-------
Production
Well
Injection
Well
I
I
-.1 I
•. n
-1'i
Petroleum
Petroleum
Stratum
Water
FIGURE D-23 FLUID INJECTION FOR ENHANCED WELL PRODUCTION
227
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D-4.2.4 Waste Recovery
It is possible that radioactive waste may be considered a valuable
resource sometime in the future, especially if the waste includes
unreprocessed spent reactor fuel. Therefore, the possibility that the
waste may be sought for some useful purpose in the future deserves
consideration.
Since authorized reentry of the repository for recovery implies both
consent of the responsible government and substantial understanding of
the situation, it can be assumed that appropriate precautions and
technologies would be employed in this case. This suggests that future
sanctioned entry would provide safeguards at least as good as, and
perhaps better than, existing ones. In any case, responsibility for any
adverse consequences would seem to rest with the future society.
Unauthorized recovery operations are discussed in the next paragraph.
D-4.2.5 Sabotage
The potential for buried waste to be used as toxins or for the
construction of nuclear explosives raises the question of a repository's
susceptibility to sabotage or unauthorized intrusion. The waste forms
would preclude any convenient conversion into nuclear explosives, and
if the wastes were used to contaminate a water supply, the effects would
become apparent only after a considerable delay. Nevertheless, it is
possible that the waste might be perceived as a resource by terrorists.
However, reaching a repository would require unusual resources and
expertise. Sinking a mine shaft would involve many people, much
specialized equipment, supplies, energy, planning, engineering and
operating skills, and uninterrupted access to the site for periods of
months. If the repository were finally breached, removing, processing,
and using the stolen waste would involve planning and engineering on a
similar scale. Also, unless the people involved possessed exceptional
skills, they would be placing themselves at great personal risk from the
waste they would be attempting to recover. Therefore, unauthorized
recovery of waste material does not appear to be a credible scenario.
228
-------
If the intent were simply to pollute a water supply with the waste,
the saboteurs would still need substantial drilling equipment,
specialized workers, free access to the site, and a great deal of
patience, since the effects of their act would not be apparent for
years, if at all. Sabotage of visible and accessible objectives, such as
a chemical plant or a surface nuclear facility, would be more likely.
Less time, material, skill, and organization, with far less risk to the
saboteurs, would be required to obtain substances with the equivalent
potential for terrorism.
D-4.2.6 Acts of War
Similar to the question of sabotage is the question of damage to the
repository through some act of war. The only credible act that could
even fracture the rock down to about 500 meters would be the detonation
(98)
of at least a ten-megaton or larger nuclear device. During a war,
it is hardly likely that bombs would be aimed at a repository. Cities
and strategic installations are far more attractive targets. In
addition, the effects on the biosphere from a damaged repository would
be insignificant compared with the other damage inflicted in such a
conflict.
D-4.2.7 Innocent Extraordinary Penetration
No buried repository of the sort considered in this study has (to
present society's knowledge) ever existed. However, a similarity can be
drawn between a repository and other hidden artifacts. The possibility
remains that curiosity or other motivation could encourage future
penetration or exploration of a repository.
For example, archeologists have excavated under pyramids and other
traces of human activity; tunnels for transportation are common in
mountainous terrain, and subway tunnels underlie many cities. The
possibility of treasure is also a strong motivation. The classic example
is the recurring effort to discover whatever may be at the bottom of a
shaft originally dug two or more centuries ago on Oak Island, Nova
(99)
Scotia. While nothing of great value has ever been recovered,
229
-------
persistent attempts during the last century to reopen the mysterious
shaft have reached depths of 100 meters or more.
While a repository is not the equivalent of a treasure trove, future
generations may have no knowledge of its function and may be intrigued
by signs of mining and the unusual care with which the openings are
sealed. There is no firm basis for determining if a repository will
become an attractive site for explorers in the future. However, if it
were to be entered by an astute investigator, its function and the
nature of the canisters should become apparent. It is more than likely
that steps would then be taken to return the repository to its original
integrity.
230
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D-5.0 NATURAL EVENT FAILURE ELEMENTS
A number of natural events and processes are modeled In this
chapter, with additional ones being discussed in lesser detail. Most of
these are geologic phenomena, although some are not, such as changes in
climate or the impact of large meteorites. In all cases the models are
simple and only intended to enable very approximate quantitative
judgments. For the evaluation of repositories at specific sites, it is
possible that quite different models, based on extensive data gathering,
might be appropriate. Nevertheless, for the evaluation of the
performance of generic repositories, it is believed that the models
developed here are adequate.
D-5.1 FAULT MOVEMENT
D-5.1.1 Summary
The repository site selection process is expected to favor sites
that are relatively stable geologically and where renewed or new
faulting is unlikely. Nevertheless, old faults are common geologic
structures in almost any location and may be expected at or near any
repository site. They may only intersect strata above or below the
repository formation, and some may even go undetected through the entire
site evaluation process. This analysis assumes the presence of a
certain number of faults on the site and, on the basis of their age and
density, estimates:
• the probability of renewed movement along the old faults,
• the probability of the occurrence of new faults.
The model consists of a constant annual rate based on the age of the
most recent fault activity. In addition, physical parameters that
characterize the groundwater flow pathway along the fault are estimated.
Releases from the repository are assumed to be by groundwater flow to
the upper aquifer. Sufficient displacement to move the entire
repository into contact with the aquifer or to the surface is not
considered possible in the time frame considered in this report (10,000
years). A summary of the analysis is given in Table D-S7. Section
231
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TABLE D-87
SUMMARY OF FAULT MOVEMENT FAILURE ELEMENT
MEDIUM
Bedded Salt
Granite
Basalt
Shan
Dome Salt
If
si
3 z
S3 S
< e
i£
£ 0
P
P
P
F
P
OF
MODEL
Annual probability
of occurrence of new
fault or movement
along old fault.
Annual probability
of occurrence of new
fault or mowsjmant
along old fault.
Annual probability
of occurrence of new
fault or movement
along old fault.
Annual probability
of occurrence of new
fault or movement
along old fau.s.
Annual probability
of occurrence of new
fault or movement
along old fault.
RELEASE
MODE
Groundweter
G^ound water
Groundwatar
Grour*d water
Groundwatar
DRIVING
FORCE
Thermally induced
convection effect
added to gradient
from aquifer inter-
connect ton.
Thermally induced
convection.
Thermally induced
convection effect
added to gradient
from aquifer inter-
Thermally induced
convection effect
added to gradient
from aquifer inter-
connection.
Thermal ly induced
convection effect
added to gradient
from aquifer inter-
connection.
SOURCE
TERM
banisters in fault zone
broken and subject to
leaching. Accumu-
lated dissolved radio-
nuclides by time of
faulting assumed
released through fault
from 100-m wide zone
around fault.
Canisters in fault zone
woken and subject to
leaching. Accumu-
lated dissolved radio-
nuclidn by time of
faulting assumed
released through fault
From 100-m wtda zone
around fault.
Canisters in fault zone
broken and subject to
caching. Accumu-
lated dissolved rsdio-
nuclicte by time of
faulting assumed
released through fault
from 100-m wide zone
around fault.
Canisters in fault zone
iroken and subject to
leaching. Accumu-
lated dissolved radio-
nuclides by time of
faulting assumed
released through fault
from 1 00-m wide zone
around fault.
Canisters in fault zone
broken and subject to
leaching. Accumu-
ated dissolved radio-
ituclides by time of
faulting assumed
rvleated through fault
Irom lOO-m wide zone
wound fault.
PARAMETERS
1st ESTIMATE
X - 2,,O^^M
Flow path 1 m wide
000 m long
K - 10~*cmftac
1 " 0.1
100 canisters in fault
zone. 5% repository
in affected surrounding
zone.
X " 2x10~8events/yi
Flow path 1 m wide
4000m long
K - 10'2 cm/sec
u • 0.1
100 canisters in fault
zone. 5% repository
in affected surrounding
zone.
X. - 5 xlO'7 events /yi
Flow path 1 m wide
4000 m long
K => 10"2 cm/sec
17-01
100 canisters in fault
zone. 5% repository
•n affected surrounding
zone.
X - 2x10-8evena/y
Flow path 1 m wide
4000m long
K = 10'4 cm/sec
n . 0 1
100 canisters in fault
zone, 5% repository
in affected surrounding
zone. '
I • 3x10-7evants/yi
Flow path 1 m wide
4000 m long
K - 10-4 cm/sac
n • 0.1
100 canisters in fault
zone. 5% repository
in affected surrounding
zone.
2nd ESTIMATE
X *> 4 x 10~7 events/yi
Flow path 1 m wide
4000m long
K - 10'4 cm/sec
TJ ° 0.1
100 canisters in fault
zone. 5% repository
in affected surrounding
zone.
X *= lO^events/yr
Flow path 1 m wide
4000m long
K = 10"2 cm/sec
T) = 0.1
100 canisters in fault
zone. 5% repository
in affected surrounding
zone.
X = 10"5events/vr
Flow path 1 m wide
4000 m long
n = 0 1
100 canisters in fault
zone. 5% repository
in affected surrounding
zone.
X • 4 x 10'7 events/yr
Flow path 1 m wide
4000m long
K - lO^cmfsec
100 canisters in fault
zone. 5% repository
in affected surrounding
zone.
X - 10'sevents/yr
Flow path 1 m wide
4000 m long
K - 10-* cm/sec
100 canisters in fault
zone. 5% repository
in affected surrounding
zone.
FLUID FLOW RATES FROM
REPOSITORY TO UPPER AQUIFER
1st ESTIMATE
tlynl
100
1000
10,000
t(yrs)
100
1000
10X100
0 (t) (m3/yrt
8.2 x 10*
6.9 x 10*
2.5 x 104
6 (t) (m3/yrl
6.9 X 106
4.4 X 106
1.9 x106
tlyrsl
100
1000
10,000
tlynl
100
1000
10,000
tlyrs)
1100
1000
10.000
6 It) Int3/yr)
8.8 x 106
7.6 x 106
3.2 x 106
6 III Im3/yr)
8.8 x 104
7.6 x 104
3.2 X104
6 It) (m3/yrl
8.2 x 104
6.0 x 104
2.S x 104
2nd ESTIMATE
tlyrs!
100
1GGO
10.OX)
tlyrsl
100
1000
10,000
6 (t) (m3/yr)
3.9 x 105
3.8 x 105
3 J x 10S
6 it) (m3/yr)
6.9 x 106
4.4 X 106
15 x 106
tlyrel
100
1000
10.0OO
tl^l
100
1000
10.000
tfyn)
100
1000
10,000
6 (t) Im^yr)
4.0 x 107
3.8 X 107
3.4 x 107
Q (t) (m3/yr|
4.0 x 10
3.8 x 10b
3.4 x 105
6 M (m3/yrl
2.0 x 10°
1.7 x 10S
1.5 xlO5
Fault may seal if flow
rate is tuff iciently small
Flow may be restricted
by availability of
Flow may be restricted
by availability of water.
Flow may be restricted
by availability of water.
Flow may be lesiiimed
by availability of water.
Fault may seal if flow
rate is sufficiently small.
Flow may be restricted
by availability of warn.
-------
D-5.1.2 provides a brief review of background material on the occurrence
and detection of faults. Detailed explanations of the model parameters
are given in Sections D-5.1.3 and D-5.1.4.
D-5.1.2 Background
Definition and examples. A fault is a fracture within the rocks of
the earth's crust along which relative movement of the two sides has
taken place. Faults can range in length from less than a centimeter to
hundreds of kilometers. Very small faults, on the order of tens of
meters or less in length, are not important for the present analysis.
In depth, faults may intersect only a single geologic formation or part
thereof, or they may extend all the way from the surface to deep in the
basement rocks. Cumulative displacement along faults, whether in the
horizontal or vertical direction, can range up to tens of kilometers or
more, representing the sum of relatively small individual movements over
an extended period. Notable examples of large faults in the United
States include the San Andreas fault, whose length exceeds 600 km, and
the Lewis overthrust fault, representing the east side of the Rocky
Mountains in Montana, with a cumulative vertical displacement of more
than 12 km. ' ' Often, a large fault is associated with a multitude
of smaller fractures, and both large and small faults may occur as a
series of subparallel features reflecting a distinct trend. (See
Figure D-24.) Faults are very common features in most geologic settings
and it is unlikely that any repository site can be found that will be
completely free from past faulting activity. For example, a detailed
geologic study of the area surrounding the proposed Charlestown nuclear
power plant in Rhode Island led to the identification of one major fault
and over 2600 minor faults and joints within five miles.
Additional faults are generally expected to be encountered on plant
(22 102 103)
sites once the overburden is removed. ' ' The important issue
is whether additional movement along faults on (or under) the site can
be expected and whether new faults might also develop.
Nature and types of faults. Faults are the result of differential
compressive stresses in the crust that exceed the strength of the rock
formation. The geometry of faults can be categorized into three types,
233
-------
(A) Nevada (Basin and Range Province)
(B) Gulf Coast Region
."TEXAS
LOUISIANA
-'^••' GULF
of
MEXICO
Source: Adapted from USGS Map M.F. 916.
FIGURE D-24 SUBPARALLEL FAULTING IN TERTIARY AND QUATERNARY PERIODS
234
-------
reflecting the stress system giving rise to the fracturing. (See Figure
D-25). Normal faults occur when the maximum compressive stress, 0 , is
vertical and the minimum compressive stress, o is horizontal. Reverse
and thrust faults (the former steeper than 45°, from the horizontal, the
latter flatter than 45 occur when the maximum compressive stress is
horizontal and the minimum vertical. Strike-slip faults occur when the
maximum and minimum compressive stresses are both horizontal. Oblique
faults represent a combination of vertical and horizontal movement.
Evolution of regional stress systems. Many geologic processes can
contribute to the development of stress systems that may cause faulting.
Examples of these processes, some of which are related, are the
following:
• Plate tectonics, involving the movement of crustal sections,
called plates, toward or away from each other-
• Slowing of the earth's rotation, with corresponding changes in
centrifugal forces.
• Earth tides, resulting from gravitational interaction with the
sun and moon.
• Changes in heat flow and temperature in the earth's crust.
• Increases in overburden stress, caused by sediment deposition,
lava flows, glaciers, rises in sea level, etc.
• Decreases in overburden stress, caused by erosion, glacial
melting, retreat of seas, etc.
• Volcanic activity, involving movement of magma through the crust.
• Diapirism, involving the penetration of plastically flowing rock
(such as salt or shale) through overlying rock.
• Dissolution, leading to settling or collapse into the resulting
voids.
• Folding and downwarping associated with the movement of the crust
toward mechanical equilibrium after some of the processes
mentioned above may have caused differential stresses.
The above list is only intended to give some representation of the range
of processes with which faulting may be associated. Two important
conclusions can be drawn. First, because at a given location many of
the processes listed occur only during specific periods in geologic
history, if at all, many (probably most) faults have exhibited movement
235
-------
(a) Normal (Gravity) Fault
(b) Reverse or Thrust Fault
(c) Strike-Slip Fault
Note: (o^ = maximum stress, a2 = intermediate stress, o3 = minimum stress)
FIGURE D-25 BASIC FAULT TYPES
236
-------
only during particular periods and have not been reactivated during
later periods with different stress regimes. Second, an analysis of
the geologic evolution of a region and the corresponding regional stress
patterns is important in predicting future faulting or fault movement.
It should be pointed out, nevertheless, that faults do represent a zone
of weakness, and therefore reactivation is occasionally experienced and
even reverse movement has been noted.
Movement along faults. Movement along existing faults depends on a
number of factors besides the relative levels of stress. Among these
are the lithology, the fluid pressures within the fault, and the nature
and quantity of material, such as rock dust, that may fill the fault.
Movement may take the form of a continual slippage (creep) or recurring
abrupt jerks (stick-slip). ' Creep may pass unnoticed unless
detected by measuring cumulative displacement, whereas stick-slip
movements are often accompanied by sensible seismicity. Depending upon
types of faults, lithology, confining pressure, temperature, rate of
movement, and other factors, the rock bounding a fault may be fractured,
polished (slickensides), folded (drag folds), or essentially unchanged.
These features are represented in Figure D-26. The rate of displacement
over time can vary considerably. The San Andreas fault has shown
occasional displacement of up to five centimeters per year although
maximum rates of one or two centimeters per year are probably more
common•
Ages of faults. Two at»es that are important in studying a fault are
the time when the fault began and the time of its most recent movement.
In many cases, these may be estimated on the basis of stratigraphy, as
sketched in Figure D-27. Since the fault shown there does not intersect
bed C, it must have begun sometime since the deposition of that bed. On
the other hand, since it does not intersect bed A, it is highly unlikely
that it has moved more recently than the period when A was deposited.
(In rare circumstances it could have moved below A without actually
moving A, although generally some manifestation of such movement, e.g.,
deformation, would be found in A.) Faults may also be dated by
associating them with a specific geologic process whose age is otherwise
well determined. For example, the salt domes of the Gulf region caused
extensive faulting and fracturing as they pushed through the overlying
237
-------
(a) Drag Folds
(b) Gouge, Breccia, Slickensides, and Subsidary Faults
V
(c) Parallel Shear Zone
FIGURE D-26 FEATURES ASSOCIATED WITH FAULTING
238
-------
/
Fault
239
Surface
-•'" '"' •'£ Marker bed A
iiSi Marker bed B
Marker bed C
Bedrock
FIGURE D-27 DATING OF
-------
rock. (See Figure D-28.) Similarly, both the development and the upper
surface dissolution of the salt anticlines in the Paradox Basin have
caused most of the faulting that has been observed there. (See Figure
D-29.) Other faults in the Gulf region were caused by slippage and
settling of new sediments as the shoreline migrated southward. Thus,
these faults parallel the shoreline and decrease in age as one moves
southward. (See Figure D-30.) There are also radiochemical, magnetic,
and mineralogical techniques for studying faults with a view to learning
about the history of their movement.
The age and nature of the most recent movement are generally the
most important data in determining whether additional movement can be
expected. Active faults are those that have experienced relatively
recent movement by geologic standards (with the period of 10,000 years
often chosen as the criterion) and that may be expected to show future
movements. Young faults include those whose most recent movement is
within the Quaternary Period (extending back about L.8 million years).
The dating of faults and the determination of their capability for
further movement are difficult problems with significant uncertainties.
There is no universal agreement among earth scientists on criteria
defining a fault that is capable of further movement; moreover, paucity
of geologic data leaves considerable uncertainty about the age and
extent of previous fault movement.
Identification of faults. Some faults, particularly young ones, are
easy to recognize by surface observation because their displacements are
manifested in escarpments or other offsets that have neither been eroded
away nor covered by later sedimentary deposits. Because faults may
either be particularly permeable or act as a barrier to groundwater flow
along permeable strata (by offsetting them), changes in surface
vegetation in linear patterns often indicate the possible presence of a
fault. These and other linear features (lineaments) visible on aerial
photographs are frequently used to detect faults. Surface geodetic
surveys may indicate changes over time that imply ground movement,
possibly along faults. The angles and depths of marker beds as observed
at outcrops or in a series of boreholes may also indicate whether some
offset has taken place. Trenches can be dug across areas of interest
240
-------
«OUNO SORfACE
SANDSTONE • " - -*
FIGURE D-28 FAULTING IN THE VICINITY OF A SALT DOME (Conceptual Drawing)
-------
Kilometers
Source: Stockton ,S.L. and A.M. Balch.The Utility of Petroleum Seismic Exploration
Data in Delineating Structural Features Within Salt Anticlines. USGS Open
File Report 78-591,1978.
FIGURE D-29 TYPICAL PARADOX BASIN SALT ANTICLINE STRUCTURE
DERIVED FROM SEISMIC AND OTHER DATA
242
-------
NJ
Circum—Gulf
T Older than late Cenozoic (>15 million years)
TT Late Cenozoic (last 15 million years)
TTT Quaternary (last 1.8 million years)
T t/ Late Quaternary (last 500,000 years)
Source: Adapted from USGS Map M.F. 916.
FIGURE D-30 AGE OF FAULTS IN THE GULF COASTAL REGION
-------
and be examined carefully for signs of displacement. Natural stream
cuts may serve a similar purpose.
Geophysical techniques such as seismic, electrical resistance, or
magnetic surveys can also be used to detect deep faults that do not
appear at the surface. For example, seismic profiles can be developed
from recordings of mechanical shock waves propagated through the rock to
an array of receivers (geophones) as diagrammed in Figure D-31. The
timing and amplitude of waves reaching the geophones can be interpreted
in terms of the depth and orientation of reflective surfaces in the
rock. If, instead of measuring the reflected signal, the refracted wave
is examined, faults may also be identified, usually by the attenuation
of energy across the fault face, as shown in Figure D-32. Whatever
techniques are used, the scale of the features to be detected depends
basically on the wave length of the seismic wave. This is itself
determined by the energy loss through the rock, with shorter wave
lengths having a greater energy loss than longer ones. The possible
resolution is approximately one-half the wavelength or, in practical
(22)
terms, in the range of ten meters. Thus, a vertical displacement of
roughly ten meters is required before a fault can be distinguished by
seismic surveys. An interpreted seismic profile is shown in Figure
D-33.
Electrical resistance surveys measure the conductivity of rock or
soil and compare the measurements with models of the expected results.
Irregularities between the measured and expected electrical resistance
may indicate the presence of a fault or other structural feature.
Electrical resistance mapping of a potential repository site would
probably use measurements taken through an array of boreholes across the
site. By determining the resistance of representative strata or rock
types at differing orientations, detecting and determining the position
of structural faults is made easier- Unfortunately, electrical
resistance surveys are complicated by a number of factors. Since
resistance surveys measure deviation from a model, the accuracy of the
survey is limited by the precision of the model. Results tend to have
several possible interpretations and are usually simplifications of real
conditions. Features must also have electrical properties different
enough from the intact rock that the contrast can be measured. Large
244
-------
Source
Geophones-
No reflection
received from
marker bed
Longer signal time
due to offset of
marker bed
Reflecting marker bed
Fault offsetting
marker bed
FIGURE D-31 DETECTION OF FEATURES BY SEISMIC REFLECTION
245
-------
Source
Refracted
signals
/
Marker
.->:•//..** V-'.?.-".Vf.tv,v
..-. '/.:•:•:: ,.::•:. .V.'.:
Refracted signals
attenuated due to
discontinuity in bed
FIGURE D-32 DETECTION OF FAULT BY ATTENUATION OF REFRACTED
SIGNALS ACROSS DISCONTINUITY
246
-------
(a) Uninterpreted
30—~~ .."""• •• iiss:."";;"^;^;^ '.%*."
(b) Interpreted to Show Structure
SW
NE
20
1 ! I
KILOMETERS
Source: USGS Open File Report 78-591.
FIGURE D-33 PROCESSED SEISMIC RECORD OF SECTION OF PARADOX BASIN
247
-------
shallow features generally show more contrast than small or deep
features, and normal variation in the rock's electrical resistance may
(22)
obscure the electrical vibration caused by a fault.
Lastly, since most earthquakes are generally thought to be caused by
movements along faults, a record of the seismicity of a region can be
helpful in understanding the potential for active faults. In
particular, the foci of earthquakes tend to lie along linear trends,
which can then be studied further for the identification of specific
faults.
New faults. While faults are among the most common structural
features in geology, few (if any) new faults have been reported in the
literature. Most apparent new faults have turned out to be extensions
of old or unmapped faults. Nonetheless, locations with a propensity for
faulting may be suggested by identifying other characteristics
indicative of the stress differential necessary for faulting. For
example, in-situ stress measurements can be made to determine the
direction and intensity of lithic stress at a particular location. If
the stresses approach the fracture strength of rock, or if stresses
increase in time, faulting is possible. Alternatively, folding,
which is indicative of stress change (see Figure D-34), also suggests
that faulting, particularly parallel to the fold axis, is possible.
Other geologic indicators, such as block tilting or warping of a basin,
suggest that stress intensification may be occurring. Conversely,
locations showing little tectonism in the recent geologic past may be
expected to have a reduced likelihood of future faulting because of the
time delay involved before sufficient stress for faulting could build.
Availability and reliability of information. The mapping of faults
has considerable importance. For example, faults may form traps that
contain petroleum, or they may pose safety risks to industrial
facilities such as nuclear power plants. The U.S. Geological Survey has
published geologic maps of all portions of the country and continues to
update them as new information becomes available. A national map of
young faults was published in 1978, based on 1975 data. As this
reference points out, the availability of data is very uneven across the
country. For example, far fewer recent searches for young faults have
been made in the mid-continent than in California. Even where extensive
248
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/Present surface
"Tensional"
normal faulting
(Undifferentiated
sediments)
Compressional"
thrust faulting
"Tensional"
normal faulting
"Tensional"
normal faulting
FIGURE D-34 FAULTING ASSOCIATED WITH FOLDING AND Tl LTING
249
-------
surveys have been made, considerable uncertainty often remains. Much of
the variability depends both on the intensity of exploration and on the
field workers' interpretations of what constitutes a "mappable fault."
Usually, only faults that can be discerned at the surface are mapped,
and these only if they show significant displacement. Furthermore, as
most faults caused by a particular stress regime are roughly parallel,
they are occasionally identified as a single large fault, rather than
many individual ones. Therefore, the actual number of faults may be
significantly higher than the number mapped. As a supplement to the
geologic maps published by the USGS, this report has drawn upon the
safety analysis reports for proposed nuclear power plants, wherein more
detailed evaluations of fault capabilities in particular areas are
reported.
D-5.1.3 Fault Movement Failure Model
The quantitative characterization of the fault movement failure
element consists of three parts:
• the probability of renewed movement along any old faults that may
be present at the repository site;
• the probability of the development of new faults at the site; and
• physical parameters to describe the groundwater flow pathway
resulting from fault movement.
The general method used for estimating the probabilities is the same for
all geologic settings and is described in the next paragraph. Its
application to specific settings will then be discussed in subsequent
paragraphs.
Renewed movement along old faults. Suppose an old fault is present
at the site and that its most recent movement has been reliably dated at
about N years before the present. The model uses the reciprocal 1/N as
an estimate of the annual probability of renewed movement along that
fault. The rationale for this approach is as follows. Movement along
faults may be regarded as a stochastic process, with the intervals
between movements analogous to the time between failures of mechanical
components in classical reliability theory. The simplest model for
250
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such a stochastic process is based upon a constant annual failure rate
X, approximately representing the probability of failure between times t
and t + 1 given that the component has not failed (fault has not moved)
by time t. According to this model, X is the reciprocal of the mean
time to failure. That is, if a type of component is known to fail after
an average duration of n, then X = i/n ±s the value of the parameter X
consistent with this observation.
Applying this analogy to the fault case, suppose it is known that
over the history of the fault, times of n , n . . . . , n, elapsed
1 £. K.
between movements. One should also add to this list the period N since
the last movement. Since fault movement has not yet recurred, N
underestimates the true value of the time to the next movement, which
may even be infinite (i.e., no new movement ever occurs). If the
process were truly stationary in time (i.e., having failure
probabilities dependent only on the time elapsed since the last event
rather than depending also on historical time) then a reasonable
estimate of the mean time to failure would be the average of the numbers
n, , n2» . . ., n, , N. (It would be biased on the low side because of
the bias involved in using N, as mentioned above. This would be
consistent with the conservative approach adopted in this study.) The
corresponding failure rate would then be the reciprocal of this average.
However, as mentioned in the previous section, movement along a fault is
strongly affected by the long-term evolution of regional stress patterns
associated with slow geologic processes. Because of these changes with
time, in estimating the mean time to failure one might wish to use a
weighted average of n, , n-, • • -, n,, N, weighting the more recent
observations more heavily. In the cases to be considered below, N, the
time since the most recent movement, is generally sufficiently great in
geological terms (tens or hundreds of millions of years) that in itself
it covers the entire period of site history relevant to whether
additional fault movement will occur. Thus, the appropriate weighted
average of n,, n2»...nK, N assigns all the weight to N, implying a
failure rate X =• 1/N. This implies that N is the only observed value
needed to estimate the failure rate from renewed fault movement.
It is not uncommon for geologists to assign, implicitly or
explicitly, a zero probability for renewed movement in the near future
251
-------
to certain old faults that are well dated and understood. Thus,
the estimation of a small positive probability by the above algorithm is
believed to be consistent with present practice and somewhat
conservative. It should be noted that this discussion further assumes
that the geology of a site is well understood and that new evolving
processes that could lead to renewed fault movement will not be
significant over the 10,000-year period of repository evaluation. (On
the other hand, it is also possible that in specific cases, regional
site investigations may lead to higher fault movement estimates, based
on a detailed understanding of the geologic processes at work.)
New faults. A region containing a potential repository site may
have had several episodes of faulting in its geologic history. For
example, there might be contemporaneous faulting during a period of
sedimentation, followed by tilting and block faulting associated with
tectonic forces. In attempting to estimate the probability of new
faulting in the region, it is reasonable to consider only the most
recent episode of faulting, because previous processes are even less
related to the present state of the region. If this most recent episode
of faulting and fault movement spanned the period from M to N years
before the present and if a fault density of f faults per repository
area (or some other measure of density) is observed, then the average
rate of new faulting over the last M years is given by f/M faults per
year per repository area. In a location with a long history of
stability since the last faulting episode, and where no new geologic
processes offer countervailing evidence, this average rate can be
interpreted as a conservative estimate of the rate governing the more
recent past and the near future. In fact, M is often more difficult to
determine than N, the latter being of greater concern in any case; and
since N is less than M, the larger rate, f/N, has been adopted for
modeling purposes. As was mentioned for the case of renewed movement
along old faults, in site-specific circumstances there may be reason to
estimate a different rate.
Combined estimate for reactivated and new faults. Suppose it is
observed that as a result of the most recent episode of faulting in a
given region (excluding minor surficial faulting), faults occur with a
density of about f per repository area. Assume further that the most
252
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recent movement is dated at about N years before the present. Then the
previous two subsections each lead to occurrence rates of f/N, in the
first case for old fault movement and in the second for new faults.
(The second calculation is probably more conservative than the first.)
Then the combined rate of occurrence of either type of fault movement is
given by :
N
With respect to the estimation of the parameter f, there are
insufficient reliable data on which to base a statistical analysis.
Some evidence for appropriate values of f can be obtained from the
following :
• Examination of fault densities from surface surveys at various
locations. Examples are shown in Table D-88.
• Fault maps prepared in connection with a number of power plant
applications .
• Seismic surveys for parts of the Delaware Basin.
• Reported spacings of faults along anticlines in the Columbia
Plateau.
On the basis of these data, it appears that for most locations it is
very unlikely to find faults spaced less than about one to two
kilometers (10 to 15 kilometers is more common) . Hence the first
estimate f = 2 faults per repository and the second estimate f = 5
faults per repository have been adopted for all geologic settings.
Therefore, the sections on the specific geologies simply associate dates
with these periods of faulting so as to calculate values of A, the
faulting failure rate.
Flow pathway. The reference repository has dimensions 2 km x 4 km.
It is assumed for the sake of conservatism that a fault intersecting the
repository cuts through parallel to the long side, so that the length of
the intersection is 4000 m. The width of the fault zone is assumed to
be one meter. The widths of fractured zones associated with faults vary
widely. Many are very small (a few centimeters) although some extend
100 meters or more. In light of the assumption of relative
253
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TABLE D-88
FAULT DENSITIES FOR SELECTED AREAS OF THE UNITED STATES
Density
(per km )
Montana
San Juan, Utah
Central Oregon
Nevada Test Site
Karnes, Texas
Sweetwater, Wyoming
Coconino, Arizona
North Michigan
Western Massachusetts
Eastern Kentucky
Bonneville, Idaho
Eastern Pennsylvania
Source: Geotechnical Engineers, Inc.
0.0236
0.2807
0.154
0.058
0.0567
0.0998
0.1737
0.1993
0.0871
0.0031
0.820
0.370
254
-------
geologic stability and careful'selection of a repository site, for both
first and second estimates a width of one meter is believed to be
adequate to model all fault movements that could reasonably occur over
the next 10,000 years. Larger zones are in fact generally associated
with growth during extended periods of activity. The porosity of the
fault zone has been assumed to be 0.1. This parameter is used only for
velocity calculations and even with this relatively high value (tending
to underestimate velocities). transit times to the aquifer system are
quite short. The only rock-specific parameter in the model is the
permeability of the fault. This depends on the strength of the rock and
will be discussed below for the various cases.
D-5.1.3.1 Bedded Salt
The first estimate for bedded salt assumes most recent faulting to
be of Permian age, and hence at least 230 million years old. This is
generally a valid assumption for the Delaware Basin, for example,
and there is evidence that in much of the Salina Basin the most recent
faulting is even of Pennsylvanian age (280 million years old). '
g
The assumption N = 2.3 x 10 years yields the value
A - — - - 2 x 10~ events/year.
N 2.3 x 108
The second estimate is based on mid-Tertiary faulting in the Paradox
Basin, corresponding to N = 2.5 x 10 years. The corresponding failure
rate is
4 x 10 events/year.
There has been more recent faulting in some evaporlte basins. For
example, faulting associated with salt dissolution in the Paradox Basin
may be of Quaternary age (1 million years old); however, the faults do
not appear to cut through the salt beds. ' ' There is probably
significant Cretaceous faulting (63 million years old) in parts of the
Salina Basin, and there is an active fault suspected to have moved
255
-------
within 100,000 years in western New York. Therefore, the second
estimate used for the calculation of X is not a "worst case," but is
intended to represent a general type of area being seriously considered
for repository siting.
The permeability of the fractured zone associated with a fault in a
salt repository could vary widely. In fact, it is highly possible for
the salt simply to deform to relieve the stresses that would induce
fracturing in adjoining strata, rather than for the salt to fracture at
all. Since salt is rather weak, any fracturing would be expected to
lead to fairly well crushed salt. The permeability of compacted crushed
salt has been estimated at about 10 cm/sec, which is the value
adopted here for both first and second estimates. Crushed shale
actually may have a lower permeability (depending upon the degree of
crushing), but for conservatism the entire fault pathway, even through
the overlying and underlying shale beds, has been assumed to have the
same permeability as the pathway through the salt.
D-5.1.3.2 Granite
The first estimate for granite is based on the assumption of an
ancient, stable batholith or other pluton. Some faulting would
generally be expected since emplacement or metamorphosis. In western
Massachusetts, Triassic faulting was the most recent faulting identified
in the geologic exploration associated with the Montague Power Plant
application. Adopting this age, IRQ million years, the
corresponding failure rate is:
— 8
2 x 10 events/year.
The second estimate is based on a more active site in the basin and
range province. Assuming that site selection avoids areas with
Quaternary faulting ("young faults"), the age would be at least one
million years, giving
X = 10 events/year.
256
-------
Less stringent site selection or inaccurate site characterization could
lead to a still higher rate.
The permeability of the fractured zone is based on the assumption
that the granite is brecciated and fractured more than pulverized, due
_2
in part to its high strength. It is believed that 10 cm/sec is a
reasonable estimate for this permeability, although a large range is
possible. This value of permeability corresponds to the high range for
silty sand and gravel (Figure D-13; see Section D-3.2) and to the
parallel plate model of ten parallel smooth fractures per meter, each of
aperture 0.5 mm.(47'50)
D-5.1.3.3 Basalt
The first estimate for basalt is based upon relatively stable areas
of the Columbia Plateau, where at least the uppermost basalt layers
(dated at eight million years) show large areas free of faults. It is
possible that the most recent faulting is still older than this, but
because of active tectonic forces in the general region it is believed
that eight million years is a reasonable age to assume. This age yields
the value:
^ * 5 x 10~ events/year.
There are certainly areas of more recent faulting within this
area. For example, a scarp in the Horse Haven uplift indicates
(31)
Quaternary movement. The second estimate is based on a site in an
area where the most recent faulting is at least earlier than Quaternary
age (one million years), yielding the value
* = 10~ events/year.
For the same reasons as in the case of granite, the permeability is
_2
assumed to be 10 cm/sec through the fault zone.
257
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D-5.1.3.4 Shale
The first and second estimates for shale are based upon the same
geologic assumptions as for bedded salt, and therefore the failure rates
are
—8
X = 2 x 10 events/year (first estimate)
X = 4 x 10 events/year (second estimate).
A permeability of 10 cm/sec has been assumed, based on the high
range of the permeability of compacted crushed shale evaluated for
, ..... (112)
backfill.
D-5.1.3.5 Dome Salt
The first estimate for dome salt is based on contemporaneous
faulting in the Gulf Interior region, where faulting continued even
after the domes stablized. The youngest faults identified in one
detailed site evaluation were dated at 13 million years. This age
yields the value
X = 3 x 10 events/year.
As one moves down to the Gulf Coast, more recent sedimentation has led
to contemporaneous faulting even in the Quaternary period. Assuming
that the site selection rules out areas with Quaternary faulting, the
minimum age of one million years to the last movement implies the value
X = 10 events/year,
which is taken as the second estimate value.
