United States Office of Water and SW-869
Environmental Protection Waste Management September 1980
Agency Washington DC 20460
&ER& Landfill and Surface
Impoundment
Performance
Evaluation
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LANDFILL AND SURFACE IMPOUNDMENT
PERFORMANCE EVALUATION MANUAL
SUBMITTED BY
Charles A. Moore, Ph.D., P.E.
GEOTECHNICS, Inc.
Columbus, Ohio
SUBMITTED TO
U.S. Environmental Protection Agency
Municipal Environmental Research Laboratory
Solid and Hazardous Waste Research Division
Cincinnati, Ohio
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Permit Writers Guidance Manual/Technical Resource Document
Preface
The land disposal of hazardous waste is subject to the requirements
of Subtitle C of the Resource Conservation and Recovery Act of 1976.
This Act requires that the treatment, storage, or disposal of hazardous
wastes after November 19, 1980, be carried out in accordance with a
permit. The one exception to this rule is that facilities in existence
as of November 19, 1980 may continue operations until final administrative
dispostion is made of the permit application (providing that the facility
complies with the Interim Status Standards for disposers of hazardous
waste in 40 CFR Part 265). Owners or operators of new facilities must
apply for and receive a permit before beginning operation of such a
facility.
The Interim Status Standards (40 CFR Part 265) and some of the
administrative portions of the Permit Standards (40 CFR Part 264) were
published by EPA in the Federal Register on May 19, 1980. EPA will soon
publish technical permit standards in Part 264 for hazardous waste
disposal facilities. These regulations will ensure the protection of
human health and the environment by requiring evaluations of hazardous
waste management facilities in terms of both site-specific factors and
the nature of the waste that the facility will manage.
The permit official must review and evaluate permit applications to
determine whether the proposed objectives, design, and operation of a
land disposal facility will be in compliance with all applicable pro-
visions of the regulations (40 CFR 264).
EPA is preparing two types of documents for permit officials
responsible for hazardous waste landfills, surface impoundments, and
land treatment facilities: Permit Writers Guidance Manuals and Technical
Resource Documents. The Permit Writer's Guidance Manuals provide guidance
for conducting the review and evaluation of a permit application for
site-specific control objectives and designs. The Technical Resource
Documents support the Permit Writers Guidance Manuals in certain areas
(i.e. liners, leachate management, closure, covers, water balance) by
describing current technologies and methods for evaluating the performance
of the applicant's design. The information and guidance presented in
these manuals constitute a suggested approach for review and evaluation
5ased on best engineering judgments. There may be alternative and
quivalent methods for conducting the review and evaluation. However,
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if the results of these methods differ from those of the EPA method,
their validity may have to be validated by the applicant.
In reviewing and evaluating the permit application, the permit
official must make all decisions in a well defined and well documented
manner. Once an initial decision is made to issue or deny the permit,
the Subtitle C regulations (40 CFR 124.6, 124.7 and 124.8) require
preparation of either a statement of basis or a fact sheet that discusses
the reasons behind the decision. The statement of basis or fact sheet
then becomes part of the permit review process specified in 40 CRF
124.6-124.20.
These manuals are intended to assist the permit official in arriving
at a logical, well-defined, and well-documented decision. Checklists and
logic flow diagrams are provided throughout the manuals to ensure that
necessary factors are considered in the decision process. Technical data
are presented to enable the permit official to identify proposed designs
that may require more detailed analysis because of a deviation from suggested
practices. The technical data are not meant to provide rigid guidelines for
arriving at a decision. References are cited throughout the manuals to pro-
vide further guidance for the permit official when necessary.
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FOREWORD
I would like to briefly discuss the philosophy upon which
this Evaluation Procedures Manual is based. The problem of trans-
port of liquids through hazardous waste landfills and surface im-
poundments is technically quite complicated. Moreover, the analytical
techniques that are currently available do not allow the problem to
be as comprehensively treated as would be desired. Nevertheless,
I have tried to avoid an approach that reverts to empiricism and
rules of thumb.
It is important to recognize that many evaluators will not
possess strong technical backgrounds in the area of transport
processes, thus this Evaluation Procedures Manual does not involve
extremely complicated mathematics. I have used linearized vers-
ions of equations and have used solutions for simplified boundary
conditions so that it is not necessary to evaluate overly compli-
cated formulae.
Nevertheless, the analytical principles upon which the
evaluation procedure is based are, in my opinion, sound ones and
should provide the foundation for future analytical developments
in the area.
This philosophical approach has three important implications:
(1) As better analytical techniques are developed, it will be
possible to modify the evaluation procedure in a rational and
consistent manner. At the design level, acceptable configura-
tions for landfills and surface impoundments will change gradually
rather than abruptly. Thus the evaluator will not be placed
in the awkward position of having to explain to the designer
that a design that was acceptable last year is seriously out
of compliance this year.
(2) Engineering firms that design hazardous waste landfills and
surface impoundments will be able to use more sophisticated
analytical techniques if they desire. For example, they may wish
to use nonlinear versions of equations or more comprehensive
boundary conditions for equations, thereby introducing more
realism into the analysis. However, because such analytical ap-
proaches are compatible with the approach being used by the
evaluator, the designer will be able to explain the reason
for differences in the results of the two analyses and be
able to more easily convince the evaluator that the more
progressive analytical approach yields an acceptable, though
hopefully more economical, design.
m
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(3) The analytical approaches presented in this manual provide a
quantitative basis upon which the evaluator and designer can
discuss possible modifications so that an unacceptable design con-
figuration can be transformed into one that is acceptable. This
approach avoids the dilemma that the designer sometimes faces of (1)
being told that a design violates an irrational rule of thumb cri-
terion, but (2) being given no guidance on how to modify the design
to comply with the intent of the requirements.
The burden is placed on the designer to provide a design that has
quantitatively documented capabilities for containment of liquids. De-
signs cannot be rationalized based on statements that the design "has
worked before" or that components whose effects have not been analyzed
"contribute to retarding liquid movement." Designers must approach liquid
routing through landfills and surface impoundments facilites as a
discrete analysis task, and they will be required to substantiate
their designs quantitatively. The Evaluation Procedures Manual implicitly
provides techniques that can be used by the designer. A logical choice
for the designer to make would be to use the same analytical procedures
to arrive at the proposed design that the evaluator will be using in
determining if the design is acceptable.
Chapters 2 and 3 describe the physical attributes of the facilities
for which the evaluation procedure has been developed. Chapter 4 provides
the analytical basis for the evaluation procedure. The fundamental physi-
cal-mathematical principles are presented and the resulting equations are
given. However, intermediate steps that involve tedious algebra are not
included in the present manual but are reserved for the technical support
document.
Chapter 5 presents the detailed evaluation procedure and serves
as a checklist. The experienced evaluator will use this chapter only.
Appendices A and B present example evaluations. Appendix C lists
symbols, and Appendix D gives sources of additional information.
In conclusion, I hope that this Evaluation Procedures Manual will
provide a straight forward, analytically sound basis for the rational
design of hazardous waste landfills and surface impoundments with
respect to their ability to provide containment of liquids.
I would like to especially acknowledge the assistance of Mike
Roulier, Dirk Brunner, Youssef Dakhoul, Jawed Umerani, Ruth Foltz and
Susan DeHart. The contributions of Dr. Vincent T. Ricca are especially
acknowledged.
