EPA-600/2-85-035
SETTLEMENT AND COVER SUBSIDENCE OF
HAZARDOUS WASTE LANDFILLS
(FINAL REPORT)
by
W. L. Murphy and P. A. Gilbert
US Army Engineer Waterways Experiment Station
Vicksburg, Mississippi 39180
Interagency Agreement No. AD-96-F-2-A079
Project Officer
Robert P.'Hartley
Solid and Hazardous Waste Research Division
Municipal Environmental Research Laboratory
Cincinnati, Ohio 45268
Municipal Environmental Research Laboratory
Office of Research and Development
US Environmental Protection Agency
Cincinnati, Ohio 45268
n^:! Protection Agency
Region V, Library
230 South Dearborn Street .,x--"
Chicago, Illinois 60604 ,•••* ,.liA4Rfc
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PEER REVIEW STATEMENT
The information in this document has been funded wholly or in part by the
United States Environmental Protection Agency under Interagency Agreement
AD-96-F-2-A079 to .US Army Engineer Watervays Experiment Station, Vicksburg,
fc
Mississippi. It has been subject to the Agency's peer and administrative
review, and it has been approved for publication as an EPA document.
ii
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ABSTRACT
Numerical models using equations for linearly elastic "deformation were
developed to predict the maximum, expected amount of settlement and cover
subsidence and potential cracking of the cover by differential settlement in
uniformly, horizontally layered hazardous waste landfills. The hazardous
»
waste landfill models represented landfills in which unsaturated wastes vere
contained in standard steel drums that vere assumed to deteriorate ultimately
in the landfill. The models vere analyzed using methods of linear elasticity |
to estimate the maximum amount of subsidence of the final cover to be expected
before and. after landfill closure and after deterioration of the waste
containers. The model landfill consisted of alternating layers of intermediate
inert cover soils and steel drums filled with simulated waste materials.
Waste, drums, waste materials, and intermediate cover soils vere assigned
values of density. Young's modulus, and Poisson's ratio for the analysis.
Landfill geometry, layer thicknesses, waste drum placement, steel drum stiff-
nesses, and laboratory consolidation tests on the soils and simulated wastes
vere also considered. To simulate postclosure waste layer deterioration,
compression of the fill was calculated for decreasing values of the Young's
modulus of the waste layers. The analyses indicate that as nuch as 92 percent
•*yf
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PREFACE
This study was authorized by the US Environmental Protection Agency
(EPA), Municipal Environmental Research Laboratory, Solid and Hazardous Waste
Research Division (SHWRD), Cincinnati, Ohio, by Interagency Agreement (IAG)
AD-96-F-2-A079 effective 1 April 1982, under the Project Title "Assessment of
Time Settlement/Subsidence Effect on Cover Systems." Final funding was au-
thorized in IAG WES-82-12 Amend AD-96-F-3-A079 effective 1 November 1982.
The study was conducted and the report prepared by Messrs* William L.
Murphy of the Engineering Geology and Rock Mechanics Division (EGRMD) end
Paul A. Gilbert of the Soil Mechanics Division (SMD), of the Ceotechnical
Laboratory (GL), WES. Direct supervision was provided by Mr. John H.
Shamburger, Chief, Engineering Geology Applications Group (EGAG), EGRMD;
Dr. Don C. Banks, Chief, EGRMD; and Dr. William F. Marcuson III, Chief, GL.
Messrs. Robert E. Landreth and Robert P. Hartley, SHWRD, were EPA project
officers for the study and provided guidance and assistance during the
investigation. The authors acknowledge the following individuals for offering
peer review of the report: Les Otte, USEPA, Cincinnati, Ohio; Dr. F. C.
Townsend, University of Florida, Gainesville, Florida; Dr» N. J. W«instein,
Recon Systems, Inc., Three Bridges, New Jersey; and S. K. Banerjl, University
of Missouri, Columbia, Missouri.
Commander and Director of the WES during the study and preparation of
the report was COL Tilford C. Creel, CE. The Technical Director was
Mr. Fred R. Brown.
iv
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CONTENTS
Page
PEER REVIEW STATEMENT .'....... ii
ABSTRACT ill
PREFACE . iv
LIST OF ABBREVIATIONS AND SYMBOLS . . . ' vii
SECTION 1: INTRODUCTION I 1
Background 1
Purpose 1
Scope ............................. 1
Approach .............. ....... 2
SECTION 2: HAZARDOUS WASTE LANDFILL CHARACTERIZATION 4
The Disposal Facility 4
The Cell Liner ........... 5
•Waste Placement and Cell Fill . 7
. Cell Cover 9
Quality Control . ....... ... 10
SECTION 3: SUBSIDENCE MECHANISMS AND RELATED PROBLEMS 11
Introduction ............. 11
Subsidence by Consolidation ..... 11
Cavity-Related Subsidence 15
Landfill Subsidence 27
Subsidence-Related Cover Problems .......... 29
SECTION 4: PREDICTION MODELS FOR MAXIMUM SUBSIDENCE 32
Introduction • 32
Purpose of Model Analysis ........ ...... 33
Conditions Assumed for Landfill Subsidence Monitoring ..... 33
Modeling of Preclosure Maximum Settlement/Subsidence 39
Modeling of Postclosure Subsidence of the Landfill as a Result
of Modulus Decrease .. ...... 48
SECTION 5: ANALYSIS OF COVER CRACKING 66
Subsidence Cracking 66
Potential Cracking by Desiccation and Shrinkage 73
SECTION 6: SUMMARY AND DISCUSSION OF RESULTS 75
Landfill Modeling .... 75
Response of Cover to Maximum Subsidence ............ 76
Response of Cover to Subsidence Cracking (Differential
Settlement) 77
Other Considerations 77
SECTION 7: CONCLUSIONS AND RECOMMENDATIONS 79
Conclusions 79
Recommendations 79
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CONTENTS (Concluded)
. - - Page
REFERENCES , 81
APPENDIX A 85
APPENDIX B 106
vi
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LIST OF ABBREVIATIONS AND SYMBOLS
Abbreviations
RCRA
FEM
PVC
ft or '
V
H
cm
sec
avg
pcf '
kg/cm2
in.
psf
cu yd
psi
HDPE
PI
LL
PCB
Resource Conservation and Recovery Act
Finite Element Method
Polyvinyl Chloride
Foot or feet
Vertical
Horizontal
Centimeter
Second
Average
Pounds per cubic foot
Kilograms per square centimeter .
Inch or inches
Pounds per square foot
Cubic yard
Pounds per square inch
High density polyethylene
Plasticity index
Liquid limit
Polychlorinated biphenyl
Symbols
H
e
AH
P
Cc
Ap
t
T
H
Thickness of soil layer
Void ratio (volume of voids to volume of solids)
Change in thickness
Change in void ratio
Total soil volume
Load on a soil mass, expressed as a pressure
Coefficient of compressibility of a soil (slope of e-log P
curve)
Change in load (pressure)
Time
A tine factor for computing tine to achieve consolidation
Length of drainage path in a soil layer
vii
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Symbols
C Coefficient of consolidation
k Permeability .
U Degree (percent) consolidation
0 Friction angle
c Cohesion
z Vertical axis coordinate
x Horizontal axis coordinate
y Horizontal axis coordinate
r Radial axis
E Young's modulus
IL ' Young's modulus of steel drum
E_ Young's modulus of composite waste/soil layer
E- Young's modulus of intermediate cover soil layer
o
Er Young's modulus of drum contents
v Poisson's ratio
CH A plastic clay .
S Subsidence
e Strain
a Stress
K Coefficient of earth pressure at rest
o
L Length of soil column
y Depth within soil column
dy Differential increment of y
Y Unit weight
AL The change in length of a soil column, or the settlement
°F Degrees Fahrenheit
(U) Radial deformation
K Bulk modulus
viii
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SECTION 1
INTRODUCTION
BACKGROUND
Settlement of sanitary and low-level nuclear waste landfills with subse-
quent damage to or compromise of the integrity of the covers Is a recognized
and documented occurrence. The U. S. Environmental'protection Agency (EPA) is
concerned that settlement within hazardous waste landfills may produce similar
subsidence problems with cover systans. The failure or distortion of the
cover system may cause consequences that are totally unacceptable to managers
of hazardous waste. Little documentation exists of the extent, potential for,
or mechanics of settlement/subsidence in hazardous waste landfills.
i •
PDRPO.SE
This study was conducted to determine the potential for settlement of
the fill and subsequent subsidence-related damage to cover systems of hazard-
ous waste landfills and to provide Information necessary for developing and
improving interim and future regulatory guidance. A goal was to develop
predictive numerical models to estimate the amount of »ttMi4|tn.ce and strain
that would be expected to occur in the landfill and cover as a result of
" ^ ^'' * $ **'
settlement. It was first necessary to characterize the hazardous waste land-
fill with respect to design, operation, and physical properties. This study
has examined the characteristics of several hazardous waste landfills with
special attention to those features expected to influence the potential for
settlement of the fill and subsidence of the final cover. Numerical models
were developed from assessment of landfill characteristics and suspected
settlement/subsidence mechanisms. The potential for degradation or compromise
of the final cover is examined through' models developed in this report.
SCOPE
The study addresses hazardous waste landfills operating under the inter-
im standards imposed by EPA under authority of the Resource Conservation and
Recovery Act of 1976 (RCRA). The predictive models developed for the investi-
gation are based on facilities operated by the commercial hazardous waste
disposal industry. Other landfill types and subsidence mechanisms operating
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in geotechnical circumstances other than hazardous waste landfill situations
were reviewed in developing hazardous waste landfill models, but the mechan-
isms and characteristics used to construct the models are those derived from
an assessment of several hazardous waste landfills operating with interim
status permits under RCRA.
APPROACH
The approach was to determine from the literature the known mechanisms
and analytical techniques of settlement and subsidence in all geotechnical
areas including mining, landfill, engineering fills, karst (geologic), tunnel-
ing and foundation investigations; to determine the mechanisms most likely to
be active in a .hazardous waste landfill; and to select the proper methods of
analysis. A review was made of literature pertinent to settlement and subsi-
dence in landfills. The initial computer data search used the information
retrieval systems DIALOG, National Technical Information Service (NTIS),
GEOREF and COMPENDEX to compile listings and abstracts of pertinent reports
and documents. Review and updating of literature continued throughout the
study. Site characterization, necessary, for model development and problem
assessment, was accomplished by contacting the hazardous w»«te disposal indus-
try and through site visits to selected facilities to obtain real data on site
geometry, liner and cover design and properties, waste and fill placement
procedures, waste and fill physical properties, compaction efforts, leachate
collection and control, subsidence experiences, and other relevant information.
Sites were selected for their location, representing several areas of the
nation and several climate and soil conditions; for their size, representing
for the most part large facilities; and for their current activity, i.e.,
their status as viable commercial landfill facilities operating under RCRA
guidance.
In addition, selected state agencies familiar with hazardous waste
disposal in their states were contacted for further information including
information about potential or existing subsidence problems, and to obtain an
indication of the amount and kinds of variation in operational procedures to
be expected nationwide. The authority for implementing RCRA interim standards
on the state level is vested in the state Departments of Health, Water Re-
sources Boards, special environmental regulatory commissions or departments,
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Natural Resources Departments, Pollution Control or Solid Waste Management
Boards, or state EPA's. Some states have multiple jurisdiction for imple-
menting the standards. The National Directory of State Agencies was used to
establish an initial list of contacts. Other regional or site-specific data
were obtained from- consulting engineeering firms and scientists and engineers
of state agencies.
Numerical finite element method (FEM) models were developed for selected
hazardous waste disposal situations using the data compiled in site character-
ization and by modifying existing FEM analytical models. The approach In the
modeling analysis was to simulate worst-case conditions that would be expected
in RCRA landfills, i.e., those situations producing the greatest amount of
settlement. Accordingly, the larger facilities where wastes are buried in
drums were used to develop the model landfill. The subsidence problem was
analyzed by modeling pre- and postclosure maximum settlement in the middle of
the landfill and differential settlement across the landfill.
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SECTION 2
HAZARDOUS WASTE LANDFILL CHARACTERIZATION
THE DISPOSAL FACILITY
The commercial hazardous waste disposal industry has developed several
•variations in the design and operation of hazardous waste Landfills to satisfy
the requirements imposed by the implementation of RCRA. The variations nation-
vide are made necessary by local geologic, topographic, and hydrologic condi-
tions, state requirements that may differ from Federal guidelines, individual
preferences by the waste disposer, and the demand placed on particular facili-
ties by prpducers of hazardous wastes. Nevertheless, a typical or "generic"
landfill can be said to possess all or most of the following characteristics:
£. Pits (cells) are excavated in native soil or rock of low perme-
ability (aboveground facilities enclosed by soil embankments are
less common).
_b. Single- or multicell construction is practiced, the cells isolated
~~ by berms and the multicell groups isolated by berms, liners, and
covers.
_c. Depths are commonly 15-50 ft, but may be as great as 100 ft.
_d_. The base of the cell is above the water table or aquifer.
£. Cells are lined with single or multiple natural or synthetic barri-
~" ers with very low permeability to water (10* to 10 cm/sec). .
_£. Cells are equipped with leachate collection and monitoring system.
£. A final cover (cap) of synthetic and/or natural materials is
installed.
ti. Wastes are placed with some care in layers generally 3 ft thick or
less and covered with less than 2 ft of crushed rock or soil fill
(intermediate cover)*. The waste and intermediate cover are alter-
nated as the cell is filled.
^i. Compaction of liners and caps is usually controlled and monitored;
~~ compaction of waste and fill is limited and is that obtained by
passage of tracked and wheeled waste placement vehicles.
^. Final cover caps of closed cells are grassed and may be equipped
with settlement plates for subsidence monitoring.
k.. Operators are required to solidify all liquids enclosed within the
~~ cell (no free liquids permitted).
* Throughout this report "intermediate cover" refers to the inert fill layer
placed over a waste layer as the cell is filled. "Final cover" refers to
the uppermost cap of the cell that provides permanent closure of the cell.
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The characteristics are discussed further is the following paragraphs.
Appendix A describes in detail the characteristics of hazardous waste land-
fills for which information was gathered for this study. • Some, but not all,
landfill construction, filling, and capping, procedures were observed firsthand
by the authors. The landfills described are believed to represent nodern
controlled waste disposal facilities operating under RCRA. They do not repre-
sent the entire range of closed hazardous waste landfills nationwide. The
practices found, and discussed here, do not necessarily comply with RCRA
guidance.
Figure 1 illustrates a generic RCRA controlled hazardous waste disposal
landfill in plan and profile. Figure 1 is a composite of many proposed and
existing designs all of which meet current RCRA requirements for long-term
containment and isolation of hazardous wastes. There are active facilities of
simpler and more complex design than that shown in Figure 1. RCRA guide-
2 ^
lines * are interim. State and local controlling government agencies and
industry interpret or meet the implied requirements in various ways. Accord-
ingly, facility design and operation vary regionally and/or within the
industry.
?*3 ~
THE CELL LINER
, • t
Cells commonly are placed below ground level in pits (often called
trenches), excavated in soil or rock of relatively low permeability, such as
clays or claystones. Aboveground landfills (impoundments) are also used but
are less common. Some areas are experiencing decreasing availability of
landfill acreage and will soon begin adding wastes atop existing, filled
hazardous waste landfills. Pits and trenches are apparently preferred by the
industry for their simplicity of construction and less critical stability
design requirements. Common practice is to require a site with a deep water
table overlain by a sufficient thickness of low permeability soil or rock.
The base of the cell is usually graded to slope toward a leachate collection
sump and monitoring well. Typical leachate collection systems are perforated
PVC pipe covered by granular fill. Graded filter design criteria were not
observed in the typical leachate collection systems. Leachate collection
systems commonly are emplaced only along the base of the cell. At least one
facility contacted, however, also installed a vertical drainage system around
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X
•era
*—s
s*-i
/
\ T r T r
\ /
•
*~ CELL 1 O- —^
t,
t
^ERMS SEPARATING CELLS
CELL 2O "*
r- -•
t. — *
*- '-9
^. CELL 3 Q* MONITORING /COLLE
WELL
moN
\
y i i i v
pT"
m
i^r^
\
covert ICAPI
SOD on PAVING
COMPACTED CLAY
SYNTHETIC LINER
LEACHATE MONITORING/COLLECTION WELL
LAYERED WASTE AND FILL
NOTE: SLOPES ARE EXAGGERATED.
LINER
COMPACTED CLAY
SYNTHETIC LINER
GRANULAR LEACHATE COLLECTION
LAYER AND BUFFER
Figure 1. Generic RCRA controlled hazardous waste disposal
landfill (see text).
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the cell riser or standpipe. Compound liners (clay plus a geomenbrane*)
encase the cells along the base and sides and may be joined with the cover
liner at closure. The compound liner commonly is a combination of. a clay
barrier and ore or more synthetic liners such as polyethylene, FVC or other
geomembrane of 30 -to 100 mil thickness. One-piece liners consisting of a
thick clay layer or in-place clay-rich soil with no synthetic liner are also
used and in fact were prevalent in the facilities visited for this study. A
layer of sandy soil or gravel may be laid down atop the liner below the first
layer of waste to serve as a buffer protecting the liner from waste placement
operations and to convey leachate to the leachate collection sump. Clay
liners are compacted with sheepsfoot rollers in lifts to a specified density,
to a specified'laboratory measured permeability to water, or to a density
corresponding to a particular permeability. The specified density commonly
represents a moisture content wet of optimum (optimum moisture content of a
laboratory soil compaction test). A vibratory roller Is used by at least one
operator on the final lift to form a smooth surface on which to place the
synthetic liner.
WASTE PLACEMENT AND CELL FILL . .. w^^,,:
Hazardous wastes being considered for land disposal and pertinent to
this study possess characteristics of ignitability, toxicity, reactivity or
corrosivity. Nuclear waste depositories are excluded from consideration as
hazardous waste fills. Waste chemistry is considered to be of only secondary
importance, and waste containment method and waste placement characteristics
of primary Importance, to the subject of this study, i.e., landfill settlement
and cover subsidence.
Wastes are emplaced primarily in steel 55-gallon drums and in bulk form.
Plastic drums and steel 85-galIon "overpack" containers, large drums contain-
ing leaking or damaged 55-gallon containers for transportation to the facility,
are present in lesser amounts. Miscellaneous wastes such as plastic sheeting,
wooden pallets, crushed drums and other containers occupy a smaller percentage
of the cell fill. Some facilities segregate wastes on the basis of, for
* A geomembrane is a synthetic impermeable liner material that may be a pre-
fabricated.polymer such as rubber or plastic or a sprayed-on emulsion such
as asphalt .
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example, acidity, alkalinity, organic content, ignitability and toxic!ty by
placing barrier berms between cells or between sections within cells. Drums
are usually emplaced closely together in a part of the waste layer or may
constitute an entire layer. Drums are placed either on end or on their sides,
the choice being more a matter of preference by the site manager than of
established advantage of one method over the other. „ However, all drums at a
given facility are placed in the same orientation. One state waste disposal
controlling agency reported the practice of isolating "soluble" (deteriorating)
wastes in separate cells so that all expected settlement occurs in a predeter-
mined location. Soluble wastes would Include drums. Other -sites handling
predominantly bulk wastes distribute the "soluble" type of waste containers
and debris throughout the fill to minimize the effects.