The permeability of a fault through a salt dome repository has been
-4
taken as 10 cm/sec, as in the case of bedded salt.
258
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D-5.1.4 Fault Movement Release Model
The purpose of this section is to calculate fluid flows through an
assumed ruptured fault. Parameters to characterize the physical pathway
have been estimated in the previous section. A number of conservative
assumptions (i.e., tending to overestimate flow rates) have been made in
the analysis so that the net effect may be to overestimate flows by one
or more orders of magnitude. For example, the capability of the
associated aquifers to produce or receive the estimated fluid flows may
be highly restricted. Faults may heal either by the plastic deformation
of the surrounding rock or by the accumulation of fill material in the
fractures. For the sake of simplicity in the present model, these
factors have not been included. If it is determined that the risk
(accounting for both probability and consequences) indicated by the
bounding calculations carried out here warrants more detailed analysis,
then it would be necessary to conduct a wider survey of specific fault
characteristics in order to improve the precision of the estimates. The
present level of detail is believed to be sufficient for this generic
analysis. For further simplification, repository resaturation is
assumed to have taken place in all cases by the time the fault movement
occurs.
In addition to transport of radionuclides by groundwater flow
through the faulted rock, there is the possibility that continued
movement of the fault may lead to physical transport of a portion of the
repository to the surface. Rate estimates show that this process would
be extremely slow, however. Further discussion is provided in Section
D-5.6.
D-5.1.4.1 Bedded Salt
It is unlikely that fault movement would occur during the period of
extensive salt creep and repository resaturation since the mechanical
stability of the site would be expected to be most certain in the time
period closest to the present. (This period has been referred to as
Period A in previous sections). Furthermore, the pressures resulting
from salt creep are sufficient to cause the relatively rapid "squeezing
259
-------
out" of fluid through degrading shaft and borehole seals during this
period as well, and so the addition of another pathway, such as a
ruptured fault, would not significantly alter this process. The fault
does have the capability, however, to lead to additional releases
through groundwater movements, and these are the movements that have
been modeled for faulting at any point in the 10,000 year period of
evaluation. The dominant driving forces are thermally induced
convection and the gradient from interconnecting the upper and lower
aquifers.
The values of the combined effective gradients tending to move fluid
through a fault are the same as those given earlier in Table D-53 (see
Section D-3.3). When these gradients are used in Darcy's law, along
with the other parameters given in Section D-5.1.3, the volumetric flow
rates shown in Table D-89 are obtained. Since these flows are not
nearly so small as those calculated for a number of other failure ele-
ments, it is natural to ask whether the conservative viscosity correc-
tion factor
c(u) = 5,
corresponding to pressurized water at about 125°C, should be
re-estimated as a function of time here so as to give more realistic
flow rates, especially at later periods, when radioactive decay will
have reduced the heat output from the wastes. From Table D-VI-2 in
Appendix D-VI, it is seen that even reducing the fluid temperature to
60 (50 is the average temperature at 10,000 years), the viscosity
correction factor would be reduced by only a factor of about two.
Therefore the original value of c(u) is retained for the sake of
simplicity.
Another area of concern that arises is whether the calculated fluid
flows might lead to considerable dissolution along the pathway. The
implications of this might include:
• a decrease in the distance between the flow pathway and waste
canisters, either by widening of the pathway or gradual plastic
flow of the salt and repository toward the fault in order to
replace salt that had been carried away; and
260
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TABLE 89
VOLUMETRIC FLOW RATES THROUGH A FAULT
(BEDDED SALT REPOSITORY)
Volumetric Flow (Q)
(nrVyr)
100 years
1000 years
10.000 years
First Estimate 8.2 x 10'
6.9 x 10'
2.5 x 10'
Second Estimate 3.9 x 10"
3.8 x 10'
3.3 x 10'
Years after repository closure.
261
-------
• an increase in fluid flow rate from the widening of the flow
channels.
This is indeed a possibility. However, another factor offsets these
problems, namely, the tendency of fractures in salt to heal themselves
by plastic flow and recrystallization. While it is beyond the scope of
this report to attempt to prove, by an analytical model or otherwise,
that the healing effect more than offsets the dissolution, the present
model may be interpreted as being based on this assumption. Other
reports have also noted the healing potential for breaches in a salt
(11,18)
repository.
The volumetric fluid flow rates in Table D-89 lead to the
interstitial velocities given in Table D-90, based on a porosity of 0.1
in the fault zone.
Estimation of the source term for this failure element requires
consideration of several processes. First, because of the possible
leaching of radionuclides prior to the fault event, the water saturating
the backfilled repository will contain an approximately uniform
concentration of each species (see Figure D-35a). The value of the
concentration may vary from one radionuclide to another depending on
leach characteristics and possible solubility limits. When the fault
pathway is established (Figure D-35b), some of the fluid will mix with
the fluid moving up from below so that some of the radionuclides in
solution will be released. This effect decreases with distance from the
fault. It is assumed for modeling purposes that the zone of influence
is a band extending 50 meters from each side of the fault. Such a zone
is expected to contain 5% of the repository area and inventory. For
conservatism, it is assumed that the initial fluid flows through the
fault from the repository to the upper aquifer contain all these
dissolved radionuclides at their initial uniform concentration. (That
is, this inventory is assumed to be depleted somewhat more rapidly than
would actually be the case.)
Second, any canisters in the actual path of the fault may be
damaged, and so the waste form is assumed to be subject to direct
leaching. (Other canisters might be given credit for container
integrity.) The material expected to be leached from canisters in the
direct flow pathway should be added to that calculated according to the
262
-------
TABLE D-90
FLUID VELOCITIES THROUGH A FAULT
(BEDDED SALT REPOSITORY)
Velocity (v)
(m/yr)
First Estimate
Second Estimate
100 years
205
975
1000 years
173
950
10.000 years
63
825
Years after repository closure,
263
-------
(a) Backfilled Watte Before Fault Event
Surrounding rock
Backfilled drift;
radionuclide concentrations
approximately uniform (in space)
ggg
Canisters in
drilled holes
in floor
%>».•>
1
(b) Backfilled Waste Drift Intercepted by Fault
FIGURE D-3S WASTE DRIFT BEFORE AMD AFTER FAULTING
264
-------
previous paragraph. It Is assumed that 100 canisters fall into this
category.
Third, continued leaching from other canisters is also expected to
occur, with movement of the radionuclides by diffusion and fluid mixing.
This contribution to the releases is expected to be much smaller than in
the previous two cases, so it is not included in the model.
D-5.1.4.2 Granite
Thermally induced convection is the dominant driving force for fault
pathways through a granite repository. The effective gradients have
been calculated as 0.11 at 100 years, 0.07 at 1000 years, and 0.03 at
10,000 years. (See Appendix D-VI) . Using these gradients in
conjunction with the parameters given in the previous section, the
volumetric flow rates shown in Table D-91 may be calculated by Darcy's
law. Corresponding fluid velocities are given in Table D-92. The
source term in this case may be treated according to the same procedure
as that given for bedded salt.
D-5.1.4.3 Basalt
The effective hydraulic gradient in the case of basalt is the
combined result of thermally Induced convection and an aquifer
interconnection. The values have been given in Table D-59 in Section
D-3.3. Using these gradients in conjunction with the parameters given
in the previous section, the volumetric flow rates shown in Table D-93
may be calculated by Darcy's law. Corresponding fluid velocities are
given in Table D-94. The source term in this case may be calculated
according to the same procedure as that given for bedded salt.
D-5.1.4.4 Shale
The effective hydraulic gradient in the case of shale is the
combined result of thermally induced convection and an aquifer
interconnection. Their values are the same as for basalt. Using these
gradients in conjunction with the parameters given in the previous
265
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TABLE D-91
VOLUMETRIC FLOW RATES THROUGH A FAULT
(GRANITE REPOSITORY)
Volumetric Flow
(tn/yr)
100 years
First Estimate 6.9 x 10
Second Estimate 6.9 x 10
1000 years
4.4 x 106
4.4 x 106
10.000 years
1.9 x 106
1.9 x 106
Years after repository closure.
266
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TABLE D-92
FLUID VELOCITIES THROUGH A FAULT
(GRANITE REPOSITORY)
100 years
First Estimate 1.7 x 10
Second Estimate 1.7 x 10
Velocity (v)
(m/yr)
1QOO years
1.1 x 104
1.1 x 104
10.000 years
4.8 x 103
4.8 x 103
Years after repository closure.
267
-------
TABLE D-93
VOLUMETRIC FLOW RATES THROUGH A FAULT
(BASALT REPOSITORY)
Volumetric Flow (Q)
(m3/yr)
100 years
First Estimate 8.8 x 10
Second Estimate 4.0 x 10
1000 years
7.6 x 106
3.8 x 107
10.000 years
3.2 x 106
3.4 x 107
Years afer repository closure.
268
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TABLE D-94
FLUID VELOCITIES THROUGH A FAULT
(BASALT REPOSITORY)
Velocity (v)
(m/yr)
100 years*
First Estimate 2.2 x 10"
Second Estimate 9.9 x 10*
1000 years
1.9 x 10A
9.6 x 104
10.000 years
7.9 x 103
8.5 x 104
Years after repository closure,
269
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section, the volumetric flow rates shown in Table D-95 may be calculated
by Darcy's law. Corresponding fluid velocities are given in Table D-96.
The source term in this case may be calculated according to the same
procedure as that given for bedded salt.
D-5.1.4.5 Dome Salt
It can reasonably be assumed that a fault intersecting a salt dome
will extend beyond the flank of the dome on one or both sides.
Consequently, a connection will be established between the upper aquifer
and the lower aquifer (or pressurized brine reservoir) extending to the
side of the dome. This interconnection provides for two driving forces
whose effect is additive. First, an aquifer interconnection gradient
tending to move fluid upward has been assumed in the generic repository
setting in dome salt (see Chapter D-2.0). Second, adequate recharge is
available to permit the establishment of a thermally induced convection
cell. The values of the effective gradients are given in Table D-97.
Using these gradients in conjuncion wih the parameters given in the
previous section, the volumetric flow rates shown in Table D-98 may be
calculated by Darcy's law. Corresponding fluid velocities are given in
Table D-99. The discussion of healing and dissolution that was
presented in the case of bedded salt also applies to this case. The
source term in this case may be calculated according to the same
procedure as that given for bedded salt.
D-5.1.5 Literature Discussion
Faulting models and parameters have been reported in a number of
other studies, several of which are summarized below.
Battelle Pacific Northwest Laboratory, working under the ONWI/WISAP
program, has developed general models for faulting at a hypothetical
site in Columbia Plateau Basalts. ' Components of the model include:
* probability of significant changes in regional tectonic forces
over the next million years;
a probability of changes in local strain ratios over the next
million years;
270
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TABLE D-95
VOLUMETRIC FLOW RATES THROUGH A FAULT
(SHALE REPOSITORY)
Volumetric Flow (Q)
(m3/yr)
100 years
First Estimate 8.8 x 10
Second Estimate 4.0 x 10'
1000 years
7.6 x 104
3.8 x 105
10.000 years
3.2 x 10A
3.4 x 105
Years after repository closure.
271
-------
TABLE D-96
FLUID VELOCITIES THROUGH A FAULT
(SHALE REPOSITORY)
Velocity (v)
(m/yr)
100 years
First Estimate 2.2 x 10'
Second Estimate 1.0 X 10"
1000 years
1.9 x 102
9.5 X 102
10.000 years
8.0 x 101
8.5 X LO2
Years after repository closure.
272
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TABLE D-97
EFFECTIVE VERTICAL HYDRAULIC GRADIENT IN A FAULT
FROM THERMALLY INDUCED CONNECTION AND
AQUIFER INTERCONNECTION
(SALT DOME REPOSITORY)
100 years
1000 years
10.000 years
Thermally Induced
**
Convection
First Estimate
0.12
Second Estimate 0.12
0.07
0.07
0.03
0.03
Aquifer
Interconnection'
***
First Estimate
0.01
Second Estimate 0.2
Total
First Estimate
0.13
Second Estimate 0.32
0.01
0.2
0.08
0.27
0.01
0.2
0.04
0.23
**
***
Years after repository closure.
it
From Table D-VI-4, Appendix D-VI.
From Chapter D-2.0.
273
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TABLE D-98
VOLUMETRIC FLOW RATES THROUGH A FAULT
(DOME SALT REPOSITORY)
Volumetric Flow (Q_)_
(m3/yr)
100 years
First Estimate 8.2 x 10
Second Estimate 2.0 x 10'
1000 years
5.0 x 104
1.7 x 105
10.000 vear;s
2.5 x 104
1.5 x 105
Years after repository closure.
274
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TABLE D-99
FLUID VELOCITIES THROUGH A FAULT
(DOME SALT REPOSITORY)
Velocity (v)
(m/yr)
100 years*
First Estimate 2.0 x 10"
Second Estimate 5.0 x 10
1000 years
1.3 x 102
4.3 x 102
10.000 years
6.3 x 101
3.6 x 102
Years after repository closure.
275
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• probability of an undetected fold as a function of both distance
from the site and degree of site investigation;
• probability of a fault associated with an undetected anticline;
• probability of shear deformation along pre-existing joints, the
cause being movement in an undetected anticline; and
• probability of rupture of a fault in the basement strata.
The last probability in this list is estimated at
X = 10 events/year.
The determination of various probabilities is associated with seismicity
data.
TASC, in work for Lawrence Livermore Laboratory, modeled
movement along old faults in a shale repository as having an annual rate
of
X « 5 x 10 events/year.
They argued that for bedded salt the probability would be less.
Consequence modeling parameters included permeabilities of 10 cm/sec
-4
and 10 cm/sec through the repository and barrier layers, respectively,
with partial healing after 70 years reducing these values by two orders
of magnitude. Fault zone porosity was estimated at 10
Claiborne and Gera evaluated faulting probabilities for a site in
southeastern New Mexico. They estimated a faulting rate of
X = 4 x 10 events/year,
based on the regional tectonic data and geometrical analysis. They
further argued that containment failure by faulting is even less likely,
involving a reduction of about two more orders of magnitude in the
failure rate.
276
-------
The KBS study' "' in Sweden estimated a fault movement rate of
X = 10 events/year
2
for a 1-km repository in that country.
A University of New Mexico study for the EPA considered the
possibility of faulting in shale and salt repositories in the Delaware
Basin. The following occurrence rates were given
X = 2.2 x 10 events/year (shale)
X = 1.4 x 10 events/year (bedded salt).
The model was based on 13 years of earthquake data and a relation
between earthquake magnitude and faulting parameters, in order to
estimate an annual average fault surface area over which movement has
been experienced. This value was used to estimate the net faulting rate
as a product of three probabilities
Pj x p2 x p3
where:
average fault surface moving per year
"l = total surface of Permian-Penn. faults
p« " probability of an old fault beneath repository
p, » probability of a rupture in old fault extending as far up as
repository.
242
For bedded salt the respective values are 0.012 km /10 km , 0.6, and
0.2, leading to the X value given above.
D-5.2 VOLCANOES
D-5.2.1 Summary
The repository site selection process is expected to avoid sites
where future volcanic activity is at all likely. Nevertheless, volcanic
277
-------
trends can cover large distances over a period of time, and occasionally
completely new volcanic centers erupt, even within stable crustal
plates. This section of the report is concerned with the intersection of
a repository by a volcanic structure that vents to the surface. The
case of subsurface intrusive structures is treated in Section D-5.3.
The model adopted here consists of a constant annual rate for
penetration of the repository and transport of material to the air and
land surface. Rates are estimated by counting the number of vents in
various areas, dividing by their age to obtain vent formation rates, and
multiplying by the probability that such a vent would intersect a
randomly cited repository in the region of interest. A summary of the
analysis is given in Table D-100.
D-5.2.2 Background
A volcano is generally defined as a hill or mountain resulting from
accumulations of congealed lava or other ejecta that have been spewed
from a vent by deep geologic pressure and heat. From the point of view
of a repository, the physical form is less important than the
probability of recurrence, the nature of the eruption, and the range of
influence. Figure D-36 illustrates a number of volcanic or igneous
features • Several important surface phenomena are described in Table
D-101.
Volcanism is usually related to areas of crustal plate collision,
where magma from a subductlon zone can be freed up through the overlying
crust, or to areas under tensional stress, where rift zones can develop.
These conditions generally are found along continental margins and
mid-oceanic rises,( although intracontinental rifts are also
found. (See Figure D-45 in Section 5.6.) Most such activity therefore
follows linear or arched trends.
During the last ten million years, the only volcanism in the
coterminous 48 states has been in the West. Most of this activity has
paralleled the Pacific Coast, but some has followed the graben of the
Rio Grande, arched southward from Albuquerque toward Las Vegas, or
extended westward from Yellowstone Park. These trends are shown in
Figure D-37. There have been only three eruptions in the 48 states
278
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TABLE D-100
SUMMARY OF VOLCANO FAILURE ELEMENT
MEDIUM
Bedded Sell
Granite
Basalt
SS
So «
35
1
s§
ES
p
P
p
NATURE
OF
MODEL
Annual occurrence
probability.
Annual occurrence
probebilrty.
probability.
RELEASE
MODE
Air and lend
surface.
Air and lend
surface.
Air and land
surface.
DRIVING
FORCE
Direct: tramport by
moving 0M> *nd
Direct tramport by
mowing OMMMd
molten rock.
moving gmt *nd
moJ ton rock.
SOURCE
TERM
Fraction of repository
Fraction of repository
brought to surfece.
Fraction of repository
irought to surface.
PARAMETERS
1st ESTIMATE
X - 1 i 10-10/yr
Fraction of repository
brought to surface is
0.4%, of which 1%h
in reeuiieule form, 9%
consists off Ins pertides
which can be easily
dispersed, end 90% is
reburled near the
surface.
Fraction of repository
brought to surface is
0.4%, of which 1%l.
consists of fine pertides
which can ba amity
Opened, and 90* is
report ed near tha
surface.
X - 6 x 10-1uYyr
Fraction of repository
irougtrt to surf ace is
M%. of which 1% is
nreepirablefonn.t*
xmsira of fins pertides
•nidi cen be eerily
aspersed, and 90% Is
aburied near the
urfece.
2nd ESTIMATE
X • 1 x 10 • 1 x 10-8/yr
Fraction of repository
brought to surfece is
0.4%. of which 1% is
hi rtapireW. form. 9%
consists of fine particles
which cen be sesiry
dlspsrsed.end9(mis
raburiad near the
surface.
X - 1 x 1f»*/yr
Fraction of repository
brought to surfece is
(U%. of which IK is
inreaplrableform.9X
consists of fine pertides
which eanbaeetlty
dtwened.andOOXit
reburiedneerthe
surfece.
RELEASE MODELING STEPS
lit EST MATE
Direct release
Direct release
Direct releese
2nd ESTIMATE
Direct relaese
Direct release
Direct releese
COMMEffTS
First estimate based on
natkmel svsrn).. Lower
rates could probebh/ ba
shing easumption, such
eslocatlaninEastor
Midwest.
First enhnsta based on
nettonel an*raga> Lower
retascouW probsoh/ be
siting assumption, such
as location In East or
Mijmaet
Based on Columbia
Plateau basalts.
-------
TABLE D-100
SUMMARY OF VOLCANO FAILURE ELEMENT (CONTINUED)
MEDIUM
S»l»
DomtStlt
LISTIC (PI
INISTIC (Dl
s*
ss
ss
p
p
NATURE
MODEL
Annual occurrence
probability.
Annual occurrence
probability.
MODE
Air and land
surface.
Air and land
surface.
FORCE
Direct transport by
moving gases and
molten rock.
Direct transport by
moving gases and
molten rock.
TERM
Fraction of repository
brought to surface.
Fraction of repository
brought to surface.
PARAMETERS
In ESTIMATE
X = 1 x I0-10/yr
Fraction of repository
Drought to surface ts
0.4%, of which 1% is
in respirable form, 9%
consists of fine particles
which can be easily
dispersed, and 90% is
raburied near the
surface.
\ " 1 x lQ-10/yr
Fraction of repository
brought to surface is
0.4%, of which 1% is
in respirable form, 9%
consists of fine particle*
which can be cosily
dispersed, and 90% to
reburied near the
surface.
2nd ESTIMATE
\ - 1 x 10-8/yr
Fraction of repository
brought to surface is
0.4%, of which l%i$
inreapirabJeform.9%
consists of fine particles
which can be easily
dispersed, and 90% is
reburied near the
surface.
X = 1 x 1O-l°/vr
Fraction of repository
brought to surface is
0.4%, of which 1%is
in re»p treble form. 9%
consists of fine particles
which can be easily
dispersed, end 90% is
reburied near the
surface.
RELEASE MODELING STEPS
to ESTIMATE
Direct release
Direct relasie
2nd ESTIMATE
Direct release
Direct release
COMMENTS
First estimate based on
national everage. Lowe)
rotas could probably be
derived from additional
siting assumption, such
as location in East or
Estimates based on
national average. Could
be refined to a lower
value for salt dome
region. First and
second estimates are the
same since from the
standpoint of volcanism.
the Gulf region shows
no variation.
to
00
O
-------
LAVA
MESA
VOLCANIC NECK WITH
LAVA ASH CONE WITH RADIATING DIKES
PLATEAU VOLCANIC DOME / CALDERAWITH
CINDER CONE
CINDER
CONE,
ON FLOOR
COMPOSITE
VOLCANO
Source: U.S. Geological Survey. Atlas of Volcanic Phenomena.
FIGURE D-36 SKETCH OF PLUTONIC AND VOLCANIC STRUCTURES
281
-------
TABLE D-101
VOLCANIC PHENOMENA WITH SURFACE MANIFESTATION
Type
Basaltic
Eruptions
Andesitic
Eruptions
Silicic
Eruptions
Phreatic
Eruptions
Maars and
Diatremes
Fumarole
Geyser
Characteristics
Mild eruptions; fluid lava; small
gaseous component; silica deficient;
regular or continuous eruptions.
«
More violent than basaltic eruptions;
viscous lava; gaseous; much ash and
cinders. Forms composite cone; may
be explosive; irregular eruptions;
often long dormant. Most prevalent
type.
Nearly rigid lava; may be very
gaseous; forms domes and spines.
Gas, fumaroles, and geysers may
be only manifestation of magma.
Steam or gas explosion. May create
crater resembling impact crater, or
may shatter existing cone. Most
ejecta fragmented, or dust and gas.
Caused by contact of water with
hot magma.
Eruption crater in country rock from
violent eruption. Steam explosion
and jet erodes crater and ejects
limited volume of volcanic material
and shattered country rock.
A crack or vent in a lava flow or
volcanic region emitting gas and fine
ejecta. May be connected to main magma
source or may be the result of trapped
gas and steam from recent eruption. A
small feature building little or no
cone.
Steam and water emitted from a channel
connecting a heat source at depth to
the surface. Little or no solids are
ejected; often displays regular cyclic
eruptions.
Examples
Hawaii, Columbia
Plateau, Stromboli
Mt. Ranier,
Tamboro, Vesuvius,
The Andes,
Paricutln, Katmai
Mt. Pelee, Crater
Lake
Taal, Krakatoa
Hole-in-the-ground,
Crater Elegante.
Numerous
Yellowstone Park,
Steamboat Springs.
232
-------
ni-- y<-'
•: v --4^A
r=^T -—;"""'" ''';":V;:'~v-^-.
MAP EXPLANATION
LARGE VOLCANO~Bu1lt mostly by repeated eruptions
at a central vent and probably active within
the last 100,000 years. Eruptions range from
quiet to explosive. Volcano flanks
-------
recently enough to have been witnessed and documented: at Lassen Peak in
1915 and Mount St. Helens in 1857 and at present (1980). The
composition of most recent eruptions from the continental volcanic
systems has been andesite or rhyolite.
D-5.2.3 Volcano Failure Model
Of concern for a repository are the frequency and predictability of
new volcanism, since there are no present plans to consider repository
sites within the range of influence of known volcanoes. With few
exceptions, new volcanism will occur close to existing volcanic features
and in regions experiencing tensional stress. The exceptions stem from
the possibility of maar eruptions (see Figure D-36) initiated by the
release of gases or steam from a subterranean heat source. These types
of eruptions appear to be less sensitive to regional stresses, but
represent a very small percentage of eruptions.
Areas of future activity can be defined only very approximately, and
predicting the timing of this future activity is even less exact.
Future estimates of the expected frequency of eruptive activity at
volcanoes or in volcanic regions are generally based on historical
records and geologic investigation, both of which vary widely in detail
and reliability from one volcanic region to another. All of the
geologic media considered in this study, except salt domes, can be found
both close to and far from areas of recent volcanism.
There are many site-specific factors that can enter into an
estimation of the likelihood of future volcanism at a repository
location. These include the distance to the nearest recent activity,
whether the site lies in the direction of a trend, regional stress
patterns and the way they have evolved over geologic time, heat flow
measurements, etc. The model used here does not incorporate geophysical
parameters, but rather utilizes a simple counting technique for roughly
estimating the order of magnitude of the likelihood of future volcanism.
Figure D-37 shows all mapped vents in the coterminous states that
have shown activity within the last 10 million years. As noted earlier,
these are all restricted to the western third of the United States.
These vents actually formed over a longer period than 10 million years.
284
-------
However, in estimating the rate of formation, it is conservative to use
this lower, more readily available figure. The map shows approximately
6 2
1300 vents over this western area of 3 x 10 km . Thus, a gross
regional average rate of vent formation is
62 7
X = 1300 vents per 3 x 10 km per 10 years
-11 2
= 4 x 10 vents/km /year.
2
For a repository of area 8 km , the corresponding rate of intersection
would be 8 times the above, or
X = 3 x 10 intersections/year.
This number does not represent either a first or second estimate for
model purposes, but is used as an example calculation to represent the
model equation
x = 8V/AT intersections/year,
where V is the number of vents formed in the area A over a period at
least as long as T. This equation will be used for various regions to
estimate appropriate values of X. The 10-million-year cutoff for data
on vents was chosen to be consistent with the USGS use of this time
frame for their volcanic hazards maps.
A simple first estimate value of X for all media except basalt can
be derived from the assumption that, with careful site selection, it
should be possible to locate a repository so that the probability of
future volcanism is less than the national average. This is because
bedded salt, granite, shale, and salt domes are either widely
distributed or concentrated in areas of negligible volcanic activity.
The national average is thus a conservative estimate of X. This value
is obtained exactly as above, except that the entire area of the
coterminous states is used, so that
(81(1300)
(7.83 x 106)(107)
= 1 x 10~ intersections/year,
Basalt is not covered by this reasoning because the only basalt deposits
being seriously considered for a repository are located in a single
region, namely, the Pacific Northwest. By their mere presence, these
285
-------
basalts are indicative of significant volcanic activity in the past.
Most of the Columbia Plateau flood basalts were apparently deposited
about 14 to 17 million years ago, but some volcanic activity continues
in locations such as Mount Lassen farther to the west. Regional stress
studies suggest that there may be locations in this region where the
probability of future volcanism is low. First estimate calculations
consider the states of Washington, Oregon, and Idaho, exclusive of the
north-south volcanic trend represented by the Cascade and Klamath
Mountains. (This latter zone is probably associated with an existing
subduction zone and hence a different tectonic zone from the region of
greater interest.) From the map in Figure D-37, the following
parameters have been estimated:
A = 4 x 105 km2
V = 300 vents
T = 107 years
The resulting value of X from the model equation is
X = 6 x 10 intetsections/year.
This number is the first estimate for basalt.
Second estimate values correspond to repository sites in locations
of modest volcanic activity over the past 10 million years. A number of
volcanic fields shown on Figure D-37 were considered, with values of A,
V, and T being estimated for each. For example, for the Flagstaff,
2
Arizona area, 85 vents are estimated to exist in a region 6400 km in
area, and the time over which these developed is thought to be at least
10 years. These parameters yield the value
X = 1 x 10~8.
It is important to note that such values should not be applied to the
specific volcanic fields from whose parameters they have been
calculated. They represent only averages, and detailed site
investigations could introduce other factors that might significantly
alter the estimate for an individual site. They are, however, believed
to be reasonable for generic calculations.
286
-------
Many of the other calculations yielded similar values, and so this
—8
value, X = 1 x 10 , has been adopted as the second estimate for all
media except salt domes. In the case of salt domes, which are not found
in any of the volcanic regions, the second estimate value is identical
to the first, i.e., 1 x 10~10.
It should be noted that in the calculation of the volcanic vent
formation rate, X, the choice of regions to be considered has a great
effect on the resulting numerical value. For example, application of
the above procedure to the eastern United States would yield essentially
zero rates. Since the values calculated by this procedure are generally
very low, it did not seem desirable to refine them by making further
site selection assumptions. Simple modifications, such as eliminating
from consideration the vents along the Pacific coastal volcanic mountain
zone, would indeed lower the rate for the rest of the country. However,
since this modification only changes the result by about a factor of 2,
it is not deemed important in these order-of-magnitude calculations.
Another modification would be to cbnsider only intra-plate silicic
eruptions. While the consequences of these would be more severe, they
would also involve lower probabilities than the already low ones
calculated, as well as the possibility of detecting developing magma
chambers that could lead to silicic eruptions over the next 10,000
years.
D-5.2.4 Volcano Release Model
The dominant release mode for the interception of a repository by a
volcanic vent is the transport of radioactive material directly to the
surface. Since the size of the vent and the nature of the eruption can
vary considerably, this analysis simply estimates parameters that would
characterize an "average" new vent.
A 2
The area of the vent is taken to be 3 x 10 m , corresponding to the
area of a circle with radius 100 m. This cross-sectional area also
characterizes the portion of the repository that would be affected, or
0.4% of the repository inventory. Of the affected contents, it is
assumed that 1% is widely dispersed as fine particulates or gases, 9% is
included with unconsolidated ash or cinder on the surface, and 90% is
287
-------
incorporated into solidified lava or welded ash. Most recent eruptions
in America have involved andesitic ejecta with fragmented, molten, and
gaseous components. The fractions assigned to each component are
thought to be reasonable for such a typical eruption. Explosive and
calamitous events, such as the obliteration of Krakatoa and Mt. Mazama
(Crater Lake), are not only exceptional, but they are apparently more
likely with large, established volcanic systems than with newer
eruptions. Similarly, maars require abundant water, a condition not
expected at most candidate repository sites. If it were desired to
model the "worst possible" case in terms of consequences, then the
probabilities would need to be revised downward accordingly.
D-5.2.5 Literature Discussion
Volcanism has been discussed in a number of repository studies.
However, models and quantitative analyses are usually not included, and
ones that are included are difficult to compare with those derived here.
The University of New Mexico/EPA study characterized volcanic
-12 -12
events with annual probabilities ranging from 2.4 x 10 to 8.1 x 10
for disruption of a repository. These probabilities are based on an
estimate of renewed volcanism in the Delaware Basin with an annual rate
-9
of 5 x 10 , in combination with a geometric argument on repository
intersection.
(3)
Claiborne and Gera, also in an analysis of the Delaware Basin,
simply state that volcanism in such a stable area is much less likely
than formation of a "great fault." In addition, they argue that the
consequences would be less than for a giant meteorite impact.
Recent probability calculations carried out for a potential
repository site at Yucca Mountain on the Nevada Test Site yield an
_9 M2i)
annual rate of 10 for repository disruption by volcanism.
Some of the calculations carried out in other studies appear to
count volcanic craters rather than individual vents, which may explain
why some of these other rates are lower than those calculated here.
288
-------
D-5.3 IGNEOUS INTRUSIVES
D-5.3.1 Summary
The previous section on volcanoes discussed extrusive igneous
activity (movement of magma out through vents to the surface or the
atmosphere). The repository might also be disrupted by intrusive Igneous
bodies (magma that moves through the earth's crust but never reaches the
surface) . The important difference between extrusive and intrusive
activity is that while extrusive activity, volcanism, can transport
waste directly to the biosphere, intrusive activity requires groundwater
as a secondary transport mechanism.
The model in this section assumes that a planar intrusive body
intersecting the repository will transport a fraction of the intersected
waste to the overlying aquifer. Waste within the aquifer will then be
leached and moved by the natural flow of groundwater. The model requires
two parameters: the probability of an intrusive intersecting the
repository, and the dimensions of the intrusive. Intrusives are common
structures, particularly in volcanic and crystalline rocks; but, by
their very nature, their emplacement has not been directly observed and
there is little information from which probabilities for intrusions may
be estimated. In the present model, the probability of an intrusive
intersecting a repository is modeled as a fraction of the probability of
faulting. Dimensions of intrusives used in the model are consistent with
those reported in the literature. It is assumed that the waste is not
sealed into the resolidified igneous rock, which may be heavily
fractured especially in zones where it encounters groundwater. Detailed
explanations of the model are given in Sections D-5.3.3 and D-5.3.4. A
summary of the analysis is given in Table D-102.
D-5.3.2 Background
Definitions and examples. Intrusive igneous rock masses are created
when magma or molten rock is injected into crustal rock below the
surface, as opposed to extrusives, which erupt at the surface. Some
intrusive bodies may be the result of extreme metamorphism and partial
289
-------
TABLE D-102
SUMMARY OF IGNEOUS INTRUSIVE FAILURE ELEMENT
MEDIUM
Bedded Salt
Granite
Basalt
Stole
Dome Salt
sa
0 SJ
ES
(O _
si
< ec
00 tU
it
a. O
p
p
p
p
f
NATURE
OF
MODEL
Annual probability
of occurrence.
Annual probability
of occurrence.
Annual probability
of occurrence.
Annual probability
of occurrence.
Annual probability
of occurrence.
RELEASE
MODE
Groundwater
Groundwater
Groundwatw
Groundwater
Groundwater
DRIVING
FORCE
Physical transport of
wastes by magma to
upper aquifer.
Physical transport of
wastes by magma to
upper aquifer.
Physical transport of
wastes by magma to
upper aquifer.
Physical transport of
wastes by magma to
upper aquifer.
Physical transport of
wastes by magma to
upper aquifer.
SOURCE
TERM
Waste material inter-
sected by magma.
Waste material inter-
sected by magma_.__
Waste material inter-
sected by magma.
Wane material inter-
Waste material inter-
sected by magma.
PARAMETERS
1st ESTIMATE
X=2x10-10
Dimensions of dike:
1 m x 4 km.
intersecting 0.05%
waste inventory.
X = 2 x 10'10
Dimensions of dike:
1 m x 4 km.
intersecting 0.05%
waste inventory.
X - 5 x 10'9
Dimensions of dike:
1 m x 4 km.
intersecting 0.05%
waste inventory.
Dimensions of dike:
t m x 4 km.
intersecting 0.05%
waste inventory.
X = 3 x 10"9
Dimensions of dike:
1 m x 4 km.
intersecting 0.06%
waste inventory.
2nd ESTIMATE
X = 4 x 10"®
Dimensions of dike:
1 m x 4 km.
intersecting 0.05%
waste inventory.
» . ID'7
Dimensions of dike:
1 m x 4 km.
intersecting 0.05%
waste inventory.
X - ID'7
Dimensions of dike:
1 m x 4 km.
intersecting 0.05%
waste inventory.
X = 4 x 10~9
Dimensions of dike:
1 m x 4 km,
intersecting 0.05%
waste inventory.
X o 5 x 10"7
Dimensions of dike:
1 m x 4 km.
intersecting 0.05%
waste inventory.
RELEASE MODELING STEPS
Material moved to aquifer and subject to leaching.
Leach characteristics of waste form assumed
unchanged, although canisters would be removed.
Material moved to aquifer and subject to leaching.
Leach characteristics of waste form assumed
unchanged, although canisters would be removed.
Material moved to aquifer and subject to leaching.
Leach characteristics of waste form assumed
unchanged, although canisters would be removed.
Material moved to aquifer and subject to leaching.
Leach characteristics of waste form assumed
unchanged, although canisters would be removed.
Material moved to aquifer and subject to leaching.
Leach characteristics of waste form assumed
unchanged, although canisters would be removed.
COMMENTS
Probabilities deter-
mined as 1% of values
for faulting.
Probabilities deter-
mined as 1% of values
for. faulting.
Probabilities deter-
mined as 1% of values
for faulting.
Probabilities deter-
mined as 1% of values
for faulting.
Probabilities deter-
mined as 1% of values
for faulting.
10
v£>
O
-------
melting of older rock, and therefore are not truly igneous. However,
this distinction is not important for the purpose of generic modeling,
and so, for the sake of simplicity, all intrusives will be regarded as
igneous throughout the discussion.
Intrusives may be classified according to a number of features,
including size, orientation, and petrography. The most important
classifications are discussed here and illustrated in Figure D-36
(Section D-5.2). The generic term, pluton, refers to any intrusive
igneous rock body, independent of structure or mode of emplacement.
Sills are planar and parallel to rock strata or contacts. Dikes are
also roughly planar, but they cut across strata. Laccoliths can be
described as very thick sills that cause doming of the overlying rock.