Charles A. Moore
October 15, 1980
IV
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CONTENTS
Page
1. INTRODUCTION 1
1.1 Purpose 1
1.2 Relationship to Other Manuals 1
?.. APPLICABLE OPERATING CONDITIONS 3
3. APPLICABLE DESIGN CONFIGURATIONS 4
3.1 Functional Characteristics of Design Modules 4
3.2 Categorization of Functions of Design Modules 8
3.3 Definition of Units to be Included in the 8
System for Control of Liquid Transmission
3.4 Liquid Diversion Interfaces 9
3.5 Construction of Liquid Routing Diagrams 9
4. OVERVIEW OF ANALYTICAL METHODS 11
4.1 Introduction 11
4.2 Horizontal Flow Through Sand and Gravel Drain Layers 11
4.3 Vertical Flow Through Low Permeability Clay Liners 15
4.3.1 Physical Principles 15
4.3.2 Overview of Analytical Approaches 21
4.3.3 Linearized Approach to Analysis 25
4.3.4 Linearized Approach to Predicting Time of 26
First Appearance of Leachate
4.3.5 Linearized Approach to Predicting Leachate 30
Flow When Liquid Has Ponded on Liner
4.3.6 Linearized Approach to Predicting Leachate 33
Flow Rates After Saturation
4.4 Effeciencies of Liner-Drain Layer Systems 34
5. PROCEDURE FOR EVALUATING PROPOSED DESIGNS 39
5.1 Outline of Procedure 39
5.2 Information Required to Use Evaluation Procedure 41
5.2.1 Input From Other Manuals 41
5.2.2 Input From Proposed Plans and Specifications 44
5.3 Summary of Outputs of Evaluation Procedures 45
5.3.1 Outputs to Other Manuals 45
5.3.2 Outputs to Determine Whether Proposed Design 45
is Acceptable
APPENDICES 47
A. Example Hazardous Waste Landfill 48
B. Example Hazardous Waste Lagoon Problem 56
C. List of Symbols 60
D. References Cited 61
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LIST OF FIGURES
Fig. No. Title Page
1.1 Relationship of this Procedures Manual to 2
other Procedures Manuals
3.1 Cross-section of landfill delineating typical 5
containment modules
3.2 Detail views of modules constituting landfill 7
cross-section of Figure 3.1
3.3 Liquid routing diagram showing intended functions 10
of components of leachate containment system
4.1 Geometry assumed for bounding solution for 12
effectiveness of sand drains
4.2 Relationship between h /L and c = e/k 16
4.3 Partially saturated soif showing menisci resulting 17
in capillary tension in pore water
4.4 Capillary potential versus mean soil grain size 17
4.5 Capillary potential as a function of water content 19
for Yolo clay (from Philip, 1969)
4.6 Computed moisture profiles for infiltration into 20
Yolo light clay (from Philip, 1969)
4.7 Relationship between hydraulic conductivity and 24
water content for Yolo light clay (from Philip, 1969)
4.8 Complementary error function 27
4.9 Simplified geometry for calculating time for liquid 29
to penetrate liner
4.10 Geometry for calculating effeciency of drain-liner 35
systems using method proposed by Wong (1977)
4.11 Geometry for calculating effeciency of drain-liner 37
systems (after Wong, 1977)
4.12 Diagram for computing effeciency of drain-liner 37
systems (after Wong, 1977)
5.1 Flow chart for procedure used to evaluate containment 40
5.2 Sources of input information for evaluation procedure 43
5.3 Output information from evaluation procedure 46
A.I Excerpt from plans for proposed landfill 49
A.2 Excerpts from specifications for proposed landfill 50
B.I Excerpt from plans for proposed lagoon 57
B.2 Excerpt from specifications for proposed lagoon 57
VI
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1. INTRODUCTION
1.1 Purpose
This Evaluation Procedures Manual has been developed to describe the
technical approach and to present equations for determining how the design
of hazardous waste surface impoundments and landfills will function in
controlling the quantity of liquids released to the environment.
The procedures described herein should allow an evaluator to deter-
mine the adequacy of designs for:
(1) compacted clay liners or synthetic liners intended to impede
the vertical flow of liquids,
(2) sand or gravel drainage layers intended to convey liquids laterally
into collection systems,
(3) slopes on such liner systems, and
(4) spacings of collector drains.
1.2 Relationship to Other Manuals
This procedures manual relates to other manuals as shown in Figure
1.1:
(1) Hydrologic Simulation on Solid Waste Disposal Sites prepared by the
U.S. Army Corps of Engineers, Waterways Experiment Station. This
manual provides the analytical basis for determining the partition-
ing of rainfall into surface runoff and infiltration. The water
that infiltrates is, in turn, partitioned into that which returns to
the atmosphere through evapo-transpiration, that which is stored in
the cover soil, and that which percolates downward into the landfill.
The last of these components, percolation, becomes the principal input
to the present manual because it is the inflow due to percolation
that must be adequately controlled as it is routed through the land-
fill. The Hydrologic Simulation on Solid Waste Disposal Sites
manual provides the inflow on a daily basis, based upon the CREAMS
model developed by the U.S. Department of Agriculture. Alternate
sources of this type of information could be provided by Use of the
Water Balance Method for Predicting Leachate Generation from Solid
Waste Disposal Sites (Fenn, Hanley and DeGeare, 1975) which is based
upon the principles developed by Thornthwaite and Mather (1955 and
1957).
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HYDROLOGIC SIMULATION ON
SOLID WASTE DISPOSAL SITES
outflow due to percolation,
below cover on daily basis
LANDFILL & SURFACE IMPOUNDMENT
PERFORMANCE EVALUATION
input quantity of water to be
adequately controlled as it is
routed through the landfill
input service life of
synthetic liners
outflow quantitites to
collector drains
LINING OF WASTE IMPOUND-
MENT AND DISPOSAL FACILITIES
output service life of
synthetic liners
input quantity of flow to
col lector drain
GENERAL GUIDANCE FOR SELECTION
OF LEACHATE TREATMENT METHODS
input quantity of leachate
to be treated
Figure 1.1 Relatioriship of this Procedures Manual to other Procedures Manuals.
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(2) Lining of Waste Impoundment and Disposal Facilities, by Henry Haxo
of Matrecon and John Pacey of EICON Associates. This manual relates
to the present manual in two ways. First, it will provide informa-
tion that can be used to determine the service life of synthetic
liners. Second, the outflow quantities to collector drains from sand
and gravel drainage layers determined according to procedures des-
cribed in the present manual will become input quantities to the
section of The Lining of Waste Impoundment and Disposal Facilities
Manual that is concerned with sizing and layout of collector drains.
(3) Hazardous Waste Leachate Management Manual by Monsanto Research.
The outflow quantities to collector drains determined in the present
manual will become an indirect input to the Hazardous Waste Leachate
Management Manual.
2. APPLICABLE OPERATING CONDITIONS
This manual has been prepared with the assumption that the operating
conditions for a hazardous waste landfill or surface impoundment meet
the basic requirements of good engineering design. For example, in
the case of landfills it is presumed that:
(1) surface water run-on has been intercepted and directed from the site
so that only the rainfall impinging directly on the landfill need be
accounted for,
(2) proper precautions have been taken to insure the integrity of cover
soils so that erosion will not degrade cover performance,
(3) synthetic liners have been properly installed so that their integrity
is assured for their design life,
(4) ground water flowing laterally into the landfill has been intercepted
or otherwise diverted around the site,
(5) artesian pressures in strata underlying the landfill have been re-
lieved so that the hydrostatic head in the artesian aquifer lies
below the base of the landfill,
(6) during construction of the landfill water on the site has been
controlled, and
(7) the designs proposed for the components of the landfill itself
form a properly functioning system.
In the case of hazardous waste lagoons it is presumed that:
(1) inlet and outlet structures have been designed and rate of flow
controlled so that there is no danger of scour of liners,
(2) freeboard design and slope protection result in no detrimental wave
action.
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This manual is not intended to provide a means of proving that a
poor design will not work. Its purpose, rather, is to allow the evalu-
ator to confirm the adequacy of the design. It is the responsibility
of the design engineer to propose an adequate design initially. Never-
theless, the principles used in the evaluation procedures described in
this manual are in accord with the established principles of engineering
analysis. Moreover, an attempt has been made to present the physical
principles employed in these evaluation procedures in such a manner that
a design engineer could, if he so desired, choose to use the same prin-
ciples in arriving at a proposed design.
3. APPLICABLE DESIGN CONFIGURATIONS
It would not be practical or appropriate in this manual to specify
exact configurations for hazardous waste landfill or surface impoundment
designs. Rather, the approach followed here is to describe analytical
procedures for evaluating the transort of liquids through simple modular
configurations. With these analytical tools at his disposial, the evalua-
tor can then interconnect several modles to simulate the specific config-
uration to be evaluated.
Figure 3.1 shows a hypothetical landfill cross-section including
final cover, waste cells, intermediate or daily cover, and a drain and
liner resting on undisturbed ground. Modules can be delineated as fol-
lows:
(1) final cover with adjacent waste cell beneath,
(2) intermediate cover with adjacent waste cells above and below, and
(3) drain and liner system consisting (from top to bottom) of adjacent
waste cell above, sand drain layer, synthetic liner and underlying
undisturbed ground.
3.1 Functional Characteristics of Design Modules
Although Figure 3.1 represents only one of a variety of configura-
tions that might be proposed, the modules will be examined in some de-
tail to delineate the functional characteristics of each unit. This
examination will form the basis for abstracting physical characteristics
to be included in the modules for which analytical techniques will be
presented. The configuration described here is hypothetical only and
does not necessarily constitute a recommended design.
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The final cover shown in Figure 3.1 is redrawn in more detail in
Figure 3.2a. It consists from bottom to top of:
(1) the waste,
(2) an undifferentiated leveling layer whose purpose is to provide
an even, reasonably firm base and controlled slope upon which to
construct the final controlled cover,
(3) a low permeability compacted clay liner to retard the rate of downward
movement of liquid,
(4) a high permeability sand or gravel drain to provide a horizontal
pathway along which liquid collected on the clay liner can be trans-
mitted to collector drains for diversion away from the landfill, and
(5) a vegetated topsoil layer to provide both an opportunity for evapo-
transpiration to return liquid to the atmosphere and to provide a
trafficable, erosion resistant surface upon which precipitation can
be encouraged to flow horizontally for collection in drains and sub-
sequent diversion away from or recirculation through the landfill.
The intermediate cover is drawn in more detail in Figure 3.2b. It
consists of:
(1) underlying waste,
(2) a somewhat controlled layer of soil whose purpose is to provide
a trafficable working surface and temporary diversion of water, and
(3) overlying wastes.