To satisfy the general RCRA requirement that no free liquids be enclosed
within the disposal cell, liquids must be solidified before burial. Bulk
liquids, for example those delivered by tank truck, are commonly impounded
behind temporary dikes in one part of the cell and "solidified" in place with
local soil, fly ash, fuller's earth, or other material before being covered.
Drummed liquids are either solidified it) the drum by the addition of absorbent
filler to the drum, or are decanted and solidified vlth&n »th« 4C*11.. Air or
void space within the drum is also minimized by addition of filler or by
crushing empty drums. Rain water entering the cell during filling operations
is solidified in the same manner as bulk liquids or is pumped out to temporary
onsite evaporation ponds. The thickness of waste layers is generally equal to
the length or diameter of a waste drum. Each layer of waste is covered with a
layer of dry crushed rock, soil, or other material spread by tracked or wheeled
vehicles. Some attempt is made to distribute the intermediate cover material
into voids around and between drums. The intermediate cover nay be specially
selected material chosen for its absorbency, neutralization effects, or non-
flammability, or reworked, crushed rock or soil stockpiled during cell
excavation. One waste disposal film listed six types of daily (intermediate)
cover that it uses within a single facility, the choice of material satisfying
the specific requirements, such as ignitability or alkalinity, of the particu-
lar waste being covered. Waste and intermediate cover layers are alternated
as the cell is filled and then a final cover is installed. Those facilities
in which most of the wastes are in dry or solidified bulk fora do not use an
intermediate cover during filling operations.
8
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CELL COVER
Design of the final cover varies. The cover typically has the following
layers: (a) a buffer layer consisting of local soils or intermediate cover
naterials which protects the barrier from the uppermost waste layer and
(b) synthetic liners similar to those of the cell liner. The central part of
the filled cell or of the final cover Is elevated so that the final cover
surface slopes away on at least a 5 percent grade, and grades as high as
8 percent were reported (Figure 1). Lutton et al. suggested 3 to 5 percent
as quoted for use in grounds maintenance. Some facility operators and regula-
tory officials stated that the final cover surface is mounded high enough to
maintain sufficient grade after expected or potential settlement of the final
cover. The Draft RCRA Guidance Document for Landfill Design, Liner Systems
and Final Cover, issued July 1982, suggested that the final cover slope be a
minimum of 3 percent to prevent ponding, and no greater than 5 percent to
prevent excessive erosion. There appear to be no data on percentage or amount
of settlement to expect in a hazardous waste landfill and presumably the final
cover height is based on intuition by operators and regulatory personnel
(Sections 4 and 5 of this report suggest means by which settlement (subsidence)
can be predicted for modeled hazardous waste landfills). The surface is
vegetated to prevent erosion of the final cover materials* fGo*paction efforts
and control for the final clay cover barrier are similar to those for the cell
liner. Settlement plates may be installed on closed cells for monitoring of
subsidence, but none were emplaced at sites contacted in this study.
Lutton et al. presented guidelines and suggested criteria for construc-
tion of solid waste landfill final covers. Layering of final cover materials
was suggested to meet the logical requirements of a landfill final cover to:
ju Vent gases generated within the cell.
b_. Isolate wastes from contact with the environment by means of a
barrier.
£. Drain water off the fill to prevent infiltration and ponding.
A. Protect the barrier layer(s) from damage by wastes or construction
"" activities.
£. Prevent erosion of the final cover soils.
The EPA guidance document suggests that the final cover should consist of
three layers. The bottom layer overlying the topmost waste layer should be a
two-conponent low permeability layer. The upper component of the bottom layer
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should below the frost penetration depth and should consist of at least 20-mil
synthetic membrane protected above and below by at least 6 in. of bedding
material no coarser than sand. The lover component should consist, of at least
24 in. of soil compacted in 6-in. lifts to achieve a hydraulic conductivity of
no more than 1 x 10" cm/sec. The middle layer of the final cover serves as
drainage and should be at least 12 in. thick, have a" hydraulic conductivity of
at least 1 x 10* cm/sec, and should be overlain by a graded granular filter
or synthetic fabric filter. The top cover layer should be soil at least
24 in. thick and capable of supporting shallow-rooted vegetation that will
effectively minimize erosion. Variations of the suggested final cover scheme
in actual practice by the hazardous waste disposal industry ranges from a
final cover consisting of a single thick clay layer to a multilayered cap of
•clay and polymeric membrane barriers, sand drainage blanket and gas-venting
layer-. At least one state regulatory agency requires an additional soil layer
equal in thickness to the local freeze-penetration depth to further protect
the final cover materials.
QUALITY CONTROL
The RCRA controlled commercial hazardous disposal waste facilities
maintain a technical staff onsite or in a regional office, or contract to
consulting engineering laboratories, for cell design, barrier compaction
design and permeability control, monitoring of leachate quality and migration,
and waste analysis.
10
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SECTION 3
SUBSIDENCE MECHANISMS AND RELATED PROBLEMS
INTRODUCTION
Section 3 di-scusses mechanisms by which settlement of materials and/or
subsidence of the surface occurs. The discussion includes all conditions,
both natural and artificial, that have been recognized to cause settlement and
subsidence. Such conditions are consolidation and compressibility, commonly
investigated in connection with soils; cavity-related conditions encountered
in natural karst regions and in underground mining and tunneling; and a vari-
ety of mechanisms identified and documented for sanitary and low-level nuclear
waste landfills. The purpose of Section 3 is to address known settlement/
*
subsidence mechanisms, evaluate them, and select the proper mechanisms for
analysis of settlement/subsidence in hazardous waste landfills. The discus-
sion of consolidation of soils is addressed again in Sections 4 and 5 concern-
ing analysis of settlement attributed to layers of soil and waste in hazardous
waste landfills. Settlements induced by seismic events are not considered.
SUBSIDENCE BY CONSOLIDATION
Primary Consolidation
Consolidation of a soil is the decrease in void ratio (volume of voids
to volume of solids) by expulsion of fluids from the voids under excess hydro-
static pore pressure (primary consolidation) and by deformation of the skele-
ton of the soil mass and compression of gases in the voids (secondary
compression). The decrease in void ratio by consolidation represents a de-
crease in volume of the soil mass and can cause the surface of the mass to
subside. The classic Terzaghi theory for one-dimensional consolidation of a
soil assumes that deformation of the soil mass is by change in volume by the
expulsion of water from the voids and that the soil is saturated (there are
also several other important assumptions, for example, see Means and Parcher,
p. 208. The change in void ratio of a soil is a measure of coosolidation.
If a mass of soil (Figure 2) is compressed, the change in its thickness AH
can be expressed as a change in the void ratio (Ae).
11
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ii
k
^
K
*
II
sT
Ae
IT
VOIDS
SOLIDS
j
AH
T
Figure 2. Relation of thickness (H), volume (V ) and
void ratio (e) of a soil.
12
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The unit deformation is
~ - 3-— (see Figure 2) . '• . (1)
Where V - total soil volume and e is the initial void ratio. Since AH'
can be expressed as Ae , and V£ as H. (Figure 2)
AH . _A£_ '
H 1 H- e u;
where H is the total thickness of the soil mass, and the amount of settle-
ment due to consolidation is then
AH-Hj-^ . (3)
An estimate of the amount of settlement to be expected in a soil sub-
jected to a load in the field can be made from laboratory consolidation tests
on representative soil samples and field loading and overburden thickness
data. The laboratory consolidation test yields a curve of change in void
ratio (e) with increasing load (p). The slope of the resulting e-log p
1. * ?-£* ., '-
curve is called the coefficient of compressibility (("_) jmatJJ • Jffrpr« ITrril as
el " 62 _ Ae "
cc * log p2 - log p2 A log p
where p, and p~ define one log cycle of pressure for the change in void
ratio («i~«2^*
Substituting for Ae in Equation 3,
C C
AH - H J-—- A log p - H i + e (log p2 - log
and since P? * PI + ^p
AH
" H j-^Tg- ^8 (PI * AP) ' ^8 PI
C P, +
•- H r-r2-
13
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or settlement
C / »_\ •
(5)
Equation 5 predicts the amount of settlement to be expected by one-dimensional
primary consolidation of a saturated soil mass of thickness E , initial void
ratio e , initial overburden stress p, , and compressibility C_ when
loaded at an increase in stress of Ap , assuming Terzaghi's assumptions are
met.
The rate of settlement, or change In soil volume with time, can be
predicted .for selected degrees of consolidation (percent consolidation) with
the equation
where
t - time to achieve average percent consolidation (U)
T « a time factor, for which a table is available relating T and U
(see Ledbetter)
Re * length of drainage path for expulsion of water from the soil voids
(for single drainage, as with soil overlying an impervious barrier,
He » H ; for double drainage, as with soil bounded above and below
by pervious zones, He « H/2 ; for multiple drainage path, as with
soil interspersed with alternate layers of pervious zones, Be -
fraction of H )
c » coefficient of consolidation, a laboratory determined value depend-
ent upon the soil's compressibility (Cc), its permeability (k) , and
the void ratio (e)
Conversely, the degree (percent) of consolidation (U) that will occur at an
elapsed time t can be predicted by solving for T in Equation 6, and then
referring to the table (T vs U) for U .
Consolidation of soils by lowering of the water table has been identi-
fied as a possible cause of ground subsidence in some locations * * * . The
effect of lowering the water table in a soil is to surcharge the soil by
Increasing the effective stress through a decrease in pore pressure. The soil
consolidates following Terzaghi's one-dimensional consolidation theory. Fang
12 •
and Cleary discuss consolidation by ground water lowering for coarse- and
fine-grained soils in confined and unconfined aquifers.
14
-------
Secondary Compression
Similar calculations can be made for settlement from secondary compres-
sion (deformation of the soil mass), which occurs sometime after primary
consolidation as most of the applied stress is transferred to the soil skele-
ton, by considering the laboratory determined coefficient of secondary
compression. Total settlement is the sum of the primary consolidation and
secondary compression settlements. If the loading 'is not instantaneous, but
instead is applied gradually as in the case of extended construction time,
time factor curves are consulted for modified values of T and U . An
example of settlement calculations for a layered saturated sludge landfill is
presented in reference 7, pp 28-33.
Primary consolidation is not expected to be the dominant mechanism for
settlement of hazardous waste landfills. Regulations prohibiting the place-
ment of free liquids in landfills, the use of leachate collection and removal
systems, and the use of liquid-absorbing stabilizing agents limit saturation
of the waste fill. Primary consolidation may occur initially, during filling,
before closure but long-term settlement should be analyzed on the basis of
deformation of the waste layers and deteriorating waste containers.
CAVITY-RELATED SUBSIDENCE
The presence of large voids, herein called cavities, within a soil or
rock mass has been recognized as a cause of subsidence of the ground surface.
Analyses of cavity-related subsidence have been made in relation to
mining12«13»14*15*16'17 natural karst (solution cavity) areas8*15'18, and
Q jo 20
landfills ' * . The relevance of subsidence mechanisms identified in karst
and mining studies to analysis of cavity-related problems in hazardous waste
disposal fills is examined in this section. Hazardous waste disposal facili-
ties can contain Initially rigid but ultimately collapsible containers that
are placed in various geometries (horizontally, vertically, and layered with
soils). They may contain highly compressible materials and their rigidity may
initially inhibit pre- and postclosure deformation of the fill. This section
discusses cavity-related subsidence mechanisms recognized in karst and mining
investigations and outlines subsidence Investigative techniques developed for
their analysis.
15
-------
Mining Subsidence Mechanisms
Discussions of mining subsidence have generally consisted of describing
tbe geometry and size of the surface subsidence trough in terms of the size
and depth of the mined-out zone associated with the trough. Sane limited
12 15 21 ' 15
attempts have been made•"•»*•'»** to explain'the failure mechanisms. Brink ,
for example, recognizes closure of the mined opening as a mechanism leading to
t
surface subsidence. He attributes the closure to movement of the overburden
into the mined opening either en bloc or differentially. En bloc movement of
rock above the opening occurs if the arch or dome of fracturing above the
mined opening does not extend to the surface (the mined opening is deep).
Differential movement (Brink's "macroplastic") occurs if the fracturing ex-
tends to the surface (the mined opening is shallow), and downward movement of
.overlying rock* and soil is by slippage along fracture planes. . Attewell and
Farmer describe the subsidence trough in terms of an active wedge.
Brauner described subsidence as continuous if a regular subsidence trough
was formed, or discontinuous if movement occurred along fractures or in col-
lapse pits (sinkholes). Other studies of subsidence in mined areas are empir-
ical, apply to specific geologic/ geographic environments, and describe the
geometries rather than explain the mechanisms of subsidence features (for
0 - .sH-5pf«W" -
example, references 13 and 16). :~~:
Mining subsidence investigations have been conducted In response to
potential or real damage to buildings and utilities in a mining area and
accordingly address the parameters of slope and curvature of the subsidence
trough, horizontal strains and displacements, and maximum subsidence.
Figure 3 diagrams the descriptive geometry commonly used in mining subsidence
investigations (Figure 3 is derived from references 14 and 16). The limits of
the subsidence trough, which is not drawn to scale relative to the mined
opening, are defined by the "draw" line constructed from the edge of the mined
21
opening to the surface. Attewell and Farmer depict the vertical angle of
the draw as 45-(0/2)°, which defines a theoretical active wedge with 0 the
effective friction angle of the soil or rock above the opening and with the
principal stress acting vertically. Maximum strains at the subsided ground
surface occur at points of maximum curvature on the subsidence curve, or
trough. The strain is a minimum and the horizontal displacement a maximum at
the inflection points and the horizontal displacement is minimum at the center
of the trough (see Figure 3).
16
-------
HORIZONTAL DISPLACEMENT
VERTICAL DISPLACEMENT
(SUBSIDENCE CURVE)
POINT OF
MAXIMUM
TENSILE
STRAIN
(ANGLE OF
DRAW, FROM
POINT OF
MAXIMUM COMPRESSIVE
STRAIN
FARMER, 19761
Figure 3. Descriptive geometry of mining subsidence investigations.
17
-------
14
Brauner attributes damage to surface structures to the slope, curva-
ture, horizontal displacement, and resultant strain in a subsidence trough.
Following Brauner, slope of the trough is the change in subsidence (vertical
displacement) with respect to the horizontal reference axis. Slope-induced
damage commonly takes the form of change in gradient of surfaces, utility
pipelines, and drainage. Curvature is approximately equal to the derivative
or rate of change of the slope and is produced by differential vertical move-
ment of the surface. Curvature- induced damage is caused by shear strain (or
angular distortion) and bending. Differential horizontal displacement dis-
torts alignments of structures on the surface.
Karst Subsidence
Definition and Significance. Karst describes a terrain characterized by
closed depressions (sinkholes) , caves and underground drainage. Karst occurs
in and overlying deposits of water-soluble rock such as limestone and is
attributed to subsurface solution and erosion of the rock. Ground subsidence
18 22
in karst terrains has been documented extensively in the United States ' ,
in South Africa ', and in Europe . Sinkholes and depressions are the
,
surface expressions of the solution channels and caverns formed underground in
the soluble rock. Formation of the sinkholes and depressions in karst terrain
can be a process of collapse of the cavern roof, of piping of overburden soils
into the cavern by downward percolating water, of collapse of the overburden
arch or bridge spanning a cavern or of sagging of stratified materials into
the cavity. Settlement within the overburden soils overlying cavernous rock
in karst terrains presents a convenient field and laboratory tested model of
cavity-related subsidence mechanisms useful in developing analyses of subsi-
dence in waste landfills where the potential for cavities exists. The geo-
logic and hydrologic processes responsible for development of the soluble rock
caverns and solution channels of karst is less analogous. Accordingly the
mechanisms responsible for the formation of sinkholes are discussed below.
Mechanisms of Sinkhole Development. A sinkhole is defined in this
report as a closed surface depression originating at depth in a cavity or
locally highly compressible zone. The sinkhole represents local subsidence or
collapse of the ground surface. Field and laboratory observations of karst
features recognize three mechanisms of sinkhole development * * : piping,
18
-------
sagging, and arch collapse. Piping is the erosion of cohesionless or low
cohesion soils through channels or slots (pipes) by water percolating down
gradient toward a base level, such as the water table. The soil erodes from
the mouth of the pipe or slot, the erosion progressing upwards by a process of
headward piping ,. Piping can form sinkholes if a sufficiently large cavern
exists below the slot to accept the eroded aaterial and if sufficient water is
18
available for transport of eroded soil. Sowers -applies the term "ravelling"
to piping erosion phenomena.
Sagging occurs in horizontally layered soils overlying a cavity if the
span of the roof of the cavity is greater than a critical value which is
8
determined- by the strength of the coils . Figure 4 illustrates documented
sagging of horizontally layered rock and soil units overlying a solution
cavity. The situation depicted in Figure 4 might be expressed by a surface
depression but would not form a collapse sinkhole unless failure or headward
erosion (piping) of the units overlying the cavern occurred. The tendency of
the overlying layers to sag and the amount of sag will depend primarily on the
cohesion or bond strength of the material in the layers. The situation of
horizontal layers spanning a void can be represented by a simple beam supported
at each end and subject to a uniformly distributed load (gravity), as Illus-
trated in Figure 5a. The tendency of the beam to sag Is explained by analyzing
1 r
the shear and bending moment diagrams (Figures 5b and 5c, respectively). The
shear stress is greatest at the supports (beam ends) and decreases linearly
away from the ends to zero at the center (Figure 5b). The bending moment,
however, is a maximum at the center of the beam (Figure 5c). The lower sur-
face of the beam at the center is placed in tension by the moment and if the
moment at the center of the span is great enough to set up tensile forces
exceeding the cohesive strength of the beam material the beam will yield, or
sag. If the span is less than the critical distance arching of stresses may
occur in the beam and the beam will not deflect.
Arching is the bridging of a cavity by overburden soils by the transfer
of load in the overburden to the sides or abutments of the cavity opening.
26
Terzaghi and Peck used a simple laboratory test to explain the phenomenon of
arching. Figure 6 illustrates the test which consists of a layer of sand
placed on a platform containing a trapdoor overlying a cavity (AB in Figure 6a).
Pressure on the platform and door is measured on a scale. Figure 6b shows the
19
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CAST
570
MS
*K>
OLACIOLACUSTHlWE
DEPOSIT
/j^LLAC.OU.OOLOM.TE
S3!
K)0
LOWCR SANOtO
OTrsUMMWCOMITE
SOTTOM Of CAVITY M
SOWING SS-tOA
CAVITY BILLED WITH SOLUTION
BOUNDED SOULOERS. HOCK
FRAGMENTS. AND SHOWN SILTY
CLAY
SCALE
10 FT
Figure 4. Sagging of horizontal strata overlying solution
cavity (reference 24).
20
-------
LOAD
I j I I < ) I V
K//////////,BEAMy//////////|
VOID
(a) UNIFORMLY LOADED BEAM SPANNING A VOID
(+) MAX
CUJ
<0
UJ 1C
10
wu.