Stocks are vertical masses, roughly round in cross section, that pierce
the country rock. Batholiths are very large stocks, apparently formed at
considerable depths.
Plutons may intrude any rock: sedimentary, igneous, or metamorphic;
and they may have any igneous petrography. Examples are found of both
acid and basic rocks forming all types of intrusive structures. Usually,
however, magmas of low viscosity tend to form dikes and sills while
those of higher viscosity form the thicker laccoliths and stocks.
Batholiths are most often granitic in composition, apparently the result
of melting of older continental rocks. Local stresses at the time of
emplacement may also affect the morphology of intrusives; high vertical
stresses favor the formation of dikes and other discordant bodies, and
low vertical stresses favor the formation of sills.
Effects on country rock. The viscosity, temperature, and chemistry
of the magma influence the range of effects accompanying intrusion.
Forcible injection tends to break free pieces of the surrounding rock,
incorporating these rock fragments in the intrusive mass as xenoliths.
Intrusion often produces secondary fracturing of the country rock. These
fractures are typically, but not always, filled by the fluid magma. The
temperature differential between the hot magma and the cool invaded rock
may produce a zone of chilling in the intrusive and heating in the
country rock, creating local areas of metastable minerals as the rocks
pass rapidly through the stable temperatures for such minerals. Chemical
alteration (metasomatism) of both magmatic and country rock occurs where
291
-------
water and other volatiles in one or both rocks react in the vicinity of
the intrusive contact. The term "contact metamorphism" is used to
describe the change in the mineralogy or fabric of the original rock as
a result of the intrusion. The area of contact metamorphism may be
extensive and contain a variety of economic minerals, depending, of
course, on the composition of the intrusive and the accompanying fluids.
The sizes and extent of intrusives can vary widely. Some sills and
dikes have dimensions reported in centimeters, while others extend for
(58 122 123)
many kilometers and are many meters thick. ' ' Classic examples
of the latter are the Palisades sill along the Hudson River, the dikes
near Shiprock, Arizona, and the dike swarms across Scotland and
England.(123>124'125) Batholiths, such as the Idaho batholith, have
2
areas on the order of 100 km or larger, while stocks are
.. (58,126)
smaller.
Intrusives are frequently associated with volcanism, as evidenced by
the numerous sills and dikes radiating from or concentric to volcanic
vents. However, not all intrusives show this relationship, although the
relationship can also be obliterated by subsequent erosion.
Depth of igneous emplacement also varies over a wide range. Some
plutons, particularly those associated with volcanism, may have been
emplaced very near the surface. Others cooled slowly and at depths of
several kilometers, as indicated by their minerals and their crystal
(122)
size. As the distance from the magma source increases, plutonic
intrusion clearly becomes less likely.
Detection of intrusives. Intrusives are most generally identified
through field surveys by stratigraphic and petrographic comparison with
surrounding rock. These basic techniques may be supplemented by drilling
and geophysical investigations of magnetic and gravitational anomalies.
Intrusives often differ markedly in magnetic properties and density from
many sedimentary rocks and may be readily detected in some situations.
The geologic history of plutons near a repository site gives some
indication of the potential for future activity. Furthermore, current
magmatic activity near a repository site may be detected through
geothermal heat flow measurements. In general, heat gradients across the
United States indicate that, except for a very few locations, rock
melting is not likely within several kilometers of the surface/
292
-------
Measurement of surface rise or ground tilt may also be used to interpret
magmatic movements at depth. However, to maintain a conservative
approach and because rates of magmatic movement are too poorly
understood, the potential advantage of geothermal or geophysical surveys
is not considered in the present model.
D-5.3.3 Igneous Intrusive Failure Model
The model developed for igneous intrusions is analogous to that used
for faulting in that it requires:
• the probability of new intrusions intersecting a repository; and
• the physical parameters to describe transport of waste by an
intrusive.
The actual formation of intrusives has seldom, if ever, been witnessed,
although some have been inferred near volcanic centers. Only a few
investigators have reported the number, size, and spacing of plutons in
(122 127)
different regions. ' Therefore, an approach using areal
densities and ages of plutons to establish the probability of their
occurrence is difficult to apply. Many plutons apparently form at
considerable depths, suggesting that the number reaching a relatively
shallow repository would be far fewer than indicated by a count of
plutons visible at the surface after extensive uplift and erosion. For
example, in one study of a granitic region, dikes were reported at the
rate of three per linear mile, or approximately 10 per square
(122)
kilometer. However, as they had been emplaced roughly 6.5
kilometers below the surface, it is clear that extrapolation to
establish representative probabilities for Intrusions into a shallow
formation would be of questionable validity.
Alternatively, the argument has been made that the rate of intrusion
is a fraction of the rate of faulting, since most intrusives apparently
fill faults or joints, while many faults or joints have no associated
(12)
intrusives. Conditions are envisioned similar to those for normal
faulting, where vertical stress is greater than horizontal stress.
Vertical faults could form, intersecting the repository and admitting
magma in the form of dikes. The magma could then carry the waste to the
upper aquifer. Horizontal flows of magma through a repository are
293
-------
considered less important since they would not carry waste to the
aquifers or nearer to the surface.
Very limited data permit only a rough estimate of the ratio of dikes
to faults. Further analysis based on geophysical considerations may be
possible for a particular region. However, to be consistent with
(12)
estimates proposed in similar studies, the present model assumes
that dikes are one percent as frequent as faults. The probability of an
_2
Igneous intrusion disrupting the repository is thus estimated to be 10
times the rate of faulting for the geologic medium, as determined in
Section D-5.1.
D-5.3.4 Igneous Intrusive Release Model
The dimensions of an intersecting dike are used to determine the
fraction of stored waste transported to the aquifer by the molten rock.
For the sake of conservatism, it is assumed that a dike would cut the
2
repository across its longest dimension. For a repository of 8 km with
sides of 2 km and 4 km, the dike would be 4 km long. The thickness of
(122)
the dike is assumed to be 1 meter. The dike would then intersect
0.05% of the repository. Also for conservatism, it is assumed that this
entire fraction is carried to the overlying aquifer and is not sealed
into the matrix of the dike. Because this transport mechanism assumes
immediate introduction of the waste into the aquifer, the contribution
of groundwater flow along the contact is Insignificant by comparison and
may be neglected. Furthermore, it is likely that this boundary will be
resealed by melting of the country rock.
This model is independent of the host rock. Accordingly, the same
parameters apply for all media discussed in this study.
D-5.3.5 Literature Discussion
Igneous intrusives have been modeled as possible failure mechanisms
in several other studies, which are mentioned below. Most of these
studies have not identified igneous intrusion as a separate failure
mechanism, but as a variation of volcanism. ' ' ' Two sources
distinguish between extrusive and Intrusive magmatlc activity, citing
294
-------
the additional requirement of groundwater to transport waste after
(12 128)
magmatic intrusion as the main distinction. ' These studies also
discuss qualitatively the effects of concentrated geothermal heat on the
natural groundwater regime and possible local perturbations in flow.
(12)
Only one study develops a failure rate for intrusives, and this is
the basis for the approach used here.
D.5.A METEORITE IMPACT
D-5.4.1 Summary
The impact of a large meteorite could cause a breach of the
repository either by directly releasing material to the air or land
surface or by fracturing the surrounding rock, thereby permitting
greater groundwater access. Meteorites large enough to create such
breaches are very uncommon. Furthermore, the potential hazard
associated with repository releases would appear to be negligible
compared with the possible effects on surface Installations, the
environment, and the surrounding population. Therefore, the following
discussion is more abbreviated than that for most other failure
elements. A summary of the parameters used to characterize this failure
element is given in Table D-103.
D-5.4.2 Background
In the history and evolution of the solar system, meteorites have
been very common, representing a process that has had measurable effects
on the planets and their satellites. Indeed, it has been theorized that
some meteorites over 1000 km in diameter may be responsible for
(129)
variations in the thickness of the crust on the earth and the moon.
From observations of cratering history on the inner planets and their
satellites and by correlation with the ages of portions of their
surfaces (e.g., by lunar rock samples), estimates have been made of
meteorite fluxes since the formation of the solar system. Figure D-38
shows how this rate has slowed since the early period of the solar
295
-------
TABLE D-103
SUMMARY OF METEORITE IMPACT FAILURE ELEMENT
MEDIUM
BeddadSaM
Granite
SataH
si
!§
J Z
II
II
p
p
p
NATURE
OF
MODEL
Annual occurrence
probability.
Annual occurrence
probability.
Annual occurrence
probability.
RELEASE
MODE
A. Lend surface
8. Groundwalar
A. Land surface
B. Groundwater
A. Land surface
B. Groundwater
DRIVING
FORCE
A. Impact
B. Thermal convection
added to aquifer
interconnection
gradient.
A. Impact
6. Thermal convec-
tion.
A. Impact
B. Thermal convec-
tion eddad to
aquifer inter-
connection
gradient.
SOURCE
TERM
A. 0.1% repository
inventory to
surface.
B. 20% cumulative
leeched nudktn
refeasfd to ground-
water. Continued
leaching of broken
canisters in fracture
or breccia zone
110%) and tur.
rounding canisters
110%).
A. 0.1% repository
inventory to
surface.
3. 20% cumulative
Inched nudides
released to ground-
water. Continued
leaching of broken
canisters in fracture
or breccia zone
(10*1 «nd sur-
rounding canisters
110%).
A. 0.1* repository
inventory to
surface.
B. 20% cumulative
leached nudides
released to ground-
water. Continued
leaching of broken
canisters in fracture
or breccia zone
110%) and sur-
rounding canisters
110%).
PARAMETERS
1st ESTIMATE
X . 4x10-H/yr
A - 0.8 km?
K - 10-«cm/stc
n - 03
X - 4x 10-H/yr
A - 0,8 km?
K " 10~* cm/fee
n - 03
X • 4 x IO-1 '/yr
A - 0.8 km?
K - lO-'cm/sac
1 • 03
2nd ESTIMATE
X • 4x10-11/yr
A - 0.8km2
K - IO4 on/tec
r, « 03
X - 4x10-1'/yr
A " 0.8 km2
K - 10-4 cm/tec
n - 02
X - 4x10-1'/yr
A • 0,6 km2
K • 10-« cm/sec
fl - 02
FLUID FLOW RATES FROM
REPOSITORY TO UPPER AQUIFER
1st ESTIMATE
tlvra)
100
1000
10.000
Q III (m3/vr)
IjSxIO7
•j
1.4 x 10'
5.0 x 106
tlyrsl
100
1000
10.000
6 It) (r»3Avrl
f
1.4 x 10'
e.8 x 10°
32 x IO8
tlyrs)
100
1000
10.000
Q It) Im3/yr)
1 J x IO7
•j
1.5 x 10
6J x IO6
2nd ESTIMATE
(yrsl
100
1000
0*00
0 It) Im3/yr)
7£.107
7^ x 10'
S.7 x IO7
t(vn)
100
1000
10.000
6 It) lr»3/yr)
1.4 x 10
8.8 x 10*
3JB x I06
tlvnl
100
1000
10.000
6 It) Im3/yrl
73 x 10
7
7.7 x IO7
&JBx107
COMMENTS
Water availability may
severely limit flows
below levels calculated.
Water availability may
severely limit flows
below levels calculated.
Water availability may
severely limit flows
below levels calculated.
VD
-------
TABLE D-103
SUMMARY OF METEORITE IMPACT FAILURE ELEMENT (CONTINUED)
MEDIUM
Shale
Dome Salt
5i
a HI
Is
p
p
NATURE
OF
MODEL
Annual occurrence
Annual occurrence
probability.
RELEASE
MODE
A. Lendeurface
B. GroundMter
A. Landawfece
B. GroundMeter
DRIVING
FORCE
A. Impact
B. Thermal connec-
tion added to
aquifer Inter-
connection
gradient.
A. Impact
B. Thermal convec*
tton added to
aquifer inter-
eormaciion
gmtitnt.
SOURCE
TERM
A. 0.1%rapo>itorY
inventory to
eurface.
B. 20% cumulative
Hater. Continued
leeching of broken
caniaten in fracture
or breceie zone
rounding canMan
<10%l.
A. ai«repoaitarv
•Memory to
aurfece.
1. 20»CMaetfve
leeched nudidei
M^ConttMcT
laachlni of broken
cenlalen in fracture
or breccia zone
(WMUandaur-
roundlai cankMn
now.
PARAMETERS
l« ESTIMATE
X - 4x10-"fVr
» - 0£kn>2
B - OJ
X - 4x10-"/yr
A - aSkn.2
* - OJ
andESTMATE
X • 4x10-"/yr
A - OJBkml
K - 10-*cm/eec
n - OJ
X • 4x10-'1ryr
A - OJBkmZ
K - 10-*cm/aac
n - 0.2
FLUID FLOW RATES FROM
REPOSITORY TO UPPER AQUIFER
1
100
1000
10,000
6 It) Im3/Vr)
1 J x 107
U.,107
6J x 106
tlyfe)
100
1000
ioxno
0 It) .107
24»107
COMMENTS
Weterenllabllrryiney
arMntv limit flam
•enerely limit f torn
bekM NHeb cakulaled
eetablitfiad by fracture
aoneatedgaofaah
dome.
ro
-------
c
0>
£
a.
o
cc
*
n
tr
o
uuu
000
100
10
1
p
i
•
i
\
i
\
V
^
k
^^
i 4 3 2 1 0
Billions of Years Ago
Note: Graph is for lunar cratering but it is representative for inner planets.
Source: Hartmann, W.K., Cratering in the Solar System. Scientific
American 236:84, January 1972.
FIGURE D-38 RELATIVE CRATER PRODUCTION RATE WITH SOLAR SYSTEM EVOLUTION
298
-------
system, when interplanetary debris was rapidly being removed by the
gravitational attraction of the planets* The rate appears to have been
roughly constant for the last two billion years.
Meteorite impacts have been much more common on earth than may
generally be realized. The surface geology of the earth is so active
that even very large craters are eroded or buried with time. Table
D-104 lists all proven or probable impact craters in the United States
with diameters of at least one kilometer. Proven structures involve
meteorite remnants, and probable structures are determined from evidence
of shock metamorphism. Many other possible impact craters have also
been identified. The list of impact craters worldwide includes a
number over 100 km in diameter. Figure D-39 is a map of proven and
probable impact craters. The highly non-uniform spatial distribution
can be attributed to the varying geologic stability of different regions
as well as to differences in the degree to which areas have been
investigated for craters.
The rate of cratering, by size, has been studied rather carefully
because comparison of this rate with actual counts of detectable
features yields information on the history and evolution of a planet and
its surface. For craters at least 1 km in diameter, the frequency of
occurrence appears to be roughly inversely proportional to the square of
the diameter. This rule has both an empirical and a theoretical
justification/130'131) Calibrating with data from well studied stable
regions of the earth, a cratering production rate, $ , has been
determined to be given by the equation
log1Q = -11.85 - 2 log1Q D.
Here D is crater diameter in km and <)> is the number of craters per
square kilometer per year at least as large as D. In particular, for
-12
D « 1 km, = 1.4 x 10 . This means that for a land surface of 7.8 x
6 2
10 km , the area of the 48 coterminous states, there should be about
1.1 x 10~ falls per year of meteorites capable of creating craters at
least 1 km in diameter. The mean time between such occurrences is the
reciprocal of this rate, or about 90,000 years. It should be noted that
D»l is near the lower limit of applicability of the given formula, but
299
-------
TABLE D-104
PROVEN OR PROBABLE LARGE METEORITE IMPACT CRATERS
Location
Kentland, Indiana
Manson, Iowa
IN THE UNITED STATES
Diameter
(km)
rizona 1.2
:, Missouri 5.6
Missouri 6
Tennessee 3.8
iana 13
32
Kentucky 6
N. Dakota 9
, Ohio 6.4
, Texas 13
nnessee 14
Age
(millions of years)
0.025
320 +
300
360 +
300
70
300
200
300
100
200 +
80
20
100
Source: Grieve, R.A.F. and P.B. Robertson. The Terrestrial Cratering
Record. Icarus 38:212, 1979.
300
-------
Source: Hughes, D.W. Earth's Cratering Rate. Nature 281:11. September 6,1979.
Based on: Grieve, R.A.F. and P.B. Robertson. The Terrestrial Cratering
Record. Icarus 38:212,1979.
FIGURE D-39 DISTRIBUTION OF IMPACT CRATERS
301
-------
for present purposes, where the emphasis is on orders of magnitude, the
formula suffices.
The geometry of craters is relevant in determining their effect on a
nuclear waste repository. There are simple bowl-like craters, as well
as ones with complex structures, including ringed ridges and peaks in
the interior and depressed sections along the boundaries. Craters up to
about 4 km in diameter in crystalline rock and 2-3 km in sedimentary
strata are usually simple, while larger ones have complex structures. A
schematic representation of a simple crater, shown in Figure D-40, forms
the basis for the analysis in this section. For a repository about
500 m deep, as in the generic models, a crater diameter of at least 1 km
is a reasonable cutoff for defining meteorite events of interest.
D-5.4.3 Meteorite Impact Failure Model
The failure model concentrates on meteorites giving rise to craters
of diameter 1-2 km because the frequency of meteorite cratering
decreases rapidly with increasing size, and the larger size impacts are
even more likely to cause widespread environmental effects of greater
importance than breaching a waste repository. The target area has been
2
taken to be 24 km., corresponding to the repository area (2 km x 4 km)
and a one-kilometer wide buffer zone around it. The failure element
consists of the center of the crater lying within this area. Using the
—12 2
production rate of <(> = 1.4 x 10 per km per yr for craters of
diameters at least 1 km, the annual failure rate is given by
A = 1.4 x 10~12 x 24
—11
= 3 x 10 events per year.
This rate is assumed to be independent of the host rock formation, since
variations in geophysical properties are not significant for the
purposes of these rough calculations. Moreover, there are no distinct
first and second estimates in this case, since this is a statistically
derived estimate and is independent of location.
302
-------
D = Crater Diameter
Source: Adapted from Innes, M.J.S. The Use of Gravity Methods to Study the Underground
Structure and Impact Energy of Meteorite Craters. J. Geophysical Research,
66 (7), July 1971.
FIGURE D-40 SIMPLIFIED CRATER GEOMETRY
303
-------
D-5.4.4 Meteorite Impact Release Model
A meteorite impact crater formed on the repository site would be
expected to be smaller than the repository, since crater sizes are
biased toward the lower end of the range under consideration. A crater
of 1-km diameter would have a cross-sectional area at the surface of 0.8
km2.
The breccia zone would not even reach 500 m in depth, and the
fracture zone at that depth would be very small. (See Figure D-40.)
For a crater with a diameter of 2 km, the breccia zone would intersect
the repository. Based on the simple geometry in Figure D-40, the area
2
of intersection would be roughly 0.8 km , corresponding to a circle 1 km
2
in diameter. For modeling purposes, this area of intersection, 0.8 km ,
has been taken as a conservative estimate of the portion of the
repository directly affected by the meteorite event. It has further
been assumed that there is sufficient fracturing or brecciation down to
the repository depth for direct releases to the surface to occur.
Because of the higher probability of meteorites at the low end of
the size scale being considered, the expected direct release to the air
and land surface is probably very small. Although there does not appear
to be an analytical or empirical model for predicting this event, it has
been assumed that 1% of the wastes in the affected zone (i.e., 0.1% of
the repository inventory) would be released to the land surface. The
remaining wastes are subject to enhanced leaching by groundwater because
of permeability increases in the surrounding rock. The hydrologic
parameters assumed for this pathway are:
K = 10 cm/sec
n = 0.2
2
and the cross-sectional area is again A = 0.8 km • Flows through this
zone can be calculated analogously to Section D-5.1.4 on fault pathways,
and in other sections. In particular, Darcy's Law is applied with the
hydraulic gradients given in Table D-105. The corresponding fluid flow
rates are given in Table D-106. These would very likely be restricted
well below the calculated values because of limitations on the amount of
water present.
304
-------
TABLE D-105
EFFECTIVE HYDRAULIC GRADIENT IN EXTENDED VERTICAL PATHWAYS
100 years
1000 years
10.000 years
Bedded Salt
First Estimate 0.13
Second Estimate 0.62
0.11
0.60
0.04
0.53
Granite
First Estimate 0.11
Second Estimate 0.11
0.07
0.07
0.03
0.03
Basalt
First Estimate 0.14
Second Estimate 0.63
0.12
0.61
0.05
0.54
First Estimate 0.14
Second Estimate 0.63
0.12
0.61
0.05
0.54
Dome Salt
First Estimate 0.13
Second Estimate 0.32
0.08
0.27
0.04
0.23
Years after repository closure.
305
-------
TABLE D-106
VOLUMETRIC FLOW RATES THROUGH METEORITE INDUCED PERMEABLE ZONE
Volumetric Flow Q
(m /yr)
Bedded Salt
Granite
Basalt
Shale
100 years
1000 years
10.000 years
First Estimate
Second Estimate
1.6 x 10'
7.8 x 10'
1.4 x 10'
7.6 x 10'
5.0 x 10C
6.7 x 10y
First Estimate
Second Estimate
1.4 x 10
1.4 x 10'
8.8 x 10
8.8 x 106
3.8 x 10
3.8 x 106
First Estimate
Second Estimate
1.8 x 10'
7.9 x 10'
1.5 x 10'
7.7 x 10'
6.3 x 10"
6.8 x 10y
First Estimate
Second Estimate
1.8 x 10
7.9 x 10'
1.5 x 10
7.7 x 10'
6.3 x 10l
6.8 x 107
Dome Salt
First Estimate
Second Estimate
1.6 x 10'
4.0 x 10'
1.0 x 10'
3.4 x 10'
5.0 x 10
2.9 x 107
6
Years after repository closure.
306
-------
The source term for the groundwater release has several components.
First, radionuclides that may have leached out into any water in the
repository before the meteorite event would be able to move with that
water up through the permeable pathway. Second, canisters in the
affected zone of the repository would probably be broken up and subject
to direct leaching after the event. Third, canisters in other portions
of the repository could also continue to contribute leached
radionuclides to the water in the repository. These radionuclides could
gradually migrate through the backfilled tunnels and drifts to the
actual release pathway. The third effect is expected to be the least
important by far, and so it has not been modeled. To account in a
conservative and simple way for the other source terms, it can be
assumed that the cumulative leached radionuclides from 20% of the
repository are released into the pathway at the time of the breach, and
that thereafter 20% of the repository is subject to continuous leaching
in the groundwater flows calculated.
D-5.4.5 Literature Discussion
Various estimates for the likelihood of a meteorite breaching the
(26 ^
repository are found in the literature. The Swedish KBS study^ cites
a rate
—13 2
X = 10 per km per year
for craters at least 100 meters deep, and on this basis dismisses this
(12)
failure element. The NRC/Sandia study uses the rate
-13
X = 2 x 10 per repository per year
2
for impacts on an area of 8 km , a value attributed to Claiborne and
Gera. These latter authors assume a reference crater at least 2
kilometers in diameter- The University of New Mexico study for
the EPA suggested a rate
-13
X = 1 x 10 per repository per year
2
for a 10-km repository. A source term for consequence calculations was
307
-------
given in this last study as 5% of the repository inventory to the air
and 5% to the land surface.
D-5.5 BRECCIA. PIPES
D-5.5.1 Summary
Deep dissolution processes in bedded salt deposits can lead to the
development of brine-filled cavities on the lower sides of the
formations. These cavities, after reaching a certain critical size, can
cause the collapse of the overlying rock and the propagation of a
(22 132 133)
chimney of broken rock up to or toward the surface. ' ' Such a
chimney structure is called a breccia pipe. It provides a permeable
pathway through which groundwater can flow and leach radionuclides from
the waste canisters. The model described here assumes that breccia
pipes develop at a constant annual rate, except that none can breach the
repository for the first 500 years after sealing because their incipient
development would be detected during site investigations. Fluid flows
are assumed to be upward, with release of radionuclides to the upper
aquifer. Significant dissolution of the salt formation around the
breccia pipe is assumed not to occur, based on qualitative
considerations of water availability and degree of salt saturation, but
healing of the column by cementation and recrystallization is also not
assumed. A summary of the analysis is given in Table D-107.
D-5.5.2 Background
Salt is a very soluble mineral, and every salt deposit shows
geologic or topographic features associated with various dissolution
phenomena. The Delaware Basin in New Mexico contains massive salt beds,
for example, but it has been estimated that this represents only about
(133)
half of the salt originally deposited there. In fact, essentially
all the salt in the Rustler Formation in that basin has been leached
out. Saline groundwater, springs, or streams associated with most salt
basins are further indications of continuing dissolution.
308
-------
TABLE D-1O7
SUMMARY OF BRECCIA PIPE FAILURE ELEMENT
MEDIUM
Bedded Seta
Gtenne
BeBlI
SMe
OomeSelt
PHCWABILIITIC (PI
DETERMINISTIC (Ol
f
NATURE
Of
MODEL
Annual occurrence
probebilltv.
N.A.
N.A.
N_A.
N.A.
RELEASE
MODE
Upeereqiiner
DRIVING
FORCE
ThermeUv induced
convection end
equifef imerconnec-
lion.
SOURCE
TERM
Ceniners in brecct*
pipe ettumed lo be
broken end subject
to leeching.
PARAMETERS
let ESTIMATE
* - Olort<500vTi
X . l(T«/vt for
t>600»r.
K - IO-2 cm/eec
1-0-2
A - 3 » 10* m'
2ml ESTIMATE
X . OlortSOOyn
K - 10-2 cnVsec
n • OJ
A • 3 » IO4 m^
FLUID FLOW RATES FROM
REPOSITORY TO UTTER AQUIFER
let ESTIMATE
tlynJ
600
1000
10.000
6 Im3(y»l
6« 107
S» 107
2 i 107
2nd ESTIMATE
t
-------
Because salt deposits can be massive (tens to hundreds of meters
thick, with some interbeds) and nearby groundwater flows may be
relatively low, dissolution may be an extremely slow process. In fact,
because salt is practically impermeable to the movement of water,
dissolution generally takes place only at the boundaries of the
deposits. Slow average rates of dissolution would not lead to breaches
of the repository for tens or hundreds of millions of years.
However, there are certain localized dissolution features that result
from much higher than average rates of salt removal. These features are
generally caused by the collapse of the overlying rocks into cavities or
voids in the soluble rocks below. Depending on the size and other
characteristics of these collapse structures, they are known by a
variety of names: kettles, sinks, swales, collapse chimneys, and breccia
pipes. The last two terms are used to denote structures that originate
near the bottom of soluble strata and extend toward the surface, being
somewhat taller than they are wide and filled with rubble (breccia) from
the overlying rock. Although the term "breccia pipe" is also used to
describe a distinct geologic structure of volcanic origin, some early
investigators of the dissolution phenomenon have used the term to
indicate collapse features with considerable vertical extent, and this
meaning is adopted here.
Physical Characteristics. Breccia pipes are roughly circular
features from a few tens of meters to more than 0.5 kilometer in
f 132)
diameter, with an average depth three times the diameter. The
upper portions are filled with broken rock ranging from small granulars
to blocks a meter or more across. (See Figure D-41.) These features
have usually been recognized only when they have reached the surface,
and limited tests have suggested that the pipes bottom near the lower
margin of the salt strata. Only a few not reaching the surface are
reported in the literature, although it is possible that many remain
undiscovered.
Sometimes, breccia pipes are seen as domes or topographic highs,
contrary to the general expectation for a collapse feature. One
hypothesis suggested to account for this structure is that dissolution
of the surrounding salt has lowered the elevation of the area below the
more resistant brecciated column. This process is enhanced by anhydrite
310
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MAGENTATS:
DISTANCE or
MAGENTA
COLLAPSE 1 •?
HORIZON 0» SU«ttCE
rciv i
H III BLANKET «*tCCi*.'.*AV4V*
AMI MECCIA
SURFACE EXPRESSION
COLLAPSED
OUTLIER
LEVEL OF PIPE IN
MISS CHEM CO MINE
(A = Anhydrite, H = Halite)
BELL CANYON
Source: Adapted from Anderson, R.Y. Report to Sandia Laboratories on Deep Dissolution
of Salt, Northern Delaware Basin, New Mexico, April 1978.
FIGURE D-41 CONCEPTUAL DRAWING OF BRECCIA PIPE IN DELAWARE BASIN
311
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in the breccia reacting with available water and catalyzed by bacterial
or organic processes to form calcite, which may be more resistant to
i , (133,135)
dissolution. '
Hvdrologic properties. Relatively few measurements have been
performed on the breccia filling the pipes to ascertain their hydrologic
properties. However, existing data indicate that very broad spectra of
porosities and permeabilities are possible. Pipes within the Carlsbad
mining district in New Mexico have shown properties ranging from those
of the intact evaporite section to those of typical gravels, with
hydraulic conductivities from 10 to 10 cm/sec and porosities from
20% to 1%.(104'133) At the time of formation, higher hydraulic
~3 (132}
conductivities are expected, in the range of 10 to 1.0 cm/sec.
Mechanisms of dissolution. When salt or other soluble material is
attacked by a solvent, the shape of the dissolved void and the direction
in which dissolution progresses depend upon a number of conditions. For
example, water in contact with the upper surface of a salt mass tends to
spread laterally. In the case of water reaching the lower boundary of a
salt mass, dissolution is upward, forming a vertical cavity, provided
relatively fresh water is supplied and brine is removed at the bottom.
These phenomena can be explained in terms of brine density. (See Figure
D-42.) Water in contact with salt dissolves the salt until it nears
saturation. The saturated brine is denser than undersaturated water and
tends to sink. If it is at the upper salt surface, the brine forms a
stratified layer at the interface, inhibiting further dissolution. On
the other hand, water dissolving the salt from below becomes saturated
with salt and sinks away, to be replaced with fresher water, promoting
further dissolution. This latter situation sets a convection cell into
motion (driven by density differences) , and the rate of convection can
be expected to increase as the water density differences are more
pronounced. Initially, the cavity thus formed at the bottom of the salt
is not large and is able to support itself. However, if dissolution
continues, the cavity may reach a critical size, become unable to
support the overburden, and collapse.
Implicit in this explanation for a dissolution mechanism developing
a vertical cavity is the need for sufficient hydraulic head to raise the
underlying water to the salt layer. Furthermore, fresh water must be
312
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(a) Dissolution from above.
Denser brine accumulates
and spreads out along top
of salt formation.
Saturation limits further
dissolution.
Water Saturated Rock
Brine Zone
Salt Bed
(b) Dissolution from below.
Density difference
between brine and fresh
water leads to convection
cell and transport of salt
away by lower aquifer.
Salt Bed
•V'.•".'•;./. ©•'-.-.
* * »\ s''
Fracture Pathway to Lower Aquifier
FIGURE D-42 CHARACTERISTICS OF DISSOLUTION FROM ABOVE AND BELOW SALT FORMATION
313
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supplied and saturated brine removed if dissolution is to continue at
any appreciable rate. Thus, an impermeable barrier separating the water
from the salt could effectively prevent cavity growth or propagation.
Detection of Breccia Pipes. Interest in detecting and surveying
breccia pipes and similar deep dissolution features is a relatively
recent development. In general, the earlier discussions of detection
methods (see Sections D-5.2 and D-5.1) apply to breccia pipes. The
generally small scale of these features, however, limits the
effectiveness of techniques such as gravitational, resistivity, and
magnetic surveys, except when such a feature is suspected. Seismic
investigations are better able to detect collapse structures,
particularly when the breccia or other filling material is characterized
by a different seismic velocity than the surrounding rock, or when the
collapse has disrupted a distinctive marker bed. The difficulties
presented by seismic work are typically related to the area that can be
investigated within an actual exploration program, and to resolution
loss with depth, which may limit interpretation of seismic records.
This is particularly true when attempting to detect breccia pipes in the
(22)
early stages of formation.
Finding breccia pipes within a large area may most easily be
accomplished through the use of aerial or Landsat photographs.
Domes, sinks, and other topographic relief can be located and selected
for further investigation on the ground. A number of pipes have been
detected in this way, and sites for more intensive seismic exploration
have been selected. The features seen on photographs are not all
collapse structures, and not all collapse structures are deep
dissolution features. Nevertheless, many apparent dissolution
depressions suggest a location deserving further study.
Of all the detection methods discussed previously, radar and
drilling may be the most precise for confirming the presence of breccia
pipes. Since radar works well in salt and could be used from
exploratory shafts and tunnels, it is likely that scanning the rock
below a repository site could detect any dissolution cavity in its early
stages. The reported effective range of radar is in excess of the salt
thickness in the generic repository model. Proponents of radar have
suggested that targets as small as a drill pipe can be detected at
314
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hundreds of meters; therefore, it is likely that natural brine-filled
cavities of a similar size could be discovered at a lesser range.
Drilling, while not an efficient method for detecting collapse
structures, may sometimes be necessary to confirm the indications of
radar or other detection methods. Drilling into a selected target would
confirm the existence of a breccia pipe and could be used to test the
Structural and hydrologic conditions of the feature.
D-5.5.3 Breccia Pipe Failure Model
The failure model for a breccia pipe consists of estimates of
hydrologic properties and probabilities of occurrence. As noted
earlier, bedded salt is the only medium to which this failure element
applies.
Probability of occurrence. The probability of occurrence of a
breccia pipe on the repository site is specified in terms of a constant
annual rate, A, after an initial period of 500 years during which the
probability is 0. An initial period of zero probability results from
the fact that it takes some time for a critical cavity to develop, and
if one were already at a significant stage of growth at the time the
repository was sealed, then it would have been detected by geophysical
techniques, such as radar, operating from the mine. The time required
(132)
for critical cavity growth is probably much larger than 500 years,
but this conservative value has been adopted to account for the
probability of waste (heat) induced acceleration of dissolutioning. The
values adopted are as follows:
_Q
First Estimate: A = 10 events/year/repository
for t >. 500 years
Second Estimate: * = 10 events/year/repository
for t L 500 years
The second estimate will be discussed first because the first estimate
was derived from it. It comes from previous studies ' and has
been normalized here to account for a different repository area. The
method used to derive this estimate can be briefly summarized as
follows. Information on areal densities of possible breccia pipes in
several evaporite basins was collected from the literature and from the
315
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study of aerial photographs. The volumetric rate of salt removal via
deep dissolution was then estimated, based on the time period during
which this dissolution has been occuring. By comparing this rate with
estimates of critical cavity size necessary for chimney initiation and
propagation at least to an upper aquifer, estimates of the rate of
formation were calculated. These numbers are comparable to estimates
developed in other more empirical surveys, based simply on the number of
features, basin area, and time period of dissolution
(132 133 135)
processes. ' ' Field investigation to determine whether the
features were deep seated was generally not carried out. While some
shallow features are surely included in the counts, there are probably
also deep features for which surficial indication was either not present
or not recognized. In spite of these limitations and sources of error,
the resulting rate still appears to be a reasonable "best estimate"
based on available data. This number was adopted as the second estimate
because it is assumed that the avoidance of features that could lead to
deep dissolution will have high priority in the repository site
selection process, and therefore a chosen site should be at least as
good as a randomly chosen one. (This would be the case, for example, if
the potential for deep dissolution is difficult to estimate for a
particular site.) The first estimate assumes that the structures
underlying a potential repository formation are simple and well mapped,
and that any underlying aquifers are heavily saturated with salt, slow
moving, at relatively low piezometric head, and well isolated from the
host salt formation in the vicinity of the repository. It is believed
that these conditions can be verified with sufficient certainty to
reduce the occurrence rate by two orders of magnitude, which leads to
the first estimate cited above.
Hydrologic processes. The following parameters have been chosen as
representative of conditions in a newly formed breccia pipe
_2
K = 10 cm/sec (hydraulic conductivity)
n - 0.2 (effective porosity)
4 2
A - 3 x 10 m (cross-sectional area)
The hydraulic conductivity is the value recommended in Reference 11 and
is in the range given in Reference 132. In fact, breccia pipes have a
tendency to heal over time, due to recrystallization of salt and
316
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cementation of the broken pieces of rock. Since dissolution is also
possible, depending on the available groundwater, healing has not been
assumed for the present model. The values of porosity and
cross-sectional area are also consistent with those in the literature.
D-5.5.4 Breccia Pipe Release Model
If a breccia pipe were to develop from underneath the repository.
eventually part of the repository would either slump or fall into the
chimney-like structure. Physical damage to the waste package would be
expected in this process, since the rock itself is generally rather
thoroughly broken. At this point the canisters would be subject to
leaching by groundwater circulating from and back to an aquifer below
the repository. The present model does not treat separately releases to
the lower aquifer. Rather, since chimney growth propagates rapidly, it
is assumed that a connection is established between upper and lower
aquifers, and that water flows upward, driven by both an aquifer
interconnection gradient and thermal buoyancy. The counterbalancing
effect of increased density from salt dissolution is difficult to
quantify; in the interest of bounding the flows, it has not been
included. Significant additional dissolution could in fact lead to the
leaching of a significant portion of the salt formation, and it is
probable that some sections of salt deposits that are known to have been
removed did so by this process. Nevertheless, field observation of
recrystallized and cemented breccia pipes through salt formations
suggests that in a carefully chosen site, this would be most unlikely.