The underlying drain and liner system is drawn in more detail in
Figure 3.2c. It consists from bottom to top of:
(1) the undisturbed native soil to which the transmission of contaminated
liquid must be controlled,
(2) a very low permeability synthetic liner to restrict and control down-
ward movement of liquids into the native soil,
(3) a high permeability sand or gravel drain whose purpose is to pro-
vide a horizontal pathway along which liquid that collects on the
synthetic liner can be transmitted to the collector drains for di-
version away from the landfill, and
(4) the overlying waste.
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vegetation
t o p s o i I
sand drain
clay liner
undifferentiated
leveling layer
waste
(a) detail of cover
waste
intermediate cover
waste
(b) detail of Intermediate cover
waste
sand drain
drain
synthetic liner
native soil
(c) detail of drain and liner system
Figure 3.2 - Detail views of modules constituting
landfill cross-section of Figure 3.1.
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3.2 Categorization of Functions of Design Units
The various layers described above perform differing functions
with respect to the transmission of liquid through the landfill.
Some are included for the purpose of controlling vertical flow of
liquids because of their low permeability; e.g. (from top to bot-
tom) the clay liner in the final cover, and the synthetic membrane
in the bottom liner. The purpose of other layers of high permeability
is to encourage flow to drains, e.g., the sand or gravel drain in the
drain and liner system. Some layers are included because they are able
to reduce the quantity of liquid available for leachate formation
due to their evapo-transpiration properties; e.g., the topsoil.
Finally, some layers serve functions not primarily concerned with
their ability to control transmission of liquids; e.g., (from top
to bottom) undifferentiated leveling layer, waste, and intermediate
cover.
3.3 Definition of Units to be Included in the System for Control
of Liquid Transmission
The above observations form the basis for the first axiom in
evaluating the adequacy of containment in a hazardous waste sur-
face impoundment:
Certain units within the design have as a primary purpose
the control of liquid transmission. These units should be
clearly delineated and their intended functions described
by the designer in the design documents. When the adequacy
of these units for performing their intended function is
evaluated they should serve to control the transmission of
liquids.
In submitting the facility plans the designer should:
(1) have specifically referred to the unit as one intended for
control of liquid transmission,
(2) have described how the unit will function to achieve this
control,
(3) demonstrate that he has quantitatively assessed control
capabilities of the unit in a rational manner, and
(4) demonstrate that the unit can be reasonably expected to
serve this function when constructed according to the speci-
fications given in the design.
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When reviewing these plans, units that do not meet all of these
criteria should be considered only to provide a safety margin above
the basic control requirements and should not be taken into considera-
tion in evaluating the adequacy of the system to meet minimum control
requirements.
3.4 Liquid Diversion Interfaces
It is evident from Figure 3.2 that many of the units that
serve to control liquid transmission occur as modules consist-
ing of an interface between two layers. There exist several
distinct interfaces above which liquids are usually transmitted
rapidly and in a horizontal direction, and below which liquids
are usually transmitted slowly and in a vertical direction.
It is the contrast in hydraulic transmissibility from high to low
that accomplishes the change in flow direction from predominantly
vertical to predominantly horizontal, thus diverting the flowing
liquids to collector systems for subsequent conduction from the site.
Exampls are:
(1) the interface between the atmosphere and the vegetative
cover,
(2) the interface between the sand drain and the compacted clay
membrane in the final cover, and
(3) the interface between the sand drain and the synthetic
membrane in the bottom liner system.
3.5 Construction of Liquid Routing Diagrams
Figure 3.3 is a liquid routing diagram showing the several
units comprising a landfill and clearly designating by the let-
ters LTC those that are considered to be part of the Liquid
Transmission Control system. Shown also is a series of lines
and arrows that explain the routing of liquid on its course through
the liquid transmission control system. The interfaces which are
composed of high transmissibility units overlying low transmissi-
bil ity units and which serve to divert flow direction from verti-
cal to horizontal are designated by the symbol DI for Diversion
Interface. This suggests the first step in the evaluation proce-
dure:
If the designer has not already done so, construct a liquid
routing diagram for the landfill. Designate the units that
are considered to be part of the liquid transmission control
system by the symbol LTC. Determine the location of diversion
interfaces and label them DI. Use arrows to show the liquid
transmission control mechanisms. If the designer has pro-
vided such a diagram, the evaluator should confirm that it
represents an appropriate diagram for use in evaluating the
proposed design.
9
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evapo-transpiration (LTC)
vegetation (LTC)
topsoll (LTC)
sand drain (LTC)
clay .liner (LTC)
undifferentiated
leveling layer
waste
intermediate cover
waste
sand drain (LTC)
synthetic liner (LTC)
undisturbed soil
Figure 3.3 - Liquid routing diagram showing intended
functions of components of leachate
containment system.
10
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4. OVERVIEW OF ANALYTICAL METHODS
4.1 Introduction
In section 3.4 it was observed that many modules intended to
control transmission of liquids through landfills and surface impound-
ments consist of an interface overlain by a high transmissibility mater-
ial (such as the atmosphere or a sand or gravel layer) and underlain by
a low transmissibility material (such as compacted clay or synthetic
membrane). The low transmissibility material diverts a portion of flow
from vertical to horizontal at the interface and allows another portion
of the flow to continue vertically through the liner. The more ef-
ficient the design, the larger will be the portion of liquid diverted
to horizontal flow. The purpose of this chapter is to examine the princi-
ciples that govern this process and to develop equations for for quanti-
quantitatively predicting the relative proportions between the flow that
is diverted to a horizontal direction and the flow that continues to move
vertically.
4.2 Horizontal Flow Through Sand and Gravel Drain Layers
Figure 4.1 shows the conditions assumed for calculating flow
in sand and gravel drain layers. Figure 4.la shows a layer of
thickness d(m) overlying a low permeability material. The system
slopes symmetrically at an angle a (exaggerated in this
drawing) down to drains spaced a distance L (m) apart. The satur-
ated permeability of the drain layer is ks (m/sec). Liquid
impinges upon the system at a rate of e (m/sec). The source of
this liquid could be rainfall, recirculated leachate or liquid
generated by the waste.
In the limiting case of a = 0 (shown in Figure 4.1b) the
shape of the water mound that accumulates in the drain layer has
been given by Harr (1962) as
1/2
h =(•£- (L-x)x) (4.2.1)
V Kc /
The maximum value of h occurs at x = L/2 for a horizontal liner and is
given by
. o,l/2
11
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I 1 1 4 I I I I I I I
J I I I I I !
t I
h h.
'ilia x
- L •
(0)
I I I I i II I I I I
F1
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As an example, consider the case of a flat liner
having drains placed 30 m 1~ 100 ft.) apart in a sand having
k = 1X10"3 cm/sec = 1X10~5 m/sec. Assume an annual rain-
fall of 100 cm/yr (39 in/yr) equally distributed in time so that
e = 3.17X10-8 m/sec.
Thus Q 97 O/^
, _/3.17X10"° m (30r nr sec \ ,. 9 ,,
max"i 4 seclXlO-5 J ( ]
= 0.84 m
An upper bound on the quantity of liquid flowing into the drains
(assuming no penetration into the liner) is given by
q = eL (4.2.4)
= 100 cm 30 m m
yr 100 cm
= 30 m-Vyr/m of drain
= 8000 gallons/year/m of drain
This calcultion is based upon the fact that at steady-state all
of the liquid that impinges on the drain layer must be carried by
the collector pipes.
Obviously, it is impractical to design an open-topped, flat-bottomed
landfill. Equation (4.2.2), however, provides a simple computational pro-
cedure for setting a bound on the thickness, d, required for the drain
layer. Thus if d exceeds hmax, there will be no danger of leachate over
filling the drain layer and rising into the hazardous waste.
The concept of a bound is often quite useful in engineering
design, particularly when considered.in conjunction with what
might be called "other factors." Suppose, for example, that in
the above calculations hmax had been found to be 10 cm (4 in).
The designer might then wish to specify that the drain layer be
made 10 cm thick under the premise that
(1) this thickness would satisfy the bound criterion,
(2) usual construction procedures make it impractical
emplacing a layer thinner than approximately 10 cm, and
13
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(3) the cost of placing the bounding thickness might not be
significantly different from the cost of placing a lesser
thickness based upon a more exact analysis.
The same rationale, of course, holds for the collector drain
lines. Designing them to accommodate a bounding flow based on
eq. (4.2.4) may be entirely feasible economically. Engineers
often consider overdesign based upon bounding solutions to be
acceptable practice in the case of one-time installations that
are located in physically inaccessible places. This is par-
ticlarly true when the impact of overdesign on the economics of
the operation is small.
In the case of the example problem, the 100 cm per year of liquid
impinging on the layer may be unrealistically high. If for example,
only 10 cm of liquid impinged upon the drain layer because
(1) the regional rainfall was less than 100 cm/yr,
(2) only a fraction of the rainfall infiltrated,
(3) losses occurred due to evapo-transpiration, and/or
(4) a portion of the inflow was diverted by overlying control
units,
then the bounding thickness would be only 0.27 m (10 in.).
This thickness is within the realm of practicality.
Alternatively, the designer could decrease L and/or choose a
sand or gravel with a higher ks (a ks of 0.1 cm/sec is
not impractical).