MAX
(b) SHEAR DISTRIBUTION ALONG BEAM
MAX
(c) BENDING MOMENT ALONG BEAM
Figure 5. Stresses on bean spanning a void (modified
after reference 25).
21
-------
B
(a) LAYER OF SAND ON PLATFORM WITH TRAPDOOR AB
B
BEFORE RELEASE
B
i
. AFTER RELEASE
(b) STRESS (PRESSURE) DISTRIBUTION ON PLATFORM
AND RELEASED TRAP DOOR
Figure 6. Test illustrating arching in soil over a cavity
(after reference 26).
22
-------
pressure distribution after allowing the trapdoor to yield under the weight of
•and. The shear forces (pressure) on the abutments (A,B) are large and those
on the door snail, a force distribution analogous to that-of the beam in
Figure 5b. .The reason is that the central column of sand above the trapdoor
is resisted by shear stresses along its boundaries (AC and BD in Figure 6a~).
Terzaghi and Peck further state that the ultimate pressure on the released
trapdoor does not exceed the weight of a mass of sand having the arch shape of
the shaded zone in Figure 6a, regardless of the height of the column of sand.
(Coates ) showed that the pressure on the trapdoor is equal to a column of
ground equal in height to the radius of the trapdoor.) If the sand has some
cohesion the trapdoor can be removed and the sand will bridge the gap and not
fall through. The pressure not carried by the trapdoor Is supported by arch-
t •.
ing action into the abutments.
_'Arch failure in overburden soils in karst terrain has been identified as
a major cause of sinkhole development by several authors * '. Figure 7
illustrates the typical karst field conditions necessary for sinkhole develop-
ment by progressive arch failure. Solution along joints and bedding planes
and in more soluble strata within the rock of Figure 7 has created caverns and
slots. The rock is 'overlain by a residuum of insoluble material and other
soils. Piping of soils clogging the slot by percolating water In Figure 7a
has progressed upward to the base of the residuum where an arched cavity (a
dome in three dimensions) has been created. Progressive failure of the arch
proceeds as shown by the dashed lines and arrows in Figure 7a until a stable
configuration is achieved, which may be an open-roofed sinkhole like that
shown in Figure 7b. The eroded collapse debris accumulates in the cavern
below or, if sufficient discharge and gradient are available in the percolat-
ing water, is carried out of the system.
8 15
Jennings and Brink observed karst subsidence in the field and identi-
fied the requirements for sinkh'ole development:
jt. Rigid abutments must exist to allow an arch to form by the process
of stress transfer (discussed above). A condition of arching must
form in the residuum between the abutments; if the span between
abutments is too great, arching cannot occur.
_b. A cavity must develop in the residuum below the arch. The initial
~~ cavity can be produced by piping as explained above.
£. A reservoir has to exist below the arch to accept material removed
as the arch enlarges. If collapse material is not removed the
23
-------
OVERBURDEN RESIDUUM
SOLUTION JOINT OR SLOT
(bt
Figure 7. Sinkhole development by arching ia karst terrain
(modified from reference 15).
24
-------
boundaries of the arch may stabilize and the arch cease to grow.
Arch progression and stabilization is discussed further, below.
d. Once an arched cavity has been established in the residuum, a trig-
gering mechanism must occur to render the arch unstable. The most
common triggering mechanism is percolating water migrating toward
the water table. Dynamic mechanisms, such as earth tremors, vibra-
tory loading by vehicles at the surface, and mining activity have
also been Identified.
Water that enters the soils of the arch decreases the capillary tension be-
* 18
tween soil grains that is responsible for the cohesive strength of the arch .
If the gradient and flow are high enough the percolating water may also erode
soils from the arch surface. Moving water also carries away collapse debris
that collects at the base of the arch and thereby produces instability in the
arch.
The mechanics of arch failure in soil were analyzed by Lobban (reported
in reference 8) who used a finite difference analogy of a soil-filled bin
equipped with a trapdoor. Lobban1s model calculated and displayed the stress
trajectories and zones of overstress for the bin with yielding trapdoor for
soils of different cohesions and shear strengths and for different boundary
conditions. Figure .8 illustrates Lobban*s model. The stress trajectories of
Lobban's model represent the propagation of stress through the soil. The
mutually perpendicular curves show the trajectories of th^^^or and minor
principal stresses. Tangents to the curves at any point represent the direc-
2g * -^fe-V-
tions of the principal stresses at the point . Lobban concluded that
(a) varying the shear strength of the soil changed the size of the overstress
zone (Figure 8) very little for given boundary conditions, but lowering the
cohesion of the soil substantially increased the span and height of the over-
stress zone, and (b) if the collapsed debris that accumulated at the spring-
ings of an arch were removed, the boundary conditions changed and a new,
larger arch configuration would form. Iterative analysis showed that repeated
removal of the collapse debris resulted finally in a stable arch configuration
that differed for different cohesion values. The stable arch configuration
might be a surface-connected trajectory, or sinkhole such as the dashed curve
of Figure 8.
•
Lobban's conclusion that a stable arch can be rendered unstable by
removal of the accumulated debris at its springings Infers that sinkholes
probably will not fora in arched soils unless sufficient percolating water is
25
-------
POTENTIAL STABLE ARCH POSITION (SINKHOLE)
AFTER ITERATIVE FAILURE ANALYSIS (SEE TEXT)
STRESS TRAJECTORIES
"TRAPDOOR' ZQN£ OF INITIAL OVERSTRESS FOR A
SOIL WITH GIVEN 4 AND C
Figure 8. Representation of Lobban's "trapdoor" mathematical
model for analyzing arch failure propogation in soil
(after reference 8),
26
-------
introduced to transport debris away from the arch and to lower the cohesion in
the soils. It can further be inferred that arching that develops in soils
overlying cavities in waste fills will not progressively.enlarge if the move-
vent of liquids within the fill is controlled and additional water is prohib-
ited from entering'the fill.
LANDFILL SUBSIDENCE
Sanitary Landfills
Subsidence mechanisms in sanitary landfills have been documented or
o 29 30 31
proposed by several investigators f * * . Mechanisms identified were:
ji. -Primary consolidation and secondary compression (nechanical).
b. Ravelling or piping of fill soils or debris into voids or cavities.
*£. Deterioration and subsequent collapse of voids or cavities in waste
• ""•' products by corrosion, oxidation, combustion (physico-chemical) or
decay (biochemical).
Sanitary landfills commonly contain large amounts of paper and other organic
q
materials that decay and significant amounts (5-10 percent reported by Sowers )
of rubber products that are compressible but elastic. Leachate control sys-
tems and liners generally are not employed in sanitary-^^agypULs nor is waste
placement generally given special attention. On the other hand, hazardous
waste landfills do not typically contain large amounts of biodegradable
materials. Therefore, subsidence mechanisms identified for sanitary landfills
are not wholly analogous to mechanisms expected to prevail in hazardous waste
landfills.
Low-level Radioactive Waste Landfills
20
Daniel addressed final cover performance for shallow-burial, low-level
radioactive waste disposal sites and reported settlements of 6 in. to several
feet. Settlement mechanisms or causes identified were:
a_. Waste consolidation.
_b_. Decomposition of organic wastes (with, presumably, subsequent me-
chanical settlement).
£. Collapse into cavities created by random dumping of wastes.
Settlements led to three types of Identified cover (cap) problems:
£. Cracks in the cap caused by differential settlement.
Jb. Collapse of portions of the cap into cavities within the pit.
£. Ponding of water in depressions in the cap caused by subsidence.
27
-------
19
Kahle and Rowlands investigated settlement and subsidence of trench
fill for the Sheffield, Illinois, low-level radioactive waste disposal facility
and identified the following causes or mechanisms of trench cover -subsidence:
£. Consolidation of the backfill soils.
Jj. Piping or ravelling of backfill soils into cavities between waste
containers or into cavities created by deterioration of wastes and
waste containers.
c. Deterioration and settlement of the wastes and waste containers.
Piping and ravelling of soils at Sheffield were believed to be aggravated by
infiltration of additional water into the fill through breaks in the trench
cap caused by traffic, shrinkage, freeze-thaw and erosion of the cap soil
cover. Consolidation of the unsaturated backfill was presumed to occur by
drainage of water from the pores (primary consolidation) and by rearrangement
of particles (secondary compression) under the fill's own weight. Deteriora-
tion of waste containers like that experienced at Sheffield is expected to
occur in RCRA hazardous waste facilities. The Sheffield waste settlement
problems were attributed to structural collapse and corrosion of containers,
particularly metal drums. Kahle and Rowlands stated that collapse of contain-
ers created cavities into which particulate materials Jc^|ldjejR|.pe and which
could lead to development of surface potholes. However, containers should
collapse only under the weight of overlying materials and therefore should not
create a cavity but simply compact, with no break in continuity with the
overlying and adjacent soil. The result of drum collapse more logically would
be compaction (secondary compression) subsidence and not piping or ravelling
into cavities. Drum corrosion might create an incipient cavity if the drum
contained free liquids or trapped gas (air) but corrosion of the drum would
probably lead to its collapse and to closing of any incipient cavity. It is
conceivable that bridging or arching of soils overlying cavities created by
drum corrosion (but not by drum collapse) might occur if more corrosion re-
sistant materials or containers surround the corroding containers to serve as,
rigid abutments to bear the arching forces of overlying soils.
Subsidence Mechanisms in Controlled Hazardous Waste Landfills. Most of
the controlled (RCRA) hazardous waste landfills addressed in the study are
recent (post - 1977) and have not as yet exhibited subsidence problems. Waste
and waste placement characteristics, fill and fill placement characteristics,
28
-------
and other operational procedures were studied for several controlled facili-
ties to predict the probable settlement/subsidence mechanisms that might be
active in the fills. The dominant mechanism is expected to be deformation or
compression of waste products, fill soils, and voids. Water contents of the
wastes may be high but the landfill will not be saturated (for reasons dis-
cussed in Section.5 of this report). Saturation will continue to decrease as
leach ate is removed via the leachate collection system. Some of the water of
the waste and fill becomes chemically bound as water.of hydration and is not
readily available as leachate. For these reasons subsidence by consolidation
will occur much more quickly than in the case of saturated landfill soils.
Calculations explained in Section 4 indicate that consolidation of intermedi-
ate cover layers will occur in a short time, prior to final closure of the
landfill.' - .
Some cavities are present in the cells at closure but the careful place-
ment, of waste containers and intermediate cover practiced In the typical
controlled facility will keep cavity size snail. Cavities created later by
deterioration or corrosion of wastes or waste containers will also be small
because containers are not allowed to contain more than 5 percent void (cavity)
space (10 percent under 1982 interim guideline revision, DSEPA ) and may not
contain free liquids. As discussed earlier, container «0iJj(**e should result
in compaction but not cavity enlargement or sinkhole development. The strin-
gent leachate collection and liner systems of the controlled facility preclude
the development of escape paths, pipes, or excessive gradients that might
trigger cavity collapse or growth.
A layer of corroded or deteriorated waste containers can be analyzed as
a deformable layer in a fill with variable layer compressibilities. A layered
fill model can be constructed using properties of typical waste-intermediate
cover materials and typical landfill geometries. Deformation and settlement
can then be calculated for fills of varying stiffnesses and the relationship
between subsidence and fill properties developed. The method used in this
report to analyze and model the deformation by settlement of typical hazardous
waste landfills is described in Sections 4 and 5.
SUBSIDENCE-RELATE) COVER PROBLEMS
Documented examples of failure (compromise) of landfill final cover
systems resulting from final cover subsidence and fill settlement are
29
-------
primarily for low-level radioactive waste repositories and sanitary landfills.
Four types of final cover compromise that have been Identified are:
a. Differential settlement of fill and final cover leading to the
~~ development of tension cracks in the fine
Figure 9A for low-level radioactive waste
development of tension cracks in the finalQcover, diagrammed in
, and for landfills3),
b. Settlement of fill and final cover leading tft ponding of water
~" on the final cover, as shown in Figxfre 9B * .
£. Local sudden collapse of final cover soils iRto underlying
~~ cavities in the fill, as shown in Figure 9C .
d_. Piping of erodible final cover soils Into underlying cavities
~~ in the fill, leading to collapse, or sinkholes, as in type £
above for low-level radioactive wastes ).
Another ty.pe of documented final cover problem not caused by settlement, but
which can lead to the development of piping failures is cracking of the final
cover by desiccation or by freezing and thawing of water in the final cover
19
soils (Kahle and Rowlands '). Cracking, if deep enough, allows water to
infiltrate and, if the water is of sufficient volume and if cavities or other
seepage paths are present within the fill, can initiate piping of erodible
final cover soils with eventual final cover collapse.
The kinds of final cover problems considered in thiss*tndy (prior to
modeling) to be most likely to occur in controlled (R&StArT^«lrdous waste
landfills were tension cracking by differential settlement and ponding of
surface water in subsidence depressions. As discussed earlier, piping and
sinkhole development are not expected to be significant because the volume of
cavities and avenues of piping within the fill will be minimized by careful
waste placement. Leachate collection systems and solidification of liquids
will help maintain unsaturated conditions. Active hazardous waste disposal
facilities examined during this study have not yet experienced significant
cell final cover difficulties attributable to settlement. Apparently insuffi-
cient time has elapsed since closure of the first cells of RCRA-controiled
facilities for settlement and subsidence effects to be noticeable. More
significantly, it may be difficult to document other than sudden cover subsi-
dence because the disposal facility operators will correct alow or minor cover
subsidences as they occur by the use of grading equipment and fill soils.
30
-------
CRACKS
'MACKS
COVE*
Figure 9. Cover problems Identified and documented for landfills.
31
-------
SECTION 4
PREDICTION MODELS FOR MAXIMUM SUBSIDENCE
INTRODUCTION
This section presents numerical methods of analyzing the deformation in
a typical hazardous waste landfill to predict the amount of settlement of the
fill and subsidence of the final cover. It nay be several years before com-
parison can be made between the numerical method results and actual field
final cover performance. The models selected to represent the typical hazard-
ous waste landfill in the numerical analysis techniques are representative of
actual landfills encountered during this study. Waste and intermediate cover
characteristics (such as densities, water content, fill and waste layer moduli
and compressibility), leachate barrier characteristics (such as permeability,
thickness, and elastic moduli), compaction procedures and specifications, and
othe'r considerations represent real materials and operational procedures found
in the hazardous waste landfill industry. The models developed and the results
of analysis presented in .this report are thought to be valid within the limi-
tations discussed and under assumptions made in Sections A and 5. '
One design consideration for hazardous waste landfills is a liner system
to serve as a barrier between waste and in situ soil which intercepts leachate
that either has been internally generated by the contained waste or is the
result of infiltration of liquid from the outside during filling. Liner
systems often consist of layers of clay compacted in place to a predetermined
water content and density to achieve a required permeability. The liner
system may consist of clay alone or clay in combination with one or more
polymeric membranes. The effect of long-term exposure to chemical waste
environment on the liner is unknown but for the purpose of this analysis it
will be assumed that the liner system remains intact for the life of the
structure.
After closure, landfills must have a final cover to prevent human (and
animal) contact with the waste, to prevent wind dispersion of the waste and to
prevent liquids from percolating into the landfill so that the production of
contaminated leachate is minimized. In this light, it is important that the
final cover system remain intact and competent because rupture of the final
cover could cause a landfill to fill up with water and overflow, spreading
contaminated waste and toxic chemicals into the environment.
32
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PURPOSE OF MODEL ANALYSIS
Simply stated, a hazardous waste landfill is a large excavated pit where
wastes are buried, sandwiched between layers of intermediate cover soil. The
intermediate cover soil and the layers of waste are subject to compression
from the weight of 'the overlying material. Surface subsidence by internal
material compression and settlement can be a problem if it is so severe that
it causes the final cover to crack or to impound rainwater which might eventu-
ally seep into and breach the final cover. Subsidence must be considered if
long-term protection is to be provided for these structures. To avoid subsi-
dence of the center of the cover and the resulting water impoundment, such
structures, might be overbuilt by the amount of expected subsidence so that the
ground contour would reach the design grade as ultimate subsidence occurred.
t
• Accordingly, an estimate of subsidence must be made. The purpose of this
chapter is to establish soil and stress conditions in a typical hazardous
waste landfill and to estimate surface subsidence for various landfill
configurations. Two analyses were made in this study: (1) to determine
maximum subsidence to be expected before and after closure at the center of a
large landfill for two waste placement configurations, and (b) to determine
the potential for cracking of the cover by stresses from ilfferential settle-
-$$!*••**•-
merit across a uniformly layered landfill.
i i
CONDITIONS ASSUMED FOR LANDFILL SUBSIDENCE MODELING
Geometric Configuration of Modeled Landfill
The geometric configuration of a landfill is governed by several factors
Including the amount of land available, size and type of equipment available
to work'the landfill, state and local policy concerning such facilities,
projected utilization, local climatic conditions, thickness and geologic
character of the native soil and rock at the site, in situ soil strength and
proximity to the water table. After considering several geometric config-
urations (see section 1), a representative configuration was chosen and is
shown in half-section on Figure 10. The excavated section is 50 ft below the
original ground surface, the pit Is 200 ft wide at the bottom, end the side
slopes are 1 vertical on 3 horizontal for a total excavated width of 500 ft.
The final cover system has approximately 5 percent (1 vertical on 20
33
-------
*. V
FTHICK TOP LINER
ALTERNATING LAYERS OF DRUMS AND COVER
DRUM LAYER « 2-FT THICK
COVER * 1.5-FT THICK
»' BOTTOM LINER
E.,l>, - YOUNG'S MODULUS, POISSON'S RATIO OF COVER LAYERS
,!
E,. M, • YOUNG'S lyiODULUS, POISSON'S RATH) OF WASTE LAYERS
SECTION A - A
Figure 10. Assumed hazardous waste landfill configuration.
-------
horizontal) slope from the original ground surface up to the crown of the
landfill for a total center depth of 62 ft. The plan of the landfill may vary
from square to a rectangle whose length is many times the.width of the section.
Landfill Contents
The landfill' is assumed to be lined with a clay layer 8 ft thick along
the bottom and 5 ft thick along the sides and top. The waste material is
assumed to be contained in 55 gallon steel drums which, inside the landfill,
can be laid on their sides or placed on end. The interior of the cell is
assumed to be filled with alternating layers of drums separated by 1-1/2-ft-
thick intermediate soil cover layers up to the top liner. The total waste-
intermediate cover fill thickness is approximately 49 ft at the center. For
the purposes of1 this analysis, the layers are assumed homogeneous and iso-
tropic which means that layers containing the metal drum will be a homogeneous
"equivalent" of metal drum, contained waste and that portion of the intermedi-
ate cover soil that is placed in the spaces around the drums. The drums are
nominally 2 ft in diameter and 3 ft long which means that the waste layer will
be 2 ft thick in the configuration where the drums are placed on their sides;
waste layers will be 3 ft thick in the configuration where drums are placed on
end. As implied in Figure 10, the cell is symmetric with respect to a vertical
axis through the center of the landfill. With this geometry and the assumption
of homogeneous material properties, it can be shown that settlement due to
gravity stress will be maximum along the vertical centerline of the structure
because of maximum cell depth at the centerline and maximum distance from the
interference of the boundaries.