As has been mentioned in the previous section, no healing of the breccia
pipe is assumed in the model.
Upward flows are calculated by Darcy's law using the parameters
given in the previous section and the hydraulic gradients given in Table
D-108. As in other sections, the version of Darcy's law here includes a
factor of 5 to account for the lower viscosity of water at elevated
temperatures. As was discussed in Section D-5.1.4, even as the
temperatures in the repository decrease after the thermal peak, this
factor does not appear to introduce excessive conservatism. Estimated
volumetric flow rates and fluid velocities are summarized in Tables
317
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TABLE D-108
EFFECTIVE VERTICAL HYDRAULIC GRADIENT IN A BRECCIA PIPE
FROM THERMAL BUOYANCY AND AQUIFER INTERCONNECTION
(BEDDED SALT REPOSITORY)
Hydraulic Gradient (i)
500 years*
1000 years
10.000 years
Thermal Buoyancy
First Estimate 0.11
Second Estimate 0.11
Aquifer
Interconnection
First Estimate 0.01
Second Estimate 0.50
Total
First Estimate 0.12
Second Estimate 0.61
0.10
0.10
0.01
0.50
0.11
0.60
0.03
0.03
0.01
0.50
0.04
0.53
Years after repository closure.
Source: First effect is from Appendix D-VI, interpolated to give values at
500 years. Second effect is from Chapter D-2.0 of this Report.
318
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D-109 and D-110, respectively. It is important to note that, as in the
case of faults, water limitations from the lower aquifer may
significantly reduce these flows. Therefore, in a real site, aquifer
capability may be the limiting factor, although it is not simply the
lower aquifer closest to the repository that needs to be considered.
The canisters in the breccia pipe include about 0.4% of the
repository inventory, based on the cross-sectional area given earlier,
and these are subject to direct leaching. Furthermore, any
radionuclides that had previously leached out of the waste packages
would also be washed out with the groundwater flowing through the
brecciated zone. It is assumed that an area with twice the diameter of
the pipe itself is affected by this process, so that the cumulative
leached inventory for 1.6% of the canisters should be assumed to be
released to groundwater upon the occurrence of the failure element.
D-5.5.5 Literature Discussion
One model used in the literature has already been referred to in Section
D-5.5.3. While there has been considerable recent geologic Interest in
learning more about the breccia pipe phenomenon, it does not appear that
other models for their occurrence or consequences have yet been
published.
D-5.6 OTHER NATURAL EVENTS AND PROCESSES
D-5.6.1 Introduction
In addition to the natural events and processes modeled earlier as
specific failure elements, other processes could have some impact on the
repository in a time frame much longer than the 10,000 year period used
as the principal focus for this study. No location on earth is expected
to be completely stable over very long periods (hundreds of millions of
years or more). Parts of the Appalachian Mountains were once low-lying
swamps, not unlike the Florida Everglades, and the Rocky Mountains also
arose from what must have been warm shallow seas. Not only have
319
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TABLE D-109
VOLUMETRIC FLOW RATES THROUGH A BRECCIA PIPE
(BEDDED SALT REPOSITORY)
Volumetric Flow (Q)
(m3/yr)
500 years 1000 years 10.000 years
First Estiamte 6 x 107 5 x 107 2 x 107
Second Estimate 3 x 108 3 x 108 3 x 108
*
Years after repository closure.
320
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TABLE D-110
FLUID VELOCITIES THROUGH A BRECCIA PIPE
(BEDDED SALT REPOSITORY)
First Estimate
Second Estimate
500 years
1 x 10
5 x 10
Velocity (v)
(m/yr)
1000 years
9 x 10
5 x 10
10.000 years
3 x 103
5 x 10A
Years after repository closure.
321
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tectonic forces raised such mountains, but. other forces have worn them
down. The ancient Appalachians once had peaks reaching 4000 meters,
roughly twice as high as at present. Some natural processes occur more
rapidly than the growth and decay of mountains; for example, glaciers
can come and go in a cycle of tens of thousands of years. The purpose
of this section is to survey a range of natural events and processes
that have not been modeled in detail in this study and to give some
indication of the rates at which they occur.
D-5.6.2 Erosion
The most prevalent natural process on land is erosion. Gravity is
the driving force, and wind, water, and ice provide the vehicles for
rapid movement of rock and soil.
Fluvial erosion (erosion by water) is the most important process at
work. No part of the United States is completely devoid of rainfall.
Rain striking bare earth dislodges soil fragments and suspends them
momentarily, moving them downhill with the general flow of water. When
water is confined to a stream or river channel, its greater volume and
velocity can move more and larger fragments greater distances. One of
the most dramatic examples of fluvial erosion is the Grand Canyon of the
Colorado River, which is roughly 20 kilometers wide and 1.6 kilometers
deep. It was incised during the last two to ten million years, with an
-4 -4
average rate of downcutting of 8 x 10 to 1.6 x 10 meters per
year. ' Although higher rates of erosion have been reported for
brief periods for unconsolidated sediments, this erosion rate of the
Colorado River is the highest for any major river system in the country,
as indicated in Figure D-43. At its sustained rate, the Colorado River
would require more than 500,000 years to strip away the overburden from
a repository located directly below the canyon. Since long-term
drainage patterns are fairly predictable, having remained largely
unchanged for millions of years, it is unlikely that river erosion would
be a serious concern for a repository even over a time span longer than
that considered in this report.
Glaciers, which are moving masses of ice, can remove great
quantities of rock and soil in a relatively short time. A glacier can
322
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Rates of Denudation (cm/1000 yrs.)
Source: Gilluly,J., A.C. Waters, and A.O. Woodford. Principles of Geology. 3rd edition.
W.H. Freeman and Co., San Francisco, 1968.
FIGURE D-43 AVERAGE RATE OF DENUDATION OF MAJOR DRAINAGE AREAS IN THE U.S.
323
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usually be classified as alpine or continental, depending on whether it
is confined to a mountain valley or covers a broader region. Glaciers
form when snowfall exceeds melting and evaporation, causing an
accumulation of ice. Eventually, the ice becomes thick enough for the
bottom layers to move plastically under the weight of the overlying ice
and snow. The ice freezes around rock and soil, breaking them free and
grinding them against the bedrock. These combined mechanisms of
breaking and grinding make a glacier an extremely aggressive erosional
force. Also, because a glacier is a relatively solid mass, it can alter
the course of streams and rivers by diverting or damming them. The
scablands of Washington and Idaho were formed when continental glaciers
diverted the Columbia River many times during cycles of ice advance and
retreat. The enormous weight of glaciers has apparently depressed some
regions up to several hundred meters, and rebound has also been
1 Q £
detected. ' ' It is possible that crustal adjustments for
depression and rebound could cause fracturing or renewed movement along
existing faults .
The alpine glaciers that carved California's Yoseraite Valley and
many of the valleys in the Cascade Range and the Northern Rockies,
gouging the land to depths of hundreds of meters, did so during their
relatively short (roughly 10,000-year) lives. The duration of these
valley glaciers is not well determined, since there was apparently more
than one episode of glaciation, nor is the erosional depth exactly
measured, since the original topography is not precisely known.
However, a rate of erosion can be estimated from the volume of material
carried off by meltwater streams. One such estimate for the Muir
Glacier in Alaska suggests that the average rate of erosion may be as
high as 1.9 cm/year. At this rate, 500 meters of rock could be
removed in 25,000 years. A study of two Icelandic glaciers determined
(137 139)
that their average erosional rates were 0.06 and 0.6 cm/yr. '
Between 6 and 60 meters of cover could be removed by such glaciers
during a 10,000-year ice age. Thus, a repository buried directly under
a valley prone to glaciation could be seriously Jeopardized within tens
of thousands of years after the onset of moving ice. While such times
are not much more than the time frame chosen for this study, the hazard
324
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can be eliminated by ensuring that a site is selected where there is no
expectation of alpine glaciation.
Continental glaciers, such as those that covered the northern
portions of the United States several times during the Pleistocene age,
account for more widespread erosion than do valley glaciers, but erosion
depths are harder to estimate. It is likely that their movement is
slower than valley glaciers' since the driving force would depend upon
differences in ice thickness between the glacier center and edge, rather
than the gradient of a valley floor. Rates of ice advance are more
difficult to establish than ice retreat since advancing ice often
obliterates evidence from which dates can be determined. Erosion by
continental glaciers is non-uniform and varies widely, but rates are in
general much less than for valley glaciers.
In addition to its erosional power, a glacier is expected to have
effects reaching far beyond the limits of the ice itself. For example,
the increased precipitation often associated with periods of glaciation
and the runoff of glacial meltwater can increase fluvial erosion in
advance of the ice. Furthermore, the presence of ice and accompanying
water will affect both surface and groundwater hydrology in a variety of
ways: diverting rivers, recharging aquifers, and forming lakes.
The timing of the next glacial epoch is speculative, at best.
However, the frequency of major glacial advances in the last several
million years suggests that another continental glacier is a real
possibility in less than 100,000 years, the average cycle time of ice
ages during the last 850,000 years. Thus, effects of a glacier upon
a repository could appear in a geologically short time. Nevertheless,
locating a repository some distance from the boundaries of Pleistocene
and recent glaciation, shown in Figure D-44, could provide adequate
long-term control against disruption of a repository from glacial
processes, if necessary.
The wind can transport fine sands and silts long distances and
against the general trend of fluvial erosion. However, the depth to
which the wind can erode is limited, especially compared with the
erosional power of water or ice. From the standpoint of a repository,
aeolian (wind) erosion is of little consequence, as it is essentially
unable to remove the overburden. The two more likely effects of the
325
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to
GLACIATED AREAS
GLACIAL LAKES
MIUS
0 160 321 482
KIIUMUtRS
|— t
FIGURE D-44 GLACIATED AREAS OF THE COTERMINOUS UNITED STATES
AFFECTED DURING PLEISTOCENE GLACIATION
-------
wind are stripping of vegetation at the site, which would increase its
susceptability to fluvial erosion, and obliteration of site markers and
survey points, which would increase the chances of the repository's
existence and location being forgotten.
D-5.6.3 Sedimentation
Sedimentation is the complement of erosion. Material removed from
one place is deposited in another. Final deposition is typically in the
ocean, but there may be many intermediate depositional stages, such as
stream beds, terraces, and sand dunes.
The effect of sedimentation on a repository is likely to be
positive. That is, any process that thickens the overburden and further
Increases the distance from the repository to the biosphere is likely to
aid the isolation of the wastes. However, some detrimental effects are
possible. Not only can extensive deposition obliterate site markers,
but the added weight of thick sediments can, by increasing the stress on
the buried rocks, induce fracturing or, in the case of less brittle
rocks, plastic deformation. Since it is expected that the repository
will be backfilled, the damage that could result from an extreme
increase in vertical stress is expected to be slight, and a general
compaction of the repository and its contents is most likely. Possible
displacement of the repository through differential sedimentation is
discussed in Section D-5.6.8.
D-5.6.4 Tectonism
Mountain building and the formation of continents, which involve
many related processes under the general description of tectonism, may
alter overburden thickness, ground and surface water patterns, erosion
rates, and permeabilities. Examples of tectonic phenomena include
faulting, folding, tilting, uplift, and subsidence. These structural
changes in the earth's crust are explained, for the most part, by two
compatible theories: continental drift and isostasy. Continental drift,
or plate tectonic theory, explains the forces necessary to cause
structural changes on the basis of collision between thin plates of
327
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crustal rock. While the relative velocities of the colliding plates are
very low, their huge masses produce extraordinary forces, sufficient to
rupture the crust. Since the deformation is primarily along the plate
margins, which are relatively specific locations, future folding,
faulting, volcanism, and the like are expected to be confined to these
limited margins, shown in Figure D-45.
The theory of isostasy views the continents as bodies of relatively
low density material floating on a dense mantle. If some portion of the
crust is higher than the rest, there must be a proportionally deep mass
of crustal rock below the rise to provide the necessary buoyancy, as
depicted in Figure D-46. If some process, such as erosion, alters the
land contour and hence the buoyant equilibrium, the crust will rebound.
A rebound in brittle rock may result in faulting, whereas rebounding
softer rocks can deform by folding.
Both theories suggest that deformation, by folding or faulting, will
be more likely in regions of previous tectonism and high relief since
these regions represent local areas of high stress in a state of
disequilibrium; either plate margins under compression or thick zones
of the crust. The importance of tectonic forces upon a repository
depends upon the rate at which structural processes may occur. Faulting
and folding may occur in the same settings and at the same rates.
However, faulting is perceived to be more consequential than folding
since folds may leave the overburden at its original thickness,
requiring considerable erosion to expose a deeply buried repository,
while a fault transecting a repository may raise it to the surface.
Therefore, the following discussion will focus on the possible results
of severe tectonic faulting. The possibility of a fault permitting
water that may have contacted the buried wastes to enter the biosphere
has been consided as a failure element.
It is also possible that repeated vertical displacement along a
fault could bring part of the repository itself to the surface. Using
an extreme rate of fault movement yields a conservative estimate of the
time required to exhume the repository. An example of a fault with a
rapid vertical displacement is the fault forming the east boundary of
Colorado's Front Range. This fault is approximately 20 million years
old and has moved roughly 1000 meters over that period. At that rate, a
328
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to
LEGEND
MAJOR EARTHQUAKES
OTHER SEVERE
?%% EARTHQUAKES
:••* VOLCANOES
Sources: Dewey. J.F., Scientific American. May 1972. Williams, H., Scientific American. November 1955.
FIGURE D-46 CRUSTAL PLATES AND REGIONS OF THE WORLD IN WHICH MAJOR EARTHQUAKES AND VOLCANOES OCCUR
-------
Note: Elevation of surface is reflected in deepening of crust.
FIGURE D - 46 ISOSTASY
330
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fault through the repository would require about 10 million years to
raise part of the repository to the surface.
It is possible that a fault could divert a stream or river course
and make the stream follow the trend of the fault, as the Snake River
follows the fault forming the face of the Teton Range in Wyoming. In
such a case, the combined river erosion and fault movement would reduce
the time before the repository might be exposed. However, this more
rapid mechanism would commence only after the creation of the
transecting fault. Given the very low probability of a new fault
occurring and the long time before the repository could be exposed, this
mechanism appears to be much less significant than the faulting failure
element discussed in Section D-5.1.
Earthquakes generally are the manifestation of movement along a
fault but, unlike a fault, their effects are felt over a wide area. In
examining the possibility of damage to a repository from quaking it was
found that damage is typically limited to surface structures and
features, and that damage to underground workings is slight, if present
at all. For open underground workings, damage from very strong
earthquakes was seen only in the portals and shallow tunnels. Deep
excavations showed no damage at all. A backfilled repository could be
expected to endure severe shaking with essentially no adverse effects.
D-5.6.5 Uplift and Downwarping
Relative movement of large regions, such as orogeny, or mountain
building, may contribute to a general degradation of the repository-
This degradation might occur through fracturing and faulting and changes
in the hydraulic regime surrounding the repository, in addition to the
tectonic mechanisms already discussed. The geologic record shows that
in the United States, present mountain ranges have arisen from the
remains of ancient mountains, and these areas would be most susceptible
to future uplifts. The time for such pronounced events as the emergence
of a mountain range or high plateau are moderately long, even in
geologic terms. For example, the Laramide orogeny, which created parts
of the Rocky Mountains, started in the Cretaceous period and has
continued into the Quaternary, spanning more than 50 million years. If
331
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such a long period is deemed appropriate in evaluating the performance
of a repository, the model of geologic failure elements previously
developed would require substantial changes to accomodate the structural
changes possible over such spans of time.
More immediate effects of changes in ground level would be shifts in
stream and river direction and the rate of stream erosion. However, as
has already been indicated, the presence of a stream near or over a
repository would not immediately affect the repository. The rate of
land tilt and stream shift would be so gradual as to be insignificant.
A region experiencing downwarplng or subsidence is likely to be
eroded more slowly than higher ground and may become a region of
deposition. In general, subsidence or deposition at or on a repository
is not a disadvantage and may increase the isolation of the contained
waste. A problem may arise, however, if subsidence and accompanying
sedimentation occur near a repository in salt. This is discussed in
Section D-5.6. 8.
D-5.6.6 Sea Level Fluctuations
The relative elevations of a repository and sea level can alter
conditions of erosion, sedimentation, and hydrology. Usually the "base
level" of erosion is sea level. Erosion does not generally occur below
that base level; instead, sedimentation takes place. The slope of land
toward the sea affects the rate of erosion, higher slopes having a
higher rate of erosion, as shown in Table D-lll. If the sea level were
to rise, a repository sited in a high plateau area may see a reduction
in the average slope (over the long run) and a corresponding decrease in
erosion. Conversely, lowering the sea level would lower the base level
of erosion and increase the gradient, increasing the rate of erosion.
However, for an inland repository site, the effects of changes in base
level would be slight, if apparent at all.
The most recent and best recorded sea level fluctuations have been
attributed to changes in the water volume of global ice caps. During
the last ice ages, sufficient water was withheld from the oceans to
produce an approximate 100-meter decline in sea level. Since then, a
general warming trend has prevailed. If this trend continues, the sea
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TABLE D-lll
ESTIMATES OF THE RATE OF EROSION UNDER VARIOUS
CONDITIONS OF CLIMATE AND RELIEF
Physiographic setting Estimated Rate of Erosion
(cm/1000 yrs)
Lowlands—Gradient - 0.001 or less
Hot moist climate with dry season 3.2
Climate with cold winter 2.9
Intermediate maritime climate 2.7
Equatorial climate (dense rain forest) 2.2
Hot dry climate (Mediterranean, New Mexico) 1.2
Mountains—Gradient « 0.01 or more
Hot moist climate (Guatemala-Mexico border) 92
Extremely snowy climate (Southeastern Alaska) 80
Semi-humid, near-glacial climate 60
High Mediterranean mountains 45
Hot dry climate (Southwestern 18
United States, Tunisia)
Source: Press, F. and R. Siever. Earth.
W.H. Freeman & Co.. San Francisco. 1974.
333
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level could rise as much as 50 meters. A repository less than 50
meters above present sea level would be inundated, but one higher than
50 meters would be relatively unaffected.
What may be most important to an inundated site is the effect on
groundwater with an advance of the ocean. Eventually, a layer of salt
water would spread over the repository and separate it from fresher
water floating on top, as shown in Figure D-47. Before equilibrium is
reached, however, the encroaching seawater may cause a reversal of the
previous groundwater flow on the site. However, the changes in gradient
and groundwater velocity would be expected to be slow and their effects
minor.
D-5.6.7 Climate
Of all natural processes influencing a repository, weather and
climate are the most variable and rapid. Climate affects virtually all
surface processes and, indirectly, many subsurface processes. The most
important characteristic of climate is precipitation, and its effect on
hydrology and on erosion and sedimentation.
Precipitation affects both surface and groundwater flows. Changes
in rates of infiltration and in the level of surface bodies of water can
modify the water table and the hydraulic potential throughout confined
and unconfined aquifers. Changes in hydraulic potential can alter rates
and directions of flows.
A more subtle influence of climate includes the types and density of
vegetation. Vegetation exerts some control on erosion and
sedimentation. As shown in Figure D-48, the amount of material stripped
from the surface actually decreases with increased rainfall. This is
because a protective cover of plant growth prevents raindrops from
striking bare soil and dislodging dirt. Also, plant roots and detritus
slow running water, entrapping soil being carried with the runoff.
More important for a repository, however, are the more dramatic
effects of climatic change. Glaciers, for example, are the result of a
shift in climate, and their disruptive effects have already been noted
In Section D-5.6.2. During the last ice age, glacial advances were
accompanied by an abundance of precipitation and a reduction in
334
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Land Surface
FIGURE D-47 FRESH WATER OVERLYING DENSE SEA WATER
335
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1000
800
T5 — .
"3 ju
> E
c £
E S
-
600
400
200
Desert
Shrub
Forest
10 20 30 40
Effective Precipitation (inches)
50
60
Source: Gilluly, J., A.C. Waters, and A.O. Woodford.
Principles of Geology, 2nd edition. W.H.
Freeman & Company, San Francisco. 1958.
FIGURE D - 48 EROSION RATES VS. PLANT COVER
336
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evaporation, giving rise to many lakes and ponds that have now dried
altogether or have shrunk to relative insignificance. Great Salt Lake
is the dessicated remnant of Lake Bonneville, which was deeper by 300
meters and covered roughly eight times the area of the present lake.
Another lake, Lake Missoula, was formed by an ice dam preventing normal
flow into the Columbia and Snake Rivers. Several times, when the dam
broke, the rush of water rapidly carved channels and formed giant
ripples in the lake bottom. A new glacial age could also bring about
the return of lakes such as Bonneville and Missoula. If these lakes
were to develop over a repository or over the recharge area of aquifers
passing through the site, decided changes in groundwater hydraulic
gradients could occur.
By selecting a site without indications of previous lacustrine
environment or where no geographic barriers form an enclosed basin, any
problems associated with future lake expansion can be minimized.
However, the importance of this site selection factor has not been
investigated quantitatively in this study.
D-5.6.8 Salt Diapirism
Because salt deforms plastically, it can be displaced, carrying a
repository with it. If the displacement is vertical, the repository
waste could actually be carried to the surface. The presence of salt
domes and anticlines in various parts of the country is evidence of the
fluid behavior of this rock.
Studies in salt tectonism have concluded that certain conditions are
essential before salt flow can proceed. ' ' Among these
conditions are an overburden of sufficient thickness to provide the
necessary stress differential for flow to start, and a salt bed thick
enough to react to the stress. While there is no clear minimum
thickness or depth, diapirism apparently needs a salt thickness of
300-400 meters and a burial depth of at least 2000 meters. The salt
thickness cannot increase after the salt deposit is formed, but the
depth of burial may increase with subsidence and sedimentation. For a
bedded salt formation under about 500 meters of cover, additional
deposits 1500 meters thick would have to accumulate before the onset of
337
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dlapirism. If deposition and downwarping of a region proceed at the
same rate, it may be possible to determine the minimum delay between
siting a repository in salt and the first salt flowage. The section of
the United States with the most rapid downwarping bounds the Gulf of
Mexico and has a average rate of approximately 5-10 mm/year. With
sedimentation keeping pace with this downward movement 150 thousand
years would elapse before the overburden would increase by the extra
1500 meters necessary even to start salt flowage.
Where salt diapirs have already formed, less or no added overburden
may be necessary to restart upward movement. Stabilized domes may be
either in static equilibrium or may have exhausted the supply of
underlying salt. In the latter case, no further movement is possible,
but in the former case, movement may be expected to keep pace with the
rate of sedimentation. For many of the salt domes of the Gulf Coast,
diapir growth appears to have occurred at about the same rate as
sedimentation. For these domes, the subsidence has increased the
distance between the top and bottom of the dome while maintaining the
top in nearly the same relation to sea level.
D-5.6.9 Salt Dissolution
High solubility is a distinctive property of salt. If water were to
have free access to salt containing a repository, eventually the
isolating rock would be dissolved away and water could attack the waste
directly. Both the bedded and dome salt deposits typically have caprock
deposits or dissolution surfaces indicating that part of the salt has
dissolved. Sometimes the salt has been lost from the entire formation;
other times the salt is lost along a horizontally moving front or
dissolution wedge. For some specific locations, the rate of salt loss
has been estimated. For example, approximately half of the salt
originally present in the Delaware Basin may have dissolved and a
dissolution wedge has moved eastward in one formation at a rate between
5 and 20 miles per million years. ^ Similarly, the Palo Duro Basin
has active dissolution fronts moving horizontally on the order of
centimeters per year and vertically at the rate of a few millimeters per
year. Very large volumes of caprock mantle some salt domes. These
338
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thick caprock deposits can indicate that as much as 6000 vertical meters
of salt dissolved from a single dome, although lesser amounts of salt
loss are more common. In some locations within the Salina Basin and the
Michigan Basin, salt beds have disappeared entirely, with remnant gypsum
indicating their previous presence. Since the rate of salt loss is
controlled by local conditions and is a continuous process, the time
that would be necessary for the dissolution of a significant quantity of
salt can and should be determined from site-specific data rather than by
repository model parameters.
339
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78-591. 1978.
112. Bechtel National, Inc. Regional Characterization Report for the
Paradox Bedded Salt Region and Surrounding Territory. For Office
of Nuclear Waste Isolation, Battelle Memorial Institute, Columbus,
Ohio. ONWI/SUB-78/42507/1. May 1978..
113. The Analytical Sciences Corp. (Giuffre, M. S. et al-)« Information
Base for Waste Repository Design, Vol. 5: Decommissioning of
Underground Facilities. For U. S. Nuclear Regulatory Commission.
NUREG/CR-0495; TR-1210-1. March 1979.
114. Bechtel National, Inc. Regional Environmental Characterization
Report for the Gulf Interior Region and Surrounding Territory. For
Office of Nuclear Waste Isolation, Battelle Memorial Institute,
Columbus, Ohio. ONWI/SUB-78/512-01600-1. November 1978.
115. Louisiana Power and Light Co. Preliminary Safety Analysis Report,
Waterford Steam Electric Station, Units 3 and 4. Docket 50382-2.
January 1971.
116. Macdonald, G. A. Volcanoes. Prentice Hall, Inc., Englewood
Cliffs, N. J. 1972.
117. Civetta, L. et al., eds. Physical Volcanology. Elsevier Scientific
Publishing Co., New York. 1974.
353
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118. Catalogue of Active Volcanoes of the World. International
Volcanological Association, Naples, Italy. 1955.
119. U. S. Geological Survey (White, D. E., and D. L. Williams, eds.).
Assessment of Geothermal Resources of the United States. USGS
Circular 726. 1976.
120. U. S. Geological Survey (Millineaux, D. R. ). Preliminary Overview
Map of Volcanic Hazards in the United States. USGS Miscellaneous
Field Studies Map, MF 786. 1976.
121. Nevada Operations Office, U. S. Department of Energy. Nevada
Nuclear Waste Storage Investigations, July through September 1979.
NVO-196-12. December 1979.
122. Fowler-Billings, K., and M. P. Billings. Geology of the Gorham
Quadrangle, New Hampshire - Maine. N. H. Department of Resources
and Economic Development Bull. 6. 1975.
123. Geology Society of Great Britain. Geological Map of Great Britain,
Second Edition. 1957.
124. Bowen, N. L. Evolution of Igneous Rocks. Princeton University
Press, Princeton, N. J. 1928.
125. Shelton, J. S. Geology Illustrated. W. H. Freeman & Company, San
Francisco. 1966.
126. U. S. Geological Survey (Maldonado, F. ). Summary of the Geology
and Physical Properties of the Climax Stock, Nevada Test Site.
USGS Open-File Report 77-356. 1977.
127. Eaton, J. P., and K. J. Murata. How Volcanoes Grow. Science
132:925. October 7S 1960.
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128. Battelle Pacific Northwest Laboratory (Scott, B. L. et al.). A
Summary of FY-1978 Consultant Input for Scenario Methodology
Development. For Office of Nuclear Waste Isolation PNL-2851.
November 1979.
129. Hartmann, W. K. Cratering in the Solar System. Scientific
American 236:84. January 1977.
130. Grieve, R. A. F., and P. B. Robertson. The Terrestrial Cratering
Record. Icarus 38:212. 1979.
131. Hughes, D. W. Earth's Cratering Rate. Nature 281:11. September 6,
1979.
132. Geotechnical Engineers, Inc. Geological Studies Pertinent to Site
Suitability Criteria for High-Lev el Waste Repositories. For
Lawrence Livermore Laboratory, UCRL 13741. May 25, 1977.
133. Anderson, R. Y. Report to Sandia Laboratories on Deep Dissolution
of Salt, Northern Delaware Basin, New Mexico. April 1978.
134. Swenson, E. A. Rates of Salt Dissolution in the Permian Basin.
USGS J. of Research 2:253. 1974.
135. Personal Communication, Thomas Gustavson, University of Texas.
December 1979.
136. Brochie, J. F., and R. Sylvester. On Crustal Flexures. J.
Geophysical Research 74: 5240. 1969.
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New York. 1971.
138. Reid, H. F. Studies of Muir Glacier, Alaska. National Geographic
Magazine 4:19. 1892.
355
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139. Okko, V. Glacial Drift in Iceland, Its Origin and Morphology.
Comm. Geol. de Finlande Bull. 170:133. 1955.
140. Rozen, A. Response of Tunnels to Earthquake Shaking. S.M.
Thesis, Massachusetts Institute of Technology. 1976.
141. Ewing, M., and J. Ewing. Rate of Salt Dome Growth. American
Association of Petroleum Geologists Bull. 46:708
142. Press, F., and R. Siever. Earth. W. H. Freeman & Company, San
Francisco. 1974.
143. Landes, K. K., et al. Geology of the Mackinac Straits Region.
Michigan Geological Society, Publ. 44. 1945.
356
-------
APPENDIX D-I
GLOSSARY
-------
APPENDIX 0-1
GLOSSARY
Andes!tic
Anticline
Aquiclude
Aquifer
An 1sotrophy
Argillaceous
Barlte
Basalt
Batholith
Breccia
Andesitic refers to volcanoes and related features
with composition part way between basalt and
silicic rock, suggestive of the mixture of wet
basalt and continental rocks at a plate subductlon
zone *
A geologic structure having rock folded into an
arch. The opposite is a syncline which has the
rock folded downward into a trough.
A relatively Impermeable geologic formation which
effectively prevents the passage of water.
Contrasts with an aquifer.
A rock formation or stratum of relatively high
permeability that may readily yield or transmit
water-
Having properties which are not the same in all
directions.
Clay bearing. Here argillaceous is used to
describe any of a range of sedimentary rocks with
clay as a major constituent, including shale,
mud stone, argilllte, and slltstone.
Barium sulfate, BaSO,. A dense mineral and chief
source of barium, barite Is used in the deep
drilling industry as an additive to drill mud to
increase its density. This helps to buoy the
weight of a long drill string and to increase the
pressure at the bottom of the hole which assists
in preventing blow-outs.
A dense, dark, hard, fine-grained igneous rock
containing iron and magnesium rich minerals and
lacking free silica. In this study, basalt is
taken to be a family of fine-grained Igneous rocks
without specifying a particular mineral
assemblage.
A body of intrusive igneous rock larger in area
than 100 km.
Broken rock with fragments larger than sand.
1-1
-------
Breccia Pipe
Catalysis
Cement with Fine
Fillers
Connate Water
Creep
Critical Cavity
Criticality
Crust
Crystalline Rock
Darcy's Law
A geologic structure steep sided and roughly
circular in plan composed of breccia. In the
context of this report, a breccia pipe is a
feature in salt formed by the collapse of
overlying rock into a cavity formed by
dissolution.
The modification of the rate of a chemical process
through the use of an agent which is not consumed
in the process .
Portland cement or similar material mixed with
clay and silt-sized inert particles instead of
coarser aggregates.
Water entrapped in a rock at the time of its
formation. Contrasted with meteoric water.
Slow plastic or viscous fluid deformation of rock
under stress.
The maximum void or cavity in rock salt able to
support itself. Cavities larger than the critical
cavity will experience the fall of rock blocks or
breccia into the cavity.
The conditions necessary for a self sustaining
nuclear chain reaction to start or continue.
Criticality is reached when a necessary quanitity
of nuclear material is brought and held in close
proximity.
The exposed rocks of the earth. The relatively
rigid outer layer of the earth exhibiting
relatively slow seismic velocities. The crust
varies in thickness from about 60 km under certain
mountainous parts of the continents to about 5 km
under the oceans.
Referring to igneous or highly metamorphic rocks
composed of minerals with crystals large enough to
be distinguished by the unaided eye.
A mathematical description of laminar fluid flow
through a permeable medium, to the effect that
flow is proportional to the hydraulic gradient*
In particular, Q = KiA, where Q is the volumetric
flow rate through a surface of area A, orthogonal
to the flow, under a gradient i. A factor c(y)
must also be included when viscosity can vary
significantly.
1-2
-------
Diapir
Differential Stress
Dike Swarm
Drilling Mud
Drill String
A geologic structure formed by the forceful
intrusion of one geologic material into overlying
material, especially the non-igneous intrusion of
a relatively plastic or fluid material, such as
salt •
Stress differences in different directions.
A cluster of dikes oriented roughly parallel or
radiating from a common point. Parallel dike
swarms are noted in the British Isles and the
Pacific Northwest. Radial swarms are common near
volcanic centers.
Fluid used to cool and lubricate the bit of a rock
drill and to float the cuttings to the surface.
Muds may be water or organic fluid based with a
number of possible additives including clays,
starches, and density modifying materials.
A length of steel pipe segments joined together
and used to operate a drill bit suspended below
the surface.
Evaporite
Fault
Felsic Rocks
First Estimate
Graben
Gravity Fault
A rock or mineral deposited when the waters in
which it was dissolved evaporated. Common
evaporites include salt, gypsum, sulfates, and
potash salts.
A fracture showing displacement of the material on
either side along the plane of the break. Faults
are distinguished from joints, the latter showing
no relative displacement.
Igneous rocks composed primarily of feldspars and
free silica (quartz), such as granite.
In this study, the conditions or event
probabilities appropriate to a repository site
selected for its particular advantages regarding a
specific criterion. For example, a first estimate
with regard to abandoned boreholes would assume a
site with no history of deep well development and
conditions unfavorable for gas or oil reserves.
A block of rock bounded by parallel gravity faults
which has moved downward in relation to the blocks
on either side.
A synonym for a normal fault. A sloped geologic
fracture along which the overlying (hanging wall)
rocks have apparently moved downward with respect
to the underlying (foot wall) rocks.
1-3
-------
Head
Horst
Hydraulic Conductivity
Hydraulic Gradient
Igneous rock
Incompetent Rock
Indurated
Intrusion
Joints
Lithology
Lithostatic Pressure
Magma
Hydraulic pressure represented by a column of
water of a given height.
The counterpart of a graben. A fault-bounded
structure which has moved upward in relation to
the rocks on either side.
The coefficient of proportionality, K, in Darcy's
Law. In this report, it is used synonymously with
permeability.
The rate of change in hydraulic head with respect
to distance.
A rock formed by the cooling of melted rock.
Rock unable to support itself or an applied force.
In engineering, incompetent rock requires
additional support.
Solidified into a massive rock. Usually used to
describe sediments which have hardened into rock,
e.g. indurated clay is shale or mud stone.
A rock body forcibly injected into pre-existing
rock or soils. Generally intrusion denotes an
igneous rock which invaded surrounding rock but
never reached the land surface.
Fractures or separations in a rock having no
apparent displacement parallel to the plane of the
fracture.
The character of rocks and rock formations,
particularly their gross features such as
structure, color, mode of emplacement, fossil
content, and stratigraphy. Also, the study of
rocks.
Pressure applied by the weight of the overlying
rock. Lithostatic pressure at a given depth can
be estimated by multiplying the weight density of
rock by the depth below the surface.
Melted rock beneath the earth's surface.
1-4
-------
Mantle
Metastable
Mine Drift
Montmorillonite
Near Field
Neat Cement
Normal Fault
Permeability
Petrography
Piezometric Head
The layer of the earth between the core and the
crust, starting about 3400 km from the center.
The mantle has higher seismic velocities than the
crust and is apparently composed of dense iron and
magnesium rich rocks.
Temporarily stable. Metastable is used to
describe minerals or other phenomena which are not
in equilibrium with their surroundings but which
require a finite disturbance to initiate a change
toward equilibrium. A typical example is a
supercooled liquid which remains liquid until made
to solidify upon the addition of a grain of the
solid phase. Metastable is not synonomous with
unstable which denotes a shift toward equilibrium
without the addition of energy or a disturbance.
A tunnel or horizontal mine opening. Particularly
a blind tunnel not connecting to others at one
end.
A clay mineral (hydrous aluminum silicate),
generally the weathering product of lava, with the
capacity to readily absorb water between crystal
layers causing marked expansion.
Within the vicinity of the waste or the repository
tunnels. Near field effects are those caused by
the presence of the waste or the repository and
are contrasted with far field effects which are
essentially unrelated to the repository or its
contents .
Portland cement mixed without fillers or aggregate
and generally used as a grout or sealing agent.
Synonym for gravity fault. An inclined fracture
along which the rocks above have apparently moved
downward with respect to the rocks below.
A measure of the ease with which a fluid can pass
through the continuous voids of a material. (See
hydraulic conductivity.)
Description of a rock including mineral
composition, grain size and shape, fabric, and
evolution.
The height to which water in an aquifer rises or
could rise if penetrated by a well. The hydraulic
head.
1-5
-------
Planar
Plastic
Pluton
Poise Units
Polymerization
Productive Horizon
Resaturation
Second Estimate
Shale
Shear Stress
Silicic
Forming a plane or flat surface. Used here,
planar describes features or structures which are
wide, long, and roughly uniform in thickness.