There are also other possibilities. Returning to
Figure 4.la, it can be seen that putting the drain system
on a slope a not equal to 0 tends to accelerate the flow
of water toward the collector system. Figure 4.1c shows the
accumulation profile, and it is very much like that of Fig-
ure 4.1b, epecially if <* is small. (In fact, the situation
of Figure 4.1b would be obtained by letting a approach 0.) The
configuration with a f 0 has some convenient properties when
compared with a = 0. The obvious one is that the hydraulic
gradient toward the drain pipe is higher. This advantage,
however, is not of greatest importance. The most signi-
ficant advantage is that if the liquid were to cease
impinging on the drain layer, the mound would completely drain
out into the collector drain pipes in a finite amount of
time if a is not equal to 0, whereas the drainage time for
a = 0 is infinitely long.
There will be a value for hmax as shown
in Figure 4.1c which is given by an expression similar to
eq. (4.2.2):
14
-------
+1 - ^tana + c (4.2.5)
where
c=f- (4.2.6)
Therefore, the evaluator may wish to encourage the
designer to adjust a, ks and/or L to comply with the bound-
ing criterion given in eq. (4.2.5). Figure 4.2 presents
hmax/L as a function of a for several values of c = e/ks.
4.3 Vertical Flow Through Low Permeability Clay Liners
4.3.1 Physical Principles
The physical laws governing liquid moving downward through
a low permeability clay liner are somewhat more complex than
those governing liquid moving in sand and gravel drain layers.
Because of the micropores that exist in clay soils, water moves
not only by the hydraulic head caused by gravitational forces
but also by capillary forces that tend to draw the liquid into
the soil. Figure 4.3 illustrates this situation. The smaller
the pore radius, the larger the capillary attraction force.
Thus soils with a high clay content will have very small micro-
pores and therefore very large capillary attraction forces. As
the grain size of the soil increases, the capillary attraction
force decreases; thus silty soils have lower capillary action
than clays. Sandy soils have such large micropores that capil-
lary attraction forces can reasonably be neglected as we in fact
did in section 4.2.
The magnitude of the attraction due to capillary action is
most conveniently measured in terms of a capillary potential, Y.
The units of ^ are in centimeters because it expresses the con-
tribution of capillary attraction forces to the hydraulic head
tending to move the liquid through the soil. Because pressure
is conveniently positive, v is negative. Figure 4.4 shows an
approximate range of values for v as a function of soil grain
size. The purpose of this figure is not to give numerical
values but rather to show that in clay sized soils the capillary
potential becomes very large.
15
-------
'max
••••••••M
L
0.10
0.08
0.06
0.04
0.02
,005
0.1
0.2
Ja tO n
.001
.0001
0.3
0.4
Figure 4.2 - Relationship between hmax/L and c = e/k$.
16
-------
gravity
capillary tension
Figure 4.3 - Partially saturated soil
showing menisci resulting in
capillary tension in pore water.
-IxlO1
(cm)
0 L-
clays silts sands gravels
mean grain size
Figure 4.4 - Capillary potential versus mean soil grain size.
17
-------
The real situation is even more complex. Because of the
variety of different grain sizes present in soils, there will
also be many different sizes of micropores. The smaller the
micropore, the larger will be the capillary force attracting
the water into the pore. As the moisture content of the soil
increases, the smaller pores fill up with liquid and thus the
capillaries tend to form in larger pores. The larger the pores
within which the capillaries form, the smaller the value of the
capillary potental. Thus, the higher the moisture content of
the soil, the lower will be the capillary potential. Figure 4.5
shows the experimentally determined relationship between moisture
content (e) and capillary potential (v) for a popular research
soil, the Yolo clay. Notice that the capillary potential passes
through 7 orders of magnitude as the soil goes from dry to
saturated. Moreover, when the soil is very dry the capillary forces
are so large that they usually dominate gravitational forces; how-
ever, as moisture content nears saturation the capillary forces
become so small that gravitational forces become dominant.
In practical applications, clay liners are usually compacted
at a moisture content well below saturation. For the Yolo clay,
the compaction moisture content might be around 0 = 0.20. From
Figure 4.5 the capillary potental of this soil just after com-
paction would be of the order of -1X10^ cm = -10 m (-33 feet).
Thus, in order for gravitational forces to be of the same order
of magnitude as the capillary forces, approximately 10 m of water
would have to be standing on top of the liner. This situation
would certainly be unacceptable in proposed landfill designs,
and would not likely be encountered in lagoons.
This leads to two important axioms in evaluating com-
pacted clay liners:
(1) during the early stages of wetting of a compacted clay liner,
capillary attraction forces will predominate over gravita-
tional forces; and
(2) as the clay liner becomes wetter the capillary forces
decrease in importance; and, when the liner is saturated,
these forces become negligible in comparison to gravi-
tational forces.
During the life of a surface impoundment, the moisture con-
tent in the liner will gradually increase from the value at which
the liner was compacted to the saturation water content. The
process will, of course, not be uniform through the depth of
the liner; rather, the top of the liner will become saturated
very quickly and a wetting front will move downward through
the liner. Figure 4.6 shows this process for the Yolo clay
under condi cons such that water is always present at the top
of the liner but the depth of standing water is negligible.
It can be seen, for example, that the wetting front moves on
the order of 75 cm (30 in) in the first 10° sec (11.6 days).
The saturated permeability of Yolo light clay is 1.2X10"5
cm/sec. 18
-------
capillary
potential,
(cm)
0 .1 .2 .3 .4 .5
moisture content, &
Figure 4.5 - Capillary potential as a function
of water content for Yolo clay
(from Philip, 1969).
19
-------
moisture content,Q
0
40 -
depth,
I (cm)
80 '
120
Figure 4.6 - Computed moisture profiles for
infiltration into Yolo light
clay (from Philip, 1969)
20
-------
Assuming saturated flow under a unit hydraulic gradient,
the liquid would require
75 cm ,sec = 6.25X106 sec = 72 days
1.2xl(T5 cm
to travel the same distance. Thus in this particular situation
the rate of initial infiltration is 6.5 times as rapid as steady
state saturated flow under a unit hydraulic gradient.
Philip (1969) showed that for infiltration into
Yolo light clay under the above conditions, a time of 1X10^
sec (11 days) is required before gravitational forces equal capil-
lary forces in importance. We know then that throughout the 75
cm of infiltration shown above, capillary forces were dominant.
(It should be noted that Yolo light clay would be a marginal liner
material. The data for this soil have been used primarily because
of their availability.)
The above discussion has important implications with respect
to the evaluation of landfill liners:
(1) If the evaluator is interested in determining the time re-
quired for saturation of a clay liner (which, in turn, repre-
sents the time to first appearance of leachate at bottom of
liner), then the approach to analysis should be based upon
the predominance of capillary forces.
(2) If the evaluator is interested in determining the rate at
which liquids will move through the liner on a long term
(steady-state) basis, then the approach to analysis should
be based upon saturated flow under gravitational forces.
4.3.2 Overview of Analytical Approaches
In this section the basic principles of analytical ap-
proaches will be described. The mathematics is com-
plicated; however, it is important that the evaluator have
an overview of these principles even though simpli-
fied mathematical equations will be given for application to
the evaluation procedure.
The theory of infiltration is based upon the premise that
Darcy's law holds for the transport process. Conceptually,
Darcy's law states that the velocity of flow of water, U, is
negatively proportional to the spatial change, v<|>, of a driving
potential function,* . The constant proportionality is k.
Thus
21
-------
U = -kA , consists of two parts:
(1) the capillary potential,^, as previously defined, and
(2) the gravitational potential, z, taken positive downward.
Thus
<|> = y - z (4.3.4)
and eq. (4.3.3) becomes
li - a f.- aCv-z) 1 u . ,_v
at ' az L az J (4.3.5a)
(4.3.5b)
3Z ^ '
k |t-k| (4.3.5C)
22
-------
2*. (4.3.5d)
3z r zz az '
The principal difficulty with eq. (4.3.5) is that the de-
pendent variable on the left side is , while the dependent
variables on the right side are y and k. This can be remedied
using the chain rule for differentiation:
- _ dk 36
3t 3z 1K de 3z; ~ de" 37 (4.3.6)
Note that the total differentials are used in the case of dy/de
and dk/de because these relationships are functions of neither
time, t, nor space, z. In fact dv/de has already been given
in Figure 4.5 for the Yolo light clay. For completeness, Fig.
4.7 presents the relationship between k and e from which dk/de
can be determined.
It is notationally convenient to define two new parameters
to represent two of the quantities in eq. (4.3.6):
D 5 k f (4-3-7>
and
K f dk/de (4.3.8)
so that eq. (4.3.6) becomes
'- afi \ 38
- K^T (4-3.9)
This equation has the desirable property that the dependent
variable is moisture content, e , on both sides. Thus it can be
solved in conjunction with initial conditions and boundary
conditions for a particular situation to give moisture content
as a function of position and time.
23
-------
12
10
permeability,
kxlO6
(cm/sec)
6
,4
0
Q ,1 .2 .3
moisture content, a
Figure 4.7 - Relationship between hydraulic
conductivity and water content
for Yolo light clay (from Philip, 1969)
24
-------
Be assured, however, that eq. (4.3.9) is not very easily
solved. Nevertheless, solution techniques are available (c.f.