Landfill Soil Conditions and Water Content
Because of regulation and practical consideration, liner systems of
hazardous waste landfill facilities are designed to satisfy a permeability
rather than a strength requirement. The maximum value of permeability per-
mitted by the EPA is 1 x 10 cm/sec. Laboratory permeability is typically
isured on remolded soil specimens which have been back pressure saturated in
triaxial chambers. The liner and intermediate cover materials used within the
landfill are almost always of the soil excavated initially from the landfill
site. For several observed sites, the excavated soil is a medium plasticity
clay whose Atterberg limits are shown in Table 1.
35
-------
Table 1
Atterberg Limits of Typical Hazardous Waste Intermediate
Cover Materials and Model Material
Site Location - Liquid Limit (Z) Plasticity Index
Alabama 32-48 (38.avg) 12-30 (18 avg)
South Carolina 65-75 (68 avg) " 20-30 (24 avg)
New York 46-54 (50 avg) 26-33 (30 avg)
Model material 56 34
(Vicksburg buck-
shot clay)
The clay chosen for use in the model is "Vicksburg buckshot" clay, a plastic
(Unified Soil Classification CH) clay whose stress-strain and strength proper-
32 33
ties are well documented ' . The clay's Liquid limit is 56 percent and its
plasticity index is 34 percent. This clay eAlbits a stress-strain behavior
typical of remolded compacted clay over a wide range of confining pressure. A
typical stress-strain response is shown on Figure. 11. The landfill sit.e is
assumed to be completely above the water table. Therefore,,.£or £he purpose of
this analysis, the degree of soil saturation is assumed to be less than
100 percent. For the mathematical model, the liner system is considered to be
well compacted clay. It is assumed to have a dry density of 113 pcf and a
water content (weight of water per weight of solids) of 19 percent for a moist
unit weight of 135 pcf. The intermediate cover soil is considered to be less
compacted than the liner soil. Frequently the intermediate cover soil is
spread over a waste layer by a piece of earth moving equipment and compacted
by driving the equipment back and forth over the soil. Lutton et al. deter-
mined by systematic correlation between laboratory compactive effort and
passes of an intermediate sized bulldozer on landfill intermediate cover
layers that 3 to 4 passes correspond to a dry density of about 92-93 pcf dry
density in a silt or clay soil with an in situ water content of about
25 percent. This patches closely with the water content and density condi-
tions of the compacted laboratory soil specimen of clay that was selected as
the model soil . For the intermediate cover material, a dry density of
92 pcf, a specific gravity of 2.8 and a water content of 25 percent corresponds
36
-------
CONFINING PRESSURE • 5 KG/CM2
HTRAIN. LEAST SQUARES HYPERBOLIC PIT
EXPERIMENTAL DATA POINTS
8 10 12
AXIAL STRAIN. %
14
16
18
20
Figure 11. Stress-strain relationship for CH soil chosen for
liner and intermediate cover. Reference 33.
37
-------
to a saturation of about 78 percent and a wet unit weight of 115 pcf, which is
believed to be a realistic and expected in situ soil condition. The vet
weight of the waste layers is also estimated to be 115 pcf for Modeling
purposes. Index properties of the modeled soils are summarized in.Table 2.
Table 2
k
Index Properties of Modeled Liner and Intermediate Cover Soils
Dry Wet
Unit Unit Water
Compactive Weight Weight Content Saturation
Effort (pcf) (pef) (2) (2) Gs
Liner clay
Intermediate
cover clay
High
Low
113
92
135
115
19
25
97
78
2.8
2.8
Boundary Conditions of the Landfill Section
For the purpose of this analysis, it will be assumed that the geometric
section of the landfill has rigid boundaries, that is, significant deformation
•takes place only within the material inside the landfill section with no
movement of the boundaries. This assumption is justified in that the exca-
vated clay is at least normally consolidated and probably quite stiff and
strong at a. depth of 50 ft below ground level. Due to unloading as a result
of excavation, some rebound may occur but exprerience has shown that rebound
is small relative to virgin compression (compression for the first tine) of
soil. Since the weight of soil removed from the section is probably more than
the weight of the waste material redeposited, normal stress at the boundaries
is decreased, therefore, no significant additional compression should occur
along the boundaries. Any recompression that does occur will only tend to
return the boundaries to their original position. These rebound and recom-
pressive excursions at the undisturbed boundaries will be so small relative to
deformation occurring inside the landfill that they will be neglected.
In addition, it will be assumed that upon excavation of the cell to
final grade, the undisturbed ground surface will be covered with either a
polymeric membrane or a layer of remolded clay that will protect the undis-
turbed soil surface and ensure that the soil will neither swell from the
possible absorption of rainwater, nor desiccate due to water loss from
evaporation.
38
-------
Two settlement/subsidence conditions are considered. The first Bakes
use of the finite element method (FEM) and looks at settlement during the
construction and filling of a hazardous waste landfill cell. The second uses
mathematical integration to develop an equation to predict subsidence due to
changes in material properties after cell closure. Both treatments are neces-
sary for completeness. The consideration of settlement during construction
may offer a method of obtaining in situ material properties based on measure-
ments made during construction. The second and most important treatment
(postclosure subsidence) is necessary because layers consisting of wastes in
steel containers (drums) will deteriorate with time and subsidence will occur
as a result.
i •
MODELING OF PRECLOSORE MAXIMUM SETTLEMENT/SUBSIDENCE
Finite Element Settlement Analysis
A finite element computer code is used to compute settlement during
filling in the geometry selected as a typical landfill cell. The code em-
34
ployed uses a five node isoparametric quadrilateral . Within this element,
~ - fe .- ^
strain is assumed to vary linearly while constant strain is iaposed along the
element boundaries to satisfy interelement compatibility.
The code itself (named AXIPLN) was written by J. L. Withian and F. H.
Kulhawy and features the use of two nonlinear materials with hyperbolic
stress-strain characteristics and one linearly elastic material and the capa-
bility to build and/or excavate elements. The hyperbolic stress-strain soil
characteristics used in this study were taken from actual laboratory test data
on the CH soil (Vicksburg buckshot clay) described above. The hyperbolic
relationship used in the computer code was determined by a least squares fit
« e
of the laboratory data in the manner described in Withiam and Kulhawy . The
actual data points as well as the fitted curve used in the analysis are shown
on Figure 11.
The code also features the "slip" element which allows transverse dis-
placement between layers of elements to release a selected limiting shear
force. Even though this capability was not utilized in the present analysis
It could be very useful in cases where soil is placed against a polymeric
membrane where a low coefficient of friction between unlike materials could
39
-------
cause slip. Another important feature of the code is that it allows the
material modulus to increase as confinement due to gravity stress or self
weight increases . This makes the analysis much more realistic since the
loading scheme in this modeling was that of building up the total .structure by
stacking one layer on top of the other and allowing vertical stress and all
around confinement to increase in a systematic experimentally verified manner
as the layers are placed. The code and its use are described in detail in
Withiam and Kulhawy35.
The minimum intermediate cover layer thickness within the cell is assumed
to be 1-1/2-ft thick which is a reasonable and practical field-observed value.
However, intermediate cover layers as thin as 6 in. and as thick as A ft have
been observed. . Because of operations involved in numerical evaluation by the
computer code,, it is necessary to maintain the aspect ratio of the finite
elements within the structure at approximately one, which means that square
elements are preferred and the most skewed quadrilateral element permitted is
one with an aspect ratio of 3. Numerical Integration is required in the
finite element procedure and numerical errors become more significant as
elements become longer and more slender. Errors are also introduced because
elements with widely dispersed aspect'ratios have different stiffnesses which
do not match properly in the same structure and which May'"ti:ot Ismtisfy compati-
bility requirements. In a structure as large as the one trader consideration
as shown on Figure 10, it would be necessary to design a grid containing
900-1000 elements to model layers 1-1/2-ft thick in order to avoid large
numbers of elements with inappropriate aspect ratios. Such a grid would prove
difficult to manage and prohibitively expensive to run on the computer.
However, an inspection of the landfill geometry and some reasonable
simplifying assumptions will allow a considerably smaller problem to be
considered. The central portion of the landfill is 200 ft wide and typically
more than 200 ft long. Maximum subsidence will, because of symmetry, occur at
the geometric center of the landfill. Maximum subsidence is the condition
sought because if it is known, the grade of the final cover can be designed on
the basis of the maximum expected subsidence and therefore the crown will
settle, in time, to the acceptable level. Therefore, a column of appropriately
layered soil, 2 ft wide, supported by vertical rollers at the edge and pinned
on the bottom will be analyzed (see Figure 12). The column is a practical,
useful and reasonable model because:
-------
--53$
-57*
49fc
47$
LINER
LINER
COVER
26
BARREL
(25)
*S*
COVER
<50
COVER
IARREL
516
COVER
BARREL
•93:
3*
LINER
©
LINER
LINER
LINER
o
fcl«
3 «
a. FINITE ELEMENT GRID
FOR BARRELS ON END
•-BSJ
LINER
COVER
IARREL
COVER
C$70
268
«64
COVER
LINER
^5;
fc. FINITE ELEMENT GRID
FOR BARRELS ON EDGE
NOTE: CIRCLED NUMBERS ARE ELEMENT NUMBERS.
UNCIRCLED NUMBERS ARE NODAL POINT NUMBERS.
Figure 12. Finite element grids chosen for landfill subsidence model.
41
-------
a. The one-dimensional subsidence of the column will simulate the most
~~ severe subsidence in the landfill.
-------
this study is along the center line of a symmetric body, movement will be one
dimensional and no shear deformation will occur. This neans thai the column
of particles along the center line vill move downward without rotating and
consequently no shear stress will develop. Confining pressure or man normal
stress increases with increased burial depth but the computer model compen-
sates by increasing the modulus of the nonlinear soils according to an expo-
nential formula derived and described in Vithiam and Kulhawy .
A linear elastic parametric study varying E and v of the waste
layers was performed. For each computer run the Young's modulus and Poisson's
ratio of the waste layers were varied. The intermediate cover layers are
assumed nonlinear and deform according to the hyperbolic constitutive rela-
tionship described above. Poisson's ratio is assumed constant for the inter-
mediate cover layers. The effects of Poisson's ratio are discussed below, but
for the present it may be stated that the value is not expected to change
enough during loading to influence the results appreciably.
Deformation will begin to occur in the prototype cell immediately after
the placement of material. The magnitude of the deformation will depend on
the stiffness of the waste and intermediate cover layers. In the model study,
properties of the waste layers are varied for each computer run to determine
the amount of settlement that will occur for those particular values and
!
Figures 13 and 14 were developed using this approach. It must be realized
that any subsidence of the final cover that occurs as a result of settlement
of the fill during construction and filling of a hazardous waste landfill will
be compensated at the time of closure by bringing the crown of the cover to
the proper elevation. For example, if 20 in. of settlement/subsidence were to
occur in the typical cell during filling, the crown would not be left 20 in.
low; it would be brought to the design elevation. Consequently, during the
building of the cell, 20 extra inches of material would have been added to the
cell. Figures 13 and 14 suggest that if the waste drum layers are very stiff,
that is if they have a sufficiently high elastic modulus which does not de-
crease during construction, the subsidence that has occurred upon capping of
the cell amounts to about 13 and 10 in. for the drums-on-their sides and
drums-on-end conditions, respectively.
Settlement/subsidence that occurs during construction is of secondary
interest because it is compensated before closure. However, the filling of a
43
-------
1 I I I I I II i I I I I I I IT I ' I I I I 111
fRE-CLOSUPE
SUBSIDENCE 10
WITH STIFF 10
WASTE LA YEftS
YOUNG'S MODULUS OF BARREL LAYERS, PSF
Figure 13, Preclosure subsidence prediction curves for
drums-on-side configuration.
-------
110 -
100 -
FRE-CLOSURE
SUBSIDENCE
WITH STIFF
WASTE LAYERS
10"
T—I I I IIMJ 1 I I I Mill 1 MINI
INTACT
DRUM
105
10*
YOUNG'S MODULUS OF BARREL LAYERS, PSF
Figure 14, Preclosure subsidence prediction curves for
drums-on-end configuration.
-------
cell represents a field loading situation and, if a cell is properly instru-
mented during construction, in situ material properties, the rate of container
deterioration and the consequent time decay of waste layer stiffnesses may be
determined. This information would be of great value in evaluating the poten-
tial for later settlement and subsidence.
Figures 13 and 14 are based on incremental loading and show subsidence
with respect to Young's modulus and Poisson's ratio.' Properties of waste and
cover materials may be back-calculated from field measurements aade during
construction. However, these measurements must be used with relationships
based on Incremental loading such as Figures 13 and 14 because the load-
deformation relationship based on "sudden loading" or "gravity release" load-
ing (discussed below) is different from that of incremental loading. The
relationships are best illustrated by Figure 15, which contains information
taken from all the incremental load computer printouts. The vertical axis of
the figure is the average vertical stress at the centerline of the cell as the
layers are placed. The horizontal axis is the subsidence expressed as a
percent of the maximum subsidence which will occur. The average vertical
stress when the structure is 62.5 ft deep (filled and capped) is about
3700 psf. The zone.of scatter around the average line is caused by the super-
position of different values of Poisson's ratio on the plot?*%iff*rent Pois-
son's ratios give rise to different confining pressures, moduli, and
subsidence. The nonlinear nature of deformation with average vertical stress
is apparent from Figure 15.
In the "sudden-loading" case, which is considered next and which ad-
dresses the solution for postclosure material properties changes, deformation
is linearly related to vertical stress. Therefore, if meaningful properties
are to be derived from measurements obtained from instrumented representative
landfills, the proper loading history must be considered.
Behavior of Intermediate Cover Layers
Due to symmetry and maximum distance from the boundary, maximum subsi-
dence will take place at the geometric center of the cell. Because of the
relatively thin (18-in. thick) unsaturated layers of intermediate cover soil
and the long period required to fill a cell (projected to be from 1 to
75 years) primary consolidation of the intermediate cover layers can be shown
46
-------
4000 i-
20 40 60 80
PERCENT MAXIMUM SUBSIDENCE
100
Figure 15. Average vertical stress vs percent maximum subsidence.
47
-------
to be essentially complete by the tine the filled cell is capped. For example
by using Equation 6 if the time for 90 percent consolidation is desired, He -
—4 2
9 in. - 23 on, T9Q « 0..85, and cv is 1.5 x 10 cm /sec, then t^. can be
computed to h» about 34 days, which is s comparatively short time In the
period of filling-a hazardous waste cell. Coefficient of consolidation, c ,
1 26 v
has been correlated with liquid limit by Terzaghi and Peck , and the upper
limit of these data is enveloped as is shown on Figure 16. The equation for
the envelope has been determined. Recalling Equation 6, if the soil interme-
diate cover layer thickness is 2Hc cm and the liquid limit of the soil in
percent water content is LL, then the time in days required for 90 percent
consolidation of the cover layers can be expressed as
i
tg0 - H* x 10 <-0168LL - 2'2> <7>
(derived from Equation 6 and Figure 16 after conversion of units) based on the
conservative envelope of Figure 16. Using this equation and a liquid limit of
60 percent (which correspoi
be computed to be .34 days.
—4
60 percent (which corresponds to a cy of 1.5 x 10 in Figure 16), tgn may
MODELING OF POSTCLOSURE SUBSIDENCE OF THE LANDFILL AS A RESULT
OF MODULUS DECREASE
Factors Contributing to Total Subsidence
Since primary consolidation in the intermediate cover layers can be
shown to be essentially complete at closure in the hazardous waste landfill
under consideration, then except for relatively small amounts of secondary
compression, postclosure subsidence will be the result of closing of cavities
and the degeneration and softening of the waste drum layers. The stress
condition in the cell at the end of filling is determined and it may be rea-
sonable to assume that it does not change after capping (closure). Therefore,
any further subsidence in the landfill will be the result of changes in the
elastic properties of the waste drum layers. The cover layers have already
been shown to contribute very little to subsidence, so for the treatment which
follows, cover layers will be ignored with only the waste layers considered to
contribute to subsidence. In equation form, total subsidence, S_ ., may be
represented as
48
-------
10-5
10-4
10-3
ID'2
UPPER LIMIT OF TfftZAGHI
AND PECK DA TA «1
10t0.0168 LL + Z81
20 40 60
LIQUID LIMIT,*
• UPPER LIMIT OF LAMBE
AMD WHITMAN DATA40
80 100
Figure 16. Coefficient of consolidation vs liquid limit.
49
-------
ST * SISL + ^V + SDV + S E
i
where
SISL * ^side-ace due to consolidation of the intermediate cover layers
S,v - subsidence due to closing of the inherent geometric layer void
space
Sjj.. - subsidence attributed to void space inside the drums. This com-
ponent is assumed to be zero, but should be quantified and ac-
counted for in a general approach
SAE " subsidence due to change in stiffness of the waste layers
The maximum volume of void, or cavity, that can be included in the land-
fill by drum placement may be calculated geometrically for drums placed on
their sides and for drums placed on end. The maximum cavity volume for the
former is 10.73 percent of the total landfill volume and for the latter is
9.31 percent. If the cavities close completely, the maximum total subsidence
must be the sum of cavity closure plus subsidence by compression of the land-
fill contents. However, actual landfill operations will reduce maximum cavity
volume because the operations do not achieve perfect dram placement and because
'JV---.,S»K..^ -i|-r •
filling of interdrum space by sifting of cover soils daring filling generally
occurs to some extent. Conversely, any unexpected void within the drums would
contribute to the volume of inherent cavity.
Deformation by Degra-
dation of Waste Layer Modulus
For the sake of simplicity and so that tine does not enter the analysis,
the treatment given here will be that of linear elasticity. The end product
of this treatment will be the amount of subsidence or the potential for sub-
sidence caused by a decreasing waste-layer modulus, given in terms of the
pertinent parameters, but the work will not address how the subsidence occurs
with time.
Assume again a central column (Figure 17) of length L and consisting
only of waste material. The cover layers have been removed. The distance
from the top of the layer to a differential element dy is y . The edges of
the column ride on rollers so that the area of the column does not change.
Plane strain conditions exist in the column. Therefore
50
-------
dy
Figure 17. Schematic of central column and coordinate
system for subsidence model.
51
-------
ey . i^Ji (Oy
-------
Therefore the strain in the differential element, dy , of Figure 17 is the
change in length divided by the original length which, expressed in differen-
tial form, becomes
Combining Equations 14, 16, and 18,
^-yfeU^
Therefore,
(20)
i • •
Integration of Equation 20 results in the summation of the deformation in all
differential elements over the length L of the column. Therefore,
1.
d (dy) - AL (21)
where
AL - the total change in length of the column.