Capable of being permanently deformed without
rupture.
A body of intrusive igneous rock.
A measure of fluid dynamic viscosity. 1 poise =
1 gm/cm-sec.
Formation of long chain molecules from short
molecules. Through polymerization, certain light
volatile molecules combine to form more rigid
dense ones.
A stratum from which mineral wealth is recovered;
especially a stratum from which petroleum or gas
is taken.
The filling of a repository with water. If a
repository is partially back-filled with rock
materials, resaturation denotes the filling of the
void spaces within the backfill.
In this study, conditions appropriate for a
repository sited in circumstances unfavorable in
regard to a specific criterion. For example, a
second estimate for undetected abandoned boreholes
would assume a site within a long abandoned gas or
oil field.
Sedimentary rock formed from clay and silt and
that is laminated and fissile. In this study,
shale is intended to denote all fine-grained clay
rich clastic sedimentary rocks including
argillites, mudstones, siltstone, graywacke, and
so forth.
A stress or force acting to cause slippage of two
adjacent parts of a body past one another.
High in silica. Silicic refers to silica rich
magmas which are typically viscous, and confined
to regions of continental crust, suggesting that
they are the result of reraelting of crustal rocks.
Typical rocks from silicic magmas are granites,
granodlorides, and their fine-grained equivalents.
1-6
-------
Sonde
Source Term
Spall
Stochastic process
Stock
Stratum
(PI. Strata)
Stress
Subcircular
Subduction
Subparallel
Tectonic
Thermally Induced
Buoyancy
Uniform Concentration
A device to obtain and transmit remote
measurements. A borehole sonde may be used to
determine the properties of rock penetrated by the
hole.
The quantity and composition of radioactive waste
contained in a repository or subject to release by
a particular breach mechanism.
To fracture concentrically, to form "onion skin"
joints where movement is largely perpendicular to
the plane of the fracture.
A process or model whose evolution over time is
governed by probabilistic factors.
An igneous intrusive which is smaller than a
batholith, steep sided, and assumed to be
cylindrical or widening with depth.
A layer of rock, especially a layer of uniform
characteristics distinguishable from overlying and
underlying strata.
A force acting to deform, usually measured as
force per unit area; may vary with direction.
Not circular in the mathematical sense but
describing a figure which is closed and convex,
approximately circular, as the cross section of a
tree trunk is subcircular-
The forcing down toward the mantle of the earth of
crustal rocks at the junction of two colliding
crustal plates.
Not parallel in the mathematical sense but near
enough to parallel that linear features do not
actually intersect.
Pertaining to the earth's broad structural
features.
Upward forces brought on by expansion of material
when heated resulting in a lower density than that
of the surrounding material. The low density
material will tend to rise through the denser
material.
Average concentration of radionuclides in
backfilled repository as a result of gradual
leaching from waste packages. May be limited
either by leach rates or by solubility limits.
1-7
-------
U-Tube Effect A term to describe water movement through a
repository involving water entering from an
overlying-aquifer at the upstream side of the
repository and returning to the aquifer at the
downstream side.
Virgin Rock Rock which is unaffected by drilling or mining.
Waste Drift A mine tunnel or drift containing waste.
1-8
-------
APPENDIX D-II
REPOSITORY RESATURATION TIMES
-------
APPENDIX D-II
REPOSITORY RESATURATION TIMES
A. INTRODUCTION
Many of the mechanisms that permit the transport of radionuctides'
from the repository to the upper aquifer require that the hydrologtc
system be in a saturated condition. Before repository construction,
essentially all the rock helow the water table (defined in the generic
repositories by the level of the upper aquifer) is saturated with water
at pressure at least equal to hydrostatic pressure. (See Figure
D-II-1).
The excavation of the repository disturbs this saturation because
water flows from the surrounding rock into the resultant cavity, as
shown in Figure D-II-2. During the operational phase of the repository,
this water, if significant, will be pumped out, as is commonly done
during mining operations. After the backfilling and closing of the
repository, water flowing down the filled shafts and/or in through the
rock walls will gradually fill the pores of the backfill until
saturation is again established. The purpose of this discussion is to
estimate the time required for such "repository resaturation" to take
place.
B. SIMPLIFICATIONS
The repository will be modeled as a rectangular solid with base area
AR, height h, mined fraction M, and backfill porosity 1. Thus, the
volume of pore space needing to be resaturated is:
For the present calculations, the following values will be used
A. - 8 km2 - 8 x 106 m2
II-l
-------
X
X
X
X
X
X
X
X
X
X
X X
X X
Siitui
X X
X X
X
X
illlHl
X
X
X
X
/OIM!
X
X
X
X
X
X
X
X
X
X
X
X
Liitul surface
Top of upper ;u|uit
-------
5 m
M - 0.25
n = 0.2 .
6 3
These values lead to a pore volume V = 2 x 10 m". Resaturation also
requires filling of the pores in the unsaturated zone of rock
surrounding the repository and in the backfilled (or sealed) shafts and
boreholes. These latter volumes are negligible in relation to the pore
volume of the repository cavity and so will be omitted from the
analysis. The resulting calculation is conservative, in that it will
predict recharge slightly earlier than in the real case.
The flow into the mined repository is driven by a pressure gradient.
The repository is initially at atmospheric pressure while the water in
the surrounding rock exceeds this by its corresponding hydrostatic
pressure. This hydrostatic pressure will be modeled as that from a
column of water extending to the top of the upper aquifer- The pressure
in the repository would gradually rise during recharge, thereby
decreasing the effective gradient. However, for the sake of these
simple conservative calculations, this effect will be ignored. For
flows through the rock itself (as opposed to flows through permeable
shafts or boreholes), it will be assumed that recharge also occurs
through the bottom of the repository and that this is equal to recharge
through the top. With respect to the latter, it will be assumed to
occur through the column of rock immediately above the repository. Edge
effects are assumed to be insignificant and, in any case, more than
balanced by the conservative assumption of equal flow up through the
floor.
C. OUTLINE OF COMPUTATIONS
The outline of the steps in the calculation of recharge times is
shown in Figure D-II-3. To illustrate the steps, several preliminary
calculations will be carried out below.
II-3
-------
SI
Oi'tt'imiiio hytliaulii:
tliadiunl (liivini) iiH:liai<|r
S2
Dclui mino total flow
rato into repository via
all pathways
S3 Determine cumulative
inflow as a function
of time
S5 Determine the time at
which cumulative inflow
reaches required volume
S4 Determine water
volume necessary to
saturate repository
FIGURE D-ll-3 COMPUTATIONAL SEQUENCE FOR RECHARGE TIMES
II-4
-------
1. Two repository-aquifer distances are represented among the generic
repositories. For bedded salt, shale, and basalt, the top of the
upper aquifer is 130 meters above the repository. This determines
the driving hydrostatic head. The head is essentially dissipated
entirely over the 100-meter barrier layer, so that the effective
gradient is:
-12JL
100
In the case of granite and dome salt, the gradient is:
230
2. Total flow rate into the repository is assumed to be the sum over
all possible recharge pathways. Each pathway is characterized by a
permeability (which may vary with time) and a cross-sectional area.
In the case of shaft recharge, the permeabilities are based on
Section D-3.2. For the first estimate, K degrades linearly from
10 cm/sec to 10 cm/sec over 10 years. The permeabilities are
more convenient to deal with in units of meters per year, to which
the conversion is accomplished by multiplying by 3.15 x 10 . The
—3 —1
linear degradation from 3.1*5 x 10 m/yr to 3.1") x 10 m/yr
corresponds to the equation:
K(t) = 3.15 x 10~3 + —
104
3.15 x 10~3 -t- 3.12 x 10~5 t (m/yr)
—8
For the second estimate, K degrades linearly from 10 cm/sec to
-4 4
10 cm/sec over 10 years. In this case, one obtains:
II-5
-------
K(t) - 3.15xlO-+--
10*
3.15 x 10~3 + 3.15 x 10~" t (m/yr)
The total cross-sectional area of the shafts will be taken as 100
2
m (e.g., four shafts, each of which is 5 m x 5 m).
In the case of borehole recharge, the first estimate calls for
degradation from 10 cm/sec to 10 cm/sec over 10 years, which
is represented by the equation:
K(t) - 1.15 x 10~3 + 3.15 x 10"4 t (m/yr).
ft /
For the second estimate, degradation from 10 cm/sec to 10
4
cm/sec over 10 years, is given by:
K(t) = 3.15 x 10~3 + 3.15 x 10~3 t (m/yr).
Each borehole has a cross-sectional area of 0.1 m".
•
3. The output of Step 2 is a function Q(t) representing the rate of
flow into the repository at time t. This rate is calculated by
Darcy's law:
100M
where v is the water viscosity at the ambient temperature in the
rock. For these calculations, u will be conservatively taken as
•
0.002 poise so that Q has the form:
5 KiA
for each pathway. The integral of this function from 0 to t gives
the cumulative inflow by time t.
II-6
-------
4. The required water volume has already been calculated to be
V = ARhMn
which has the numerical value
V - 2.0 x 106 m3
for the parameter values that have been adopted. This represents
the initial pore space at the time of repository sealing. Tn the
case of salt, which is a plastic medium that tends to flow under
applied stress, the pore space will decrease as a function of time
due to the overburden pressure. The modeling of creep behavior is
discussed in greater detail in Appendix D-VII, where representative
numerical results are estimated. For the present calculations, the
pore space has been assumed to decrease linearly to 0 (an
approximation) over a certain period following sealing of the
repository. For first estimate calculations, this period has been
taken to be 200 years. For second estimate calculations, this
period has been taken to be 1000 years. The slower rate of creep
represents a less desirable situation with respect to this
mechanism because more water can enter the repository before the
salt has effectively sealed itself tight.
5. The equation:
Q(t) = V
is solved for t in order to determine the recharge time.
D. BEDDED SALT RESATURATION TIMES
For a repository in bedded salt, resaturation would generally be
restricted to two sets of pathways: permeable shaft and borehole seals.
II-7
-------
The bulk rock permeability is too low to contribute significantly to the
inflow.
First estimate. Using parameters given earlier, the Inflow due to
shafts is given by:
QL - 5 KiA
- 2.048 + 0.02048 t
so that the cumulative amount of water present is:
Q - 2.048t + 0.01024 t2 .
Similarly, assuming 60 borehole pathways (50 to upper aquifer, 10 to
lower), they contribute an amount of inflow given by:
i$ - 0.123 + 0.0123 t
so that the cumulative amount of water present is:
Q2 - 0.123t + 0.00614 t2 .
Since the pore space in the first estimate case is given by:
Q - (2 x 106)(200 - t)/200
for t between 0 and 200 years, resaturation Is achieved at the time t
which satisfies the equation:
Q - Qx + Q2 .
II-8
-------
This value of t is approximately 200 years (199.883) and the
3 3
corresponding water volume is 1.2 x 10 m" (1171).
Second estimate. Second estimate parameters lead to the formulas:
•
Qj_ = 2.048 + 2.048t
Q1 = 2?048t + 1.024 t2
•
Q2 = 0.123 + 0.123t
2
Q2 = 0.12^t + 0.061 t
(2 x 106)(1000 - O/1000
The resaturation time in this case is approximately 720 years, with a
5 3
corresponding water volume of 5.6 x 10 m .
E. GRANITE RESATURATION TIMES
For a repository in granite, there are three sources of inflow:
permeable shaft seals, permeable borehole seals, and flow through the
bulk rock. Because the cross-sectional area for flow through the bulk
rock is so much larger than for shafts and boreholes (almost five orders
of magnitude), and because this difference is not balanced by a
correspondingly lower permeability, the flow through the bulk rock
dominates.
The permeability values given in Section D-3.1 for the first
estimate case lead to the formulas:
Q = 5 KiA
3 3
= 2.8 x 10" m /yr for t < 100 yr
- 2.8 x 104 m3/yr for t 1 100 yr
7 3
The value of A used here is 1.6 x 10 m , twice the area of the
repository, to account for recharge from both above and below the
II-9
-------
repository. The cumulative inflow by 100 years after repository closure
is thus:
Q(100) = 2.8 x 103 x ]02
= 2.8 x 105 m3
In order for resaturation to be complete, an additional inflow equal to
f O
1.72 x 10 m is necessary, in order to give the required total of 2 x
10 m . At the rate of 2.8 x 10 nf /yr, this would take an additional
61 years, so that the resaturation time would be approximately 161
years .
For the second estimate case, the inflow over the first 100 years is
Q = 2.8 x 105 m3/yr
so that resaturation takes place almost immediately, i.e., about 7 years
after closure. Since the calculated value is so small, it does not
extend into the peak thermal period. Therefore, the conservative
viscosity assumption (0.002 poise) is overly conservative. This
observation also applies to subsequent calculations, but since the times
would be rather short in any case, there is no need for a more refined
calculation.
F. BASALT RESATURATION TIMES
As in the case of granite, the dominant inflow for resaturation is
through the bulk rock.
The parameter values given in Section D-3.1 for the first estimate
case lead to the inflow rate:
Q = 3.3 x 10 4 m3/yr
over the first 100 years, which implies resaturation at about 61 years
after repository closure. In the second estimate case, the permeability
11-10
-------
is two orders of magnitude higher, so that resaturation takes place in
less than one year (0.6 year).
G. SHALE RESATURATION TIMES
The parameters that govern resaturation times are identical to those
for basalt. Therefore, the first and second estimates of resaturation
times for a repository in shale are 61 years and 0.6 years,
respectively.
H. DOME SALT RESATURATION TIMES
The analysis of resaturation of a repository in a salt dome is
similar to the case of bedded salt. There are two parameter changes to
be accounted for. First, since there is no lower aquifer immediately
below the repository, only 50 borehole pathways should be included.
Second the vertical gradient in shafts and boreholes is 1.1 instead of
1.3. Using the same notation as earlier, the first estimate
calculations yield the functions:
Qj = 1.73t + 0.0086 t2
Q = 0.086t + 0.004 t .
Since the pore space is
(2 x 106)(200 - t)/200
for t between 0 and 200 years after repository closure, resaturation is
again achieved at the time t which solves the equation
Q - Q! + Q2 •
This value of t is approximately 200 years (199.91) and the
corresponding water volume is 865 m .
11-11
-------
Similarly, for the second estimate, the following functions apply:
Q = 1.73t + 0.86 t2
Q2 = .086t + 0.04 t2
Q = (2 x 106)(1000-t)/1000 .
The result is a resaturation time of 748 years with a corresponding
water volume of 5.0 x 10 m .
I. SUMMARY OF CALCULATIONS
Resaturation times calculated earlier are summarized in Table
D-II-1.
J. QUALIFICATIONS
The numerical results of this section have been derived under a set
of specific assumptions and parameter values. Depending on the manner
in which the repository is designed, the resaturation times calculated
here may or may not be reasonable estimates of the time before which
certain release mechanisms can become operative. A particularly
complicating factor is the fact that engineering choices which may add
to repository integrity with respect to one breach mechanism may detract
from its integrity with respect to another. Examples of this are
discussed below.
Porosity of backfill. Since the rate of inflow to the repository is
fixed by the pathway parameters, the recharge time will be increased if
the volume V of water required to saturate the repository is increased.
7 3
The limiting case of no backfill yields a volume V = 10 m and hence
recharge times five times as long as those calculated above.
Nevertheless, the use of highly porous (and hence permeable) backfill
would aid the movement of radionuclides through the repository should
some breach pathways be established.
11-12
-------
TABLE D-II-1
CALCULATED RESATURATION TIMES
Medium First Estimate Second Estimate
(yrs) (yrs)
Bedded Salt 200 720
Granite 161 7
Basalt 61 0.6
Shale 61 0.6
Dome Salt 200 748
11-13
-------
Bulkheads. It is possible that the repository designs will include
sealing off waste drifts and segmenting tunnels with carefully
constructed bulkheads. These measures will reduce the potential for
water and radionuclide transport through the repository. At the same
time, if these barfiers are essentially impermeable, they also seal off
portions of the repository from certain inflow sources, such as
permeable shafts and boreholes. The result will be that the segments of
the repository which include (or are close to) the water sources may
become resaturated rather soon. In this case, mechanisms for hydrologic
transport of radionuclides may become operative sooner than envisioned
from the times calculated earlier. For repositories in which
resaturation through the bulk rock dominates, this factor is not
important.
K. CONCLUSIONS
While resaturation mechanisms may delay the initiation of potential
radionuclide transport from the repository, for the reasons cited in the
previous section it is recommended that considerable care be exercised
in applying credit for this delay in assessing repository performance.
It is a matter that should be investigated when specific repository
plans are being evaluated, at which time the uncertainties may be
sufficiently resolvable to allow greater credit for this factor in the
repository performance assessment.
11-14
-------
APPENDIX D-III
METHODOLOGY FOR DISSOLUTION CALCULATIONS
-------
APPENDIX D-III
METHODOLOGY FOR DISSOLUTION CALCULATIONS
A. INTRODUCTION
The dissolution mechanisms discussed here apply exclusively to
repositories in salt. Similar problems do not arise with the other host
rocks under consideration.
Breach mechanisms that permit water to flow from a repository in
salt to an aquifer may develop either by gradual processes (e.g., shaft
seal degradation) or abrupt events (e.g., faulting). In either case,
the water may dissolve and carry off some of the salt, thereby perhaps
worsening the breach. The harmful effects could consist of the
formation of a less resistive pathway for the water and hence greater
water flow, the accessibility of more canisters to leaching, or
structural changes in the surrounding rock.
The purpose of this appendix is to estimate the rate at which such
dissolution could take place, consistent with other assumptions in the
report. Throughout, the following constant value for salt (NaCl)
solubility in water is used:
0.37 gm/cc water = 0.168cc salt/cc water.
This is the solubility of salt at about 100 C. The concern here is for
boreholes and shafts that have been filled and sealed according to the
specifications given elsewhere in the report. Dissolution during the
operational phase of new wells drilled in the future is assumed to be a
problem that the drillers will have to meet in engineering their
systems. For the sake of conservative calculations (i.e., tending to
overestimate the dissolution), it will be assumed that water leaving the
salt layer through the breach pathway is saturated with salt.
III-l
-------
B. BOREHOLES
In Section D-3.3, the degradation of a sealed borehole has been
modeled as a deterministic process. The parameters assumed were:
2
Area, A = 0.1 m
Porosity,
0.1
Permeability, K = 10
-8
- 10
-8
10
(for the first estimate,
t in years, K in cm/sec)
K
10
-8 + 10 - 10
10
8
(for the second estimate,
t in years, K in cm/sec)
These parameters enable the calculation of flow as a function of
hydraulic gradient. For conservatism, the viscosity will be taken as
0.0022 poise, which has been used elsewhere for flow calculations. (See
Appendix D-VI for the dependence of viscosity on temperature.)
Dissolution is expected to be greatest at the point where unsaturated
water enters the salt layer. As a consequence, it is conservative to
assume uniform dissolution in estimating dissolution at the repository
level. Calculations here are consistent with the generic stratigraphies
and repository assumptions given earlier in the report.
•
A water flow rate Q through the filled borehole corresponds to a
•
salt dissolution rate equal to 0.168 Q. If the borehole has radius r
III-2
-------
and length L through the salt, then the rate of change of the radius is
3
given by:
dr_ = 0.168 Q
dt 2-rrrL
s
For bedded salt, L = 100 m for a borehole extending to the lower
S
aquifer. For dome salt, L = 230 for a borehole extending to the
• s
repository. Recall that Q is given by:
for a hydraulic gradient i. The computational procedure is to proceed
as follows :
1. Compute Q(t) =
2. Compute Q(t) by integrating Q(t) and using the initial condition
Q(0) S0.
3. q(t) = 0.168 Q(t) is the cumulative volume of salt removed.
4. Compute r(t) from the formula
where r is the initial radius. This formula simply derives
from volumetric considerations.
5. Compute -7^ , if it is of interest, from the earlier formula
_ q(t)
dt 2irr(t)L
s
•
For ease of computation, the integration of Q(t) is worked out below,
III-3
-------
4
where K is assumed to degrade linearly from KQ to K^ over 10 years:
K K
K(t) = [K + ^-7- ° t] [10"2][3.15 x 107]
0 104
_2
where KQ and K, are in cm/sec and K is in m/yr - The factor 10
converts centimeters to meters and the factor 3.15 x 10 converts
seconds to years. As long as the other parameters remain constant,
f~ r\ -j
Q(t) - Q(0) = J[K + 1 " ° t] [10" ][3.15 x 10
Q U ^Q^
K K
Q(t) = [Knt + 1- ? t2] [3.15 x 105] [.~
u 2 x 1(T
Note for future reference that the expression inside the integral sign
•
is Q(t) . Note also that dissolution may change the value of A for the
section of the borehole within the salt, but as long as the changes are
very small, corrections for this change need not be introduced. For
significant dissolution over a large extent of the borehole, Darcy's law
would no longer apply since there would essentially be a conduit for
water flow.
Using the scheme just outlined, the numerical results shown in
Table D-III-1 are obtained. These calculations suggest that, at least
within the parameter range under consideration, the change in r is
relatively slow. Therefore, the derivative dr/dt may be approximated by
the formula:
ll = 0.168 Q
dt = 2irr L
o s
III-4
-------
TABLE D-III-1
CHANGES IN BOREHOLE RADIUS AS A RESULT OF DISSOLUTION
(Using a gradient i - 0.01, rQ - 0.18))
Time
(years)
First Estimate
r(meters)
Second Estimate
r(meters)
Bedded Salt
100
500
1000
5000
10,000
0.1800
0.1800
0.1800
0.1803
0.1811
0.1800
0.1800
0.1801
0.1826
0.1903
Dome Salt
100
500
1000
5000
10,000
0.1800
0.1800
0.1800
0.1801
0.1805
0.1800
0.1800
0.1800
0.1812
0.1846
III-5
-------
instead of by the original formula:
T 0.168Q
dt
s
The difference is in using r , the original radius, instead of r, which
always results in a conservative calculation (i.e., tending to
overestimate dr/dt) because r is greater than or equal to rQ. For the
case of bedded salt, using L = 100 m and r - 0.18 m, this yields the
S O
formula:
= 1.485 x 10~3 Q
Similarly, for dome salt, using L - 230 m and r =0.18 m, one obtains
~ - 6.458 x 10"4Q .
As an example of the application of these formulas, consider the value Q
= 0.875 m /yr, which is the value calculated in Section D-3.4 for first
estimate fluid flows at 1000 years after repository closure. Tn the
_3
case of bedded salt, the resulting value of dr/dt is 1.3 x 10 m/yr-
This slow rate of increase is or would probably be compensated for by
salt creep, which would tend to close any channels created by
dissolution. For example, rough calculations suggest that dr/dt for an
_3
open borehole at repository depth would be about -3 x 10 m/yr, which
would more than balance the dissolution. Further discussion of salt
creep may be found in Appendix D-VII.
Dissolution around other breach pathways can be analyzed in a manner
exactly analogous to the examples worked out above for boreholes. The
values in Table D-III-1 roughly scale with the gradient, so that the
effects of the larger second estimate gradients in certain cases are
apparent.
III-6
-------
APPENDIX D-IV
METHODOLOGY FOR DIFFUSION CALCULATIONS
-------
APPENDIX D-IV
METHODOLOGY FOR DIFFUSION CALCULATIONS
A. INTRODUCTION
In the case of a breach of a nuclear waste repository, either by a
gradual process (e.g., borehole plug degradation) or a distinct event
(e.g., faulting), there are basically two processes for movement of
radionuclides from the canisters to the release pathway. These
processes are convection and diffusion. Convection, the carrying of
radionuclides by moving water, may be driven by several mechanisms,
which are discussed elsewhere in this report. Molecular diffusion,
driven by a concentration gradient, is the principal subject of this
appendix.
A simplified plan view of a portion of a repository is shown in
Figure D-IV-1. The canisters of wastes are emplaced in holes in the
floor of the waste drifts. For purposes of this appendix it has been
assumed that the waste drifts are 5 m x 5 m in cross section, although
most of the formulas will first be worked out in terms of a parametric
cross-sectional area A. The waste drifts may be quite long, say 500
meters, and the canisters may be placed at intervals on the order of 5
to 10 meters.
Potential breach mechanisms, such as faults and boreholes, may
intersect the waste drifts, the main tunnels, or simply the rock
pillars. (The pillars are expected to cover 50-90% of the total
repository area.) The drifts and tunnels will be backfilled with
porous material. The pillars may also be porous, due either to basic
rock porosity or to fracture systems. In any case, diffusion is through
porous media, not simply through bulk fluid.
B. BASIC PRINCIPLES AND HYPOTHESES
The basic goal here is to calculate the rate of mass transport from
a "source" to a "sink". The source is one or more canisters of nuclear
waste, and its strength is determined by the concentration of material
IV-1
-------
• Waste drift
Waste drift • •
Main
tunnel
• Waste drift •
Waste drift • •
Canisters
FIGURE D-IV-1 PLAN VIEW OF PORTION OF REPOSITORY (NOT TO SCALE)
IV-2
-------
at Its boundary. In general, this concentration will vary from one
radionuclide to another. The concentration will be bounded by the
solubility limit of the relevant species, which in many cases is very
small, and it may be further limited by the rate at which the species
can be leached from the canister/waste-form package. The sink consists
of a release pathway, such as the portion of a borehole passing through
the repository. (Transport along the release pathway is generally
dominated by convective forces, which are discussed elsewhere in this
report.)
Molecular diffusion is driven by a concentration gradient in the
same way that heat conduction is driven by a temperature gradient or
fluid flow by a pressure gradient. The basic mathematical model is thus
a partial differential equation, which for steady-state problems is
simply the Poisson equation (reducing to the Laplace equation away from
sources and sinks). The purpose here is not to derive or assume this
body of mathematical theory, but rather to present simple,
self-contained models that are sufficiently accurate to predict
diffusional mass transfer in the present case. Geometric
simplifications, always intended to err on the conservative side, will
be employed freely. The purpose is generally to reduce problems to a
single dimension.
The fundamental principle that the diffusion rate is proportional to
the concentration gradient takes the form:
J = D
dx
in one dimension, where
J = flux rate (mass per cross-sectional area per time) . The
direction of movement is understood to be from regions of
higher concentrations to lower ones. With this convention, no
minus sign is needed in the equation.
D = diffusion constant. This depends on the fluid, the porous
medium, the diffusing solute, and the conditions present.
C(x) = concentration of the solute at distance x from the sink.
This equation, called Pick's law, is exactly analogous to Darcy's law
IV-3
-------
for fluid flow in a porous medium. J will be a function of x. The
total mass transport rate q through any cross-sectional area A will be
obtained as the product JA. The two sections that immediately follow
use Pick's law to calculate diffusion rates in certain fundamental
cases.
C. DIFFUSION THROUGH A TUBE OR TUNNEL (MODEL A)
Consider the situation sketched in Figure D-IV-2a. Suppose the
concentration at the left end is kept fixed at C2 and that at the right
end at C, , where C« > C, . The corresponding concentration gradient and
flow is strictly one dimensional, and may be modeled as in Figure
D-IV-2b. As long as the porous medium is uniform (an assumption used
throughout), the concentration will change uniformly, so that:
C(x) - £ (C - C )
Thus the diffusive flux is:
D(C - C.)
J = ± ±_
and the mass transport rate q is:
D(C2 -
where A is the cross-sectional area.
While it would be desirable to have measurements of the diffusion
coefficient D for the given solute in the given medium, such data are
not generally available for the materials of interest in this study.
Indeed, the diffusion rates in water are not well known and must often
be approximated from other known values. Given the diffusion rate in
water, the rate in the water-saturated porous medium may be
approximated. We shall do this by multiplying the tunnel
cross-sectional area A by the porosity n of the backfill material, since
nA better represents the effective cross section through which the
diffusive flux acts. The effective pathway through a real medium is
IV-4
-------
Source boundary
(Concentration
Sink boundary
(Concentration C1)
(a)
(b)
TUNNEL
C(x)
FIGURE D-IV-2 DIFFUSION ALONG A TUNNEL
IV-5
-------
also not expected to be the straight line suggested in Figure D-IV-2b,
but this distance multiplied by a "tortuosity" factor. Since for many
porous media this factor is still less than 2, it is not incorporated in
the present analysis. Therefore, accounting for porosity but ignoring
tortuosity, the mass transport may be calculated approximately by:
q =
D(CZ - c1)An
This formula and the corresponding model will be called Model A.
D. DIFFUSION IN AN ANNULAR REGION (MODEL B)
The situation to be analyzed in this section is shown in Figure
D-IV-3a. The cylindrical source will be used to bound the contributions
from several point sources located on or outside such a cylinder.
Because of symmetry, flow is strictly horizontal and radial and may be
analyzed with the aid of Figure D-IV-3b. Steady-state flow requires an
identical rate of mass transport through every intermediate boundary.
As x increases, the boundary area increases proportionately, so for the
same mass transport rate, a smaller flux rate holds. Since flux rate
\
and concentration gradient are proportional, the concentration varies
non-uniformly in this case.
The reasoning just described actually enables the calculation of
mass transport. Whatever the steady-state overall mass transport rate
•
may be, it must hold that q is the rate of material movement through any
intermediate cylindrical boundary; that is, for all x,
JA
(D 3-)
dx
IV-6
-------
Borehole passing through
repository (sink)
Repository
horizon
Cylindrical source of material
diffusing toward borehole
Intermediate boundary
at radius x
Source
FIGURE D-IV-3
CYLINDRICAL SOURCE AND SINK LEADING
TO DIFFUSION IN AN ANNULAR REGION
IV-7
-------
where h is the height of the cylinders. Therefore:
dC q
rr~ " ~ o i-
dx D • 2irh
• constant
Simply calling the constant B, it follows that!
dC = B_
dx x
C(x) - Bin x + E
for another constant E, yet to be determined. If boundary conditions
are specified in the form:
C(r1)
C(r_) « C-
(sink)
(source)
where r., and r_ are the radii of sink and source respectively, it is
easily seen that:
~ C
tn(x/r
IV-8
-------
The corresponding mass transport rate is thus:
• •
D • (r ) • 2irr.h
dx 1 1
D .
D
C - C,
i. . 2-rrr-h
Cancelling the r,'s and now inserting the porosity factor, we obtain:
2irDhn(C2 -
This formula and the corresponding model will be called Model B. Note
that for conservative calculations one wants to err on the side of
underestimating r2 and overestimating r, .
E. EXAMPLE: DIFFUSION INTO MAIN TUNNEL
Consider the situation previously shown in Figure D-IV-1. If flow
through the main tunnel is initiated by some mechanism, such as
degrading shaft seals at either end, the release of material along waste
drifts to the tunnel may be primarily from diffusion. We shall model
this situation as shown in Figure D-IV-4 for radionuclides whose
concentration is limited by a relatively low solubility limit C^* It is
conservative to replace the first canister by a planar source at
concentration C~, and fill the entire waste drift cross section.
Furthermore, the remaining canisters in the drift cannot contribute to
the mass transport, since the hypothetical source has maximal
concentration. (There could not be a net concentration gradient driving
IV-9
-------
Hypothetical
sink
Hypothetical
source
First canister
FIGURE D-IV-4 GEOMETRY FOR DIFFUSION INTO MAIN TUNNEL
IV-10
-------
material toward it from the right). We take as the sink the entrance
from the main tunnel to the waste drift. This is the situation in Model
A. Nominal parameters will he taken as follows:
A -
n =
D =
C2 -
Cl "
L =
25 m
0.2
io-6
io-5
0
20 m
2
2
cm /sec
Ci/m3 (Ci
9
curies)
The corresponding mass transport is found to be:
q • 8 x 10~9 Ci/yr.
This represents the maximum contribution of one waste drift to the main
tunnel by diffusion, according to the parameter values given above.
It is important to compare this mass transport with that possibly
driven by other forces. In particular, consider the following question:
What hydraulic gradient acting along a waste drift would result in the
same transport rate? A permeability of K - 10~ cm/sec and a viscosity
of v - 0.005 will be used in answering this. The unknown gradient 1
causes fluid flow at the rate
Tot"
Assuming that this water is saturated with the solute in question, i may
be found to be:
8 x 10~9 - 1.6 x IO3 x i x 10~5
i - 5 x 10~7.
This is an extremely low gradient and suggests that much care should be
IV-11
-------
exercised before diffusion is regarded as the dominant transport
mechanism.
F. EXAMPLE: BOREHOLE THROUGH A PILLAR
The repository pillars may be considered as long rectangles of
constant width w; a borehole drilled randomly through such a pillar will
have its expected distance from a wall approximately equal to w/4. For
the present calculations we shall take w = 16 m, so that the expected
shortest distance from borehole to drift will be 4 m. In fact, the
borehole may receive material from the nearby drift as well as from the
one on the opposite side of the pillar. An upper bound on diffusional
transport may be obtained by using Model B, with nominal parameters as
follows:
rl •
C1 •
1
h =
r2 =
C2 =
n -
D =
0.2
0
5 m
4 m
io-5
10
io-6
m
Ci/ra3
O
cm Is
The corresponding mass transport is found to be:
Q - 3.3 x IO"11 Ci/yr
As earlier, it is important to compare this with the potential transport
by a convective process. By the analogous structure of Darcy's and
Pick's laws, the equation corresponding to Model B for fluid flow rate Q
may be written:
ZirKhAp
100p«,n(r2/r1)
IV-12
-------
where Ap Is the head difference and p is the viscosity.
Taking u - 0.005 and K - 10~9 cm/sec, this yields:
Q » 7 x 10"3 x Ap m3/yr.
—5 3
If this fluid is saturated at 10 Ci/m , say, then Ap may be found
from:
3.3 x 10~U = 7 x 10"8 x Ap
5 x 10 m = Ap
Along a distance of 5 m of the borehole, the pressure drop corresponding
-3
to a gradient of 0.001, say, will be 5 x 10 m. Therefore, no matter
what the pressure in the waste drift, it will differ from that in part
of the borehole by at least 2.5 x 10~ , which is five times the
difference needed to approximate diffusional transport. This suggests
that diffusion will not dominate this process.
G. TRANSIENT BEHAVIOR
If the repository is breached some time after the canisters have
corroded and radionuclides have diffused through the repository, then
initially the mass transport out through the release pathway will be
greater than its steady-state value. This is because the maximum
concentration C* determined by solubility limits may be experienced very
close to the breach, leading to a high concentration gradient and hence
a high diffusion flow. The initial flow is best approximated by
assuming it is at concentration C~ of whatever other initial values may
be estimated for that point in time.
Exit flows at concentration C2 should continue to be used in the
models until steady flow has been obtained. A conservative approach for
dealing with this factor may be developed as follows:
1. Determine the radionuclide flow rate (in Ci/yr, say) out the
release path.
IV-13
-------
2. Determine the initial stored radionuclide content in the
diffusional pathway being modeled. (Concentration limits x
water volume).
3. Determine how long it would take for the quantity calculated in
Step 2 to be removed by the rate from Step 1.
4. The time calculated in Step 3 may be used to shift to a
steady-state diffusion model. In fact, for the Model A
situation, one half of this time suffices.
This calculation is not intended to determine the time at which
steady-state behavior is achieved, but it shifts the mass transport rate
in time so that the cumulative amount released by any point in time is
greater than or equal to the actual value. In this sense it is a
conservative approach.
IV-14
-------
APPENDIX D~V
METHODOLOGY FOR U-TUBE CALCULATIONS
-------
APPENDIX D-V
METHODOLOGY FOR U-TUBE CALCULATIONS
A. INTRODUCTION
The purpose of this section is to analyze the flow through the
repository for the conditions outlined in Figure D-V-1, where the
degrading shaft seals and the permeable tunnel backfill lead to an
alternative path from point A to B. While this additional path may tend
to decrease slightly the driving potential (head) between points A and
B, it is conservative to ignore this effect. Since the overall
resistivity of the alternative path is in general still considerably
higher than that of the aquifer, this assumption is probably not overly
conservative.
B, MATHEMATICAL FORMULATION
Darcy's formula will form the basis for the present analysis. In
its simplest form, it appears as follows:
Q - KiA
where
•
Q - flow rate through pathway cross section
K « hydraulic conductivity, also referred to loosely as the
permeability
i - hydraulic gradient
A " cross-sectional area
The hydraulic conductivity, in units of length per time, depends not
only on the medium through which water is flowing, but also on the
water's viscosity, which varies with temperature. The numbers reported
in the literature are ordinarily for water at relatively low
temperatures (a20°C) at which the viscosity is approximately 0.01 poise.
Since the hydraulic conductivity is inversely proportional to the
viscosity, the reported K values must be divided by the ratio y/0.01
V-l
-------
Flow
Gradient i
Shaft
Mine tunnel
Shaft
Aquifer
FIGURE D-V-1 TYPICAL U-TUBE SITUATION
V-2
-------
when the viscosity U is expected to deviate significantly from 0.01
poise. This might be the case, for example, with water flowing through
the repository during its period of high thermal output. A table of
viscosity values is given as Table D-V-1. Dependence on pressure is not
sufficiently important to require consideration for present purposes.