Philip, 1969, and Parlange, 1971a, b, c, 1972a, b, c, d, e, f),
and the evaluator should be prepared to accommodate the innova-
tive designer who has manipulated the undesirable mathematical
attributes of eq. (4.3.9) into desirable design attributes for
landfill liners.
However, for purposes of evaluating landfill liner designs
it is necessary to transform eq. (4.3.9) into a more tractable
form. In doing this it is important that the essential attributes
of eq. (4.3.9) not be lost in a sea of empiricism. The basic form
of eq. (4.3.9) must be retained, but it should be written in
a way such that it can be solved with a reasonable amount of effort,
An approach to accomplish this was described by Philip (1969) and
involves linearizing the equation.
4.3.3 Linearized Approach to Analysis
The principal difficulty with eq. (4.3.9) is that the trans-
port coefficients D and K are not constants; they vary greatly
with position, z, and time, t. Both quantities can easily undergo
excursions of value of several orders of magnitude. Nevertheless,
it is possible to write eq. (4.3.9) in linearized form:
M. = A/D* 11 \_ K* 21 (4.3.10)
3t 3Z \U 3Z ) 3Z
where the tilde implies approximation based upon the linearizing
assumption of D* and K* constant. Under these conditions eq.
(4.3.10) becomes
_ r\ ^
i§. - n* 3 6 i/*89 (4.3.11)
3t " U 2 " K 37
Linearization, of course, has its price. First, the
results of eq. (4.3.11) may be in error—for example 9 may differ
significantly from e. Second, the values for D* and K* must be deter-
mined from laboratory experiments that approximate field conditions
as closely as possible.
Nevertheless, integral properties such as infiltration rates
and distance of advance of the wetting interface can be predicted
with acceptable accuracy by means of the linearization technique.
25
-------
4.3.4 Linearized Approach to Predicting Time of First Appearance
of Leachate
In the early stages of infiltration (i.e., when the liner
is wetting up) the first term on the right side of the eq. (4.3.11)
will dominate. (Careful examination of the manipulations in eqs.
4.3.5a through d shows that the D* term represents the capillary
attraction part of the process.) The eq. (4.3.11) can be written
(4.3.12)
We now impose the following initial and boundary conditions:
(1) At initial time (t=0) assume that the moisture content is
equal to e^ throughout the depth of the liner:
e = e. for z> 0 and t = 0 (4.3.13)
(remember, z is positive downward).
held at the saturation moisture content, e :
(2) At all times at the boundary (z=0) the moisture content is
.ion moisture content, e :
= es for z = 0 and t >_ 0. (4.3.14)
The solution to eq. (4.3.12) for the initial and boundary
conditions of eqs. (4.3.13) and (4.3.14), respectively, is:
= 61 + (es - e.) erfcf
(4.3.15)
where erfc is the complementary error function as given in Figure
4.8. This function can be called in most computer programming
languages, and is tabulated in many books of mathematical tables
(c.f., Crank, 1975).
Equation (4.3.15) is not particularly useful for the
evaluation procedure because we are not especially interested
in predicting moisture content profiles. More practical for
the evaluator would be the ability to predict the time required
for the wetting interface to penetrate the clay liner. This
26
-------
erfc(X)
1.0
.9
.8
.7
.6
5
.4
.3
.2
.1
1.0
X
1.5
2.0
Figure 4.8 - Complementary error function.
27
-------
can be done easily if a few simplifying approximations are
made. These are illustrated in Figure 4.9. The principal sim-
plification lies in the assumption that the soil extends below
the depth represented by the thickness of the liner. Thus the
"infinite depth" solution of eq. (4.3.15) is applicable. It
is also assumed that the wetting interface has reached
the bottom of the liner when an amount of moisture has entered
the top boundary sufficient to saturate the soil to a depth, d,
equal to the thickness of the liner. The relationship for the
total amount of liquid entering up to time, t, is given by
Mt = 2(es - 01)
(4.3.16)
The quantity of liquid required to saturate the liner to a
depth, d, is given by
M. =
(4.3.17)
Equating (4.3.16) and (4.3.17) yields
(4.3.18)
Though only approximate, eq. (4.3.18) does yield a bounding
value for use in evaluating the delay time that a clay liner pro-
vides.
It should be pointed out that for relatively thick liners
or for soils having relatively low capillary potential, it would
be more appropriate to apply eq. (4.3.11) without neglecting
the last term. In this case the solution for the initial and
boundary conditions given by eqs. (4.3.13) and (4.3.14), respectively, is
given by Philip (1957) as
(4.3.,9)
which is slightly more complicated than eq. (4.3.15); and in
addition requires that the designer provide an appropriate value
for K*. In order to predict the time required for the wetting
front to penetrate the liner, we write the expression equiva-
lent eq. (4.3.16):
28
-------
moisture content,
depth,
i
Figure 4.9 - Simplified geometry for calculating
time for liquid to penetrate liner,
29
-------
"t = (es - ei
D* ,
erf
erfc
4D*
(4.3.20)
which would produce the penetration time, t.
Introducing eq. (4.3.17) into eq. (4.3.20) gives:
(4.3.21)
Eq. (4.3.21) cannot be solved explicitly as was eq. (4.3.18); how-
ever, trial and error solution can be used to solve for the
penetration time, t.
4.3.5 Linearized Approach to Predicting Leachate Flow When
Liquid Has Ponded on Liner
In the case of a surface impoundment lagoon where liquid
has ponded on the top of the liner, eq. (4.3.6) still holds,
however the boundary conditions become
e =
for t = 0 and z > 0
(4.3.22a)
and
= h for z = 0 and t > 0
(4.3.22b)
For these mixed boundary conditions the most efficient solution
procedure involves re-examining eq. (4.3.5d):
30
-------
3^__3/,3!\ _3k_
3t ~ 3Z \ 3Z / " 3Z
(4.3.5d)
with
D = k
do
(4.3.7)
and
- dk
- cle"
(4.3.8)
Now from eq. (4.3.5d)
d§_ 3t_ _ 3 /. 3¥_
df 3t 3Z \ 3Z
32
(4.3.23a)
D at 3z\3z/ "dedvsz
(4.3.23b)
_
D 3t " 3Z 3Z
\ . Kk a*.
; D 3Z
(4.3.23c)
3t
JL J_ 3*
k 3Z
3
(4.3.23d)
31
-------
This diffusion equation in 0
(4.3.25a)
and
= hg for z = o and t ^ 0
(4.3.25b)
where Y-J is the value of capillary potential corresponding
to the initial moisture content, 6|. The solution to eq.
(4.3.24) subject to boundary conditions (4.3.25) is:
erfc
(4.3.26)
Eq. (4.3.26) can be used to predict the first appearance
of leachate using the following approach. It will be assumed
that the wetting interface has reached a distance, d, equal to
the thickness of the liner when the moisture content at the base
of the liner is (6-j +es)/2; or when
6 .+6
1 S
Thus in eq. (4.3.26) set
and z = d:
32
-------
,.+es =
erfc
d-K*t
2/D*t
+ exp -s*- erf
dK*t
\
(4.3.27)
4.3.6, Linearized Approach to Predicting Leachate Flow Rates
After Saturation
After the clay liner has become saturated, the flow process
is dominated by gravitational forces, the capillary potential
approaches the pressure head in the water, hn, and the water
content (which is at saturation) no longer changes with time.
In this case in eq. (4.3.5a):
36
at
(4.3.28)
and
(4.3.29)
where ks is the saturated hydraulic conductivity, more commonly
referred to as the Darcy coefficient of permeability. Equation
(4.3.5a) becomes .
' »(yz) 1 (4.3.30a)
0 =
3Z
(4.3.30b)
= k
(4.3.30c)
or
where
32h
= 0
h - hp - 2
(4.3.30d)
(4.3.31)
33
-------
is the total hydraulic head (remember, z is positive down-
ward). Equation (4.3.30d) is known as the LaPlace equation.
The solution for flow velocity is simply obtained as
v = k.
3h
(4.3.32)
The total quantity of liquid passed by the clay liner in time,
At, is given by
q = kc
ah
(A)At.
(4.3.33)
For the Yolo light clay with ks = 1.2x10"^ cm/sec, a unit
hydraulic gradient, an area of 1 square foot, and a time of 1 year:
q -
1.2X10"5 cm 1 ft2 1 vr 31.5X1Q6 sec
ft 7.48 gal
sec
yr 30.5 cm
ft*
= 93 gal/yr/ftr.
(4.3.34)
4.4 Efficiencies of Liner-Drain Layer Systems
The efficiency of a liner-drain layer system is a quanti-
tative measure of the proportion of liquid that moves through
the drain layer and is collected by the drain collector lines,
relative to the proportion that seeps into the liner. Wong
(1977) proposed an approximate technique for quantifying
this, based upon saturated Darcy flow in both the drain layer and
the clay liner. Figure 4.10 describes the geometry assumed
in his calculations.
34
-------
I
C
£ ^
"w ^
Q 05
>» O
u ^
u
0*
u
r—
3
t.
O
a.