Combining Equations 20 and 21 -wwr* »«•
_T
and
Note that Equation 23 contains no stresses and suggests that the subsi-
dence that is at the cell center and therefore maximum, varies directly with
the density of the waste fill and with the square of the waste depth and
inversely as the stiffness, E . This means that a column of material with
density Y , length L and elastic properties E and v will deform an
•mount AL if suddenly "released to gravity" from a completely weightless
state. Mow from this point, if the elastic modulus E begins to decrease and
deteriorates from an initial value E^ to a final value E~ then the result-
ing subsidence will be
53
-------
u - 2.) . „ „ . (24)
and if the change in elastic modulus is known, s may be computed directly
from Equation 24. -S » ALf - AL^ and Equation 24 is derived by direct
substitution of ALf and AL^ into Equation 23.
Effect of Poisson's Ratio
Poisson's ratio (v) logically changes and influences the results as
subsidence occurs, but the manner in which it changes is not clearly
40
understood. Lambe and Whitman suggest that the value of v can usually be
estimated with satisfactory accuracy as 0.35 for soils of low saturation and
0.5 for fully saturated soils. The value of 0.5 will enforce material incom-
pressibility and consequently no subsidence will occur at that Po is son's
ratio. At the opposite extreme, a Poisson's ratio of zero indicates behavior
where a vertical stress causes vertical strain but no tendency for horizontal
strain. A material such as loose snow has a 'Poisson's ratio approaching zero.
Practically, waste in a hazardous waste landfill will be neither of these
60
extremes but something in between. Lambe and Whitman • artecgniced the diffi-
culty of making an exact evaluation of Poisson's ratio for use in any problem,
but suggested that the value usually has a relatively small effect on engi-
neering predictions. Craig states that during consolidation Poisson's ratio
decreases from the undrained value to the drained value at the end of
consolidation. The decrease does not affect the vertical stress and slightly
decreases the horizontal stress, but this decrease is neglected in the
Skempton-Bjerrum method of consolidation settlement prediction.
/ *?
Al-Hussaini performed K tests on sand under conditions of triaxial
compression. During the K_ tests, radial strain was not permitted and the
horizontal and vertical stresses were measured and vertical strain occurred.
The ratio of horizontal to vertical stress under these conditions is, by
definition, KQ . These tests showed that KQ remained constant during loading
up to axial pressures of 300 psi. Since KQ and Poisson's ratio are related
in linear elasticity by the equation
1 + K
o
54
(25)
-------
if K remains constant during deformation then so does v , Poisson's ratio*
Al-Hussaini shows that for the material being tested the value of K varies
o
from about 0.6 at a relative density of 20 percent to a value of about 0.4 at
a relative density of 100 percent. Equation-25 would suggest a corresponding
variation in Poisson's ratio of about 0.38 down to 0.29 for the cane range of
relative densities. Donaghe and Townsend performed R tests on a very
plastic clay (liquid limit - 79, plastic limit - 26) and showed a change in
K from 0.52 to 0.64 over an interval of axial stress from 7 psi to 85 psl.
This is a change in Poisson's ratio from 0.34 to 0.39.
The conclusions of the above investigators suggest cither that Poisson's
ratio does not appear to vary significantly during deformation or that a
change in Poisson's ratio does not affect the results significantly. Tor
these and also the reason that no analytical plan has yet been formulated to
vary Poisson's ratio during loading, it will be assumed that the value remains
constant. Settlement and4 subsidence, then, will occur primarily as a result
of a decrease in the Young's Modulus, E , of the waste layers.
Use of the Subsidence Equation
This paragraph explains how the subsidence equations end accompanying
curves are used to compute the expected subsidence caused by degradation of
wastes in a landfill. Equation 23 has been graphically represented on
Figures 18 and 19 for the typical cell under consideration with on-side and
on-end drum disposal, respectively. For the on-side drum disposal configura-
tion, the typical fill has 14 drum layers at a thickness of 2 ft for each
layer for a total compressible thickness of 28 ft. Similarly, the total waste
layer thickness for the on-end drum disposal configuration is 33 ft. There-
fore, the values for L in Equation 23 are 28 and 33 ft, respectively. The
value for waste material density is taken to be 115 pcf in the typical cell.
The value of the material elastic constant, Young's modulus, is varied and the
subsidence curves are shown for four values of Poisson's ratio. As an example,
assume that in a waste cell 62.5 ft deep at the center, there are 28 ft of
drum-waste layers (on-side configuration) with an average density of 115 pcf.
Say that the initial Young's modulus and Poisson's ratio were determined to be
5 x 10 psf and 0.35, respectively. This establishes one point on Figure 18
(drums on their sides). How say it is determined from laboratory tests or
55
-------
IIIIIII!
EXAMPLE: POST-CLOSURE SUBSIDENCE
BY DEGRADATION Of WASTE
LAYERS • 33.7-0.7 • 33.0 IN.
7.0
6.5
6.0
5.5
5.0 5
o
4.5 <
&
CM
3.5 S
Z
"I
i
2.5
2.0
1.5
1.0
as
107
YOUNG'S MODULUS. PSF
Figure 18. Post-closure subsidence prediction curves for drums
placed on their sides.
56
-------
POST-CLOSURE SUBSIDENCE. IN.
g S 8 tt
m
-
0
1
p
U1
1 1 1
b i" b
1 1 1
M w u
O* O Ul
1
b
1
*>
in
-
jn in o> ft «a
o in b ui b
PERCENT STRAIN (62.6 FT-DEEP LANDFILL)
-------
extrapolated from field experience and measurement that the Young's modulus of
the waste drum layers could decrease to 1 x 10 psf with the value of Poisson's
ratio unchanged. This establishes the second point on the figure and there-
fore the subsidence that would occur as a result of this change in:modulus ct
constant Poisson's."ratio (v - .35) is the change in ordinate from the first to
the second point which is
33.7 - 0.7 inches - 33 inches (see Figure 18)
The same value would be obtained by using Equation 24 and substituting in the
values Y » 115 pcf, L - 28 ft, v - 0.35, E. « 5 x 105 psf and E- - 1 x
4
10 psf. Additional subsidence prediction curves can be generated with
Equation 23 for other landfill geometries by applying different values of L
(total waste-layer thickness), Y (waste layer density) and, if justified, v .
Equation 23, Figures 18 and 19, and Equation 24 can be applied to hazardous
waste landfills of any depth, with either on-end or on-side layered waste
placement configuration, and for any waste/container stress-strain moduli and
densities. The above example demonstrates the general use of the subsidence
curves and equations. The following paragraphs evaluate the vaximum subsi-
dence expected to occur for worst case conditions in landfills composed of
representative materials.
Estimate of Maximum Expected
Subsidence for Representative Moduli
Drums on Their Sides. Steel drums buried on their sides may be ideally
represented by an elastic cylinder subjected to the application of external
pressure only. The drum has a typical wall thickness of 0.050 in., an inside
diameter of 22.25 in., a Young's modulus of 30 x 10 psi and a Poisson's ratio
of 0.29. From the basic assumption, typical dimensions and material proper-
44
ties, the equations of an elastic hollow cylinder were rearranged to show
that the effective elastic modulus E_ of such a cylinder subjected to an
isotropic change in external pressure is
E.. • 9.7 x 10 psf*t where E^ • modulus of the drum (26)
* See derivation in Appendix B.
58
-------
The repeating geometric unit representing the Idealized drum buried on its
side is shown on Figure 20* The space shown shaded above the drum is assumed
to be filled with soil. The space below the drum is taken to be an air cavity
so that maximum subsidence may be estimated. The intermediate cover layers
have been shown above to be unde forming in the terminal condition (closure of
the landfill) so they have been removed. Therefore for the purpose of analysis
the cell can be considered to consist of stacks of the basic building blocks
of Figure 20.
The soil in the system is taken to be the same clay described above for
use as intermediate cover. Consolidation tests performed on this material at
/e
the indicated density within the stress levels of interest show that the
constrained secant modulus of this soil is approximately 104,000 psf .
If it is assumed now that the clay present above the drum is subjected
to the same uniform pressure as the drum and that the total volume change in
the system is the sum of the volume change of the drum and the volume change
of the soil, then it can be shown that the elastic modulus of the composite
system with intact drums is related by
f
where E_. - Initial elastic modulus of the composite system, in psf
E • Elastic modulus of intermediate clay cover material, in psf
£_ - Elastic modulus of the waste drum, in psf
If now the moduli of 104,000 psf (Eg) and 9.7 x 10 psf (E^) are substituted
into Equation 27, then a value of 900,000 psf (E.^) is obtained for the initial
composite. From E_. , Equation 23 and Figure 18, it can be determined that
for a Poisson's ratio of 0.35, the corresponding initial elastic subsidence in
the representative landfill under consideration is approximately 0.4 in. Now
assuming that the contents of the drums were initially liquids and that the
contents were solidified by adding an absorbent material such as kiln-dried
fuller's earth (crushed claystone), then after the steel of the drum has
completely corroded away, the waste contents will be .subjected to compression
by existing gravity stress.
Consolidation tests were performed on two commercially available absorb-
ent earth compounds to obtain typical constrained modulus values for these
59
-------
VOID fCAVITY)
Figure 20. Geometric configuration of drum buried on its side.
60
-------
materials. Both materials were soaked in water for 48 hours to allow for the
maximum possible absorption of water. The materials were then spooned into an
oedometer (one-dimensional consolidation device) to simulate the probable low
density achieved by the field practice of pouring the material into a drum
half filled with liquid. The specimens were then loaded up to 55 psi in the
oedometer in five or six increments allowing complete drainage under each
increment. The results of the loading are shown on Figure 21.
The first material is sold commercially as a Compound to absorb oil
spills. It is basically a calcium bentonite clay stone which was removed from
a quarry, crushed, then kiln-dried at 1100*? (calcined). The resulting mate-
rial has the appearance of a coarse angular sand with hard granules which
remained hard and intact after soaking. The constrained secant modulus of
this material was measured to be about 1,000 psi or 144,000 psf (see Figure 21).
The second material is sold commercially as an absorbent for use commonly
as "kitty litter." The material is identical in composition to the first
material except that after crushing, it is kiln-dried at only 300*F (i.e., it
is noncalcined) . The resulting material had the same physical appearance as
the first material but after soaking became soft and plastic and the resulting
modulus was measured to be about 275 psi or 40,000 psf. Since the objective
was to estimate maximum subsidence, the lower modulus of 40,000 psf (the
noncalcined claystone) was used in the calculations. - •• :f •
Referring again to Figure 20, the final configuration vat analyzed in
exactly the same manner as the intact drum configuration except that for the
final configuration the drum volume is replaced by elastic material with a
modulus of 40,000 psf (the modulus of the noncalcined claystone). If a similar
analysis is performed assuming that the two materials will compress as if
loaded by an isotropic pressure then the equivalent elastic modulus may be
shown to be
. e
E-f -- £—§ - (28)
ir Eg + 4Ec (1/2 - ir/8)
where E-f - Final elastic modulus of composite system, in psf
E - Elastic modulus of intermediate clay cover in psf
EC - Elastic modulus of drum contents in psf
* See derivation in Appendix B.
61
-------
60 i-
tu
e
Sf
0/i. ABSORBENT MATERIAL
PERCENT STRAIN
Figure 21. Constrained elastic moduli of two simulated
waste materials.
62
-------
If the values of 40,000 psf for modulus of drum contents and 104,000 psf for
intermediate cover modulus are substituted into Equation 28, then the equiva-
lent composite modulus is computed to be 48,000 psf. The corresponding subsi-
dence for this value is 7 in. taken from Figure 18. Now if the initial value
of 0.4 in. is subtracted, then the resulting subsidence is 6.6 in., which
•
corresponds to 0.89 percent strain in a total height'of 744 in. (62 ft). But
this is not all the subsidence that can occur. The air void (cavity) beneath
the drum can be shown to be 10.73 percent of the total volume. If this space
closes completely during subsidence, then the total value will be the sun of
the two or 10.73 + 0.89 • 11.62 percent (approximately 87 In.) for the maximum
expected subsidence. If all the waste drums are assumed to contain 10 percent
i •.
(allowable) void space, the additional 10 percent represents an additional
7.9 percent waste layer cavity volume (drums occupy 79 percent of the waste
layer for drums on their sides). The total estimated subsidence considering
10 percent void space in the containers would then be 11.62 + 7.9 * 19.52 per-
cent or 145 in. (12.1 ft). However, it seems unlikely that all the drums
would contain the maximum 10 percent allowable void space.
• Drums on End. ' Similarly,-if drums that are buried on end are represented
-••:•;•-. mtjpfffty^ '
by hollow steel cylinders that carry the axial compressive load without buck-
ling then the effective elastic modulus of such a structure can be shown to be
EJJ - 3.86 x 107 psf * (29)
which corresponds approximately to zero initial subsidence on Figure 19.
When the drum has completely corroded and the remaining material is
taken to have a modulus of 40,000 psf then the final value of subsidence taken
from Figure 19 is 11.7 in. This corresponds to 1.56 percent strain in a
height of 750 in. It can be shown that the cavity space between drums in the
densest possible stacking configuration comprises 9.31 percent of the total
volume. If this space closes completely during settlement then the total
value will be 1.56 + 9.31 - 10.87 percent (approximately 82 in,) for the
maximum expected subsidence (drums-on-end). If all the waste drums are assumed
to contain 10 percent (allowable) void space, the additional 10 percent
* See derivation in Appendix B.
63
-------
represents an additional 9.1 percent waste layer cavity volume (drums on end
occupy 91 percent of the waste layer). The total estimated subsidence consid-
ering 10 percent void space in the containers would then be 10.87 + 9.1 -
19.97 percent or 150 in. (12-1/2 ft). However, it seems unlikely that all the
drums would contain the maximum 10 percent allowable void space. The effects
of the calculated cover subsidence are discussed in "Section 6 of this report'.
The analyses for the estimation of maximum subsidence were necessarily
approximate but do lend analytical credence to the estimates. Material prop-
erty values used in the analyses were values which either were measured spe-
cifically for this treatment (as in the case of the drum filler material) or
taken from, data obtained from tests on material believed to be very similar in
nature and behavior to material used in waste disposal operations.
The analyses show that most (86 to 92 percent) of the subsidence that
might.'occur will be the result of closing the cavity space associated with
drum disposal. The estimate of maximum expected subsidence assumes that none
of the cavity space is filled during construction and that the space closes
completely during subsidence. This leads, of course, to the most liberal
estimate of subsidence.. Actually, two occurrences during construction will
reduce the cavity space giving rise to less subsidence, first, precise ar-
rangement of drums in a landfill is practically impossible. Material will
fall into the cavity space underneath and between drums as a result of less
than perfect placement. The degree of cavity filling will be dependent on
material, water content, and drum placement. .Obviously, there is a greater
opportunity for the cavity space to be filled in upright drum disposal because
of the vertical cavity spaces.
Secondly, for drum-on-side disposal, the analysis assumes radial
deformation. It is more probable that the cylinder will flatten into an
elliptical shape and intrude into the cavity space. This will reduce the
cavity space during construction and lead to less subsidence in the terminal
condition. Unaccountable factors which might lead to less subsidence are:
a_. The unquantifiable filling of expected cavity space during construc-
tion of the landfill.
Jb. Arching or bridging over cavity space which results in the cavity
~~ remaining occluded for all time.
-------
c. Thixotropy or the gain of strength with time at constant water
~" content vithin the cover layers. This will enhance arching or
bridging.
d. Reaction of soil with waste material which enhances soil strength.
Unaccountable factors which will tend to increase subsidence are:
a. Excessive and unexpected creep in the intermediate cover layers.
b. Soil reaction with waste material and biodegradation which diminishes
~~ soil strength and increases compressibility.
c. Unexpected cavity space in containers.
65
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SECTION 5
ANALYSIS OF COVER CRACKING
SUBSIDENCE CRACKING . '
Cracking due.to subsidence is a problem occasionally encountered in
embankment dams and levees. If cracking develops, rainwater can percolate .
into cracks and result in some combination of erosion, reduced soil strength,
and slope stability problems. If similar cracking occurs in the covers of
hazardous waste landfills, rainwater will percolate into the cracks and pose
the very serious threat of breaching the cover and filling the cell with water
which would then have to be handled and disposed as contaminated leachate.
Therefore it was considered necessary to analyze the hazardous waste structure
under consideration for subsidence cracking.
*
Approach
The finite element grid used for analysis of subsidence cracking is
shown in Figure 22, and represents the discretization of the configuration
shown in Figure 10. • The restriction of maintaining the elements comprising
the structure to no more than a 2:1 aspect ratio was largely observed. The
• - 'jjKf~J. „ -
cover and liner thicknesses are approximately the same as that used in the
central column study (Section 4) but the waste is modeled by fewer layers.
Fewer layers were necessary because of the aspect ratio restriction of the
elements and the rapid increase in the required number of elements as layers
became thinner and more numerous. A model using many more elements would be
expensive to run and would not yield better information because it is differ-
ential settlement, not total settlement, that determines the stresses in the
cover.
The liner and top cover of the cell consisted of a compacted clay with
the same nonlinear elastic stress-strain properties as the material assumed in
the liner system of the analysis in Section 4. The waste layers were modeled
as a linear elastic material so that the compressibility and volume change
characteristics might be varied systematically. The moist density of the
liner was assumed to be 135 pcf and that of the waste, 115 pcf. The cell was
loaded and allowed to settle under gravity.
66
-------
f '
•3
Figure 22. Finite element grid used to analyze hazardous waste landfill.
-------
Results of Cracking Study
The evaluation of the assumed cell geometry for cracking consisted of
examining the computed stress field for values of negative minor principal
stress. For the geometry and soil conditions assumed, the minor principal
stress field was co'ntoured and is shown in Figure 23. The figure shows that
the stress field is well behaved with no remarkable stress concentrations or
»
singularities, and the values are all positive, indicating that there are no
tensile zones. The material of the body remains in compression and there is
no tendency for cracking, i.e., there is insufficient differential settlement
in the modeled landfill to produce stresses that would cause the cover to
crack in the manner illustrated in Figure 9A (Section 3).
The 'subsidence across the cell was evaluated. Several waste material
i
compressibilities were evaluated from which it was determined that subsidence
could"be normalized in terms of the maximum subsidence across the cell. These
results are presented in Figure 24 and show that subsidence at the center line
is 100 percent of the maximum subsidence and is zero at the outermost limit
(250 ft from the center line) of the cell. Vertical subsidence at any distance
across the cell may then be determined by multiplying the influence factor
(the Z subsidence in Figure 24} by the maximum subsidence, phich occurs at the
center line for the desired distance. For example, a maximum subsidence value
may be chosen from Figures 18 and 19 and the resulting subsidence determined
all across the cell by using Figure 24.
The contour of the subsidence across the cell is shown in Figure 25,
which is simply an inversion of Figure 24. Figure 25 shows that in the deepest
part of the cell where the bottom is horizontal, subsidence is virtually
constant, the value at the point where the bottom starts to slope upward being
about 80 percent of the maximum value. This demonstrates numerically that the
deepest part of the cell subsides almost uniformly and Justifies the central
column analysis used above in Section 4. Subsidence then decreases rapidly at
an increasing rate as the edge of the cell is approached.
Factors Affecting Cracking
The results of the cracking analysis are further examined in this
section. Lefebvre and Duncan46 concluded from a finite element analysis of
embankment dams that stress is a better criterion than strain for determining
68
-------
In
8
VO
Figure 23. Contours of minor principal stress in landfill.