Consideration of viscosity, as outlined above, leads to the
following revised form of Darcy's law:
0 _
* 100U
where the dimensions are as follows:
K length /time
i dimensionless
A length squared
100P dimensionless (actually, poise/0.01 poise)
•
Q length cubed/time
The factor
lOOy
is sometimes called the Darcy velocity. It has the units of length/time
but should be interpreted as a flux: volume per cross-sectional area per
unit time. When the Darcy velocity is divided by the porosity n, an
approximation to the average fluid velocity is obtained.
Darcy's law may be considered from the point of view of its
electrical analog, Ohm's law:
I-
where
R = resistance,
E « the voltage over the resistance, and
I = the current.
In the present case, the porous medium is the resistance, the head drop
is the voltage! and the flow rate is the current. If the gradient i
V-3
-------
TABLE D-V-1
VISCOSITY OF LIQUID WATER AT ATMOSPHERIC PRESSURE
Temperature Viscosity
(°C) (poise)
20 0.0100
40 0.0065
60 0.0047
75 0.0038
100 0.0029
125 0.0022
150 0.0018
Source: American Institute of Physics Handbook, 1972.
Data compiled from other sources.
V-4
-------
originally derives from a head drop A over a length L, that is,
then the basic equation is
_
* 100UL
from which the parameter correspondence is seen to be:
resistance
voltage
current
This correspondence is useful in analyzing series and parallel flow
paths, as in the present problem.
C. ANALYSIS IN PARAMETRIC FORM
The following symbols will be used for the parameters characterizing
the situation shown in Figure D-V-1:
A head drop from A to B
D, distance from A to B which also equals length of mine tunnel
K^ permeability of filled mine tunnel
A. cross-sectional area of mine tunnel
n, porosity of filled mine tunnel
D« length of each shaft
K2 permeability of filled shafts
A- cross-sectional area of each shaft
^2 porosity of filled shafts
As mentioned earlier, the slight change of head difference between
points A and B, due to the development of an additional pathway between
V-5
-------
them will be omitted from the analysis. Thus, the problem amounts to
three resistances In series, as sketched In Figure D-V-2.
The flow rate Is thus:
Interstitial velocities In each segment are given by:
v. .--a.
v
2
Head drops over Individual segments are proportional to the resistances,
so that:
A -
2
where the subscripts 1 and 2 correspond to tunnel and shaft,
respectively.
V-6
-------
left shaft tunnel right shaft
100MD,
FIGURE D-V-2 SERIES RESISTANCE MODEL FOR U-TUBE CALCULATIONS
V-7
-------
D. NUMERICAL RESULTS
Of particular importance in this report is the upward vertical
gradient i, in the so-called right shaft. On the basis of the previous
discussion, this can be calculated from the equations:
"2 A
a. + 2cu L,
i z t
al + 2°2 L2
where i is the gradient in the upper aquifer. For calculational
purposes, the variable inputs will generally be i, K. , and K_. The
gradient i will vary between first and second estimates, taking the
value 0.002 and 0.02, respectively. K, has the value 10~ cm/sec for
j •*-
salt and 10 cm/sec for granite, basalt, and shale. K- is a function of
time due to the assumed gradual degradation of the shaft seals. The
first estimate is:
K2 - 3.15 x 10~3 + 3.12 x 10~5 t
and the second estimate is:
K2 - 3.15 x 10™3 + 3.15 x 10~3 t,
both based on Section D-3.2.3. The other parameters have been given
previously in this appendix. Corresponding values of i« are summarized
in Table D-V-2. Note that while the gradients decrease with time, the
flow rates would actually increase since the total resistance of the
series pathway is decreasing.
A similar U-tube effect occurs with sealed boreholes. Assume that
50 boreholes penetrate to the repository and that they are located
randomly. Then the resulting flow would be downward in roughly 25 holes
V-8
-------
TABLE D-V-2
HYDRAULIC GRADIENTS IN VERTICAL SHAFTS DUE TO U-TUBE EFFECT
Hydraulic Gradient (1)
Medturn
Years*
First Estimate
Second Estimate
Bedded Salt
Granite
Basalt
Shale
Dome Salt
100
250
1,000
10,000
100
1,000
10,000
100
1,000
10,000
100
1,000
10,000
100
250
1,000
10,000
0.033
0.030
0.019
0.00 A
0.017
0.017
0.017
0.040
0.040
0.036
0.040
0.040
0. 036
0.016
0.015
0.012
0.003
0.036
0.015
0.004
0.0004
0.167
0.121
0.033
0.363
0.200
0.036
0.363
0.200
0.036
0.032
0.015
0.004
0.0004
*Years after repository closure.
V-9
-------
and upward in the other 25, and the mean distance (projected to a plane
parallel to the direction of aquifer flow) between the boreholes in
these two sets would be 2000 m, half the length of the repository.
Using area and permeability parameters given in Section D-3.3.3, the
vertical gradients shown in Table D-V-3 may be calculated.
V-10
-------
APPENDIX D-VI
EFFECT OF THERMALLY INDUCED BUOYANCY
ON VERTICAL FLOW
-------
APPENDIX D-VI
EFFECT OF THERMALLY^INDUCED BUOYANCY ON VERTICAL FLOW
A. INTRODUCTION
The heat generated by radioactive wastes in a repository will
decrease the density of any water present. The reduced density will
result in an upward force (due to buoyancy) for any water column
extending from the repository to the upper aquifer. The water column of
interest may include all the water contained in rock pores or fractures
above the repository, or may be the water present in a specific breach
of containment pathway such as a slightly permeable borehole. The
situation is illustrated in Figure D-VI-1. Note that the emphasis is on
the water above the repository, not on the rock itself, and therefore
reference is to the (generally moving) column of water. This phenomenon
has been discussed elsewhere * ' , although various conclusions have
been drawn concerning its significance. These previous discussions have
been based on numerical solutions to two-dimensional fluid-flow
equations and on other fluid-mechanical techniques. The purpose of this
appendix is to discuss the question in terms of basic physical
principles, without numerical simulations or advanced analytical
techniques. This approach should serve to clarify the important factors
and lead to useful numerical approximations of the forces created by
this buoyancy effect.
B. SIMPLIFICATIONS
Any vertical movement of the water in the rock surrounding a
repository will be superimposed on the prevailing, largely horizontal
flow pattern. However, the water velocities through the surrounding
rock are sufficiently small that these horizontal forces and motions can
be omitted from the analysis without significantly affecting the
results. In fact, it is also conservative to ignore such motions
because they tend to decrease the density gradient and hence the
buoyancy effect. In the absence of horizontal flows induced by regional
VI-1
-------
Land surface
Aquifer
!;^— Water column acted on by
ll upward buoyancy forces
t
Repository
FIGURE D-VM CONCEPTUAL FRAMEWORK FOR BUOYANCY ANALYSIS
VI-2
-------
groundwater movement, there will still be horizontal flows induced by
the differential vertical forces that result from density differences in
the water column under consideration. The resulting flow pattern has
the general shape shown in Figure D-VI-?. However, these horizontal
components may also be ignored for the present approximate analysis, as
becomes especially clear by redrawing the previous figure with Identical
horizontal and vertical scales. See Figure D-VI-3.
C. OUTLINE OF APPROACH
The structure of this analysis is illustrated by the sequence of
drawings in Figure D-VI-4. Figure D-VI-4a shows two vertical columns of
water connected by a tube at the bottom. Heating of the left column
results in a lower density, so there is a tendency for water to move
through the connecting tube from right to left. The driving force for
this motion can be maintained approximately constant by inlet and outlet
pipes to maintain constant water levels, as shown in Figure D-VI-4b.
The same driving force and flow rate can be obtained by considering an
equivalent difference in water levels, rather than water densities.
This difference is shown in Figure D-VI-4c. In order for the flow to
achieve a steady state, the driving force must be balanced by an equal
and opposite resisting force. In the present case, the dominant
resisting force comes from the low permeability of the medium through
which the water flow?. While it may be argued that the corresponding
repository situation implies that this resistance should be present in
both columns of water, at the outset of the analysis the conservative
assumption of resistance only in the rising column will be used. This
is shown in Figure D-VI-4d. The driving force can be represented by the
effective hydraulic gradient over this vertical column, calculated by
dividing the excess height of the right column over that of the left
column (= head) by the length of the left column. (The effect of
resistance in the right column is discussed later In this appendix.)
VI-3
-------
Land surface
Aquifer
\ N / / /
=M= •
• Repository
/ /
FIGURE D-VI-2 CONVECTIVE FLOW PATTERN
M t I I I I! I I 1
SCALE: 1 cm = 460m
FIGURE D-VI-3 SCALE DRAWING OF REPOSITORY
• Land surface
• Aquifer
VI-4
-------
(a)
"2
/\
Heat
/\
Heat
(0
(d)
I
1
FIGURE D-VI-4 CONCEPTUAL DEVELOPMENT OF BUOYANCY MODEL
VI-5
-------
D. OUTLINE OF COMPUTATIONAL APPROACH
In order to apply the conceptual model described earlier, the
following data are needed:
• Temperature distribution in the overlying rock at the time of
interest.
• Water density as a function of temperature.
• Water viscosity as a function of temperature.
• Permeability of the water column pathway.
• Effective porosity of the water column pathway.
These data enter into the computational framework illustrated in Figure
D-VI-5. The output of such computations consists of volumetric flow
rates and travel times for water from the repository to the aquifer when
driven by the thermally induced buoyancy effect. For the purposes of
this study, this output may be interpreted as a lower bound on travel
time and hence a conservative estimate. The equivalent hydraulic
gradient is also important for comparing this driving force with other
driving forces.
In addition to model limitations previously noted, the following
factors are also not included:
• Effect of dissolved material on density and viscosity.
• Effect of fluid flow on underlying temperature distribution.
Dissolved material could have a significant effect on density in case
the water passes through a highly soluble medium such as salt. In this
case, the vertical column moving upward would contain more dissolved
material, and this would tend to counteract the buoyancy effect. It is
therefore conservative to omit this factor. The effect of dissolved
material on viscosity is too small to warrant consideration. It is also
conservative to omit the effect of fluid flow on the temperature
distribution, since this effect is to decrease thermal, and hence,
density gradients. Furthermore, the amount of heat transfer that can be
accomplished by the fluid flow appears to be rather small (<10%)
compared with the total heat transfer.
VI-6
-------
81
S2
S3
S4
86
S7
89
Pick time t.
Obtain temperature
distribution from
other documents.
Compute corresponding
density distribution.
Compute mass of
vertical column
of water
85
Compute mass of column
of water at normal tem-
perature.
Determine vertical force
on column and corres-
ponding pressure.
Convert to equivalent
hydraulic gradient.
88
Compute water
viscosity for ambient
conditions.
Determine flow rates and
interstitial velocity by
Darcy's law.
810
Determine travel time
from repository to aquifer.
FIGURE D-VI-5 INFORMATION FLOW CHART FOR BUOYANCY COMPUTATIONS
VI-7
-------
E. DISCUSSION OF INDIVIDUAL STEPS
SI: Because the temperature profile varies with time, these
calculations need to be repeated for the points in time that are of
interest.
S2: Temperature distributions for various points in time have been
given for salt and granite in the Task B Report. Temperature
distributions for basalt, granite, and shale have been given
(A)
elsewhere. These distributions depend significantly on several
factors, such as: age and composition of wastes, areal density of
waste, thermal conductivity of surrounding rock, heat capacity of
surrounding rock, etc. For purposes of the present calculations, we
will assume the temperature distributions indicated in Figures
D-VI-6 through D-VI-10, which are "generic" approximations based on
the aforementioned sources.
S3: The density of liquid water may be estimated from standard
reference data. Table D-VI-1 summarizes selected numerical values.
Pressures are not given with these data, but the effect on density
of pressure changes in the range of 1 bar (atmospheric) to 50 bars
(approximate hydrostatic pressure at 500m depth) is too small to
warrant consideration in this approximate analysis. One notes that
50 bars is sufficient pressure to prevent boiling at 250°C.
Given the temperature distribution in a vertical column of water,
the corresponding density distribution is then calculated by means
of the data in Table D-VI-1.
S4: Previously, the column of water under consideration has always
extended from the repository level to the upper aquifer. In the
case of many breach-of-containment mechanisms, there is no question
about this choice. For some calculations, however, it may be
preferable to consider a column of water extending from the upper
aquifer down to some point below the repository.
VI-8
-------
360
-5 460
f
560
Time: 10 yr.
(100,460)
I
100 200 300
Temperature °C
360
460
f
w
Q
560
Time: 100 yr.
(50,360)
(250,460)
),560)
100 200
Temperature °C
300
360
•§ 460
a
0)
Q
560
Time: 1,000yr.
% (100,360) 360
\ I
\ (150,460) | 460
/ 1
/
/ (100,560) 560
-
-
-
Time: 10,000 yr.
(50,360)
(50,460)
(50,560)
I i |
100 200 300
Temperature °C
100 200
Temperature °C
300
FIGURE D-VI-6 TEMPERATURE DISTRIBUTION FOR BEDDED SALT REPOSITORY
VI-9
-------
Time: 10 yr.
260
460
f
660
(20,230)
(100,460)
(20,660)
I
_L
100 200
Temperature °C
260
€
I 460
a
0>
a
660
Time: 100yr.
(20,230)
(20,660)
I
300
_L
100 200
Temperature °C
(250,460)
300
260
J 460
OJ
Q
660
Time: 1000 yr.
(35,230)
(125,460)
100 200
Temperature °C
260
460
£
660
Time: 10,000 yr.
(20,230)
(50,460)
I (30,660)
300
100 200
Temperature °C
300
FIGURE D-VI-7 TEMPERATURE DISTRIBUTIONS FOR GRANITE REPOSITORY
VI-10
-------
360
I
I
0)
O
460
560
Time: 10 yr.
360
a
4)
•§ 460
a
Q)
O
560
I
I
Time: 100 yr.
•I
I
100 200
Temperature °C
300
100 200
Temperature °C
300
360
w
I 460
560
Time: 1000 yr.
360
.§ 460
a
a>
Q
560
Time: 10,000 yr.
100
200
300
100
200
300
Temperature °C
Temperature °C
FIGURE D-VI-8 TEMPERATURE DISTRIBUTIONS FOR BASALT REPOSITORY
VI-11
-------
360
-460
560
Time: 10 yr.
(20,410)
(100,460)
I
I
100 200
Temperature °C
300
360
I
1 460
f
V
Q
560
Time: 100 yr.
(50,360)
100 200
Temperature °C
(250,460)
300
360
S
0>
,§ 460
£
0)
Q
560
Time: 1000 yr.
\ (100,360) 36°
\ 8
) (150,460) ^ 46°
/ °
/(100.560) 560
I I I
Time: 10,000 yr.
—
••
-
(50,360)
(50,460)
(50,560)
100
200
300
Temperature C
100 200
Temperature °C
300
FIGURE D-VI-9 TEMPERATURE DISTRIBUTIONS FOR SHALE REPOSITORY
VI-12
-------
Time: 10 yr.
260
.§ 460
(100,460)
(20,510)
I
I
100 200
Temperature °C
300
260
S 460
a
0)
a
660
Time: 100 yr.
(30,230)
(30,660)
L_
I
100 200
Temperature °C
(230,460)
300
260
E 460
660
Time: 1000 yr.
(110,460)
(80,660)
I
100 200
Temperature °C
300
260
•=• 460
f
0)
Q
660
Time: 10,000 yr.
(50,230)
(50,230)
(50,230)
I I
100 200
Temperature °C
300
FIGURE D-VI-10 TEMPERATURE DISTRIBUTIONS IN SALT DOME REPOSITORY
VI-13
-------
TABLE D-VI-1
DENSITY OF LIQUID WATER
Temperature (°C)
20
30
40
50
60
70
80
90
100
110
120
130
Density (gm/cm )
.99823
.99568
.99225
.98807
.98324
.97781
.97183
.96534
.95838
.9510
.9434
.9352
Temperature (°C)
140
150
160
170
180
190
200
210
220
230
240
250
Density (gm/cm )
.9264
.9173
.9075
.8973
.8866
.8750
. 8628
.850
.837
.823
.809
.794
-------
The following two principles should be kept in mind:
a. The vertical velocity of the water column is proportional
to the effective hydraulic gradient acting upon it.
b. The effective hydraulic gradient acting on a vertical water
column (due to buoyancy) is proportional to the average
density of the column.
These principles will now be applied to a repository whose vertical
thermal profile has the form given in Figure D-VI-lla. The
corresponding density profile is given in Figure D-VI-llb. A column
of water extending down just to the repository has some average
density Pj, as shown in Figure D-VI-llc. The slightly longer water
column shown in Figure D-VI-llc has a lower average density because
the addition has a density P_ which is less than PI . To confirm
that this would increase the velocity of the column, simply note
that the relatively high buoyancy force in the lower segment would
tend to "push" the column above it. This effect continues to
require consideration of longer columns until a point is reached
where the average density of the column equals the density of the
next additional increment. In calculations of this type, the
maximum point will often be only roughly approximated. Examples of
situations in which such longer water columns will need to be
considered include the following:
• Baseline flow through repository (no breaches).
• Boreholes penetrating some distance below repository.
• Faults extending below repository.
The determination of the proper water column to consider and its
average density provides the information needed to determine its
mass (or, equivalently, mass per unit cross-sectional area). The
numerical differences resulting from consideration of longer water
columns are generally not very large.
S5: The density of a corresponding column of unheated water may be
conveniently and conservatively estimated as 1 gm/cm . With this
density, the mass of a column is easily determined.
VI-15
-------
Depth
a)
Upper
aquifer
Repository
M
Depth
b)
Upper
aquifer
Repository
c)
d),—t
e)
P2
Temperature
Density of water
FIGURE D-VI-11 DETERMINING WATER COLUMN WHOSE VERTICAL VELOCITY IS MAXIMAL
-------
S6: Let L represent the length of the water column under
o
consideration and let p* be its average density in gm/ctn . Then for
every square centimeter of cross-section, the gravitational force is
P*Lg, where g is the acceleration due to gravity. The opposing
buoyant force due to a column of unheated water is 1-Lg, and so the
difference is (1-P )Lg.
S7: This force corresponds to a hydrostatic head of
(l-P*)Lg
Pg
when measured in terms of water at an arbitrary density p.
Variations in p between p* and 1 do not significantly affect this
value, so that the computationally convenient value, p = 1 g/cm ,
will be used. Thus, the equivalent head is given by
(l-p*)L
This yields a hydraulic gradient i given numerically by
i - l-p*.
Note that i is dimensionless. It is strictly equal to the quotient
(l-p )/l, where 1 and P* ai
cancellation of the units.
(l-p )/l, where 1 and P* are both in gm/cm , thereby leading to the
S8: The viscosity of water is relatively insensitive to pressure
in the range under consideration. Its dependence on temperature is
shown in Table D-VI-2.
Because of this temperature dependence, no single viscosity value
actually covers the entire water column. Nevertheless, an estimate
based on average temperature can be made in order to permit the
application of Darcy's law (see below).
S9: The vertical flow of the water column will be approximated by
Darcy's law:
n - Ki
Q Too"
VI-17
-------
TABLE D-VI-2
VISCOSITY OF LIQUID WATER AT ATMOSPHERIC PRESSURE
Temperature Viscosity
(°C) (poise)
20 0.0100
40 0.0065
60 0.0047
75 0.0038
100 0.0029
125 0.0022
150 0.0018
Source: American Institute of Physics Handbook, 1972.
Data compiled from other sources.
VI-18
-------
where:
* 32
Q - flow quantity (cm /cm /second)
K - permeability (hydraulic conductivity for water at
viscosity 0.01, in cm/sec)
i - hydraulic gradient (dlmensionless)
W - viscosity (poise, equal to gm/cm/second)
The denominator 100P allows for corrections due to different
viscosities, although the numerical effect is at most about half an
order of magnitude. Furthermore,
S10: The travel time T from the repository to the upper aquifer is
given by the quotient
where D is the distance and v is the velocity. Note that D is the
correct parameter here even if a longer column of water (i.e., L >
D) is under consideration.
P. SAMPLE CALCULATIONS
The detailed computation of thermally induced convective flows is a
matter for the consequence calculations in specific
breach-of-containment mechanisms. Several examples will be worked out
here.
1. Baseline Flow Through Granite Repository at 100 Years
The temperature distribution shown in Figure D-VI-7 corresponds
to the density distribution shown in Figure D-VI-12. Calculations
show that a water column of approximate length L • 305m has maximum
vertical velocity. In particular, a running average density is
recorded as the column length increases from L-0, and the Increases
are terminated when the density equals (approximately) the density
VI-19
-------
210
260
310
360
410
3 460
I
Q
510
560
610
660
I
I
.78 .80 .82 .84
.86 .90 .92 .94
Water density (gm/cm )
.96 .98 1.00
FIGURE D-VI-12 WATER DENSITY DISTRIBUTION FOR BASELINE GRANITE REPOSITORY AT 100 YEARS
VI-20
-------
of the next increment. The corresponding average density value is
P* =• 0.899. This yields a hydraulic gradient of
. i =» i - p* = 0.1.
The other parameters will be taken as follows for this sample
calculation:
—9
K = 10 cm/ sec
U = .0022 poise (taken at 125°C)
n = 10~4
D = 230 meters
These numbers lead to a fluid velocity:
v
4.5 x 10 cm/sec
~ 1.4 m/yr
and hence a travel time:
= — = 162 years.
—8
Note that if the permeability were 10 cm/sec, then the travel
time would be about 16 years.
2. Flow Through Leaky Borehole Penetrating to a Bedded Salt
Repository at 1000 Years
In this case, the length L is fixed at 100 meters, the
distance from the repository to the upper aquifer. The temperature
range is 100°C - 150°C, as shown in Figure D-VI-6. It is
sufficient to estimate the average density to be P* = 0.94, based on
Table D-VI-1. This results in a gradient i = 0.06. Other
parameters will be taken as follows:
K = 10 cm/sec
M = 0.0022 poise
v =• 0.1
D - 100 meters
VI-21
-------
These numbers lead to a fluid velocity:
v =• 2.7 X 10~5 m/sec
=8.5 m/yr
and hence a travel time:
T = 12 years.
3. General Results
Tables D-VI-3 and D-VT-4 show the effective hydraulic gradients
on vertical columns of water extending between the upper aquifer
and the repository or some point below it. (The difference between
these two cases is usually not very great and is often blurred by
the interaction between breach pathways.)
G. CALCULATION OF RELEASE TIMES
The transit times calculated earlier are useful for estimating
the instantaneous transport rates at particular moments in time.
However, if several hundreds or thousands of years are required for
the distance from repository to aquifer to be traversed, the change
in velocity over time must be accounted for. As an example of this
kind of calculation, consider the case of a gradually degrading
borehole seal. The question is: when do radionuclides first appear
at the aquifer? For a granite repository, ignoring the effect, if
any, of repository resaturation time, the permeability of the
-8
borehole is assumed (second estimate) to degrade linearly from 10
-4 4
to 10 cm/sec over 10 years. A formula for K is thus:
-4 -8
-8 12 - =
10
10"8 + 10~8t
io~8 (i+t) .
VI-22
-------
TABLE D-VI-3
EFFECTIVE HYDRAULIC GRADIENT DUE TO .BUOYANCY OF A COLUMN
OF WATER BETWEEN UPPER AQUIFER AND REPOSITORY
Bedded Salt
Granite
Basalt
Shale
Dome Salt
10 years
0.02
0.01
0.02
0.02
0.02
Time after closure
100 years 1000 years
0.12
0.10
0.12
0.12
0.12
0.10
0.06
0.10
0.10
0.07
10,000 years
0.03
0.01
0.03
0.03
0.03
VI-23
-------
TABLE D-VI-4
MAXIMUM EFFECTIVE HYDRAULIC GRADIENT DUE TO BUOYANCY OF A COLUMN
OF WATER BETWEEN UPPER AQUIFER AND SOME POINT BELOW REPOSITORY
10 years 100 years 1000 years 10,000 years
Bedded Salt 0.03 0.13 0.11 0.04
Granite 0.02 0.11 0.07 0.03
Basalt 0.03 0.13 0.11 0.04
Shale 0.03 0.13 0.11 0.04
Dome Salt 0.03 0.13 0.08 0.04
VI-24
-------
The average density of the water column would be approximately that
at the 350 m depth (at least for all times after 100 years). From
the data in Figure D-VI-7, this can be estimated as on Figure
D-VI-13. The analytic approximation to the temperature curves
enables straightforward computations. Now we perform a sequence of
velocity calculations according to the earlier outline. The
porosity is taken as 0.1. The results are summarized in Table
D-VI-5; and it can be seen that for the first few hundred years
(excluding about the first 50-70 years), the average velocity is
approximately 1 m/yr. Thus, it requires about 200 years to cover
the distance from repository to aquifer. The first releases by this
mode would then be expected at about 250-300 years after
emplacement.
H. RESISTANCE OF RECHARGE PATHWAY
The model which has been used in the calculations thus far was
sketched as Figure D-VI-4d and is repeated as Figure D-VI-14a in
this section. The true physical situation is more closely
represented by Figure D-VT-14b, in which the column on the right,
called the recharge pathway, is also modeled as offering some
resistance to fluid flow. In this case, the total driving potential
remains the same, but it is dissipated over the two columns, so that
the potential acting on the release pathway (the left column) is
less. It was pointed out earlier that to ignore this factor is a
conservative approach. The purpose of this and the following
sections is to estimate the degree of conservatism involved and to
provide a more realistic model to use where appropriate.
The representations in Figures D-VI-4 and D-VI-14 are useful in
determining the effective pressure differential tending to move
fluid through the system, but once this has been determined (as in
previous sections) it is simpler to use the model in Figure D-VI-15a
with the electrical series resistance analog in Figure D-VI-15b.
VI-25
-------
120
t 90
ui
oc
I
£
I
60
30
100
T * -30log10t
T * - 60 Iog10t + 270
I
1000
TIME (t)
10000
FIGURE D-VI-13 APPROXIMATE TEMPERATURE PROFILE AT 350m IN GRANITE
VI-26
-------
TABLE D-VI-5
CALCULATION OF VELOCITY FOR VARIOUS TIMES
<
l-l
N>
t
100
200
300
400
500
1000
2000
3000
4000
5000
10000
T(at 350m)
120
111
106
102
99
90
72
61
54
48
30
it
.943
.950
.954
.958
.959
.965
.977
.980
.986
.989
.996
i
.057
.050
.046
.042
.041
.035
.023
.020
.014
.011
.004
P
.0023
.0026
.0027
.0029
.0029
.0033
.0039
.0047
.0050
.0056
.0082
K(cm/sec)
1.0 x 10~6
2.0 x 10"6
3.0 x 10~6
4.0 x 10~6
5.0 x 10~6
1.0 x 10~5
2.0 x 10~5
3.0 x 10~5
4.0 x 10~5
5.0 x 10"5
1.0 x 10~4
v(m/yr)
.8
1.2
1.6
1.8
2.2
3.3
3.7
4.0
3.5
3.1
1.5
-------
(a)
(b)
1
I
FIGURE D-VI-14 RECHARGE RESISTANCE INCORPORATED IN EARLIER BUOYANCY MODEL
Flow direction
(a)
Recharge
Discharge
(b)
-~-vwvwv—vwvwv-
FIGURE D-VI-15 SIMPLIFIED CONCEPTUAL MODEL FOR RECHARGE RESISTANCE
VI-28
-------
(The electrical analog has been discussed at greater length in
Appendix D-V.) The resistance of a pathway segment is given by
.-IL-
KA
where L is the length, K is the permeability, and A is the
cross-sectional area. Non-uniform pathways may be approximated by
series or parallel combinations of resistances, which may then be
reduced to an equivalent simple resistance. In cases where the
water viscosity changes appreciably during transit (because of
temperature gradients), this factor may be incorporated in the
resistance term:
a a L • IQOU
KA
where p is the viscosity (in poises). For a potential drop (head)
over a series of resistances, the drop over each .one is proportional
to its resistance. In particular, for a drop A over ct and a** the
effective potential acting on the discharge path is
"2
A.
The calculations of the previous sections were based on the
conservative assumption ou « a. so that A. - A.
The following sections will discuss the application of the
present model to particular breach-of-containment mechanisms. The
estimation of appropriate values of A- and L_ can be quite difficult
because of the complicated geometry of the flow patterns.
Furthermore, one must be careful in applying steady state models to
systems in which parameters are changing over time.
I. RECHARGE THROUGH BULK ROCK
The approximate shape of the streamlines for the baseline flow
through granite is sketched in Figure D-VI-16. The shortest
recharge pathway would be from the aquifer rather close to the
repository and its length could be almost as small as that of the
VI-29
-------
Land surface
Aquifer
FIGURE D-VI-16 QUALITATIVE ESTIMATE OF STREAMLINES
VI-30
-------
discharge path. A longer length would generally be associated with
larger cross-sectional areas for the same flow, thereby tending to
counteract the effect of longer length or resistance ( <*= L/KA).
As a consequence, one can imagine recharge paths with as little
resistance as the discharge path, which would entail dividing the
earlier calculated flows by a factor of 2. This difference is not
significant in the order-of-magnitude calculations being carried out
here; consequently, this effect has not been taken into account in
determining first arrival times at the aquifer from the thermally
incuded convection mechanism.
For determining long-term cumulative releases to the aquifer it
is important to check whether the present calculations grossly
overestimate the flow rates and, if so, what correction factors
might be appropriate. In order to simplify the geometry, the model
shown in Figure D-VI-17 will be used. The repository is modeled as
2
a hemispherical surface with radius 1 km, giving an area of 2^(1) =
2 2
6 km , or slightly less than the real repository area of 8 km".
(The smaller area in the model will tend to slightly overestimate
the recharge resistance.) The recharge paths are assumed to be
oriented radially, so that the equipotential surfaces would be
hemispherical. (This underestimates recharge near the aquifer and
overestimates it deep in the rock.) Thus, the hydrostatic head, h,
is a function of r alone in this model.
If water passes through the repository at the flow rate §, then
in fact the same flow must pass through every concentric
hemispherical surface. Since by Darcy's law, flux is proportional
to pressure or head gradient, it follows that
Q = K. ^ • 2,r2
dr
and that this quantity is actually independent of r. (K is the
permeability; h is the head.) Viscosity is assumed to be that at
low temperatures, so no correction factor is incorporated. It would
be possible to incorporate lower viscosities near the repository,
due to higher temperatures. In comparing the relative resistances
of the recharge and discharge pathways, this factor would tend to
VI-31
-------
a) Three dimensional view
Repository
Equipotential surface
for recharge streamlines
b) Two dimensional side view
Repository
Recharge streamlines
FIGURE D-VI-17 HEMISPHERICAL REPOSITORY RECHARGE MODEL
VI-32
-------
increase the relative weight of the recharge pathway. Integration
of the above differential equation for h, between arbitrary radii r.
and r_, yields
Ah - h(r2) - Mr,) . ^ < JL - JL ) .
An equivalent resistance for the recharge path is then
Ah 11 Is
M <•» M
Q *
The cumulative resistance from r. - 10 m to r_ » » is therefore
a . JL _L_
recharge 2rrK
It has previously been seen that the discharge resistance is given by
L
Discharge " KA
6 9
and in the present case, L « 230m and A - 8 x 10 nr. Therefore,
o . - 1.6 x 10~4 x K
recharge
"discharge - 2.9 x 10~5 x K
In this case the recharge resistance is larger by roughly a factor of
20.
VI-33
-------
The cumulative fraction of the total resistance between r^ - 1 and
an arbitrary value r- is given by the factor
1 - l/r2
for which selected values are shown in Table D-VI-6. It is clear that
the preponderance of the resistance to recharge flow is close to the
repository. The reason is that the effective cross-sectional area for
recharge increases faster than the corresponding distance from the
repository.
The implication of a recharge pathway resistance of 10 or 20 times
that for discharge would be to decrease the corresponding flow rate by
the same factor. Whether this factor should be incorporated depends on
an additional factor, which is discussed in the next section.
J. NON-STEADY-STATE FLOW
The calculations in the previous sections have been based on the
assumption of steady state flow. This assumption may underestimate
actual flow in case there are transient sources of fluid closer to the
discharge path. A potentially important source consists of the void
spaces in the repository backfill and in the surrounding rock. Changes
in temperature and hydrostatic pressure in a rock mass can cause changes
in void space volume with the result that water can be stored or
released. If the potential changes in total stored water are
substantial, compared with the volumetric flows being calculated for
certain failure elements, then the recharge resistance assumes less
importance because the water may be coming out of storage instead.
Figure D-VI-18 illustrates a potential storage release mechanism. The
VI-34
-------
TABLE D-VI-6
FRACTION OF TOTAL RECHARGE RESISTANCE
BETWEEN rx - 1 km AND GIVEN r2
r2 (km) fraction (1 - l/r2)
2 1/2
3 2/3
4 3/4
5 4/5
n-1
"
VI-35
-------
(a)
(b)
Rock with fractures
and pores before
repository resaturation
Expansion of openings
by hydrostatic pressure
during resaturation
(0
Partial contraction of openings
due to decrease in hydrostatic
pressure from heating of water
and corresponding density change
FIGURE D-VI-18 PORE WATER RELEASE MODEL
VI-36
-------
extent of this mechanism obviously depends on the timing of resaturation
compared to the peak thermal period, both of which depend on many site
and repository parameters.
Since the purpose of this section is primarily to estimate whether
the quantities of water available from storage could be an important
factor to consider, two example calculations will be carried out, one
for the water stored in the repository backfill and one for the water
stored in the rock itself.
From Appendix D-II, the void space volume in the backfill is
f Q
expected to be about 2 x 10 m . The actual volume is a function of the
effective stress on the backfill, which equals the total stress minus
the effect of fluid pressure. If the overburden has shifted so that the
backfill has voided mechanical equilibrium, then the total stress
remains essentially constant, so that changes In fluid pressure imply
equal changes in effective stress, although in the opposite direction.
These changes in effective stress change the volume, primarily because
of grain movement. The parameter that measures this effect is the
compressibility a, defined as the fractional volume change per unit
change In effective stress. Representative volumes are shown in Table
D-VI-5, which also shows the compressibility of water. The change in
hydrostatic pressure due to changes in density of the overlying water
has been discussed earlier in this report. For a granite repository
with a distance of 260m from the repository to the water table, a change
from P - 1 to P « P* « 0.95 results in a pressure change of 17 psi at
the repository depth. With a normal compressibility of 10 psl , the
3
corresponding volume change would be 340m . This number is larger than
a number of flow rates calculated in the main text, in which case
recharge resistance might not be an important factor.
Similarly, the storage capacity of the bulk rock may be considered.
-4
Using a porosity value of 10 , the void space volume in the rock below
the repository down to a depth of 1000m is given by
V - (8 x 106m2) (540m)10~4
5 3
- 4 x 10 m
—7 -1
With a compressibility of 10 psl and a pressure change of 17 psi,
the water released would equal the change in rock volume, given by
7.3 x 103 - (8 x 106m2)(540m)(10~7 psi"1)(17 psi).
VI-3 7
-------
Note that since the rock volume is so much larger that the water volume
stored in voids, the compressibility of the water itself has little
importance here. At the rate calculated above, the flows through bulk
rock could not be met for long using this source of water. Obviously, if
the parameters were different, then possibly the compressibility could
have some effect on the flow calculations.
K. CONCLUSIONS ON RECHARGE RESISTANCE
For the case of flow through granite, it appears appropriate to
decrease by an order of magnitude the effective hydraulic gradients
*
calculated by the formula i = 1- P , in order to account for the
resistance of the recharge pathway. In basalt and shale, water is
available from the lower aquifer. For large breaches, such as faults,
recharge can occur through the fault itself, and no recharge resistance
should be included. This appears to be a conservative approach, but not
overly so. For small breaches, such as boreholes, sufficient recharge
resistance can be assumed through the repository, so that significant
resistance along this part of the system cannot be assumed.
VI-38
-------
REFERENCES APPENDIX D-VI
1. Dames & Moore. Technical Support for GEIS: Radioactive Waste
Isolation in Geologic Formations. Vol. 21: Ground Water Movement
and Nuclide Transport. For Office of Waste Isolation, Union Carbide
Corporation. Y/OWI/TW-36/26. April 1978.
2. Ka'rnbra'nslesa'kerket (KBS). Handling of Spent Nuclear Fuel and Final
Storage of Vitrified High Level Reprocessing Waste. Stockholm,
Sweden. December 12, 1978.
3. Apps, J.A., et al. An Appraisal of Underground Radioactive Waste
Disposal in Argillaceous and Crystalline Rocks: Some Geochemical,
Geomechanical, and Hydrogeological Questions. Lawrence Berkeley
Laboratory. LBL-704. June 1978.