2
c:
c
i
o
en
35
-------
The approach postulates that at some initial time a rec-
tangular slug of liquid is placed upon the saturated liner to
a depth h0. The liquid flows both horizontally along the slope
of the system and vertically into the clay liner. The fraction
of liquid moving into the collector drain system at time, t, is
given by
-i- = l - -}- (4.4.1)
so *1
and the fraction of liquid seeping into the clay liner is given
by
Ji_
hn "
where
s
V kTTW <4-4-3'
<«•«•«>
V$1
and
s = length of saturated volume at time, t (cm)
h = thickness of saturated volume at time, t (cm)
SQ = initial length of saturated volume = L/2 sec(a) (cm)
hQ = initial thickness of saturated volume (cm)
ksi = saturated permeability of the material above clay liner (cm/sec)
kS2 = saturated permeability of the clay liner (cm/sec)
a = slope angle of the system (°)
d = thickness of the clay liner (cm).
Figure 4.11 shows the geometry at some time, t.
The efficiency of the liner is easily determined with
reference to Figure 4.12 which graphs h/hp versus S/SQ and
t/t]. Equations (4.4.1) and (4.4.2) can be solved paramet-
rically in t/tj, to yield the line shown on the figure. (The
line is actualTy a curve; however, for practical liner-drain
layer configurations it can be approximated as a straight
36
-------
Figure 4.11 - Geometry for calculating effeciency
of drain - liner systems, (after Wong, 1977)
h/h,
1.0
t/t.
Figure 4.12 - Diagram for computing efficiency
of drain - liner systems.(after Wong, 1977)
37
-------
line.) In this case the efficiency of the system is given
by the area labelled f in Figure 4.12. This area is most easily
determined by calculating the value of h/ho when t/t] = 1.0
(or S/SQ = 0). This value is called n and can be obtained by
solving eq. (4.4.2) with t/t] = 1.0:
The value of n can be either positive or negative; however, most
efficient designs will have n>0. The efficiency is given by either
f = -- for n^O (4.4.6)
or
(4.4.7)
Thus the efficiency varies from 0 to 1.0.
The quantity of liquid draining out of the system is given
by:
amount collected in drains = f x hQ (4.4.8)
and the quantity of liquid seeping into the liner is given by:
amount seeping into liner = (1-f) x hQ (4.4.9)
As an example, consider a system having a Yolo clay liner
(ks2 = 1.2X10~5 cm/sec) that is 75 cm thick, overlain by a
gravel layer having k$2 = 0.1 cm/sec. The entire system
slopes at 4 ft/100 feet and the drain spacing is 30 m. Assume
that an initial slug of liquid 10 cm thick impinges upon the system.
38
-------
a = 2.3° (4 ft/100 ft)
ksi =0.1 cm/sec
kso = 1.2X10'5 cm/sec
a = 75 cm
SQ = L/2 sec a = 30 m/2 sec (2.3°) = 1500 cm
From eq. (4.4.4),
„ /1500 1/1.2X10 i „„*. /o i°\ a n£
C = I -=?F|| T 1 c°t vt.o ) -uo
From eq. (4.4.5), '
i 75 e-.06 75
n = ] + 10 cos(2.3°) " 10 cos(2.3")
= .507
and from eq. (4.4.6)
* 1+-507 _ 7r«
f = __- /M
Thus 75% of the liquid is diverted to the drains.
5. PROCEDURE FOR EVALUATING PROPOSED DESIGNS
5.1 Outline of Procedure
The procedure for evaluating proposed designs as shown
in Figure 5.1 is as follows:
(1) select a typical cross-section through the landfill from
the design drawings (more than one cross-section may
require evaluation);
(2) construct a liquid routing diagram as shown in Figure 3.3;
(3) isolate liquid diversion modules consisting of low permeability
layers overlain by high permeability drain layers;
(4) determine the amount of liquid impinging upon the first module;
(5) calculate the bounding height of free standing liquid within
the drain layer using eq. (4.2.2) or (4.2.5);
(5a) compare the ratio of this height to the thickness of the
drain layer with the ratio deemed to be appropriate for the
site-specific conditions;
39
-------
j Tj select typical cross-section _ j
4 _ ,
J2J construct liquid routing diagram j Fig. 3.3 [
assess the ade-
quacy of the
thickness
6a
tabulate partial
sums of retention
times
1
1
—
13 I isolate liquid diversion modules
determine amount impinging
calculate bounding
height of free
standing liquid
Eq. 4.2.2 or 4.2.5
calculate time for
liquid to penetrate
liner
Eq. 4.3.18 or 4.3.21
assess
efficiency of
liner-drain nodule
use (a) impingement
rate from step 4 or
(b) steady state seep-
age rate from step 7
as input
li
calculate steady
state seepage rate
through liner
Eq. 4.3.32
calculate
efficiency of
liner-drain module
Eqs. 4.4.4-"4.477
NO
was last liner
the bottom 1 iner?
In
calculate total
retention time by
summing partial
retention times
t*.
assess the adequacy,
of the retention
time
YES
assess the
appropriateness of
the steady state
seepage rate
Fig. 5.1 - Flow chart of procedure used to evaluate containment.
40
-------
(6) calculate the time required for water to completely permeate
each clay liner using eq. (4.3.18) or (4.3.21);
(6a) tabulate the retention time for the modules;
(7) calculate the steady-state seepage rate through the saturated
liner using eq. (4.3.32);
(8) calculate the efficiency of the liner-drain module using
eqs. (4.4.4), (4.4.5), and (4.4.6) or (4.4.7);
(8a) compare with the efficiency deemed to be appropriate for
the site specific conditions;
(9) determine whether or not all modules in the liquid routing
diagram have been evaluated;
(10) if there are more modules, use the lesser of (a) the impingement
rate from step 4 or (b) the steady-state seepage rate calculated
in step 7 as the impingement rate on the subsequent module;
(11) if this module is the last module, compare the steady-state
seepage rate calculated in step 7 with the steady-state
seepage rate deemed to be appropriate for the site specific
conditions;
(12) if this module is the last module, also calculate the total
retention time by adding the partial sums from step 6a for
each module;
(12a) compare the retention time calculated in step 12 with the
retention time deemed to be appropriate for the site
specific conditions.
Table 5.1 summarizes the equations used in the procedure.
5.2 Information Required to Use Evaluation Procedure
The input required to use the evaluation procedure is shown
in Figure 5.2.
5.2.1 Input From Other Manuals
Input required to use the evaluation procedure is obtained
from two other manuals:
(1) The Hydrologic Simulation on Solid Waste Disposal manual
provides input to step 4 (amount of liquid impinging on first
module). This quantity is available on a daily basis as the
quantity, Q. The evaluator may wish to express these values
on a monthly average basis. Alternatively, monthly percola-
tion can be determined using the Water Balance Method of Fenn,
Hanley, and DeGeare (1975).
41
-------
Table 5.1
Summary of Equations
Eg. Number
4.3.32
4.4.4
Equation
2\ 1/2
f. f. . C.
(or 4.2.5)
4.3.18
(or 4.3.21)
"max |
t -
N
\ /
TT d2
4 D*
v = k.
h
C = -4 r^- COt a
d k
si
Purpose
Predict maximum rise of liquid
in sand drain
Predict time to first apperance
of liquid at base of clay liner
Predict steady state seepage rate
through saturated clay liner
Predict steady state seepage rate
through saturated clay liner
4.4.5
4.4.6
or
4.4.7
1 +
f =
hgCOSd
f =
f* rl
e" - . Predict steady state seepage rate
nO through saturated clay liner
if n>0
if n < 0
Predict steady state seepage rate
through saturated clay liner
Predict steady state seepage rate
through saturated clay liner
42
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information from Hydro!oqic
Simulations on Solid Haste
Disposal Manual
information from Lining of
Waste Impoundre'it R Disposal
Facilities nanual
information • '"otn proposed
plans and specifications
information obtained by
considering site specific
conditions
] 2
1 3
i
.diversion"module" (?
i
Q
d,.ic
\
V \\\
o \\\ \\
|6a
T
I
10
,«J1.d2.K1.K2
:<>t!
N
E
Fiaure 5.2 - Sources of inout infornation for evaluation procedure.
43
-------
(2) The Lining of Waste Impoundment and Disposal Facilities manual
provides effective permeability coefficients and design lives
for synthetic membranes to be used as input in step 6,7, and
8, respectively.
5.2.2 Input From Proposed Plans and Specifications
The evaluator will obtain several essential pieces of
information from the proposed plans and specifications for the
surface impoundment:
(1) the typical cross-sections to be used in step 1 should be
obtainable from the plans. These cross-sections will be
used to construct the liquid routing diagrams of step 2.
In addition, the designer may have provided liquid routing
diagrams in these documents;
(2) the liquid diversion modules may have been delineated by
the designer in the specifications and may also be shown on
the plans; and
(3) the following information must be provided in the plans and
specifications for each module:
(a) the thickness of the sand or gravel drain layer (to be
used in steps 5 and 8);
(b) the thickness, d, of the clay liner (to be used in steps
6, 7, and 8);
(c) the coefficient of permeability, kgn , for the sand or
gravel drain layer (to be used in steps 5 and 8);
(d) the infiltration coefficients, D* and K*, for the clay liner (to
be used in step 6);
(e) the initial compacted moisture content, 9.., for the clay
liner (to be used in step 6);
(f) the saturation water content, 0 , for the clay liner
(to be used in step 6);
(g) the coefficient of permeability, kS2, for the saturated
clay liner (to be used in steps 7 and 8);
(h) the slope, a, of the clay liner (to be used in step 8);
(i) the length, sg, from the high point of the liner to the
drain (to be used in step 8).