-------
100 200
HORIZONTAL DISTANCE FROM CENTERLINE, FT
300
Figure 24. Percent subsidence vs distance from centerline.
70
-------
5%SLOP£
Figure 25. Vertical subsidence across a trapezoidal landfill.
-------
if cracking will occur. The minimum principal stress value was the variable
they examined to determine if cracking would occur. For example, if the value
of the minimum principal stress became negative in a region, then the soil
(Which was assumed incapable of carrying tension) was presumed to nave cracked
in that region.
Examination of the calculated stress condition in the hazardous waste
disposal cell investigated in this report revealed that tensile stresses do
not develop anywhere in the structure as modeled. Landfills with nonuniform,
nonhomogeneous contents were not modeled and nay produce tensile stresses and
resultant cracking. However, certain parallels nay exist between these waste
cells and the embankments examined by Lefebvre and Duncan . Based on a
comparison with embankments there nay be several reasons why tensile stresses
do not develop in the waste cells under consideration:
/£. The material in the hazardous waste landfill is placed in an exca-
vated pit which is a "bathtub-like" structure and will contain and
support most of the waste material completely. It is assumed that
once the cell has been filled back to the original ground level, a
fairly gentle 5 percent slope will be used to build up to the crown.
In an embankment dam, very often the sides slope up to the crest at
IV on 3H, for a fairly steep 33 percent slope. Thus there is proba-
bly a core severe loading condition in embankment daas than in
hazardous waste landfills just due to slope steepness.
b. Lefebvre and Duncan concluded that large zones of tension are more
~" likely when an embankment dam material is very stiff. It has been
observed that the fill material in hazardous waste landfills is
typically not well compacted and the soil exhibits plastic rather
than brittle behavior (see Figure 11). Compaction in the field is
accomplished by driving a piece of construction equipment back and
forth over the waste layers. This does not accomplish a high degree
of compaction and, therefore, the waste layers in the cell are not
very stiff. The top cover and bottom liner are typically compacted
wet of the optimum water content to achieve a permeability require-
ment rather than a strength; therefore because of the high water
content at compaction, the cover materials are more plastic and less
stiff and brittle than they would be if a design strength and den-
sity had been the target of the compaction. Therefore because of
the filling technique and compaction of hazardous waste landfills,
the contents are more flexible and therefore less likely to develop
zones of tensile stress than are embankment dams.
c. Lefebvre and Duncan concluded that as the embankment becomes
"~ successively stiffer than the foundation, the size of the tensile
zone and the magnitude of the tensile stresses increase. The con-
struction of an embankment dam always involves applying more load to
the foundation underneath that structure than had previously existed
72
-------
simply due to the additional weight of the embankment. The addi-
tional load will cause foundation deformation. In the case of
hazardous waste landfills, the disposal cell will consist of a pit
excavated in natural ground. The foundation material at the bottom
of the cell was undisturbed ground before excavation, it, had been
compressed by, say, 50 ft of overburden soil for geologic time, and
was at least normally consolidated. The waste material which was
then placed into the cell was not well compacted and probably less
dense than the excavated natural material. Therefore no additional
load was applied to the foundation as a result of filling the cell
with waste and it is likely that no additional deformation took
place in the stiff foundation material. Therefore it was assumed in
this study that the hazardous waste landfill under analysis rests on
a rigid foundation. This assumption also has basis In field
observation. At several sites it was observed that as hazardous
.waste cells were excavated, the natural material at depth became so
.stiff that it had to be ripped out by large and powerful bulldozers.
Therefore the undisturbed foundation material is, in fact, much
stiffer than the waste contents of the cell and, accordingly, any
tensile zone which develops in the cell should be vanishingly small
since the ratio of the modulus of the waste material to the modulus
of the foundation is small.
POTENTIAL CRACKING BY DESICCATION AND SHRINKAGE
The cracking described above is strictly associated with stress and
strain conditions due to body forces acting on deformable cell contents which
were assumed elastic. Another mechanism which can cause cracking is shrinkage
and involves the loss of water from soil by evaporation. Here too tensile
stresses develop as a result of soil volume decrease and the accompanying
shrinkage tensile strain. However, the difference between shrinkage cracking
and subsidence cracking is that water content must decrease in order to develop
shrinkage cracks, whereas cracks due to settlement are assumed to occur at
constant water content.
Certain clay minerals are susceptible to shrinking and therefore
cracking. Clays rich in the mineral montmorillonite are notorious for shrink-
age cracking behavior. Shrinkage cracking may be controlled in desiccating
environments by treating exposed soil surfaces to prevent evaporative water
loss.
Sherard found in a study of embankment dams that transverse cracks in
dams may be caused by shrinkage when the surface of the embankment is allowed
to dry out after compaction. He says that it is sometimes not possible to
differentiate between shrinkage and settlement cracks and that shrinkage due
73
-------
to drying nay accelerate and aggravate the development of cracks due to settle-
ment and increase the widths of settlement cracks.
Surface shrinkage cracking is not the concern of this'report, but it is
important to realize that the potential for this type of cracking floes exist
and its occurrence.is independent and exclusive of settlement cracking; how-
ever, the problems resulting from the two types of cracking are similar. Many
>. 5
investigators have studied shrinkage cracking, and Lutton, et al. have summa-
rized several practical solutions to this problem. It should be noted that
shrinkage cracks due to water loss through evaporation may occur in hazardous
waste landfill covers. The two types of cracks nay be virtually indistin-
guishable and will cause similar detrimental effects. Shrinkage nay pose a
* • *
severe threat to cover systems in climates and seasons of high evaporative
water loss, and in such climates appropriate defensive measures should be
taken. Another potential problem of shrinkage or settlement cracks is the
»w
accumulation and freezing of water in open cracks. Water expands by about
9 percent upon freezing and the expansion could open cracks farther and aggra-
vate conditions.
74
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SECTION 6
SUMMARY AND DISCUSSION OF RESULTS
LANDFILL MODELING . !
Several commercially operated landfills observed during this study were
large pits excavated in natural earth to depths of 50 to 100 ft. The natural
t
earth was typically a soil or rock of low permeability. Landfill structures
observed were generally lined with clay and/or synthetic polymeric membranes
and equipped with a leachate collection and withdrawal system. The structures
were typically filled with alternating waste layers 2 to 3 ft-thick and inter-
mediate coyer layers about 1-1/2 ft thick. After filling, the landfills are
capped with a permanent clay cover layer which is continuous with the sides
and bottom liner system. A polymeric membrane may or may not be used in the
cover,. A representative model landfill section chosen for the purpose of
mathematical analysis and demonstration for this Investigation Is 50 ft deep
and 200 ft wide across the cell bottom. Sides slope up to the original ground
level at 3 horizontal on I vertical and the cover layer slopes up to the crown
at 5 percent to give a total depth of 62.0 ft at the center of.the landfill.
The model landfill is assumed to be constructed and ^dJrls&ssxsetly *s several
observed representative landfills. —--"
Solidified material buried in steel drums is expected to sake up the
most significant portion of the waste in the cells under consideration. A
mathematical equation based on the theory of elasticity was developed to allow
calculation of maximum subsidence. Use of the equation requires input of
waste properties such as density, depth of burial, and stiffness (Young's
modulus). Subsidence occurs as a result of postclosure cavity collapse and
waste-drum deterioration and softening. The mathematical equation predicts
subsidence as a result of waste layer softening which is simulated by lowering
the Young's modulus of the layers.
The equations developed in this report and their related subsidence
prediction curves apply as well to horizontally layered landfills of varying
depths, physical properties and geometries and are not restricted to landfills
with the specific dimensions presented in this report. The analyses are for
homogeneous and 1sotropic materials in layered, unsaturated waste cells.
-------
Subgrade materials are presumed to be rigid (noncoapressible). The site-
specific amount of maximum subsidence depends on the fill depth and the physi-
cal properties of the waste, fill, cover and liner materials. Waste properties
are presumed to show the most site-specific variability of all the contributing
materials and are critical to the accurate prediction of subsidence. Strengths
and stress-strain data of actual or simulated waste materials would permit
more effective predictions of expected subsidence with the models developed
for this report.
RESPONSE OF COVER TO MAXIMUM SUBSIDENCE
Analyses of the numerical settlement models developed for this study
indicate that the maximum landfill cover subsidence that would be expected
under worst-case conditions (deep fill, deteriorated drums and low-stiffness
waste layers) would be approximately 11-1/2 percent which for the representa-
tive landfill would result in a final cover slope of about 2 percent from the
crown to the landfill boundary. Most of the subsidence '(around 10 percent)
occurs by closing of cavities Incorporated during filling. The 11-1/2 percent
subsidence would not create ponding (negative slope) for the representative
landfill assuming a 5 percent cover slope (12.5-ft crown) was established at
closure. The resulting 2 percent slope is, however, less than the minimum
- - -^-^VM^^E ".-
suggested by EPA (3 percent) to promote drainage. Drainage off the cover is
desired to prevent infiltration of standing or slow-draining precipitation
with the danger of filling and overflowing the landfill (the bathtub effect)
and of creating excessive leachate. An additional subsidence of 8 to 9 percent
must be considered if drums are assumed to contain the maximum allowable
10 percent void space when placed in the fill. However, an assumption that
all the drums would contain 10 percent void is considered realistic by the
authors.
This study has shown that consolidation of the unsaturated intermediate
cover (fill) layers occurs relatively soon and prior to closure. Landfills
whose waste layers consist predominantly of waste-filled steel 55-gallon drums
will experience additional settlement after probably several years during
which time the drums and waste deteriorate to progressively lower elastic
moduli and strengths. Estimations of waste layer and fill moduli for intact
and deteriorated waste container conditions were made and applied to the
prediction curves to derive the 11-1/2 percent maximum expected subsidence.
76
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RESPONSE OF COVER TO SUBSIDENCE CRACKING (DIFFERENTIAL SETTLEMENT)
The analysis of the assumed hazardous waste disposal cell described
shows that tensile cracking does not occur within the body of the landfill
configuration modeled for this analysis. For the soil and filling: techniques
assumed, the stresses which would cause tensile cracking do not develop. The
stress and displacement fields observed In the landfill body are well behaved
and smooth with no unexpected singularities. There are several reasons for
this, Including the fact that the landfill material behaves plastically,
yielding rather than rupturing. The foundation completely supports the waste
material and Is very stiff relative to the waste cell contents. An analysis
of the vertical surface displacement shows that vertical movement is maximum
in the center of the cell and subsidence is almost uniform over the flat-
i •.
bottomed portion of the cell. This confirms that a central column analysis of
subsidence is justified, and allows the subsidence at any point across a
typical cell, to be estimated if the center subsidence is known. Tensile
stresses from differential settlement occurring in other landfills (nonuniform
waste layers, for example) were not analyzed.
OTHER CONSIDERATIONS " ,^,,,.., ,
~" % *
The settlement models for this study were developed under the assumption
that drained, unsaturated conditions prevailed within the landfill and that
containers of free liquids were not Included in the fill. It is prudent to
consider the effects on settlement of including substantial volumes of free
liquids, or stabilized liquids that become unstable with tine, in the landfill.
A liquids-filled waste drum that had deteriorated sufficiently would release
its contents into the surrounding soil or soil-like intermediate cover or into
bulk wastes surrounding the drum. Assuming the surrounding fill and bulk
wastes were less than 100 percent saturated the freed liquids would be absorbed
into the pore spaces and would Increase the saturation of the fill materials.
Stabilized or "solidified" liquids that might be released after deterioration
of drum contents would be expected to act similarly, but with a smaller volume
of liquid. The Intermediate cover layers placed will be compacted with con-
struction equipment as discussed earlier. Regardless of the compactive effort
applied, two conditions of compaction are possible; compaction wet of optimum
water content and compaction dry of optimum water content. If the layers are
77
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compacted wet of optimum, allowed to consolidate to 100 percent consolidation
undar the applied load, and then exposed to free liquid (water)* volume change
45
of the clay layer will usually be insignificant . However, if the layers are
compacted dry of the optimum water content, two effects might conceivably be
expected as a result of post-closure release of liquid; the cover layer could
tend to absorb liquid and swell (increase in volume) or collapse (decrease in
volume) upon exposure to the liquid. Laboratory investigation has shown
that collapse of soil usually occurs at low water contents and at high stress
levels, which would mean that the layers at greater depths in the landfill
would tend to collapse. Volume change due to collapse is irreversible, that
is, the settlement or subsidence due to this phenomenon is not recoverable.
Swell usually occurs in soils at low water contents and low stress levels,
which would mean for this study that layers at shallow depths in the landfill
would tend to swell when exposed to water. Swell, however, may be reversible
in that, as surplus water which was absorbed into the soil diffuses with tine
into dryer regions of the layers, shrinkage may occur and the coil may tend to
return to its original volume.
Laboratory tests suggest that to minimize the problem of either swell or
collapse of intermediate cover layers, compaction wet of the^tt>ptiBum water
content is desirable. In practice, waste and intermediate cover layers of
hazardous waste landfills are placed at the existing water content of the
soils and no special compactive efforts are made.
At this time, no specific statement may be made regarding the effects of
liquid released in a landfill. The ultimate effects of such releases would
depend on site-specific factors such as the amount of liquid released, the
water content of the layers at the time of compaction, the mineralogy of the
intermediate cover layers, the compaction characteristics of the layers and
the stress levels within the layers exposed to liquids.
78
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SECTION 7
CONCLUSIONS AND RECOMMENDATIONS
CONCLUSIONS •
Conclusions reached as a result of the study are:
a. The dominant mechanisms of settlement of the fill and subsidence of
~~ the covers of horizontally layered hazardous waste landfills are
expected to be closing of the inherent drum-placement void spaces
and compression of cell contents including intermediate cover soils,
waste, and waste containers. Cavity related piping and sinkhole
phenomena are not expected to play a major role in predicted
subsidence. This conclusion is based on review of representative
active waste disposal practices in industry and government and
analysis of documented and theoretical subsidence mechanisms re-
ported in other, .related activities.
i .
-------
Drums or other containers of wastes should be filled to minimize the
volume of void within the containers. Much of the potential settle-
ment from compressibility can be eliminated by preventing the inclu-
sion of cavities in the waste placement process, is the typical
hazardous waste landfill.
_b. Layering .of waste and intermediate- cover in thin lifts BO that some
~~ compactive effort is achieved during filling.
£. Control of liquids by installation of efficient leachate collection
*~ systems and stabilization of liquid wastes to prevent saturation of
the fill and to allow consolidation to occur as rapidly as possible.
£. Installation and monitoring of cover settlement plates so that the
subsiding surface can be maintained at the proper slope. Hazardous
waste landfills should be documented, instrumented, and monitored
after closure. Subsidence of the cover as well as the settlement of
Internal waste layers should be monitored with time in an effort to
•gain understanding of postclosure internal changes, how they occur,
and Wow they affect the overall behavior of the landfill. Many of
the mechanisms at work within these landfill cells can be understood
only by study and experience with representative landfill cells.
The data obtained by field monitoring will permit evaluation and
improvement of settlement/subsidence prediction models developed in
this study. Landfill operators should remember that, while the
cover surface can be maintained at a proper runoff slope by the
addition of soil or other material, the internal cover liner, wheth-
er a clay layer or a flexible membrane liner or both, may have been
deformed and stressed by subsidence. Internal cover liner damage or
deformation cannot be remedied by simple cover Efface cosmetic
actions. . ^ .,,
£. Placement of a buffer thickness of intermediate cover soils above
~ the uppermost waste layer and beneath the final cover to lessen the
potential for collapse of the cover directly above locally compres-
sible zones such as deteriorating drums.
80
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REFERENCES
1. Wright, N. D., and Allen, G. P. 1980. The National Directory ef State
Agencies, 1980-81, Heraer and Company, Information Resources Press,
Arlington, VA;
2. U. S. Environmental Protection Agency. 1980. "Hazardous Waste and Con-
solidated Permit Regulations," Federal Register. May.
3. . 1982. "Hazardous Waste Management System; Permitting Re-
quirements for Land Disposal Facilities," Federal Register, July 26.
4. Giroud, J. P., and Goldstein, J. S. 1982. "Geomenbrane Liner Design,"
Waste Age. September, pp 27-30.
*
5. Lutton, R., J., Regan, G. L., and Jones, L. W. 1979. "Design and Con-
struction of Covers for Solid Waste Landfills," Report No. EPA-600/2-79-
165, Municipal Environmental Research Lab, U. S. Environmental Protection
•Agency, Cincinnati, OH.
6. Means, R. E., and Parcher, J. V. 1963. Physical Properties of Soils.
Chas E. Merrill Pub. Co., Columbus, OH.
7. Ledbetter, R. H. 1976. "Design Considerations for Pulp and Paper-Mil1
Sludge Landfills," Report. No. EPA-600/3-76-111, Municipal Environmental
Research Lab, 0. S. Environmental Protection Agency, Cincinnati, OH.
8. Jennings, V. E. 1966. "Building on Dolomites in the Transvaal," in The
Civil Engineer in South Africa, pp 41-62.
9. Sowers, G. F. 1973. "Settlement of Waste Disposal Tills," Proceedings
of the Eighth International Conference on Soil Mechanics and Foundation
Engineering, Moscow, Vol 2, Part 2, pp 207-210.
10. Whiteman, C. D., Jr. 1980. "Measuring Local Subsidence with Extensome-
ters in the Baton Rouge Area, Louisiana, 1975-79," Water Resources Tech.
Rep. No. 20, Louisiana State Department of Transportation, Baton Rouge,
LA.
11. Winslow, A. G., and Wood, L. A. 1979. "Relation of Land Subsidence to
Ground Water Withdrawals in the Upper Gulf Coast Region, Texas," in
Mining Engineering. October, pp 1030-1034.
12.. Fang, H. Y., and Cleary, T. F. 1976. "Subsidence," in Analysis and De-
sign of Building Foundations, edited by H. Y. Fang, Envo Publishing Co.,
pp 467-517.
13. National Coal Board. 1975. Subsidence Engineer's Handbook. Mining
Department.
81
-------
14. Brauner, G. 1973. Subsidence Due to Underground Mining, Part II. u. S.
Bureau of Mines Information Circular I.C. 8572, U. S. Government Printing
Office, Washington, D. C.
15. Brink, A. B. A. 1979. Engineering Geology of South Africa. Vol. 1.
Building Publications Pretoria, South Africa.
16. Gray, R. E., Gamble, J. C., McLaren, R. J., and Rogers, D. J. 1974.
"State-of-the-Art of Subsidence Control," Repor.t ARC-73-111-2550, Appala-
chian Regional Commission, Washington, D. C.
17. Wardeli, R. 1969. "Ground Subsidence and Control," Mining Congress
Journal, January, pp 36-42.
18. Sowers, G. F. 1976. "Settlement in Terranes of Well-Indurated Lime-
stone," in Analysis and Design of Building Foundations, ed. by E. Y.
Fang, Envo Publishing Co., pp 701-727.
i' •-.
19. Kahle, R., and Rowlands, V. 1981. "Evaluation of Trench Subsidence and
Stabilization at Sheffield Low-Level Radioactive Waste Disposal Facility,"
ffUREG/CR-2101, U. S. Nuclear Regulatory Commission.