4. Dames & Moore. Technical Support for GEIS: Radioactive Waste
Isolation in Geologic Formations. Vol. 20: Thermomechanical Stress
Analysis and Development of Thermal Loading Guidelines. For Office
of Waste Isolation, Union Carbide Corporation. Y/OWI/TM-36/20.
April 1978.
5. Chemical Engineers Handbook. R.H. Perry and C.H. Chilton, eds. 5th
Edition. McGraw-Hill Book Company, New York. 1973.
6. Freeze, R.A. and J.A. Cherry. Groundwater. Prentice-Hall, Inc.,
Englewood Cliffs, N.J. 1979.
VI-39
-------
APPENDIX D-VII
SALT CREEP
-------
APPENDIX D-VII
SALT CREEP
A. INTRODUCTION
When subjected to loads for extended time periods, many materials
undergo gradual plastic deformation subsequent to the initial elastic and
plastic response. This gradual deformation is known as creep and, of the
geologic media under consideration, it appears significant only in the case
of salt deposits. This suggests a possible advantage of salt for waste
containment because certain breaches may tend to be "self-healing" through
plastic creep. This appendix provides the basis for analysis of this
healing process by examining the creep closure of cylindrical openings in
salt. The principal mathematical method used is a standard engineering
approach for the analysis of three-dimensional creep. In the following
analysis, this method is combined with empirical data and a stress analysis
of a circular opening to produce estimates of closure times.
B. MATHEMATICAL CHARACTERIZATION OF STEADY-STATE CREEP
This analysis will be based on a steady-state uniaxial creep law due to
(2)
Heard. The law may be stated as follows:
- in-6 -11833/6 5.5 (1)
e = 3 x 10 e a v '
where
° » applied stress (bars)
9 = temperature ( K)
e = strain rate (sec )
After conversion of stress units to psi and evaluation at 60°C, the
equation becomes
e = 1.1 x ICf20 a5'5
VII-1
-------
Since this is a uniaxial law, it is necessary to develop a
generalization to describe creep in response to a three-dimensional stress
field. In the development, the stress field is represented by three
mutually orthogonal principal stresses denoted o., a^t a$ an<* their
corresponding strains e , e., e . The basic assumptions, based on
observations of plastic flow, are that during creep there is no change of
volume and that the principal shear strain rates are proportional to the
principal shear stresses. Under the assumption that the strains are small
compared to unity and that there is no rotation of the strain axes, these
assumptions may be expressed mathematically as
or ei "*" £2
- °2 °2 * °3
where C is a constant at a given point and time in the stressed body.
Together, equations (2) and (3) imply that
- f C
In order to fully characterize the three-dimensional creep, it remains to
determine the constant C based on the uniaxial creep law of Equation 1.
There are a number of approaches to this, but a standard technique
(supported by experiment) is to assume that in steady-state
three-dimensional creep,
VII-2
-------
«„*)
*
•
where e , o are, respectively, the octahedral strain rate and octahedral
stress as defined by:
o* - - ((al - a2) + (o2 - a3) + (o3 - o^]
Combining this with Equation 4 and the uniaxial law, Equation 1, it
follows that:
1.1 x 10~2°(o*)4'5[a1 - i
1.1 x 10~20(o*)4'5[o2 - f
e3 » 1.1 x 10"2°(o*)4'5ta3 - | (ax + o2)]
This provides the required description of three-dimensional creep in
response to a general stress field.
C. APPLICATION TO CLOSURE OF A LONG CYLINDRICAL OPENING
In order to model the creep closure of a borehole or tunnel shaft, the
above result can be interpreted for the case of a long circular cylindrical
opening. The stresses result from the ambient lithostatic pressure. It
will be assumed that the creep is steady state, the medium is isotropic,
and the cylinder is very long in relation to its radial dimension. From
(3)
the literature (e.g. ), it can be demonstrated that, based on these
assumptions and if the pressure in the borehole is much smaller than
lithostatic pressure, the following principal stresses are present at the
VII-3
-------
boundary.
Q0 = 2p (6)
ar - °
where p is the lithostatic pressure and the principal stress directions are
taken along the cylindrical coordinate axis.
*
It follows that the octahedral stress, a is given by
r I
°* = -r [(ar - °e)2 + <°r - °z)2 + (oe - °z)2]2
= 1.2p
Application of Equation 5 implies that the radial strain rate is given by
er = 1.1 x 10'2°(o*)4-5[ar - \
-------
assumptions were made. Some of the most important are:
• The creep closure is characterized as a steady-state process,
• The surrounding salt is completely homogeneous.
• The creep behavior is described as
** -20 SS-1
e - 1.1 x 10 (a*) ° yr
where
e* = octahedral strain rate
*
a = octahedral stress
• The creep process occurs without net change of volume.
• The principal shear strain rates are proportional to the principal
shear stresses.
The first two assumptions are made to permit an analytical estimate of
closure rates for a generic repository. To eliminate these assumptions
would require detailed finite element analysis, which is not feasible in
the absence of site-specific information. Such an analysis is not,
however, expected to alter the order of magnitude of the results. The
third assumption is based on the most recent empirical impure data obtained
for the WIPP project and is felt to represent the best available
information on salt creep under expected conditions in the vicinity of a
repository. The final assumptions are standard in the analysis of plastic
creep and are based on extensive observations of creep processes.
The result of the analysis is that the opening will close
according to the following relation:
VII-5
-------
, „ -1.1 x 10~2 t
r(t) =• r e
where
r « initial radius
t = time since opening was created
r(t) - radius at time t .
The breach-of-containment mechanisms discussed in this report involve holes
in the range of 10 cm to 5 m in radius. Table D-VII-1 summarizes the
resulting closure of holes in this size range.
From the governing equation it is clear that both radius and
cross-sectional area, considered as functions of time, are concave up, so
that between any two points they are bounded by the linear function
connecting those points. For simplicity, therefore, cross-sectional area
can be modeled as a linear function of time, equal to 0 at a time when the
opening may be regarded as essentially closed. Since for long tunnels or
holes the volume can also be modeled in this fashion. For non-circular
openings, closure can be considerably faster than for circular ones and it
is, in general, conservative to use the closure rates for the latter. For
backfilled openings, the fractional rate of change of the pore space will
be taken to be the same as for the open holes. To cover all these cases,
two very simple rules have been adopted, therefore. For first estimate
calculations, the void space of an open or backfilled opening in salt is
assumed to decrease linearly to approximately zero in 200 years. This
number is consistent with the above calculations. For second estimate
calculations, the void space is assumed to decrease to approximately zero
in 1000 years. Slower creep could result from the nature of the overburden
and interbeds, as well as from impurities in the salt itself.
VII-6
-------
TABLE D-VII-1
ESTIMATED CLOSURE RATES OF CYLINDRICAL OPENINGS IN SALT
Radius (m)
Percent/closure Times (vrs)
50
90
99
60
210
420
O.lm initial
5 x 10
-2
1 x 10
-2
1 x 10
-3
5 m initial
2.5
0.5
0.05
VII-7
-------
REFERENCES
1. Finnie, I., and W.R. Heller. Creep of Engineering Materials.
McGraw-Hill Book Company, Inc., New York, 1959.
2. Sandia Laboratories (Dawson, P.R. ). Constructive Models Applied in
the Analysis of Creep of Rock Salt. SAND 79-0137. Jan., 1978.
3. Timoshenko, S., and J.N. Goodier. Theory of Elasticity. McGraw-Hill
Book Company, Inc., New York, 1951.
VlI-3
-------
APPENDIX D-VIII
CANISTER CAPABILITIES FOR LONG-TERM
ISOLATION
-------
APPENDIX D-VIII
CANISTER CAPABILITIES FOR LONG-TERM ISOLATION
A. INTRODUCTION
The systems under consideration for nuclear waste isolation offer
many barriers for waste containment, including the waste form itself,
the canister and overpack materials, the vault sleeve and backfill
materials, and the geologic formation. The geologic environments
currently being investigated are salt and hardrock formations, as well
as sediments on the ocean floor. The waste may be directly disposed as
spent fuel rods or may be altered to a different form. This appendix
will consider the protection that may be expected from the canister and
overpack layers.
B. CANISTER SYSTEM DEVELOPMENT
There are four steps in the development of a canister system:
1. performance criteria development and environmental
specifications;
2. materials development;
3. canister design; and
4. system demonstration.
These steps may be worked on concurrently but they must be completed in
sequence.
The development of performance criteria will set lifetime goals for
the canister. It must be determined whether the canister should remain
intact for (a) retrlevability purposes, about 25 years, (b) the high
radio/thermal activity period, 500-1000 years, or (c) the radionuclide
lifetimes, up to 10 -10 years. The controlling failure mechanisms and
rates for a given material will depend upon many environmental
parameters, which in turn will vary with the geology and the waste form.
Estimates for several parameters are given in Table D-VIII-1. These
estimates have not been designated as design criteria but have been
useful guides for experimentation.
VIII-1
-------
TABLE D-VTII-1
ISOLATION ENVIRONMENTS*
Geologic Formation Maximum
and Waste Type Temperature Pressure Chemistry
Bedded Salt
Transuranic-Low
Level Waste
30
Spent Unreprocessed
Fuel 70-100
High-level Waste
250
Sub-seabed Sediments
High-level Wastes 200
Shale, Hardrock, Tuff
High-level Waste 250-300
14.5 MPa Dry (1/2%) 95% Nad
17.9 MPa Dry (1/2%) 9«%
17.9 MPa Dry (1/2% H,0) , 98% NaCl
with potential localized
intrusion of
NaCl-KCl-MgCl. brine (due
to thermally induced
brine migration)
55 MPa Seawater-saturated
sediments (40% solids)
Atmospheric Air + steam for » 100
years, then possibly
inundated groundwater
*Does not take radiolysis into account
Source:
Braithwaite, J.W., and N.J. Magnani. Corrosion Considerations
for Nuclear Waste Management. In: Scientific Basis for Nuclear
Waste Management, G.J. McCarthy, ed., Plenum Press, N.Y. , 1979.
VIII-2
-------
Once the design goals and service conditions are set, input from a
materials development program is necessary. Laboratory experiments can
generate general corrosion rates, but it is also important to quantify
the susceptibility of materials to localized corrosion that will result
in accelerated corrosion rates. Localized corrosion mechanisms include
pitting, crevice corrosion, and stress-corrosion cracking. The
following sections will summarize the materials development work in the
United States and Sweden.
When the materials are sufficiently characterized, an integration of
the information should result in a canister design that can meet the
lifetime goals in the specified environment. It is not clear whether a
single barrier or a multi-barrier system will be preferred. A
multi-barrier system must be designed carefully, so that the presence or
failure of one barrier will not inadvertently hasten the failure of
another- This effect could occur by galvanic corrosion if two metals
are in contact or when the corrosion product of one barrier could be
especially aggressive to another barrier.
C. U.S. MATERIALS DEVELOPMENT PROGRAMS
The materials development program in the United States is in an
early stage. Many materials are being evaluated but no specific systems
have yet been singled out. The broadest-based U.S. study has been at
Sandla Laboratories where a number of metals have been evaluated as
(1 2)
potential high-level waste canister materials. ' Laboratory
investigations there have measured coupon weight losses for periods of
2-8 weeks in autoclaves. The solutions modeled brine from salt
formations and seawater from sub-seabed sediments. Temperature,
dissolved oxygen, and moisture content were also varied. Sandia has
also been active in bench-scale heated salt block experiments as well as
full-size heated field tests. As a result, Sandia has selected eight
metals for further study. The criteria for selection included corrosion
resistance as well as metal cost and availability. The eight metals
are: 1018 mild steel; Corten A steel, ; lead; 90-10 cupronickel;
SS-Ebrite 26-1,(b); Monel 400,(c); Inconel 600,(c); and Ticode 12.(d)
VIII-3
-------
Table D-VIII-2 summarizes the corrosion rates of these materials in a
brine and a seawater solution.
It appears possible to design an overpack material to last thousands
of years if general corrosion is known to be the only corrosion
mechanism at work. This conclusion is similar to that presented in the
Task B Report. Autoclave experiments provide general corrosion rates
but are not very helpful in providing accelerated rates resulting from
local corrosion mechanisms.
Work under way at Battelle's Pacific Northwest Laboratories (PNL)
will complement the results from Sandia and continue the broad-based
approach. Autoclave experiments will provide further data on
corrosion rates utilizing both groundwater solutions and brine. PNL
will investigate ceramic and polymeric materials as well as metals.
The materials development program at Savannah River Laboratory has
been limited to studying canisters for vitrification (through either
continuous or in-can melting). The canister lifetime goals have not
been in the range of thousands of years but rather are intended for
interim storage and shipping purposes. Overpack materials are not being
studied.
Trademarks: (a) U.S. Steel Corporation, (b) Allegheny Ludlum
Industries, (c) Huntington Alloys, and (d) TIMET.
VIII-4
-------
TABLE D-VIII-2
CORROSION RATE IN BRTNE AND SEAWATER OF THE
EIGHT CANDIDATE MATERIALS
Brine Seawater
(mm/yr) (mm/yr)
1018 Mild Steel 1.7 0.4
Gotten A Steel 0.9 0.2
Lead 0.5 0.3
90-10 Cupronickel 0.14 0.07
SS-Ebrite 26-1 0.016 0.005
Monel 400 0.03 0.1
Inconel 600 0.009 0.005
Ticode 12 0.0006 0.005
Source: Braithwaite, J.W., and M.A. Molecke, High Level Waste Canister
Corrosion Studies Pertinent to Geologic Isolation. NRG
Conference on High Level Radioactive Solid Waste Forms, Denver,
December 19-21, 1978.
VIII-5
-------
D. SWEDISH PROGRAM
The Swedish Corrosion Institute and its research group seem to be
somewhat ahead of the United States in regard to the four steps of
canister development. Granite rock has been specified as the geologic
environment. Three specific alternatives for the disposal of spent fuel
in hardrock formations have been recommended:
1. reprocessed waste in a 6 mm-thick titanium canister with a
100-mm thick lead lining,
2. spent unreprocessed fuel in a 200-mm thick pure copper canister;
and
3. spent unreprocessed fuel in 100-mm thick aluminum oxide canister
produced by hot isostatic pressing.
The feasibility of manufacturing aluminum oxide canisters by means
(4)
of hot isostatic pressing (HIPing) has been demonstrated. HIPing is
a process that produces very dense ceramic bodies without excessive
grain growth but is normally applied to much smaller samples. An
aluminum oxide lid can be sealed onto the main body, also by means of
HIPing. The flat surfaces that form the seal must first be polished to
a flatness of + 25 ym.
Aluminum oxide is in its highest oxidation state and is therefore
very stable in groundwater. It will, however, be hydrated on surfaces
in contact with water, which may result in flaking. This reaction is
very slow and aluminum oxide should easily resist the action of
groundwater for a million years. Being a ceramic, it is very
susceptible to slow crack growth, which could lead to delayed failure.
In order for this to occur, a surface defect and tensile stresses, both
of sufficient magnitude, must be present. The stresses may be due to
residual stresses from fabrication or applied stresses from rock
movement. Care must be taken during fabrication of these canisters to
minimize defects and residual stresses. Nondestructive evaluation
techniques may be used to verify the maximum defect size before final
disposal.
A copper canister was also designed for the isolation of
unreprocessed spent fuel assemblies. ' It is to be made from very
pure oxygen-free high conductivity (OFHC) copper. The fuel rods are to
VIII-6
-------
be stripped from the metal components of the assembly to maximize space
usage. After the rods are placed in the copper container, the spaces in
between will be filled with lead. Three copper lids are then electron
beam welded to seal the can.
Copper is a relatively noble metal and free oxygen and sulfide are
the only constituents of groundwater that can potentially cause
corrosion. Considering all of the sources of free oxygen and sulfide in
the repository, a weight loss estimated at 60 kg will occur after a
million years. This loss corresponds to an average corrosion depth of
0.5 mm or a maximum depth of 2.4 mm if the top of the canister is
attacked more heavily. Copper is not highly susceptible to pitting but
it can occur in some cases. Using an empirical model, the maximum
attack depth after one million years is predicted to be 60 mm or 30% of
the wall thickness.
In Sweden, the storage container for vitrified reprocessed waste has
/a \
been designated to be a lead-lined titanium canister. The waste is
to be cast into or melted in a stainless steel cylinder. These
stainless steel cans will be placed in the prefabricated lead-titanium
canister and any extra space filled with molten lead. The container
will be sealed by a welded-on titanium lid. Both the lead and the
titanium are to be very pure.
Titanium develops a passivating layer of Ti02» which forms
spontaneously and protects against corrosion. Assuming a constant
corrosion rate, the 6-mm thick casing should last beyond thousands of
years. Pitting, crevice corrosion, and stress-corrosion cracking do not
appear to be problems. The initial prediction of lifetime was thousands
(8)
of years, but a recent report has downgraded the lifetime of the
(9)
titanium shell. This revision was based on a slight risk of delayed
failure from the presence of hydrogen, causing penetration of the
titanium in a rather short time. Hydrogen can diffuse through the
titanium and become concentrated at defects. This action results in
embrittlement, and possibly delayed fracture, at tensile stresses much
lower than those normally involved. Small amounts of hydrogen will be
present in the fabricated titanium and hydrogen may also evolve as a
corrosion product. It is very difficult, however, to predict the extent
to which this evolved hydrogen will be absorbed. Although this type of
VIII-7
-------
delayed failure has never been found in unalloyed titanium, it is not
completely understood, and thus, the risk of its occurring cannot be
eliminated completely. Therefore, no lifetime limit has been predicted
for the titanium casing.
Pure lead is also very corrosion-resistant. Because of the titanium
casing, any attack on the lead would be localized, with the rate
dependent upon the amount of available oxygen. Estimates of this
quantity lead to a predicted lifetime of thousands of years for the 100
ram-thick lead lining. According to Swedish estimates, the total lifetime
of the lead-lined titanium canister in groundwater is given as thousands
of years, although it probably will be tens of thousands of years.
E. SUMMARY
The canister development program in the United States is not at the
stage where it is possible to make an estimate of canister lifetime.
Specifications for the service conditions must be set and considerable
materials development work is still needed. When this is all integrated
into a canister design, a lifetime evaluation will be possible.
However, from results to date of the U.S. program and taking into
account the Swedish work on specific canister systems, it seems highly
likely that it is possible to design a viable canister that will last
thousands and possibly tens of thousands of years.
VIII-8
-------
REFERENCES - APPENDIX VIII
1. Braithwaite, J.W., and N.J. Mag nan1. Corrosion Considerations for
Nuclear Waste Management. In: Scientific Basis for Nuclear Waste
Management, G.J. McCarthy, ed. Plenum Publishing Corporation, New
York. 1979.
2. Braithwaite, J.W., and M.A. Molecke. High Level Waste Canister
Corrosion Studies Pertinent to Geologic Isolation. Presented at
Conference on High Level Radioactive Solid Waste Forms, sponsored by
the Nuclear Regulatory Commission, Denver, Colorado, December 19-21,
1978.
3. Personal communication, MaxKrelter, Pacific Northwest Laboratories.
4. Savannah River Laboratory (Rankin, W.N.) Compatibility Testing of
Vitrified Waste Forms. Report DP-MS-77-115 (rev. 2/15/78).
5. Mattsson, E. Corrosion Resistance of Canisters for Final Disposal
of Spent Nuclear Fuel. In: Scientific Basis for Nuclear Waste
Management, G.J. McCarthy, ed. Plenum Publishing Corporation, New
York. 1979.
6. Karnbranslesakerhet (KBS). Handling and Final Storage of
Unreprocessed Spent Nuclear Fuel. Stockholm, Sweden. 1978.
7. Ibid. Copper as Canister Material for Unreprocessed Nuclear Waste
Evaluation with Respect to Corrosion. Technical Report 90,
Stockholm, Sweden. 1978.
8. Ibid. Handling of Spent Nuclear Fuel and Final Storage of Vitrified
High Level Reprocessing Waste. Stockholm, Sweden. 1978.
9. Ibid. Corrosion Resistance of Titanium Canisters Lined with Lead
for Final Disposal of Reprocessed and Vitrified Waste from Nuclear
Reactors. Technical Report 107, (in Swedish), Stockholm, Sweden.
1978.
VIII-9
-------
APPENDIX D-IX
THERMAL STRESS CRACKING IN SALT
-------
APPENDIX D-IX
THERMAL STRESS CRACKING IN SALT
A. INTRODUCTION
The purpose of this appendix is to present a set of rock mechanics
calculations undertaken to assess the possibility that fracture pathways
would develop from the repository to the upper aquifer, especially in
the case of a repository in salt. Two types of stress have been
addressed: thermal stresses and stresses around mined openings in rock,
with emphasis on the former.
The existence of a repository and the heat released by it alter both
the state of stress and the mechanical properties of the host formation.
While stress concentrations around underground openings have been
studied extensively, thermal stresses complicate the problem; for much
of the time, these thermal stresses are dominant. Should the total
applied stresses exceed the strength of formations surrounding the
repository, fractures may breach the geologic barrier.
B. BASIS FOR ESTIMATION
Analysis of stresses about manmade underground works has been
undertaken with varying degrees of sophistication for about thirty
(1 2 3)
years. ' ' In-situ stress measurements generally confirm the
predictions of analytical models within the normal limits of accuracy of
geomechanics.
With few exceptions, analyses of stresses and strength in
geomechanics are deterministic. Material properties are specified as
constant over large regions; it is then possible to analyze and compare
them with strengths. Results are expressed as the ratio of available
resisting strength to driving load in specified models of failure; the
ratio is commonly called the "Factor of Safety" (FS). Because no
sources of uncertainty are included in these analyses, quantitative
estimates of probabilities of failure are not possible. Through long
experience, rules of practice for acceptable Factors of Safety have
IX-1
-------
emerged. The extrapolation of "acceptable" FS to unique cases is
difficult, however.
The most important mode of failure considered in estimating the risk
of high-level waste (HLW) escaping the repository is the formation of
continuous channels connecting repository and aquifer. Traditional
stress analyses predict zones of failure, rather than fractures.
Generally, the stress field is compared with rock strength and for these
regions in which strength is exceeded by stress, the rock is said to be
(4)
"failed" or "plastic". A typical result is shown in Figure D-IX-1.
The conclusion of this type of analysis is that zones of failure develop
adjacent to the repository, but beyond about one opening diameter from
the repository (expected) stresses do not exceed (expected) strengths.
The expected FS against failures that extend beyond the failed zone is
typically much greater than 1.0.
Stress analysis can be made with varying levels of sophistication.
Assumptions can be made about alternative deformation behavior (e.g.,
elasto-plastic, strain-hardening, strain-softening, etc.), about the
influence of jointing, and the like. Yet, the predictive results are
qualitatively the same: in some regions adjacent to the opening,
stresses exceed strengths; in regions away from the opening, stresses do
not exceed strengths. The shapes of failed zones are sensitive to
geometric details (i.e., sharp corners concentrate stresses locally).
For the purpose of estimating risks such conclusions are Inadequate,
since they do not follow the development of the fracturing all the way
to the aquifer.
At present, there are no modeling techniques for rock fracturing
that incorporate uncertainty. Thus, an approach to this problem was
developed specifically for the present analysis. This approach treats
rock properties as random variables, and calculates the reliability of
host formations against failure in particular modes, under
deterministically predicted stress fields. The approach and its
underlying assumptions are presented below.
The purpose of this analysis cannot be to calculate precise
probabilities for a breach of the geologic barrier through
overstresslng, because such calculations are not possible in the present
state of geomechanics. Rather, the purpose is to establish whether the
IX-2
-------
0 yr
0.1 vr
1.0 vr
5.0 vr
30 .vr
Note: Dotted areas indicate regions within the rock for which applied stresses
exceeded strength.
Source: Mathab, M.A., J.L. Ratigan, and D.R. McCreath. Stability of a Radioactive
Waste Repository in the Canadian Shield. 18th U.S. Symposium on Rock
Mechanics, 1977.
FIGURE D-IX-1 RESULTS OF STRESS ANALYSIS STUDIES PERFORMED FOR WASTE
STORAGE IN FORMATIONS OF THE CANADIAN SHIELD
IX-3
-------
inherent uncertainties in rock properties within a bedded salt formation
chosen for its uniformity lead to important uncertainties on breaching.
A limiting equilibrium model is constructed which, while typical of
geotechnical models, is only one of many that could have been used.
Reasonable estimates of material property uncertainty and spatial
variability are propagated through the model. Average salt properties
are sufficient to protect the repository against breaching; the question
is whether there is a significant probability that worse-than-average
properties may occur in such a way that breaching becomes possible.
This analysis yields a prediction that is more qualitative than
quantitative; the numerical results are accurate, not to an order of
magnitude, but to a few orders of magnitude.
Many numerical models have been developed for studying stress and
temperature distributions around potential repository openings, and many
mechanisms of breaching failure have been studied. All of these studies
have led to consistently high deterministic factors of safety. The
present analysis estimates whether such factors of safety may lead to
significant probabilities of the development of release pathways.
C. FAILURE THEORY FOR ROCK
Rock, including salt, is a frictional material the strength of which
depends on two properties: one independent of ambient stresses,
generally called the "cohesion"; and one dependent on ambient stresses,
generally called the "friction angle". Rocks display greater strength
under confinement than when unconfined, and this increase in strength is
dependent on the confining stress.
The Mohr failure criterion for rock is shown in Figure D-IX-2,
plotted with normal stress as abscissa and shear stress as ordinate.
Following this criterion, failure occurs when the shear stress on a
plane, T, exceeds some monotonic function of the normal stress on the
plane, a,
T ra g(o) (1)
IX-4
-------
SHEAR
STRESS
r
•FAILURE
ENVELOPE
(TENSILE)
°3 °
NORMAL STRESS
(COMPRESSIVE)
Note: Semi circles represent loci of stresses for planes of varying orientation with major
principal stress o\, minor principal stress o3, and intermediate principal stress Oj.
FIGURE D-IX-2 MOHR FAILURE CRITERION FOR ROCK
IX-5
-------
Equation 1 is sometimes approximated by the linear relationship
T « C + a tan •
where C is the "cohesion", and 4>, the "friction angle". Equation 2 is
commonly called the Naviser-Coulomb criterion. The Mohr failure
criterion (Equation 1) has been empirically verified, and is widely
used.
Under high pressures, Mohr envelopes for rocks typically become
flat, and the materials behave cohesively. Failure strengths cease to
be dependent on normal stress. While the slope of the Mohr envelope
gradually changes, a bilinear approximation is often used Instead
(Figure D-IX-3). The inferred transition pressure between frictional
and cohesive behavior depends on the particular rock and the ambient
temperature. Transition pressures decrease with increasing temperature,
with the rate of decrease dependent on the particular rock. In salt,
strength behavior above some transition pressure is usually assumed to
be purely cohesive, while in other rocks (e.g., crystallines) strength
at high stresses still exhibits slight stress dependence. Transition
stresses for salt are anticipated to be within the range of stresses
predicted for repositories at 460 meters.
Intact rock is not perfectly elastic, but displays ductility (i.e.
nonlinearity in stress vs. strain) at high shear stresses (Figure
D-IX-4). Post-failure behavior can range from strain-hardening to
strain-softening, with some materials like salt displaying more ideal
plasticity.
Deformation properties of rock are not important in comparing
stresses with strength, but they are important in predicting stresses in
the first place. According to elasticity theory, elements of rock
continue to withstand and transmit stresses in a linear way up to and
(theoretically) beyond what are known to be their failure limits. In
reality, however, rock is not perfectly elastic, and incremental
stresses are redistributed around failed elements, replacing sharp
stress concentration with broader bands of lower stress.
Much work has been performed over the past ten years in numerical
analysis of subsurface stresses using assumptions of various
IX-6
-------
to
00
Lul
QC
FRICTIONAL
BEHAVIOR
COHESIVE
BEHAVIOR
'TRANSITION
PRESSURE
(EXPANSIVE)
NORMAL STRESS
(OPPRESSIVE)
FIGURE D-IX-3 Bl LINEAR APPROXIMATION TO CURVED MOHR ENVELOPE
IX-7
-------
oo
LL)
OH
OH
Sj
VOLUMETRIC
(EXPANSIVE)
STRAIN
(COMPRESSIVE)
FIGURE D-IX-4
TYPICAL DEFORMATION BEHAVIOR FOR
BRITTLE ROCKS
IX-8
-------
complexities (e.g. elastoplastic analysis, plastic analysis, etc.).
Changes of these assumptions lead to changes in predictions of stress
distributions and failure zones. Of course, as pointed out before,
changes in failure zones predicted by a totally deterministic analysis
have little practical importance in an overall safety analysis program.
It is useful, however, to emphasize the point that assumed relationships
of deformation affect stress predictions.
The cost and effort involved in performing stress analysis
incorporating complicated deformation properties must be balanced
against the increase in information, actually derived. With few
exceptions, inelastic stress calculations must be made numerically,
typically using finite element or finite difference techniques. Besides
estimating bulk and shear moduli for the rock, one must estimate various
transition stresses and moduli in each zone of the stress-strain
relationship.
All of these properties can be reasonably estimated for a particular
site, although the accuracy of the estimates depends on the extent of
the exploration and testing program. Tn performing non-site-specific
studies, however, such estimates are difficult; this difficulty extends
to estimating an appropriate modulus for the elastic case. Therefore,
one must ask whether more sophisticated deformation relations are useful
in the present application. In any case, uncertainty in estimating
moduli probably leads to more uncertainty in stress predictions than do
the differences among different deformation models.
Rock masses differ from intact rock in that the former are cut by
pervasive and nonpervasive fractures and inhomogeneities that affect
mechanical behavior. Most important of these features are joints, i.e.,
one or more sets of subparallel fractures separating the rock mass into
blocks. Joint systems are geologic in origin and exist prior to
repository construction, with their character and extent determined by
lithology and geologic history.
Joints affect the behavior of rock masses by lowering deformation
moduli and by introducing planes of weakness. The degree to which
either of these effects occurs depends on the density of joints, their
sizes, and their physical properties (i.e. shear and normal stiffness,
and frictional resistance). All of these properties are site-specific.
IX-9
-------
Common practice in analyzing the behavior of jointed rock masses is
to use continuum models, but to modify deformation moduli and strength
parameters by reduction factors. Sometimes anisotropy is also
introduced. Discontinuum models for jointed rock require information
specific to the rock mass and opening geometry. '
Salt is a low-viscosity material that can flow under stress and in
which fractures heal quickly. Therefore, salt formations are thought to
be sparsely jointed, if at all. Variations introduced by assuming salt
to be intact are probably within the error band of present analysis,
which among other uncertainties includes those from site-to-site
variability.
D. EMPIRICAL DATA ON SALT STRENGTH
1. Rock Salt Properties
The literature was searched for empirical data on the mechanical
and thermal properties of in situ salt, in order to estimate values
for the following parameters:
1. thermal conductivity and heat capacity,
2. Young's (deformation) Modulus and Poisson's Ratio, and
3. strength parameters (cohesion and friction angle).
Such an estimate was difficult because of the lack of
comprehensive published information on the subject, and because
these properties vary with temperature and the strain rates. Some
simple assumptions were therefore made in the study. Where
necessary, the available published data were extrapolated to the
conditions of the model repository, which were taken to be:
_ y i o
temperatures from 0 to 300 C; strain rates from 10 to 10 min-1.
2. Thermal^Properties
Thermal conductivity has been measured in several studies
dealing with waste repositories/7'8'9'10^ Findings from the
literature are summarized in Figure D-IX-5. Reported values of
IX-10
-------
10
8
.c
CO
>-
o
Q
§ 4
o
estimated range
at roon temp.
polycrystalline
latural rock salt **
ingle crystal
NaCl t
assumed for
analysis *
estimated
range at
room temp.
100 200 300 400
TEMPERATURE (°C)
500
600
700
Sources: * Arthur D. Little, Inc. Task B Report.
**Westinghouse Astronuclear Laboratory, A Study of Borehole Plugging in
Bedded Salt Domes by Earth Melting Technology. WANL-TME-2870, 1975.
t Kaufman, D.W. (ed.) Sodium Chloride: The Production and Properties of Salt and
Brine. Reinhold Publishing Co., N.Y., 1960.
FIGURE D-IX-5 THERMAL CONDUCTIVITY OF ROCK SALT
IX-11
-------
thermal conductivity are in the range 1-10 Btu/(f t-hr-°C), and the
values decrease with increasing temperature. '
Many of the laboratory data reported in the literature are from
tests on single crystals of salt, so the properties of
polycrystalline salt (i.e. rock salt) had to be estimated from
sparse data. The curve labeled "rock salt" in Figure D-IX-5 was
extrapolated from tests on polycrystalline salt at room temperatue
(24°C), using the trend observed in single crystal tests.
Specific heat data are shown in Figure D-IX-6. ' Reported
values of specific heat are in the range 8-11 Btu/(gm- C), which is
in the upper range of values for other rocks, and are
temperature-dependent. Specific heat increases with increasing
temperature.
Density data are shown in Figure D-IX-7. ' While the data
are sparse, a range of 1.95-2.2 seems appropriate. As expected,
this range is somewhat below that of most rocks. As with other
properties of salt, density is temperature-dependent, decreasing
with increasing temperatures.
3. Mechanical Properties
Estimation of elastic properties for salt, Young's Modulus and
Poisson's Ratio, is complicated by temperature-dependence and
viscosity. Creep from viscosity at low strain rates decreases the
deformation moduli reported in the test results.
Published values of Poisson's Ratio for rock salt are shown in
Figure D-IX-8.(11'14'15) Within the range of temperatures of
interest for the repository, a Poisson's Ratio of about 0.22 is
appropriate. It should be noted that thp Poisson's Ratio enters
2 _i
stress calculations through the term (1-v ) (where v is the
Poisson's Ratio) which means that stress predictions are not
sensitive to minor uncertainties in the ratio.
Published data on Young's Modulus for rock salt are shown in
Figure D-IX-9. ' ' Temperature trends in both dynamic and
static testing are similar, the modulus decreasing slightly with
increasing temperature for the range 0-300°C. The disparity between
IX-12
-------
X
CM
I O-
CD
CV
CO
O
LU
O- I--/
*
**
TOO
200
300
400
500
600
700
TEMPERATURE: (°c)
melting
temperature
800
900
inno
Sources: "Arthur D. Little, Task B Report.
**Gera, F. Review of Salt Tectonics in Reaction to the Disposal of Radioactive Waste in Salt Formations.
Geological Society of America. 83,1972.
tKaufman, D.W. (ed.). Sodium Chloride: The Production and Properties of Salt and Brine. Reinhold Publishing Co.. N.Y., 1960.
FIGURE D-IX-6 SPECIFIC HEAT OF ROCK SALT VS TEMPERATURE
-------
I
M
*-
2.4
2.2
2.0
1.8
o>
s1'6
'Z
c
tt)
1.4
1.2
1.0
melting I temperature
I
100 200 300 400 500
Temperature (°C)
600
700
800
900
1000
Sources: 'Arthur D. Little, Task B Report.
**Gera, F. Review of Salt Tectonics in Reaction to the Disposal of Radioactive Waste in Salt Formations. Geological Society of
America. 83,1972.
tKaufman, D.W. (ed.). Sodium Chloride: The Production and Properties of Salt and Brine. Reinhold Publishing Co., N.Y., 1960.
FIGURE D-IX-7 DENSITY OF ROCK SALT VS. TEMPERATURE
-------
l/i
0.4
0.3
as
CC.
O
'§.
0.2
0.1
I
I
I
I
I
100
200
300
600
700
melting
temperature
I
800
900
400 500
Temperature (°c)
Sources: Westinghouse Astronuclear Laboratory, A Study of Borehole Plugging in Bedded Salt Domes by Earth Melting Technology. WANL-TME-
2870,1975.
Hunter, L., and S. Siegel. The Variation with Temperature of the Principal Elastic Moduli of NaCI Near the Melting Point. Physical
Review, 61,1942.
Starfield, A.M., and W.C. McClain. Project Salt Vault. J. Rock Mechanics and Mineral Sciences, 10, 1973.
1000
FIGURE D-IX-8 POISSOIM'S RATIO VS. TEMPERATURE
-------
o 5
x
ji
I 4
ui
"5
2! 3
•Dynamic Modulus — Average Values for Polycrystals.
(derived from Single Crystal Data of Reference 14)
_]••— Elastic (reload) static modulus (data from Reference 16)
Static value for Lyons, Kansas Rock Salt (from Reference 15)
Initial static modulus (data from Reference 16)
k«-Backfigured from in-situ test (from Reference 15)
'Static" Modulus - Values for Grand Saline, Texas Dome Salt (from Reference 8)
I
li
Melting
Temperature
100 200 300 400 500 600
Temperature (°C)
700
800
900
1000
FIGURE D-IX-9 YOUNG'S MODULUS OF ELASTICITY VERSUS TEMPERATURE
-------
dynamic and static testing is much greater than the temperature
effect, which suggests that strain rate and not temperature is the
dominant test variable.