44
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5.3 Summary of Outputs of Evaluation Procedures
The output of the evaluation procedure will be used in
the manner shown in Figure 5.3.
5.3.1 Outputs to Other Manuals
The output of the present procedure will be used as input
to the Lining of Waste Impoundment and Disposal Facilities manual.
Specifically, the quantity of liquid moving through sand and
gravel drain layers and collected in drain lines as determined
in step 8 will dictate the quantity of water to be carried by the
collection pipes. Moreover, this quantity will become an indirect
input to leachate treatment considerations.
5.3.2 Output to Determine Whether Proposed Design is
Acceptable
The comparison of the proposed design's performance with
conditions appropriate for the particular site (performed in
steps 5a, 8a, 11, and 12a) will determine whether the proposed
design is acceptable with respect to control of leachate.
45
-------
information to be used in
Lining of Waste Impoundmen
in
& Disposal Fac. Manual
information to be used to
evaluate acceptability J 3 J
of design i—L
l!£
1 E
I
6a
LL
I
10
Fioure 5.3 - Output information from evaluation procedure.
46
-------
APPENDICES
47
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APPENDIX A
Example Hazardous Waste Landfill
A landfill is to be located in a critical groundwater region.
The landfill contains a section devoted to hazardous waste. This
section is isolated by a sand drain layer and compacted clay liner
both above and below the hazardous waste section. Figures A.I and
A.2 contain excerpts from the plans and specifications, respectively.
Solution to Hazardous Waste Landfill Problem
The solution procedure follows that recommended in the flow
chart of Figure 5.1.
Step 1. Select typical cross-section.
The plans give only one typical cross-section (Figure A.I),
so this cross-section is selected for analysis.
Step 2. Construct liquid routing diagram.
Excerpt 1 from the specifications deals with the leachate
control system and will provide the basis for constructing the
liquid routing diagram. The modules that are considered to be a
part of this system are the vegetated cover, the intermediate sand
drain and liner system, and the bottom sand drain and liner system.
The intermediate cover was not included because the designer provided
inadequate data to allow the evaluator to analyze its effects.
(LTC)
Liquid Routing Diagram
DI
(LTC)
V
48
-------
all slopes 9.6%
waste
vegetated
soil cover
Intermediate
cover
intermediate
sand drain layer
and clay 1 iner
hazardous waste
bottom sand
drain layer
and clay liner
native soil
Figure A.I - Excerpt from plans for proposed landfill.
49
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-excerpt 1-
CONTROL OF LEACHATE
Leachate will be controlled
by vegetated final cover, by
an intermediate sand drain layer
underlain by a compacted clay
layer, and by a bottom liner
overlain by sand. The clay for
both liners is compacted at 2%
above optimum water content and
to 95% of Standard Proctor
density. The sand layers are
carefully placed at controlled
thickness. Collector pipes are
placed as shown on the plans.
Intermediate cover will also
provide some degree of control
of liquid flow rates.
-excerpt 3-
LABORATORY TESTS ON CLAY
Laboratory permeability tests
were performed on the clay com-
pacted at 2% above optimum mois-
ture content to field density.
Water was initially allowed to
diffuse into the sample under
negligible hydrostatic head so
that the linearized diffusivity,
D*, was determined to be 5x10 "6
cm/sec. After D* was established,
back pressure was applied to
hasten saturation of the sample.
After saturation, the coefficient
of permeability, k , was found to
be? xlO"6 crn/sec.
-excerpt 2-
LABORATORY TESTS ON SAND
Laboratory permeability
tests were performed on the
sand compacted to the field
density and then saturated.
The coefficient of permea-
bility was found to be
1 x 10"? cm/sec.
Figure A.2 - Excerpts from specifications for proposed landfill
50
-------
Step 3. Isolate liquid diversion modules.
There are two liquid diversion modules: the intermediate
sand drain and compacted clay layer and the bottom sand drain and
compacted clay liner.
Step 4. Determine the amount of liquid impinging on the intermediate
module.
To accomplish this, the results of a water balance calculation
were used as input to the present analysis. The data for percolation
below the cover for a typical year are:
MONTH PRECIPITATION PERCOLATION(cm)
January 0 0
February 0 0
March 12.21 1.83
April 6.48 3.25
May 9.47 2.51
June 10.6 0.05
July 9.27 0
August 9.04 0
September 8.56 0
October 5.18 0.61
November 1.7 1.6
December 0 0
Annual 72.51 9.85
Two values will be used for analysis:
3.25 cm mo day hr min
Apr ~ mo 31 days 24 hrs 60 min 60 sec
= 1.2X10"6 cm/sec
Step 5. Calculate bounding height of free standing liquid.
Excerpt 2 from the specifications shows that the sand to be
used in the sand drain layers has a saturated permeability of
ks = 1X10-2 cm/sec.
Using eq. (4.2.5) for L = 30 m, ks = 1X10"2 cm/sec,
e = 1.2X10-° cm/sec and a = 5.48° (9.6%) gives:
51
-------
c =
1X10"^
h - 30 m /.2Xl(T7n[tan2 (5.48°) +
max ' 2 1.2X10-4
1.2X10
hmax = 8-2 cm
which is less than the design value of 30 cm.
Step 5a. Because hmax is less than 30 cm, the design is
acceptable.
Step 6. Calculate time required for liquid to appear at bottom of
liner.
Excerpt 3 from the specifications provides a value for linearized
diffusivity of D* = 5X10~5 cm /sec. Using this value in eq. (4.3.21)
with d = 75 cm (from Figure A.I) gives
. _ TT d2 _ (3.14U75)2 cm2 sec y_£ = 97
~ ~A~ n* ~ f\ 9 7 £/.
4 u 4 (5xlO~b) cm^ S.lxlO7 sec
Step 6a. Tabulate partial sum.
Partial sum = 27.5 years.
Step 7. Calculate steady-state seepage rate through saturated liner.
Excerpt 3 from the specifications provides a value for the
saturated coefficient of permeabiity of ks = 2X10~6 cm/sec. Using
this value in eq. (4.3.32) gives, for unit hydraulic gradient:
52
-------
2x10"5 cm (1)
sec
= 2 x 10~6 cm/sec
as the steady-state seepage rate.
Step 8. Calculate efficiency of liner-drain module.
The required data were obtained as follows:
SQ = 15 cos(5.48 ) = 15.1 m (plans, Fig. A.I)
d = 75 cm (plans, Fig. A.I)
k$2 = 2X1Q-6 cm/sec (excerpt 3 from specs., Fig. A. 2)
ksi = 1X10-2 cm/sec (excerpt 2 from specs., Fig. A. 2)
a = 9.6% = 5.48° (plans, Fig. A.I)
h = 3.25 cm = April percolation.
From eq. (5.1.4)
cot a
= 15.1 m 100 cm 2X10"6 cm sec cot (5.48°)
_o
75 cm m 1X10 sec cm
= 0.042
From eq. (5.1.5)
„.(,*
_
cosa / hQ cosa
3.25 cos(5.48°)
= (1+23.18)(.958)-(23.18) = -.015
53
-------
From eq. (4.4.7) since n<0
1 = 49%
n) 2(1 + .015)
Step 8a. Compare with efficiency appropriate for the site.
While adequate site-specific information is not available for
this site, the value of 49% is marginal. Values well in excess of 50%
would be more acceptable.
Step 9. Was liner the bottom liner?
No, therefore go to step 10.
Step 10. Use steady-state seepage rate of 1.2xlO~6 cm/sec from step
4 as amount of liquid impinging on bottom liner, then go
to step 5 for bottom liner. (Note that the rate of
2xlO~° cm/sec from step 7 exceeded the available mois-
ture.)
Step 5 and 5a. Same as for intermediate module.
Step 6. Same as for intermediate module.
Step 6a. Partial retention time = 27.5 years.
Steps 7,8, and 8a. Same as for intermediate module.
Step 9. Was liner the bottom liner?
Yes, therefore go to Step 11.
Step 11. Compare steady-state seepage rate from Step 4 with rate
appropriate for the site.
While adequate site-specific information is not available,
2xlO~° cm/sec could be acceptable.
54
-------
Step 12. Calculate total retention time.
Total retention time = 27.5 + 27.5 = 55 years.
Step 12a. Compare total retention time with that deemed v,o be
appropriate for the site.
While site-specific information is not available, 55 years
could be adequate.
55
-------
APPENDIX B
Example Hazardous Waste Lagoon Problem
The solution procedure follows that are recommended in the
flow chart of Figure 5.1. However, Steps 3, 5, 5a, 8 and 8a are
not applicable.
Step 1. Select typical cross-section.
The plans give only one typical cross-section (Figure B.I),
thus this cross-section is selected for analysis.