20. Daniel, D. E. 1983. "Shallow Land Burial of Low-Level Radioactive
Waste," ASCE Journal of Ceotechnical Engineering, Vol 109, No. 1,
pp 40-55.
21. Attewell, P. B., and Farmer, I, W. 1976. Principles of Engineering
Geology. John Wiley and Sons, Inc., New York, pp 535-536.
22. Franklin, A. G., Patrick, D. M., Butler, D. K., Strohm, W. E. Jr., and
Hynes-Griffin, M. E. 1981. "Foundation Considerations in Siting of
Nuclear Facilities in Karst Terrains and Other Areas Susceptible to
Ground Collapse," NUREG/CR-2062, U. S. Nuclear Regulatory Commission.
23. Herak, M., and Springfield, V. T. 1972. Karst, Elsevier, Amsterdam.
24. Millet, R. A., and Moorhouse, D. C. 1973. "Bedrock Verification Program
for Davis-Besse Nuclear Power Station," in Specialty Conference on Struc-
tural Design of Nuclear Plant Facilities, Vol. 1, ASCE, pp 89-113.
25. Nash, W. A. 1957. Sehaum's Outline of Theory and Problems of Strength
of Materials, Schaum Publishing Co., New York.
26. Terzaghi, K., and Peck, R. B. 1948. Soil Mechanics in Engineering
Practice, John Wiley and Sons, Inc., New York.
27. Coates, D. F. 1970. Rock Mechanics Principles, Mines Branch Monograph
874, Halifax.
28. Smith, V. D. 1964. "The Condition of Stress Around a Simulated Mine
Opening," in Proceedings of the Rock Mechanics Symposium. Ojueens Univer-
sity, Ottawa, Canada.
82
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29. Yen, B. C., and Scanlon, 6. 1975. "Sanitary Landfill Settlement Rates,"
Journal of the Geotechnical Engineering Division. ASCE, Vol 101, No. GTS,
May, pp 475-487.
30. Rao, S. K., Moulton, L. K., and Seals, R. K. 1977. "Settlement of Refuse
landfills," in Proceedings of the Conference on Geoteehnieal Practice for
Disposal of Solid Waste Materials. University of Michigan, ASCE, New York.
31. Sittachitta, P., Yee, W., and Chang, J. 1976. "Settlement Performance
of Test Embankments Constructed Over Sanitary Landfill," Transportation
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Transportation.
32. Strohm, V. I. 1966. "Preliminary Analysis of Results of Division Labo-
ratory Tests on Standard Soil Samples," HP No. 3-813, U. S. Army Engineer
Waterways Experiment Station, Vicksburg, MS.
33. Donaghe, R. T. 1971. "Effects of Strain Rate in Consolidated-Undrained
Triaxial Compression Tests of Cohesive Soils," Report 2, Miscellaneous
Paper S-70-8, U. S. Army Engineer Waterways Experiment Station,
Vicksburg, MS.
34. Doherty, W. P., Wilson, E. L., and Taylor, R. L. 1969. "Stress Analysis
of Axisymmetric Solids Utilizing Higher-Order Quadrilateral Finite Ele-
ments," Report No. S.E.S.M. 69-3, Structural Engineering Laboratory, Uni-
versity of California, Berkeley, CA.
35. Withiam, J. L., and Kulhawy, F. H. 1978. "Analytical Modeling of the
Uplift Behavior of Drilled Shaft Foundations," Geotcchnical Engineering
Report 78-1, School of Civil and Environmental Engineering, {Cornell Uni-
versity, Ithaca, NY.
36. Wu, T. H. 1967. Soil Mechanics, Allyn and Bacon, p 152.
37. Desai, C. S., and Christian, J. T. 1977. Numerical Methods in Geoteeh-
nieal Engineering, McGraw-Hill.
38. Wright, D. K., Gilbert, P. A., and Saada, A. S. 1978. "Shear Devices
for Determining Dynamic Soil Properties," Earthquake Engineering and Soil
Dynamics, ASCE Specialty Conference, June.
39. Amenzade, Yu. A. 1979. Theory of Elasticity. Translated from the
Russian, Mir Publishers, Moscow.
40. Lambe, T. W., and Whitman, R. V. 1969. Soil Mechanics. John Wiley and
Sons, Inc., New York.
41. Craig, R. F. 1978. Soil Mechanics, 2nd Ed,, Univ. of Dundee.
42. Al-Russalni, M. M. 1980. "Comparison of Various Methods for Determining
Ko," Laboratory Shear Strength of Soil. ASTM STP 740.
83
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43. Donaghe, R. T., and Townsend, F. C, 1975. "Effects of Anisotropic Ver-
sus Isotropic Consolidation in Consolidated-Undrained Triaxial Compres-
sion Tests of Cohesive Soils," U. S. Army Engineer Waterways Experiment
Station, Technical Report S-75-13, Vicksburg, MS.. •
44. Tinoshetiko, S. Strength of Materials, Vol II, Advanced Theory and
Problems, Van'Nostrand Reinhold Company.
45. Peterson, R. W. "The Influence of Soil Suetidn on the Mechanical Behav-
ior of Unsaturated Soil," U. S. Army Engineer Waterways Experiment Sta-
tion, under review for publication.
46. Lefebvre, G., and Duncan, J. M. 1974. "Finite Element Analysis of
Transverse Cracking in Low-Embankment Dams," Contract Report S-74-3,
TJ. S. Army Engineer Waterways Experiment Station, Vicksburg, MS.
47. Sherard, J. L. "Embankment Dam Cracking," in Embankment Dam Engineering -
The Casandre Volume, Ed. by R. C. Hirschfeld and S. J. Poulos, John Wiley
and Sons.
84
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APPENDIX A
This Appendix presents information on design, construction, and opera-
tional characteristics for several active commercial hazardous waste landfill
facilities located 'in several regions of the country. The 10 sites discussed
were sufficiently documented during this study regarding characteristics
Influencing landfill settlement to allow summaries to be made of their
operations. The information presented may be of use in other study areas
concerning hazardous waste disposal. Table Al summarizes the operating char-
acteristics of the sites and describes the geometry of typical landfills
(cells, pits, trenches, and cut and fill). The sites are not named but are
identified' by number only.
The column headings of Table Al are clarified here. Landfill type clas-
sifies the landfills as belovground (includes pits and trenches, which may be
divided into cells or subcells), combination above and belovground fills, and
valley cut and fill, which is in effect a hybrid somewhere between landfill,
surface impoundment, and waste pile (EPA designations). The geometry of
typical or largest-sized individual landfills for a facility is described by
the excavated depth (before lining and filling), the bottom dimension of the
excavation, the interior side slopes, and the approximateMtfca In plan. The
actual or relative slope of the fill base is given because the slope is usually
part of the leachate collection system design. The slope of the top surface
of the final cover is shown where known. The column for subgrade (in-place)
material describes the native soil or rock underlying the landfill and in
which the landfill is placed. The specifications (specs) and descriptions of
landfill liners and the final cover are given where known.
Leachate collection systems vary in their complexity, but are commonly a
system of drain pipes and granular material designed to intercept and carry
the leachate to a central collection point where -it is removed by pumps. The
forms in which wastes are buried in the landfill, for example in containers or
in bulk fora, are described. Many facilities segregate wastes on the basis of
physical or chemical compatibility by placing them in different cells or
subcells within the landfill, and the practice is indicated as shown in the
table. The column for waste drum placement refers to the manner in which
55-gallon steel drums, common hazardous waste containers, are placed within
85
-------
Table Al Characteristics of Selected Hazardous Waste Landfills
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the fill for burial. The waste layer thickness describes the waste layer
separated by interim cover or fill layers of soils or other inert materials.
Some landfills bury primarily bulk wastes, which are spread in thin or thick
lifts and commonly for which no intermediate cover is used. Where;intermedi-
ate cover is used its thickness and composition are described in the table.
The method by which liquid wastes are stabilized, or solidified, and the
k
agents used, are shown. The year in which the first hazardous wastes were
buried in the facility is given where known. Many sites contacted in the
study had a history of multiple ownership, many of which predate RCRA. There-
fore, there are sometimes older fills onsite for which little information is
available regarding contents or construction. The information shown in the
table for'Site No. 10 was not derived firsthand and is less complete than
•information for the other sites. A narrative description of Sites 1 through 9
follows.
Site No. 1
This facility is located in the eastern U. S. and occupies about
2400 acres of plant area. The owners consider the site ideal for hazardous
waste landfilling because it is underlain by a considerable thickness of
claystone and silt stone of low permeability and relativej.y.jmgh strength. The
first hazardous wastes were buried at the site in 1977. The landfills are
large pits excavated in the claystone to depths of up to 100 ft with near-
vertical side slopes except for the upper 20 ft which Is a remolded soil re-
placing weathered material and is cut back to 2V on 1H. The bottom of the pit
is typically 300 ft square and is graded to slope to one side at about
5 percent. Earlier cells were only 30 ft deep. The landfills are single-cell,
that is the wastes and waste containers may be placed anywhere within the
large pit during filling operations and no berms or other dividers are used to
subdivide the pit.
The pit is excavated to grade and a one-piece liner consisting of 2 ft of
crushed native claystone is emplaced along the base and compacted with sheeps-
foot rollers to specification. Compaction is specified at 95 percent Standard
Proctor and is monitored. An 8-f t thickness of the clay liner is maintained
against the sides of the pit as the filling progresses. The leachate collec-
tion system is an 8-in.-thick blanket of washed gravel enplaced atop the
bottom liner, a perforated PVC collection pipe along the toe on the low side,
87
-------
and a 4-ft-diam concrete riser for access to collected leachate. Landfilled
wastes seen to be divided evenly between drums and bulk solids and solidified
liquids. Drums are placed on their sides (horizontally) and closely packed.
An area of drums may abut an area of bulk wastes and other debris.. The waste
layer when completed is covered with 12 to 18 in. of excavated, stockpiled
native claystone. The intermediate cover materials are spread with motorized
scrapers and Do-equivalent bulldozers. Waste and intermediate cover are
alternated to within 8 ft of the ground surface. The upper 8 ft of the pit is
filled with crushed, remolded claystone in 1-ft lifts to the came specifica-
tions as the bottom liner, to form the final cover. The center of the final
cover is crowned to produce an unspecified slope on the tspper surface.
Figure Al -illustrates the construction of a pit of Site No. 1 in cross section.
Bulk liquid wastes are solidified before burial by mixing then with
absorbents such as cement kiln dust in temporarily isolated mixing cells
within the pit. The mixture is then spread into the landfill. The resultant
mixture is strong enough to support heavy tracked vehicles. Liquids in drums
are solidified by adding a commercial absorbent, kaolinitic clay or "fuller's
earth," to the drum contents. Drums are filled to within 5 percent full to
prevent occurrence of voids. • Empty drums and other containers are crushed
before burial. Rain falling into the pit has to be con*iAer«4 contaminated
and must be treated as liquid waste, i.e., it'must be isolated and solidified
before burial, which reduces available landfill space. Retention of rainwater
is a common operational problem in pit-type lined landfills in regions of
moderate to high rainfall.
Site No. 2
Site No. 2 is in the eastern U. S. and occupies approximately 268 acres
of plant area. The first.landfill was opened in 1978. The base levels of the
pit-type landfills lie totally within a siliceous claystone, which when ex-
tracted and crushed produces an efficient commercial absorbent (fuller's
earth). The absorbent properties of the excavated claystone make it ideal as
a solidification agent for liquid wastes and, In the less pure font, as inter-
mediate cover fill for landfill operations. The claystone formation is only
50-65 ft thick and the depth of the landfill pits are limited to 40 ft after
30 to 40 ft of sandy clay overburden is removed. A water-bearing sand under-
lies the claystone at a depth of 10 to 15 ft below the base of the excavated
88
-------
00
to
8-FT COMPACTED FINAL COVER
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WASTE AMD WASTE DRUMS
Figure Al. Cross section of landfill of site number 1.
-------
pit but artesian pressure places the piezometric surface 10 to 20 ft above the
pit base. The typical pit is rectangular in plan, aeasures 200 by 500 ft at
the base and the sides are cut to a 3 horizontal on 1 vertical elope. The
landfill pit is divided into three cells by constructing earthen berms across
the pit. The berms are reconstructed with each lift until the pit is closed
and capped. The bents permit isolation of chemically or physically incompati-
ble wastes, specifically organic, acid, and alkalirfe wastes. Wastes consist
primarily of bulk solid and solidified materials and solidified waste in steel
drums. Figure A2 illustrates the construction of a landfill for Site No. 2,
in cross section.
The pit is excavated to grade, covered immediately to prevent drying and
cracking, -and a dual liner consisting of a 5-ft-thick layer of remolded,
i •,
compacted clay overlain by a 30-mil-thick blanket of Hypalon, a fiber rein-
forced synthetic geomembrane, 'is installed. The 5-ft clay liner is compacted
wet of optimum in 1-ft lifts with sheepsfoot rollers to a laboratory deter-
—8
mined density that corresponds to a permeability to water of 10 cm/sec. The
clay for the liners and cover is borrowed from overburden materials. Quality
control of liner and cover compaction specs is maintained by a consulting
laboratory. Permeability (k) to water is measured in a triaxial chamber on
-,-.-,i*< • . >,
remolded compacted specimens back pressure saturated, yield permeability
tests are not conducted on the clay liner but field density checks are made
using a densitometer or balloon volumeter. A plasticity Is chosen that will
—8
give the desired permeability of 1 x 10 cm/sec. The desired plasticity
occurs at a dry density of 92-93 pcf and a water.content of 25 to 30 percent.
Optimum density of the compacted clay, obtained by standard Proctor compaction,
is 112-113 pcf and occurs'at a water content of 15 to 20 percent. The clay
has a liquid limit of about 50 percent, a plastic limit of 21 to 29 percent
and 84 to 85 percent passes the No. 200 sieve. The in-place water content of
a typical laboratory sample was quoted as 28.5 percent, the saturation
93.3 percent, and the void ratio as 0.82. The specific gravity of the grains
is 2.68. A vibratory roller is used on the final lift of the clay liner to
provide a smooth surface for the geomembrane. A 2-ft-thick blanket of sandy,
clayey overburden soil is spread atop the Hypalon liner to serve as a buffer
to protect the liner and to assist the leachate collection system. A leachate
collection system of A-in.-diam PVC drain pipe is placed within the 2-ft sandy
90
-------
• SYNTHETIC LINER
TOP SOIL
COMPACTED CLAY
SANDY SOIL
CONCRETE RISER
LAYERED WASTES AND FILL
LAYERED WASTES AND FILL
HAULAGE ROAD
BERMS BETWEEN CEL LS
LEACHATE COLLECTION
5 FT COMPACTED CLA Y
Figure A2. Cross section of landfill of site number 2.
-------
soil layer and leads to a 4-ft-diam concrete sever pipe riser at the center of
each cell. The concrete riser is carried upward as filling progresses by
adding 5-ft sections of pipe. Figure A3 shows construction details of the
leachate collection system. A row of waste drums is placed along each side of
each collection pipe to protect the pipe. The slot formed between the drums
is then backfilled with washed gravel. A geotextile, a 50-mil nonwoven fabric,
is laid across the drum-gravel surface to prevent washing of fines into the
gravel. Normal waste-fill procedures are then started.
The first layer of wastes, consisting primarily of steel drums and solid-
ified wastes, is emplaced on the sandy layer, and then covered with about 2 ft
of the crushed, dried "fuller's earth" absorbent. The absorbent is spread
with rubber-tired front-end loaders and light crawler tractors so that it
sifts down between the waste containers and completely covers the waste layer.
The absorbent fill varies in particle size from dust (clay-sized) to perhaps
1/4 in. The operation observed probably results in some bridging of the fill
over voids. Waste containers are closely stacked, however, and large voids
probably are not created during filling of the cell. Waste drums are placed
on end (long axis vertical). Waste and fill layers are alternated up to the
top of the cell and the cells within the section are then capped. One ft of
sandy clay is placed atop the last waste/fill layer. Twenty-mil PVC with a
30-mil factory-bonded Hypalon edging is then bonded to the Hypalon liner to
envelop the cells. A 2-ft-thick blanket of clay is compacted atop the syn-
thetic liner to the same specs as the liner clay. Finally 18 in. to several
feet of topsoil caps the cells. The cap is grassed and settlement plates or
supposed to be installed. To date, no settlement plates have been installed
but were scheduled for installation. All wastes brought into the facility are
weighed and classified and when added to the cell are mapped on a 3-axis
system so that their positions are known.
All liquids handled by the facility, including those in containers and in
bulk, are solidified by the addition of crushed and dried "fuller's earth"
absorbent. Liquids in drums are treated within the drums or if the drums are
full they are partially emptied into other drums and both drums of liquids
then treated. Leaking or damaged drums acquired off-site or brought to the
site are repackaged in 85-galIon "overpack" steel drums. Emptied drums are
usually crushed along the long axis to a thickness of about 8 in.
92
-------
CONCRETE RISER
WASTE DRUMS
DRAINPIPE
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I
I
,-J
PLAN
• GEOTEXTILE FILTER CLOTH
WASHED GRAVEL
2 FT SANDY SOIL
DRAINPIPE
SECTION A - A
Figure A3. Leachate collection system for site number 2.
93
-------
Partially full drums are refilled with absorbent so that air space (void) is
reduced. Bulk liquids are usually transported to the facility by tank truck.
The trucks drive directly to the* top edge of the pit where they discharge
their loads into the appropriate cells by laying the discharge hose onto the
pit slope and opening the valve. In the early stages of cell filling the
hoses do not reach the bottom of the cell but discharge directly onto the 3 on
k
1 side slope. Associated erosion of the slopes in several places by gullying
was observed during the site visit but erosion reportedly does not compromise
the side liner. The liquids run into a pit within the cell where they form a
pool that is solidified by addition of absorbent material. Most of the waste
drums appeared to be in good condition but some were damaged, partially
crushed, or punctured. Some sheet plastic, used to cover and- line waste
transportation trucks, is buried along with other waste. Wooden pallets are
also observed in the waste fill. Larger containers, such as truck tank cars,
are crushed and included occasionally in the cells in addition to the 55 and
85-gallon drums. Plastic drums are sometimes disposed of. The solidified
bulk liquid wastes attain a consistency sufficient to support the wheeled and
tracked earth moving vehicles that operate in the pits.
Site No. 3
The facility is located in the eastern U. S. The site was not visited
for this study but information was obtained through correspondence with site
personnel. The landfills are partially below grade but most of the volume of
the fill is placed aboveground behind retaining dikes, and would probably be
classified as surface Impoundments by EPA. Early fills at the site were 1 to
2 acres in area and were capped and closed in 1978. A presently active area,
or cell, is 3-5 acres and a planned cell will be 14 to 17 acres in size. The
cells are excavated into glacial till and clay. A 10-ft-thick remolded clay
liner is installed along the base and interior 1 on 1 slopes by compacting in
6-in. lifts to achieve a permeability to water of no more than lO~ cm/sec.