To determine the variation in Young's Modulus with strain rate,
it was necessary to make several assumptions and to use published
creep test data. It was assumed that static moduli reported in the
literature (Figure D-IX-10K ' were tested at a strain rate of
-2 -1
about 10 min . This would correspond to 10% strain in 10
minutes. It was also assumed that dynamic moduli reported in the
4
literature correspond to strain rates of about 10 per minute.
In addition, values of elastic moduli have been back-calculated
from published unconfined creep tests. Uniaxial creep tests for
rock salt, as shown in Figure D-IX-11, were used to determine
the strain at various compressive stresses and temperatures
corresponding to strain rates of 10~ , 10~ , and 6 x 10~ min ,
from which values of Young's Modulus have been determined (Table
D-IX-1) .
Finally, the strain-rate dependence was estimated by rearranging
Starfield and McClain's equation for empirically observed
deformation in rock salt pillars,
e - (0.65 x 10~37) ( )°*25 (T + 273)9'5 o3'0
(3)
where
c « strain
t - time in minutes
T « temperature in C
and
a = uniaxial stress in psi, into the form
u.5o
IX-17
-------
106
M
x
t-«
oo
J 10s
jo
LU
•S 1Q4
o
103
Figure
D-IX-9
104
Estimated
Value of E
•
Versus e
Temperature °C
20° 65° 100° 200'
Hendron
Starfield
•
A
O
A
V
102 1 10'2 10^ ID"5 1Q-8
Strain Rate (cm/cm/mm)
Sources: Hendron, A.J. Mechanical Properties of Rock. In: Stagg, K.G., and O.L. Zienkiewicz, eds. Rock Mechanics in
Engineering Practice. John Wiley & Sons, New York, 1968.
Starfield, A.M., and W.C. McClain. Project Salt Vault. J. Rock Mechanics and Mineral Sciences, 10,1973.
10-
FIGURE D-IX-10 YOUNG'S MODULUS OF ELASTICITY OF ROCK SALT VS. STRAIN RATE
-------
TOTAL
STRAIN
(*)
e = 10"4/hr
e = 10"5/hr
400 800
TIME (hours)
1200
1600
•Temp. 65°C
"Temp. 23°C
Note: Stress is indicated along curves in kg/cm2.
Source: Hendron, A.J. Mechanical Properties of Rock. In: Stagg, K.G., and O.L. Zienkiewicz, eds.
Rock Mechanics in Engineering Practice. John Wiley and Sons, New York, 1968.
FIGURE D-IX-11 UNIAXIAL COMPRESSION CREEP TEST FOR ROCK SALT
IX-19
-------
T°C E(105psl)
23
65
ro
o
20
100
200
10
10
-5
-6
6x10
-5
-7
10
10
-6
6x10
-7
20(7) 4x10
-4
10
10
10
-5
-8
10
10
-11
-5
10
10
10
10
-8
-11
-5
-B
-11
525
750
2800
525
TABLE D-IX-1
UNIAXIAL COMPRESSIVE CREEP TEST DATA
0.(
In) E(10 psi) a(p>l) e(ln/ln)
TEST DATA(2*
11 5.25 1750 0.008
0.0135
" 0.0155
n 3.75 " 0.023
0.0355
" 0.0425
TPCT nATA^- '
E(105pst)
2.19
1.30
1.13
0.761
0.493
0.412
0.0075
9.99
9.92
9.27
9.83
8.56
3.72
7.46
2.27
0.28
3.73
4500 0.0125
BACK-CALCULATED FROM CREEP EQUATION
3.60
(19)
1750
9.72
7.73
2.54
6.16
1.38
0.158
7.33
0.078
0.0079
o(pei)
2250
2250
e(ln/ln)
0.020
0.0435
0.0/.85
0.0115
0.065
9.41
6.16
1.38
4.30
0.701
0.075
0.359
0.037
0.0037
I .13
0.517
0.464
0.714
0.346
-------
where strain rate, e, is in rain" . Values of modulus from this
equation were computed for various stress levels at room
temperature, for strain rates of 10 , 10~8, Id'11 (Table D-IX-1).
Although these values differ from those back-calculated from creep
test data, the trends are similar.
Combining information from each of the above sources leads to a
best estimate of modulus over the temperature and strain-rate ranges
of interest, as shown in Figure D-IX-10. This estimate would
suggest an approximately constant modulus in the range below 10
min , which is the range of thermally applied stresses for the
repository. The value of E in this range is about 3 x 10 psi.
Published values of the coefficient of linear thermal expansion
(18 )
were reviewed. ' The coefficient is only slightly
temperature-dependent (increasing with increasing temperature), but
over the range of interest (0-300°C) the values vary only from 4.03
to 4.7 x 10 C . For the purposes of this analysis, the
coefficient of expansion was assumed not to vary with temperature.
Rock salt sheared at constant temperature and strain rate
exhibits either brittle or ductile behavior, depending on the
confining stresses. Above the brittle-ductile boundary, the Mohr
envelope is flat, (i.e., a constant shear strength for all confining
stresses). In the ductile range, however, the shear behavior is
strain-hardening.
The brittle-ductile transition was assumed to occur, as shown in
Figure D-IX-12, where the curved Mohr envelope for peak behavior
crosses the residual envelope, oriented at the angle of sliding
(19 20 21)
friction. '*' The angle of residual friction was derived from
Figure D-IX-13 to be about 29°.<16»17»22) Reports in the literature
vary from as low as 20° to as high as 40°, with most estimates lying
between 25° and 35°.
A simple (c,) linear approximation to the Mohr envelope called
the Mohr-Coulomb Criterion (Figure D-IX-14) was conservatively
IX-21
-------
20'
M
?
[S3
o (psi x 1000)
Note: TEMP°C * 24° n ^
#150°
"250°
##300°
Sources: Handin, J., and R.V. Hager, Jr. Experimental Deformation of Sedimentary Rocks Under Continuing Pressure: Tests at High Temperature.
Bulletin, American Association Petroleum Geologists, 42: 2892-2934,1958.
Stokes, R J. Mechanical Properties of Polycrystalline NaCI. Proceedings British Ceramics Society, 6: 187—207,1966.
Baidyuk, B.V. (ed.). Mechanical Properties of Rocks at High Pressure and Temperatures. Consultants Bureau Translation, New York, 1967.
FIGURE D-IX-12 SUMMARY OF PUBLISHED SHEAR STRENGTH DATA
-------
NJ
U>
n (kg/cm2)
Sources: Fodor, I., and K. Tokes, Neve Forschungen Uber die Physikelischen and Mechanischen Eigenschaften des Rumanischen Steinsalzes.
Theme 3, No. 78: 705-709. Proceedings 1st Congress International Society Rock Mechanics, Lisbon, 1966.
Serata, S., S. Saknrai, and T. Abachi. Theory of Aggregate Rock Behavior Based on Absolute Three-Dimensional Testing (ATT) of Rock Salt.
Proc. 10th Symposium on Rock Mechanics, 1969.
Hedron, AJ. Mechanical Properties of Rock. In: Stagg, K.G., and O.L. Zienkiewicz, eds. Rock Mechanics in Engineering Practice.
John Wiley and Sons, New York, 1968.
FIGURE D-IX-13 MOHR COULOMB ENVELOPE AT LOW STRESS LEVELS
-------
Td
uniaxial
tension
test
tension, a.
model peak/
ductile
ad =
compression, a
n
tan
FIGURE D-IX-14 LINEAR MOHR - COULOMB ENVELOPE STRENGTH MODEL
-------
assumed to predict peak shear strength for constant temperature and
strain rates. This model is expressed as
o tan
n
P IT,
I d
where
C 2
Td - °t/2
2t ,
d j. ,
a. tan <}>
L t u _
O. • T,/tan d>
ad p
(5)
n >
(6)
tan
-------
800
600
o
o
oc
i
LU
400
200
STRESS (kg/cnr)
FIGURE D-IX-15 STRENGTH LIMITS OF ROCK SALT VERSUS TEMPERATURE
IX-26
-------
where T is the ductile shear strength and o the tensile strength.
These values of shear and tensile strength were used in the
strength model previously discussed, so that:
for v
°a < °d
J4.8 x 103 -540> /tan
|T(°C) + 74 )
T • C(T) + o tan 4> K(T)
p v ' n P
where ,
C(T) -
2
7.07 x 106
T + 1160
» •
5
4.79 x 103
T + 74
4.79 x 105
T 4- 74
**
A
540 1 7'08 X 10 3£(
J*tW T JW\
T + 1160
*y (10)
(11)
. + tan .79 x 10'
T + 74
- 540
-I
r.os x 10;
T •»- 1160
360o tan
(13)
where T is temperature in C,
o is norrail srress,
n
o is the brittle-ductile transition stress, and
$ is the residual fraction angle.
For
Tp Td T + 74
- 540
IX-27
-------
The strength model is, therefore, in terms of only two exogenous
variables (temperature and applied normal stress) and one material
constant (the residual sliding coefficient of friction).
E. STRESS PREDICTIONS
To make predictions on the behavior of a rock mass, both the
mechanical rock mass properties (strength, deformability, and
permeability) and the state of stress must be estimated. These
parameters and stresses are not independent.
1. In-situ Stresses
Prior to construction, a repository site will be in some state
of stress depending on the rock formations and recent geologic
history. For flat-lying sites in tectonically quiet regions, the
principal stress directions will be very nearly vertical and
horizontal. Figure D-IX-16 presents data summarizing in-situ
vertical stress measurements from several sources and from sites
(23)
distributed across North America. The common assumption of
2
gravity stresses for the vertical direction, about 0.23 kg/cm /m (1
psi/ft) of depth, is slightly below the average of these
measurements, but the scatter in the data is large. Among other
sources of this scatter are large measurement errors from the way
in-situ stresses are measured (see, e.g., (2).
Typical densities for rock masses are in the range of
3 3
2560 kg/in . Salt is somewhat lower, or about 2240 kg/m . Thus, the
2
assumption 0.23 kg/cm /m (1 psi/ft) is reasonable, particularly
since the analytical results are insensitive to moderate changes in
vertical and horizontal stresses.
Horizontal stresses within a given profile typically vary
proportionally with vertical stresses. The ratio of horizontal to
vertical stress is therefore defined and assumed to be constant
either for an entire profile or for individual strata or sequences
of strata,
o,
K = -£ (15)
a
v
IX-28
-------
DEPTH (m)
0
150 1
304
460
610
760
915
assuming deqsity of
assuming
stress
.23 kg/cm /m
70 140 210 280 350
VERTICAL STRESS (kg/cm2)
Source: Lidner, E.N., and J.A. Halpern. In-Situ Stress Analysis. 18th U.S. Symposium on
Rock Mechanics, 1977.
FIGURE D-IX-16 APPROXIMATE VERTICAL STRESSES FOR SEVERAL
SITES IN NORTH AMERICA
-------
Figure D-IX-17 shows data summarizing in-situ measurements of
(23)
horizontal to vertical stress ratio, K. As for vertical
stresses, the data show wide scatter. Typical values of K,
particularly in tectonically quiet regions, were assumed to be from
0.5 to 2.0 (i.e., the average horizontal stress varies from half to
twice the vertical stress). A best estimate of the stress ratio was
taken to be 1.0.
Salt, having low viscosity, deforms continuously under small
shear stresses, and within short geologic times (i.e., hundreds
rather than tens of thousands of years). Thus, for the purpose of
non-site-specific analysis, a stress ratio of 1.0 is appropriate.
Any other stress ratio would produce shear stresses, induce viscous
flow, and over time neutralize stress differences. A stress ratio
of K = 1.0 was used in analysis, and the sensitivity of results to
variation within the range of 0.5 1. K L 2.0 was tested.
2. Concentration of Stress
Construction of an opening within a uniform stress field
concentrates the stresses, with the exact form of the concentration
a function of the geometry of the opening and the deformation
properties of the rock mass. Typical results for elastic media are
shown in Figure D-IX-18. Analytical expressions of the concentrated
stress field exist for elastic isotropic and anisotropic media and
(24)
many common geometries. Analytical expressions do not exist for
most inelastic assumptions, although solutions can be obtained
numerically.
Waste repositories will not have a single opening, like a long
cylinder, but will have a series of parallel openings approximating
a rectangle in the horizontal plane. Stress distributions about
this series of openings will be more like those from an infinite
series of holes in a medium rather than a single one (Figure
D-IX-19). The present analysis considered only a single opening,
however.
IX-30
-------
DEPTH (m)
AVERAGE oh / a
Source: Lindner, E.N., and J.A. Halpern. In-Situ Stress Analysis. 18th U.S. Symposium on Rock
Mechanics, 1977.
FIGURE D-IX-17 MEASURED STRESS RATIOS FOR SEVERAL SITES IN
NORTH AMERICA: HORIZONTAL STRESS *
VERTICAL STRESS
IX-31
-------
PRINCIPAL
STRESS
V r^;^^O
\yVv^"^^ I
^^^fefci£7
QX>
^%*,.>$S?'(iv '?$^~^£g.
II'! I
SHEAR
STRESS
Source: Savin, G.N. Stress Distributions Around Holes. NASA Technical
Translation, TTF-607.
FIGURE D-IX-18 STRESS CONCENTRATIONS ABOUT CIRCULAR
OPENINGS IN HOMOGENEOUS, ELASTIC MEDIUM
UNDER VERTICAL STRESS FIELD
IX-32
-------
maximum tangential stress at wall
-3
^A^r^*-
H O ® O =
0123456
S/r
If If t It t I
Hsh-
o 00
h n M n »
0 12 345 6
S/r
Source: Savin, G.N. Stress Distributions Around Holes. NASA Technical
Translation, TTF-607.
FIGURE D-IX-19 STRESS CONCENTRATIONS ABOUT A ROW OF OPENINGS
IN ELASTIC MEDIUM
IX-3 3
-------
The bases for choosing to consider a single opening were the
following:
First, use of analytical expressions available for stresses
about a single opening reduced computational effort and allowed
larger parametric studies.
Second, the region of significant stress concentration
extends only to about one diameter away from the opening.
Series of openings at separations greater than two diameters can
be modeled as if each were isolated. Increases in maximum
stress concentrations for multiple openings spaced at one
diameter (i.e., 2 diameters o/c), over single openings in
(2)
elastic materials is less than 10%. Therefore, errors
introduced by considering only one opening were small.
Third, uncertainties in the conclusions of this analysis
are dominated by uncertainties in material properties and the
thermal field.
Stresses generated about an opening in a homogeneous medium
depend on the deformation properties of the medium, in particular on
whether the material is elastic or inelastic (and on the form of
inelasticity in the latter case) , and on the ratio of moduli and
Poisson ratios if the material is anisotropic. The simplest case,
of course, is elasticity.
While elastic solutions, as used in the present analysis, depend
on assumptions that are not precisely correct for real rock masses,
there are several arguments for their use.
First, any stress-strain relationship must be verified for real
conditions. In many cases inelastic relationships are as difficult
to verify as elastic ones. Given many alternative inelastic
relationships, each leading to a somewhat different stress
distribution, a choice must still be made among them. Errors
introduced by using an elastic assumption may not be any greater
than errors associated with various inelastic assumptions.
Second, appropriate moduli values are difficult to estimate even
in the elastic case. Estimation is more difficult for inelastic
cases, and more moduli must be estimated. Errors introduced by
selecting poor parameter values may be larger than those introduced
by using elastic theory.
IX-34
-------
Third, elastic solutions are analytically and computationally
convenient. Therefore, larger parametric uncertainty is a primary
source of predictive uncertainty in this analysis; results from
parametric studies are likely to bound predictions made using other
models.
Fourth, given the widespread use of elastic analyses, there is
accumulated experience with these solutions, which aids in
interpreting the results. This also means that results of the
present analysis are more easily interpreted by those who were not
directly involved in obtaining them.
For these reasons, stress distributions in the present analysis
were calculated using elastic theory, and parametric studies were
used to bound the range of uncertainty.
3. Thermal Stress
The major source of stress in geologic media about a repository
appears to be the thermal field. Salt has a coefficient of linear
thermal expansion, a , of about 40 x 10~ 0C~ . Rock temperatures
predicted by several studies, including the present one, may reach
200-250°C at the repository wall. Because deformation of repository
formations is constrained, this thermal field will induce
significant stresses.
Prior to repository construction, the in-situ thermal field will
be uniform, but increasing linearly with depth. For geologically
stable regions (i.e., nonvolcanic), a temperature gradient of 1 C
for 60-80 m is typical. Ambient temperature at 450 m (1500 ft) in
bedded salt is expected to be about 30 C.
Heat generated within the repository will be a function
primarily of (1) waste type and age at burial, (2) time after
O S 96^
burial, and (3) spatial canister density.v"' The conditions
considered were 10 years aging and 150 kW/acre for heat generation
density, consistent with the" Task B report. For analysis, a
1X-35
-------
temperature (increase) profile similar to the Task B results were
used. This profile was expressed analytically as:
AT(°C) = 222 exp (-1.1 x 10~5 r2) (16)
where r = distance from repository.
This profile was assumed to .be isotropic in the salt.
The time for peak mine temperatures differs in different
analyses; fracturing probabilities are related primarily to the
temperature profile and not to time (relation of shear stresses
through viscous flow was neglected, which is a conservative
assumption). Therefore, the results of stress analyses in the
present case are not significantly affected by these time
differences. For analyses, a time of 100 years to maximum mine
temperature was assumed.
Stresses generated by the thermal field were calculated assuming
the repository salt formations to be isotropically elastic with
uniform deformation properties. Parametric analyses were performed
by varying deformation moduli.
Elastic thermal stresses around the underground repository were
derived by adapting a solution for the thermal stresses in a thin
(27)
circular disc. This solution is valid for temperature
distributions symmetric about the center of the repository, and
requires that the modulus of elasticity, Poisson's Ratio, and
coefficient of thermal expansion be constant with temperature and
location.
Expressions for radial and tangential thermal stresses are:
(17)
VI~IT
~/T(r)dr
IX-36
-------
6 1-v-
-« /"
~
T(r)dr + aT(r)
(18)
where: E
v
a
r
R
T(r)
modulus of elasticity
Poisson's Ratio
coefficient of thermal expansion
radial distance from center of repository
radius of repository
temperature increase above ambient at radius r
Rewriting equation 16 in general form as:
T = T e
max
-Br'
(19)
where: T= maximum temperature increase (at repository wall)
in 3. A
B = constant
Substituting into the equations for stresses yields,
•,-&($* [•-*-•*])
(20)
'e
IX-37
-------
Radial thermal stresses are zero at the repository wall (r - R)
and at infinity, and are compressive everywhere in between;
tangential stresses are maximum at the repository wall, zero at
infinity, and may be compressive or tensile in between.
It is Important to note that thermal stresses .ire directly
proportional to the modulus of elasticity of the rock salt. Errors
in this modulus result in equally large errors in thermal stresses.
Since there are little data on the elastic modulus of rock salt at
high temperatures and low strain rates, the potential for error in
estimating thermal stresses is large.
Since all stress calculations assume elastic material behavior,
total stresses around the repository are obtained by superimposing
the region (in-situ plus stress concentrations around the cavity)
and thermal stress fields.
F. STOCHASTIC FRACTURE MODEL
1. Model Construction and Assumptions
The probability of fracturing between the repository and an
overlying aquifer was analyzed by modeling rock properties as
( 2 8}
second-order homogeneous random processes, and calculating the
reliability of potential fracture paths against shear failure
(Figure D-IX-20).
The assumption of second-order homogeneity* for rock properties
implies that mean properties are constant in space or may be
described by a deterministic trend, that the point variance of
properties is spatially constant, and that the autocorrelation of
properties (i.e., the degree to which adjacent points in the rock
mass have similar properties) is a function only of the vector
*"Homogeneity" and "stationarity" are equivalent terms for spatially
varying and temporally varying parameters, respectively. Although
usage varies, "homogeneity" has been adopted in this report.
IX-38
-------
DEPTH (m)
0
surface
380
460
540
repository
__ . -j. aq'u}fer
£iii
FIGURE D-IX-20 POTENTIAL FAILURE PATHS BETWEEN REPOSITORY
AND AQUIFER
IX-39
-------
distance separating points (Figure D-IX-21 presents these concepts).
Second-order stationarity assumptions for geologic materials are
(29)
generally accepted.
Three sets of rock properties are important for analyzing
reliability: strength parameters, deformation parameters, and
thermal parameters. The first set controls the available resistance
of rock to various modes of failure, while the latter two control
stresses generated in the rock. In the present analysis, only
strength parameters were assumed to be stochastic; deformation and
thermal parameters were assumed to be deterministic. This means
that analyses were performed on a stochastic strength field subject
to deterministic stresses. The errors introduced by this limitation
are thought to be within the scope of the desired objectives of the
study. In more precise studies, and in particular for site-specific
analyses, techniques for incorporating uncertainty in the stress
field should be used. Because analysis of stochastic stresses
involves differential rather than integral fields, their solution is
more complicated.
A failure mode analyzed in the present study was the development
of shear zones between repository and aquifer. For this analysis, a
limiting equilibrium approach was used with driving forces along
potential shear paths balanced against resisting forces. Kinematic
admissibility was not considered (i.e., potential shear paths were
not limited to those on which continuous relative movements were
possible) . The requirement of kinematic admissibility, constraining
the set of potential shear surfaces, would yield somewhat higher
reliabilities than those from the present analysis.
Alternative modes of fracturing, in particular the development
of propagating cracks by redistributing stresses at increments of
(31)
crack were not considered. Pre-existing anomalies in repository
formations (e.g., faults) are treated in Section D-5.1. The
limitation of other failure modes, other than limiting equilibrium
shear failure, affected numerical results, but differences are
thought to be within small multiples rather than orders of
magnitude. Site-specific analyses should include both the
probability of non-flaw inhomogeneities and progressive fracturing.
IX-40
-------
horizontal axis
randomly
variable
material
property
mean
point variance
autocorrelation '
distance
FIGURE D-IX-21 SCHEMATIC DESCRIPTION OF ROCK STRENGTH
IX-41
-------
Both of these are important in predicting stress fields and should
be treated in conjunction with spatially varying deformation and
thermal properties.
Figure D-IX-20 illustrates plane strain failure paths considered
in this analysis. Various fracture geometries were analyzed, of
which the least reliable was selected for detailed analysis. The
failure path geometry used in detailed analysis consisted of a log
spiral emanating from the repository at an angle (45 - 4>/2),
connecting to a vertical line continuing to the aquifer. This is a
(32 33)
geometry of fracturing observed in model tests . ' In analyzing
failures for a given set of parameters, a search routine was adopted
that searched for the minimum reliability surface. In general,
minimum reliability and minimum FS surfaces are not the same.
Overall reliability against plane strain shear faiure was taken
as that of the least reliable surface. With an infinite number of
potential surfaces, the reliability of the least reliable path is
only an approximation to the reliability of the system. However,
due to high correlation of stresses and strengths along adjacent
surfaces and the spatial narrownesss of low FS clusters,
correlations of FS for alternative paths are high. Therefore, the
reliability of the minimum surface is a good approximation to the
system reliability.
The reliabiity of an individual path to shear failure was
determined by integrating predicted shear stress along the surface
and comparing this driving force with the integral of available
resisting shear stress. (Figure D-IX-22.) The driving force was
determined by decomposing the stress field at each point along the
failure surface into a normal stress, s , and a shear stress, t, and
numerically integrating over the surface,
DP
S
'./ "*•
where DF is the total driving force along path S, and ds is the
differential curve length.
IX-42
-------
DEPTH (m)
0
surface
shale
380
460
aquifer
'
repository
540
aquifer
FIGURE D-IX-22 STRESS AND RESISTANCE ALONG POTENTIAL
FAILURE SURFACE
IX-A3
-------
The resisting force was determined by decomposing the stress
field and integrating over the failure criterion,
RP - /*[C(T) + a u(T)]ds
eJ R
where RF is the resisting force along path S, C(T) is the
temperature-dependent cohesion parameters, and {J(T) is the
temperature-dependent coefficient of friction (y(T) = tan 4>(T)). A
tilde indicates a random variable.
Resisting force, a function of two random variables, is itself a
random variable with some mean and variance. The reliability index
of shear failure along path S was defined as:
where E[ ] indicates expectation, and V[ ], variance. A reliability
index was used because it is non-parametric (i.e., does not depend on
distribution assumptions).
With no loss in generality, thermal reduction factors K(T) and
H(T) may be introduced such that
C(T) = K(T)C(24°) = K(T)c,
W(T) - H(T)y(24°) = H(T)p.
K(T) and H(T) were assumed to be monotonically decreasing functions of
temperature, evaluated on the basis of empirical evidence.
Using reduction factors, moments of the resisting force along path
S can be derived as:
IX-44
-------
E[RF] » J{K(T)E[c] + o ,H(T)E[M]}ds
S nl
VfRF] -/^>{K1(T)Kj(T)Cc(r) + 0^(1)0^
•(I)Cp(r)}d.1dSj (23)
where subscripts i and j indicate arguments for the double integration,
and
Cc(r) = autocovariance function of cohesion
Cu(r) = autocovariance function of coefficient friction
r = surface distance between points i and j.
On the basis of empirical evidence, a bilinear Mohr-Coulomb failure
criterion was assumed. Up to some transition stress, a, (T2), the salt
was assumed to have a failure criterion specified by the parameter pair
(C, w) ; above the transition stress, a perfectly cohesive failure
criterion specified by the parameter pair (C, u - 0) . The transition
stress was assumed to be monotonically decreasing with increased
temperature.
Introducing a transition from frictional to purely cohesive
behavior required that the potential breach path be divided into two
segments, one on which a >o,(T) and one on which a
-------
The analysis was expanded to three dimensions by considering
cylindrical failure surfaces formed by translating the least
reliability plane-strain path (Figure D-IX-23). As a first
approximation, the failure surface was taken as one autocorrelation
distance (r ) wide. The question addressed in the three-dimensional
analysis was how much the plane-strain reliability index is reduced
by considering the potential for failure anywhere around the
repository.
Considering only one opening of the repository, there is an
infinite number of potential failure surfaces because the assumed r
wide surface could be anywhere along the opening length. Let the
surfaces be indexed by the location of their center points. Because
adjacent surfaces overlap, their total resistances can be highly
correlated*
The total shear resistance is calculated as for the plane-strain
path, but now averaged over a larger two-dimensional surface. Thus,
the variance in the total resistance is reduced from that of the
most critical path. For a surface of width r this variance
reduction is to 37%, and the corresponding standard deviation
reduction to 61%.(28)
Assigning the total resistance of a surface to its midpoint at
the repository wall, a correlated one-dimensional random process is
defined. Breaching occurs if at any place along the opening, the
resistance drops below the driving forces. This is equivalent to
the one-dimensional random process crossing a level (J standard
deviation from the mean, where 6 is the single-surface reliability
index. For large 6, the probability of .at least one level crossing
in length L of repository opening is:
Pr = L exp(-B2/2) (25)
IX-46
-------
FIGURE D-IX-23 THREE-DIMENSIONAL MODEL
IX-47
-------
where 6 is a length measure formed by integrating the
autocorrelation function between negative and positive infinity (for
/2 g\
exponential autocorrelation <$ = 2r ).
Applying Equation 25 yields the probabilities of failure at peak
thermal stresses. If the peak thermal stresses occur at about 100
years, and if the cumulative probability of failure is assumed to
increase linearly with time, the failure rate over the first hundred
years would be two orders of magnitude lower than the values implied
by Figure D-IX-24.
The results of the analysis for the reasonable and somewhat
conservative 20% variation in salt properties indicate exceedingly
low probabilities of breaching failure even when multiple failure
surfaces are considered. These probabilities are obviously not
precise and should be considered only as indicators.
2. Parametric Inputs and Results of Analysis
Parameter values chosen for sensitivity studies bounded those
values found in the literature (Table D-IX-2). For a specific site
these values would have to be evaluated from exploration and
testing. Results were not sensitive to Poisson's Ratio, lateral
stress ratio, the anisotropy ratio of autocorrelation, or the form
of the autocorrelation function.
Results of plane strain analyses for coefficients of variation
in material properties, are shown in Figures D-IX-24 and D-IX-25.
Trends within the results are the following:
1. Thermal stresses predominate, thus the probability of
fracturing is sensitive to the thermal field. Time trends
in reliability reflect time trends in rock temperatures.
2. The probability of fracturing interconnecting repository and
aquifer decreases as the separation distance between
repository and aquifer increases. The relationship is not
linear; by decreasing the separation some proportion, the
probability is increased by a greater proportion.
IX-48
-------
TABLE D-IX-2
PARAMETER VALUES USED IN ANALYZING RELIABILITY AGAINST
SHEAR FAILURE BETWEEN REPOSITORY AND AQUIFER
Parameter
Young's
Modulus
(psi)
Poisson
Ratio
Point Coefficient
of Variation*
Autocorrela-
tion Length*
(feet)
Lateral
Stress Ratio
Low
5.0 x 10'
5/50
Most Probable
5.0 x 104
0.22
10
10/100
High
5.0 x 10!
20/200
0.5
1.0
2.0
Standard deviation divided by mean.
** -1
Distance at which correlation reduces to e
IX-49
-------
oa.
x"
I
If
20
16
12
8
4
0
0.1
10
Time (yrs)
100
FIGURE D-IX-24 CALCULATED RELIABILITY INDEX AS A
FUNCTION OF TIME
12
10
oa.
x 8
0)
=5 4
QC
2
0
50 100
Distance to Aquifer (m)
20%COV
40%COV
150
200
FIGURE D-IX-25 CALCULATED RELIABILITY INDEX AS A
FUNCTION OF DISTANCE TO AQUIFER
IX-50
-------
3. Probabilities of fracturing are sensitive to deformation
modulus and point variance of strength properties. Care
must be taken in estimating these parameters for
site-specific studies.
G. RECOMMENDATIONS FOR STOCHASTIC ANALYSIS IN SITE-SPECIFIC STUDIES
Stress analyses of site-specific repositories should incorporate
uncertainties. In general, this is not now done. Current analyses are
primarily deterministic, allowing estimates only of mean safety factors
and not probabilities. The analysis performed here, owing to
limitations of time and effort and in keeping with the overall
objectives of the present study, serves only as a first approximation to
a comprehensive stress analysis of a particular repository.
In analyzing a specific repository, the present analysis should be
expanded to account for the uncertainties discussed below.
1. Stress Field Uncertainties
Uncertainties in the stress field are generated by uncertainties
in deformation and thermal properties of repository formation, and
by uncertainties in the regional stress field. These sources of
uncertainty are coupled. Moreover, for a specific site, uncertainty
will be contributed by estimation error. Despite the extensiveness
of site exploration programs, uncertainties always exist in site
characterization. These estimation uncertainties are increased by
the conflicting objectives of placing as few new borings as possible
into the geologic barrier.
The approach to modeling uncertainty in stresses would be to
approximate deformation and thermal properties as second-order,
homogeneous stochastic processes, and solve the differential field
equation for means and variances. These solutions would most likely
be numerical, as through uncertain finite element analysis. This
would result in process statistics for stresses as a stochastic
field (e.g., (30). Using a model of this sort, estimation error
based on sampling could be quantified.
IX-51
-------
2. Crack Propagation Analysis
The present analysis has treated limiting equilibrium shear
failure as the criterion of fracturing. Alternative criteria should
be considered. Of particular importance would be the consideration
of fracture propagation in which stress concentrations are
recalculated for increments of fracture extension. The same
stochastic model of strength, deformation, and thermal properties
could be used to yield probabilistic predictions.
3. More Accurate Geometric Model of Repository
The present analysis has used a simplified idealization of the
repository as a cylindrical opening in a uniform material.
Site-specific studies should model repository geometry based on
actual layouts. Although this would add analytical complexity,
certain idealizations (e.g., infinite rows of identically shaped
openings) are tractable.
4. Elasto-plastic Media
For specific sites, more complicated deformation models should
be introduced, based on test results on site materials.
5. Jointing and Pervasive Inhomogeneities
Salt has been modeled using continuum mechanics. In materials
other than salt (e»g., basalt, shales), jointing will significantly
influence the mechanical behavior of the rock mass. Appropriate
allowances must be made for the effects of Joints, either by
augmenting bulk mechanical properties or by introducing discontinuum
models.(5'17»3>
IX-52
-------
6. Pore Water Pressures
Pore water pressures affect rock mass strength by reducing
available frictional resistance in accordance with the effective
stress concept,
T - C + (a - u) tan 6,
where T = the available shear resistance and
y - the pore water pressure.
No consideration has been given to pore water pressures in this
analysis. Recent work indicates that water pressure may be
incorporated in stochastic analyses.
H. DERIVATION OF STOCHASTIC REDUCTION FUNCTIONS
For the derivation of mean and variance of stochastic resistance for
constant temperature, cohesive condition, consider an elemental volume i
(Figure D-IX-26) along the potential failure path L:(a, b). The
resistance to shear displacement at this point, assuming Mohr-Coulomb
failure criterion, is:
(26)
Tr,i = Ci + ai tan *i
where
T » the maximum available resisting shear stress,
r»1
c. and . » the cohesion and friction angle at the point, and
a = the stress normal to the potential failure path at i. o.
is assumed known, based on stress calculations; however
both c. and tan $ , the material properties, are assumed to
be second-order homogeneous random variables.
The maximum available resisting shear force along path L is the integral
of the available shear resisting stress, or
IX-53
-------
-60
15%COV
-50
-40
.o
(D
•§ -20
oT
o
O)
O
-10
20%
30%
40%
10
100
Total Length of Opening
1000
m
FIGURE D-IX-26 PROBABILITY OF BREACHING
IX-54
-------
RF(L) - / Tr ± ds - / ct + o± tan $± ds (27)
The expectation of Equation 27 is
E[RF(L)] - E[/ c± + o1 tan ^ ds] (28)
- / Elc^ds + / o^ E[t
an
Defining the new variable,
= tan
the expected resisting shear force becomes
E[RF(D] - / Elc^ds + /a1Elwi]d. (29)
This value is easily calculated once o is known as Etc.] and E[w.] are
constant across space, given the assumption of statistical homogeneity.
The variation of Equation 26 requires somewhat more labor to determine.
By definition,
V[RF(L)] - E[(RF(L) - E[RF(L)])2]
IX-55
-------
- E*[RF(L)J (31)
4 + o^ds • f(c± + otv
- [/Etc.] - ot ElVi] ds]
• - -, c + o c y v ) ds^sj (32)
ds]2
(33)
Cc
-------
along any potential failure path. Correlation lengths will of course
differ for different paths, based on the orientation of the chord joining
their endpoints. Second, the path length between any two points i and j is
used in calculating correlation rather than the chord length between them.
This allows line integrals to be taken along the path. As long as the
correlation length, r , is small relative to the path curvature this second
assumption introduces little error.
(35)
Following the arguments of Popoulis , the double integral of
Equation 34 can be reduced to a single integral. The function Cc(i,J)t
depending only on the distance r » li-jll, is constant within the shaded
area of Figure D-IX-27:
Cc(i,j) - Cc(r) (35)
The area of this strip is (L - r)dr when L is the total path length
from a to b.
Thus Equation 34 becomes
V[RF(L), . //^((J) ds.ds., - / (L - r) ee(r) dr <36>
r-0
For the common autocovariance function (Figure D-IX-28)
C.(r) - °l e'r/ro (37)
2
where is ttie Point variance; the variance of resisting force
becomes:
IX-57
-------
L-r
FIGURE D-IX-27 REDUCTION OF DIMENSION IN VARIANCE
CALCULATIONS
IX-58
-------
0.5
0.4
0.3
0.2-
0.1 -
e-(r/r0)
0.1 0.2 0.3
i i
0.4 0.5
FIGURE D-IX-28 NORMALIZED VARIANCE OF AVERAGE STRESS
FOR TWO AUTOCOVARIANCE FUNCTIONS
IX-59
-------
V[RF(D] - f (L-r) o 2e"r/r°dr
J n C
r-0
L
o (38)
+ 1) -
,L
'o
Dividing by L leads to the variance in the average resisting stress,
which is a function only of the ratio l/rQ»
This is graphed in Figure D-TX-29.
For the autocovariance function:
C (r) - a
(40)
IX-60
-------
II
f-H
o
•p
o
O
•o
0.0
TOO
FIGURE D-IX-29
APPROXIMATE REDUCTION FACTOR AS
FUNCTION OF AUTOCORRELATION DISTANCE
IX-61
-------
L
V[RF(L)] - f (L - r) a^ e ° dr
o
*• i *
-..«/ »' fe
(42)
Substituting the approximation
2
erf(z) = 1 - (0.3A8t - 0.09587(+0.74785t)e~z (43)
t - [1 + 0.47047Z]"1
allows Equation 42 to be calculated numerically.
IX-62
-------
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