Step 2. Construct liquid routing diagram.
Excerpt 1 from the specifications states that the compacted
clay liner constitutes the only leachate control system. Because
there are no diversion layers the liquid routing diagram is quite
simple.
liquid
J
compacted
day
(LTC) Liquid Routing Diagram
native
soil '
t
Step 4. Determine amount of liquid impinging on the clay liner.
Amount consists of a static head of 2 meters.
56
-------
1iquid
waste
T
compacted clay
liner
75 cm
*
native soil
Figure B.I - Excerpt from plans for proposed lagoon.
-excerpt 1-
CONTROL OF LEACHATE
Leachate will be controlled
by a clay liner. The liner will
be compacted at e. = .24 moisture
content and to 95% of Stand Proc-
tor density. The saturated mois-
ture content is 9 = .495.
-excerpt 2-
LABORATORY TESTS ON CLAY
Permeability tests were per-
formed which yielded linear-
ized transport coefficient
values of K* = 2.3X1Q-8 m/sec
and D* = 1.3X10-1! m2/sec.
At a moisture content e. =.24,
the capillary potential was
¥ = .002 cm = 2X10-5 m. At
0 = (e. + e )/2 = .37,
-------
Step 6. Calculate time required for liquid to appear at bottom
of liner.
The time required for first'appearance of leachate is determined
using eq. (4.3.27) with y =2X10-5m, h = 2m, d = .75 m. * = 2.3XKT8
m/sec, D* = l.SXlO^V/sec, * at (e. + eJ/2 = 1.3X10-4m:
erfc .75-2.3X10"8t
2 /1.3XKHH
exP . .75+2.3X10^
1.3X1Q-'1 2 '1.3X1 0-1 U
Trial and error solution yields a retention time for the liner of 235
days.
Step 6a. Tabulate partial sum.
Partial sum = 235 days.
Step 7. Calculate steady-state seepage rate through saturated liner.
Excerpt 3 from the specification provides a valu£ of the
saturated coefficient or permeability of ks = 1.2X10~b cm/sec. This
value can be used in eq. (4.3.32) with
3 h = 200 cm + 75 cm = 275 cm
and
9 z = 75 cm
to give
q = 1.2X10"5 cm 275 cm 1 ft2 1 yr ft 31.5X106 sec 7.48 gal
sec 75 cm 30.5 cm yr ft3
= 340 gal/ft2/yr
as the steady-state seepage rate.
58
-------
Step 9. Was the liner the bottom liner ?
Yes, therefore go to Step 11.
Step 11. Compare the steady-state seepage rate from Step 7 with
rate appropriate for the site.
Site-specific information is not available; however, the rate
of 340 gal/ft2/yr is quite low.
Step 12. Calculate total retention time.
Total retention time is 235 days.
Step 12a. Compare with total retention time appropriate for the
site.
Site-specific information is not available.
59
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APPENDIX C
List of Symbols
c = constant defined by eq. (4.2.6)
C = constant in eq. (4.4.4) 2
D = diffusivity of partially saturated soil (cm /sec)
D* = linearized diffusivity (cm^/sec)
d = thickness of layer (m or cm)
e = liquid impingement rate (m/sec)
f = fraction of liquid collected by drain
h = hydraulic head (cm)
hQ = initial liquid head on liner (cm)
hp = pressure head (cm)
K = partially saturated permeabilty (cm/sec)
K* = linearized permeability (cm/sec)
ksl = saturated permeability of drain layer (cm/sec)
ks2 = saturated permeability of clay layer (cm/sec)
L = distance between drains (m)
n = parameter defined in eq. (4.4.5) (cm)
q = flow quantity (gallons/year)
Q = percolation rate from cover (cm/sec)
s = distance to trailing edge of draining liquid (cm)
SQ = distance from drain to break in slope (cm)
t = time (sec)
t-| = time for complete drainage (sec)
v = flow velocity (cm/sec)
x = horizontal coordinate (cm)
y = vertical distance (cm)
z = vertical coordinate (cm)
a = slope angle of liner or drain layer (°)
<}> = hydraulic driving potential
v = capillary potential (cm)
e = volumetric water content
ei = initial water content
QS = saturation water content
e = water content predicted by linearized equations
8 = partial differentiation
v = spacial gradient
-------
APPENDIX D
References Cited
Crank, J. (1975) The Mathematics of Diffusion. Clarendon Press,
Oxford, 398 pp.
Fenn, D. G., K. J. Hanley, and T. V. DeGeare (1975) Use of the
Water Balance Method for Predicting Generation From Solid
Waste Disposal Sites, Office of Solid Waste Management Pro-
grams, SW-168, U.S. Environmental Protection Agency, Cin-
cinnati , Ohio.
Green, W. H. and Ampt, G. A. (1911) Studies on Soil Physics, 1.
The Flow of Air and Water Through Soils, J. Agr. Sci., V. 4,
No. 1, pp. 1-24.
Harr, Milton E. (1962) Groundwater and Seepage. McGraw-Hill Book
Company, New York, 315 pp.
Klute, Arnold (1952) A Numerical Method for Solving the Flow
Equation for Water in Unsaturated Materials, Soil Sci.,
V. 73, pp. 105-116.
Mein, Russell G. and Larson, Curtis L. (1973) Modeling Infil-
tration During a Steady Rain, Water Resources Research,
V. 9, No. 2, pp. 384-394.
Parlange, Jean-Yves (1971a) Theory of Water-Movement in Soils: 1.
One-dimensional Absorption, Soil Sci., V. Ill, No. 2, pp.
134-137.
Parlange, Jean-Yves (1971b) Theory of Water-Movement in Soils: 2.
One-dirnensional Adsorption, Soil Sci., V. Ill, No. 2, pp.
170-174.
Parlange, Jean-Yves (1971c) Theory of Water-Movement in Soils: 3.
Two- and Three-dimensional Absorption, Soil Sci., V. 112,
No. 5, pp. 313-317.
Parlange, Jean-Yves (1972a) Theory of Water-Movement in Soils: 4.
Two- and Three-dimensional Steady Infiltration, Soil Sci.,
V. 113, No. 2, pp. 96-101.
Parlange, Jean-Yves (1972b) Theory of Water-Movement in Soils: 5.
Unsteady Infiltration from Spherical Cavities, Soil Sci.,
V. 113, No. 2, pp. 156-161.
61.
-------
Parlange, Jean-Yves (1972c) Theory of Water-Movement in Soils: 6.
Effect of Water Depth Over Soil, Soil Sci., V. 113, No. 5,
pp. 308-312.
Parlange, Jean-Yves (1972d) Theory of Water-Movement in Soils: 7.
Multidimensional Cavities Under Pressure, Soil Sci., V. 113,
No. 6, pp. 379-382.
Parlange, Jean-Yves (1972e) Theory of Water-Movement in Soils: 8.
One-dimensional Infiltration with Constant Flux at the Sur-
face, Soil Sci., V. 114, No. 1, pp. 1-4.
Parlange, Jean-Yves (1972f) Theory of Water-Movement in Soils: 9.
The Dynamics of Capillary Rise, Soil Sci., Vol. 14, No. 2,
pp. 79-81.
Philip, J. R. (1957) The Theory of Infiltration: 1. The
Infiltration Equation and Its Solution, Soil Sci., V. 83,
pp. 345-357.
Philip, J. R. (1957) The Theory of Infiltration: 2. The Profiles
of Infinity, Soil Sci., V. 83, pp. 435-448.
Philip, J. R. (1957) The Theory of Infiltration: 3. Moisture
Profiles and Relation to Experiment, Soil Sci., V. 84,
pp. 163-178.
Philip, J. R. (1957) The Theory of Infiltration: 4. Sorptivity
and Algebraic Infiltration Equations, Soil Sci., V. 84, pp.
257-264.
Philip, J. R. (1957) The Theory of Infltration: 5. The Influence
of the Initial Moisture Content, Soil Sci., V. 84, pp. 329
339.
Philip, J. R. (1957) The Theory of Infiltration: 6. Effect of
Water Depth over Soil, Soil Sci., V. 85, pp. 278-286.
Philip, J. R. (1957) The Theory of Infiltration: 7. Conclusion,
Soil Sci., V. 85, pp. 333-337.
Philip, J. R. (1969) Theory of Infiltration, Adv. in Hydrosci. 5:
215-305.
Smith, Roger E. (1972) The Infiltration Envelope: Results from
a Theoretical Infiltrometer, J. of Hydrology, V. 17, pp.
1-21.
Thornthwaite, C. W. and J. R. Mather (1955) The Water Balance,
Publications in Climatology, Laboratory of Climatology,
Vol. 8, No. 1.
62
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Thornthwaite, C. W. and J. R. Mather (1957) Instructions and
Tables for Computing Potential Evapo-transpiration and the
Water Balance, Publications in Climatology, Laboratory of
Climatology, Vol. 10, No. 3.
Wong, J. (1977) The Design of a System for Collecting Leachate
from a Lined Landfill Site, Water Resources Research,
V. 13, No. 2, pp. 404-410.
'US GOVERNMENT PRINTING OFFICE 1980-757-064/0182
63
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