An 80-mil high density polyethylene (HDPE) geonembrane liner is then emplaced
atop the clay and a buffer of 1 to 2 ft of additional clay is laid atop the
geomembrane. The cell is divided into as many as 5 subcells by clay berms to
allow segregation of wastes. The subcells isolate heavy metals, pseudometals
(arsenic, antimony, bismuth, etc.), organics, flammable wastes, and toxic
wastes. The subcell base is graded to slope toward an exterior berm at
94
-------
2 percent, and a leachate collection system is installed. A 1-ft-thick graded
stone filter blanket covers the base of the subcell and directs leachate
(primarily rainwater) to a 42-in. concrete cylinder riser. .During operations
side riser pipes assist in removing leachate. Figure A4 diagrams a Site No. 3
landfill in section.
Wastes are primarily in steel drums. The first layer of drums is placed
directly atop the leachate layer, the drums in upright (on-end, vertical)
position. A 6- to 12-in. layer of intermediate cover is spread atop each
waste layer as fill progresses. The composition of the intermediate cover
varies with each subcell for waste compatibility, and may consist of clay,
limestone, ashes, or specialized covers. The intermediate cover fill receives
some compaction from the tracked vehicles used to apply it. The final cover
consists of 3 ft of compacted remolded clay atop the last waste layer, followed
by a HDFE geomembrane liner, about 18 in. of clayey soil and a 6-in. top layer
of topsoil. The final cover surface slopes away from the center at 8 percent,
as constructed.
All liquids, in drums and in bulk, are chemically analyzed and treated
with absorbent or stabilizing agents the composition of which is determined by
the chemistry of the waste. Classification of wastes also permits accounta-
bility and mapping of all wastes buried in the landfill.
Site No. 4'
Site No. 4 is located in the south central D. S. near the Gulf Coast.
The site covers 86 acres of which 50 acres are available as landfill. The
landfills are pits excavated belowground in clays and silty clays with occa-
sional lenses of silty sands. Each cell is approximately 3 to 5 acres in
area, 50 ft deep, and has side slopes of IV on 2.5H. The base of the cell
slopes to one side. Cells are lined by placing 4 ft of remolded compacted
clay-rich soil against the base and sides, nsing a sheepsfoot roller and
placing in 6-in. lifts. The state requires compaction at 95 percent of Stand-
ard Proctor. Liners mst have a permeability to water no greater than 10*
cm/sec. In excavating the cells, a large pit area is excavated to grade and
divided into smaller areas of cells by the use of temporary clay berms. In an
active cell, therefore, three sides may consist of adjoining waste fill slopes,
and the other side of the native soil cut slope. The temporary clay-soil
berms protect the operating cell from contamination by the adjoining waste
fill.
95
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VO
'TOP SOIL
• LOOSE CLAY
. HOPE LINER
, COMPACTED CLAY
LEACHA TE COLLECTION RISER
QAS VENT
INTER. COVER LAYERS
COMPACTED CLAY
Figure A4. Cross section of landfill of site number 3.
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The leachate collection system consists of slotted 6-in. PVC pipe laid
down every 100 ft along the side slopes from the ground surface down into the
center of the cell. A granular soil layer is emplaced along each section of
pipe along the base of the cell. Wastes are primarily bulk solid* and solidi-
fied liquids. Drums comprise only an estimated 10 to 15 percent of the waste.
Solidification is achieved by mixing cement kiln dust with the bulk liquids in
mixing pits. The resulting mixture is spread along' the working base of the
cell in thin (6-in. to 1-ft) lifts and receives some compaction by D-5 and D-8
Caterpillar dozers. If steel drums of wastes are included in the fill there
are no more than three stacks of drums vertically within any location of the
cell and 2 to 3 ft of solid bulk wastes are placed between drum layers, with
at least '5 ft of bulk waste between the lower drum layer and the cell base.
Empty drums are crushed before being placed in the fill. A final cover is not
planned for this facility because the site manager has applied for a permit to
construct surface impoundments atop the existing landfill.
Site No. 5
The site is located near the Gulf Coast in the south-central U. S. The
facility occupies about 450 acres most of which is dedicated to land farming,
a method of disposing of Class II and milder wastes (Class I wastes are haz-
-- -.-*«&fc$:'- - ,
ardous materials) by incorporating them into the topsoil with a disc harrow.
Approximately 18 acres of the facility are currently u«ed for below grade
landfilling. Four active cells, or trenches, are being worked. Wastes,
almost totally in bulk form, are segregated by type in different trenches:
one for iron oxide catalyst, one for sludge (solidified), one for organics,
and one for acid mixed in a stabilizing agent. This is a relatively small
facility taking wastes from a few local suppliers. The first wastes were
landfilled in 1980.
The landfill trenches are 15 ft deep, approximately 80 by 110 ft on the
base and about 170 by 200 ft at the top, with IV on 1.5H side slopes. The
trenches are excavated in clays, silty clays, and silty sands. Water-bearing
strata occur variably at a depth of about 25 ft but artesian pressure places
the piezometric level at a depth of 3 to 4 ft below ground surface. An ancient
sand-filled stream channel traverses the site and if intercepted by an exca-
vated trench the sand is removed to a depth of a few feet and that area of the
trench wall backfilled with clay-rich material. Alternately, no liner is
97
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required if 4 ft of in-place clay-rich soil exists in the cut trench walls and
base. Clay-rich soil is defined by the state as having a water content
30 percent, a plasticity index (PI) of 15, and 30 percent passing the No. 200
sieve. A compacted liner of 3 ft of remolded clay-rich soil is emplaced prior
to landfilling the.trenches. The liner is compacted to 95 percent Standard
Proctor density. A consulting engineering laboratory monitors site construc-
tion requirements with subsurface exploration techniques and runs field den-
sity tests on compaction. Typical test results for liner soils are: light
gray to red clay, Standard Proctor compaction maximum dry density 94.6 pcf,
optimum water content 26 percent. Typical in-place conditions of the clay-
rich soil »ere 24.8 to 31.0 percent water content and 87.0 to 99.7 pcf, or
90.2 to 103.4 percent Standard Proctor. Laboratory constant head permeability
tests on back-saturated samples of the clay-rich strata yielded permeability
—8 —9
to water of 10 to 10 cm/sec.
Leachate collection is achieved .by emplacing a 4-in. slotted PVC pipe in
the center of the trench in a 6-in.-thick blanket of pea gravel covering the
trench base. The trench base slopes toward one end where a right-angle bend
in the 4-in. PVC pipe directs leachate to a riser and sump. Figure A5 dia-
grams a typical trench in section. The bulk solidified wastes and other solid
debris are deposited in the trenches by end dumping over a vertical face 15 ft
high which is advanced along the trench axis toward one end. A cover of 4 ft
*
of clay-rich soil caps the trench,
Site No. 6
The site is located near the Gulf Coast in the south central U. S. The
facility occupies about 440 acres most of which is dedicated to landfilling
operations. Part of the site originally was operated as a hazardous waste
landfill under different owners but merged with the current owners and ex-
panded in 1981. The landfills are individual pits or trenches 12 to 17 ft
deep excavated in silty, sandy clay generally less than 20 ft thick and under-
lain by silty and sandy soils. The piezometric level is at about 2-3 ft depth
(belowground surface). The trenches are typically 100 ft wide by 400-500 ft
long at the top with 1 on 1 side slopes. The trench bottom slopes toward the
axis of the trench. A liner is not required as long as there is 4 ft of
in-place clay-rich soil (see definition for Site No. 5) in the trench, walls
and floor. The leachate collection system is a single 4-in. slotted PVC pipe
98
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vO
vO
S«//W AND MANHOLE
COMPACTED
CLAY-RICH
BACKFILL
GRAVEL BLANKET
*» f*r
PVC DRAIN PIPE
SAND STRATUM
Figure A3. Croas section (end view of trench of site number 5)
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laid down the center on the bottom of the trench and up the end or side slope
to aboveground. The pipe is covered with a variable thickness and amount of
crushed rock. • •
Most of the waste is in bulk solid and solidified liquids. Ho intact
steel drums are buried, but empty crushed drums are placed in small quantities.
The facility incorporates a jet mixing technique to stabilize liquids. Liquids
*
are loaded into a mixing pit and a tank truck injects Portland cement kiln
flue dust at high pressure and velocity through a hose at the bottom of the
mixing pit. Mixing and absorption appear to be quite complete with the method.
The solidified wastes have a consistency resembling silty soil when placed
into the burial trench. Bulldozers equipped with pyramidal treads for better
compaction distribute the wastes along the long axis of the trench toward one
end along a low sloping waste face. Final covers are not planned because the
owners will apply for a permit to construct waste Impoundments atop the exist-
ing landfills. In connection with the impending construction of embankments
for the aboveground impoundments, a consultant conducted stability analyses on
the proposed embankments and a consolidation analysis of the waste fills and
in-place soils. The results of the analyses indicated that the mixture of
Class I (hazardous) wastes and flue dust was stronger than the unmixed Class II
wastes. The hazardous waste/flue dust mixture was less compressible than the
stiff natural clay-rich soil with respect to primary consolidation.
Site No. 7
This site is located in the desert southwest. The facility's hazardous
waste disposal landfills have been in operation since about 1970. The plant
occupies 80 acres with 18 acres dedicated to chemical waste disposal. Disposal
is in large pits divided into cells by berms of native soils. The pits are
50 ft deep, excavated in a horizontally bedded clay 90 ft thick below the pits
that appears to be derived from volcanic ash falls. The upper several feet of
strata are bedded clayey sands and gravels. The site managers consider the
in-place clay a natural liner, and measured permeabilities to water are 10
_o
to 10 cm/sec. Ground water is over 300 ft deep. Evaporation in the desert
climate far exceeds precipitation. The active pit observed was 540 ft square
with near-vertical side slopes. The pit was divided into four cells of unequal
sizes for the segregation of acid, alkaline, organic, and PCB wastes.
100
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The facility installs no leachate collection system in the pits but maintains
monitoring veils around the site. At the current rate of filling the active
cell is expected to take 12-14 years to fill. .
Most of the waste is buried in steel drums, which account for, an estimated
90 percent of the waste containers. Some bulk waste and other containers
including wooden boxes and crates and transformers are also buried. Drums are
placed on edge (horizontally) in stacks two or three drums deep. Six inches
of soil (intermediate cover) separates each drum stack from the next higher
stack. Some compaction of the Intermediate cover is achieved by the rubber-
tired motorized scraper used to spread the cover. Several tiers of wastes may
be placed in one part of the pit before the adjacent area is used, and there-
fore the pits cannot be considered as being horizontally layered with respect
to waste placement. Liquids (paints, sludges) in containers were buried in
earlier pits prior to 1980, but BO free liquids have been burled subsequently.
The high evaporation rate at the site helps reduce the liquid content as the
pit is filled. Liquid wastes are stabilized with several agents including
cement flue dust, bentonitic clay, and fuller's earth. Fill proceeds to
within 3 ft of ground level, then a cover of the excavated clay strata is
applied and crowned 2 ft at the center for a total cover; Hiickness of 5 ft at
the center and 3 ft at the pit edges, which yields a cover slope of less than
1 percent.
Site No. 8
This site is located on the west coast in arid to semiarid climate (evap-
oration is approximately five times precipitation). The facility occupies
approximately 280 acres with a 1900 acre buffer of land surrounding the working
portion of the site. The facility incorporates holding ponds for liquid
wastes and landfills for burial of solid hazardous wastes. The landfills are
positioned in dry valleys between hills, the mouth of the valley dammed to
create an impoundment. This facility is not a true landfill but should proba-
bly be classified as a hybrid between landfill, surface impoundment and
wastepile. The landfill area is excavated down to fresh rock (marine siliceous
siltstone to claystone or clayshale with some sandstone), cut to 1 on 1 side
•lopes, and then lined and filled. A perched water table exists beneath the
site but is insignificant as an aquifer. The site has had at least two owners
prior to its present ownership. The presently active landfill was started in
1979. Earlier ownership dates at least to 1968.
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The liner is 2 ft of compacted remolded clay from the claystone «ubgrade.
The liner is compacted with a special compactor with cleated feet to a desired
permeability to water (measured typically 10~ to 10~ cm/sec). The leachate
collection system consists of french drains installed along the inside toe of
the cut and leading down-valley to a collection sump and 18-in. metal riser at
the center of the barrier dam. As the fill proceeds upward the fill surface
v
is terraced back toward the head of the valley and a new riser and leachate
system installed at the new level. Figure A6 diagrams the fills in profile
and plan.
Wastes almost totally have been bulk solidified liquids but some burial
of drums is planned. Vastes are dumped over the edges of the fill and mixed
with sufficient clayey material moved in from the edges of the valley to
stabilize the liquids. The material is then spread into the fill in thin
lifts'by a bulldozer. The waste surface is then compacted to a reported
80 percent of Standard Proctor by the special compactors. Typical wastes
received are paint residues, sludges, and metal-contaminated soil. Some solid
debris such as fiber drums, minor paper and plastic debris, and wooden pallets
are also included occasionally. An extensive system of runon-runoff drainage
ditches is constructed around the fills to divert rainwater fron the fill
surface. The planned depth of the landfill before closure is about 100 ft.
The final cover has not yet been designed.
Site No. 9
This facility is also located on the west coast in an arld-seniarid
climate. The facility operates holding ponds and lagoons for liquid wastes
(chiefly oil field related wastes) and recently (1978) began landfilling solid
hazardous wastes. The plant occupies 250 acres and is surrounded by a buffer
of plant-owned land of approximately 4300 acres. This facility like Site
No. 8 also operates by filling in dammed valleys. The natural valleys are
excavated to fresh rock, a diatomaceous (siliceous) shale and claystone, the
aide slopes graded to about 1 on 1, a clay barrier dam installed at the lower
end, and the valley filled. The in-place material is of sufficiently low
permeability to water (1 to 3 x 10" cm/sec and 78 percent passing the No. 200
sieve) that presumably no further lining is required to retain leachate. The
claystone is 500 to 1000 ft thick at the site and there are no known aquifers
below it. The natural down-valley slopes of the landfill areas are 3 to
102
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WASTE FILL
LEACHATE COLLECTION RISERS
BARRIER DAM
FRENCH DRAINS
LINER
PROFILE
PLAN
(NOT TO SCALE)
Figure A6. Landfill of site number 8.
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10 percent. The 12-ft-thick barrier .dams are constructed with care by com-
pacting clay in lifts and keying about 4 ft into fresh rock. Leachate collec-
tion is by gravity drainage down valley to a perforated FVC pipe in a gravel
curtain against the landfill side of the barrier dam, the pipe sloped to a
central collection-sump with riser. There are five separate landfills that
vary in capacity from 47,000 cu yds to 172,000 cu yds. The maximum planned
depth before closure for the largest landfill is about 85 ft.
Approximately 90 percent of the landfilled wastes are in steel 55-gallon
drums. The drums are placed in single layers, closely and carefully stacked
on end across the landfill surface. Each waste layer is separated from the
next higher layer by 4 ft of crushed native diatonaceous fill as the interme-
diate cover. The site managers estimate that a completed fill will contain
73 percent of inert intermediate cover material and only 27 percent waste
material. Wastes are segregated by reserving each landfill for one kind of
waste. The fills are separated by several tens of feet of inplace claystone.
The separate landfills are for solid PCB's, solvents/pesticides, heavy metals/
sludges, caustics/cyanides, and acids. Figure A7 diagrams the largest landfill
(the solvents/pesticides fill). The PC8 landfill contains many large wooden
crates approximately 3*4 ft square containing contaminated •oil* Electrical
transformer bodies are also buried. Liquid wastes in drums are solidified by
the producer before delivery to the landfill. Vetmiculite (an expanded mica)
reportedly is a common solidifying agent. The final cover has not been de-
signed for these landfills.
104
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EVENTUAL TOP OF FILL
LEACHATE COLLECTOR
BARRIER DAM
BARRIER DAM
PLAN
(NOT TO SCALE)
Figure A7. Landfill of site number 9.
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APPENDIX B
DERIVATIONS OF EQUATIONS FOR YOUNG'S MODULUS
(1) Young's modulus of drum subjected to uniform external pressure.
The assumption is Bade that a drum lying on its side will be subjected to
a uniform pressure • AP aad that
where
(U) , « radial deformation of the drum at radius b.
b - outer radius of the drum (- 11.175 in).
a - inner radius of the drum (- 11.125 in).
E » Young's modulus of the drum aaterial (steel, E - 30 x 10 psi).
v - Poisson's ratio of drum material (steel, v - 0.29).
A unit thickness will be chosen so that the initial volume V^ - vr . If the
final volume is V, - ir(r + Ar) then the change in volume of the system
neglecting higher order terms is
AV - Vf - V - ir (2r Ar) (2)
i
and
AV m 2-n rAr _ 2Ar (3)
V * ir r2 " r
which becomes by substituting in equation (1)
AV 2AP Fa2 + b2 1 (4)
V " E Lb2 - a2 ~ J
and if one dimensional compression is assumed, the modulus of the drum, E_ is
~ . f 2 . ^21 (5)
vhich becomes upon substitution
- 67352 psi (6)
- 9.7 x 106 psf
106
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(2) Composite Young*s modulus of soil/drum configuration for drums on their
sides.
The assumption Is made that the two-component system (the drum and soil,
see Figure 20) will compress hydrostatically under pressure, i.e., the bulk
modulus of the system can be computed from • '
where
AP - the increase in pressure applied to the system.
AV
—- - volumetric strain of the system.
For the assumed, condition of one dimensional compression, the bulk modulus, K ,
is equal to the Young's modulus,
f
* ' * -ffiBT (8)
The change in volume of the drum as a result of a change in 'pressure is equal
to
(9)
Similarly, the change in volume of the affected soil is
, D2
Es
where
D -drum diameter.
£ » Young's modulus of the soil.
The total change in volume of the system is therefore
AVTOTAL
and
VD AP D2 (1/2 - ir/8) AP
(12)
230 South Dearborn Street ^ 107
Chicago, Illinois 60604
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The volume of the drum is » D /4 and the total volume of the system is D
for unit thickness. Therefore, equation (12) reduces to
*VTOTAL . A0 I TT . (1/2 - ir/8)
_ _ _ (13)
VTOTAL ~ |4E~ ' E-
which when combined with equation (8) yields
E m V m D S
composite T it Eg + 4E (1/2 - w/8) (14)
(3) Composite Young's modulus of soil/drum configuration for drums on end.
The assumption is made that for the drums standing upright (on end), a
uniform pressure Ap is applied over the top -surface of the drum and that the
contents will initially contribute no stiffness to the system. Therefore the
total force applied to a drum is
F - AJ AP (15)
2
where A_ is the total area of the top of the drum and equal to if b . The
deflection, S , of the drum is
* . -PL MO
« • Tjj-j (16)
where
L « drum length
E - Young's modulus of drum material (for steel, E - 30 x 10 psi)
2 2
A « area of the material of drum » T (b - a )
b • outer drum radius » 11.175 in.
c « inner drum radius - 11.125 in.
Therefore
But the strain in the drum is the ratio g- and the applied stress is AP .
Therefore the effective Young's modulus of the drum is the ratio
108
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