SW-869
Revised Edition
LANDFILL AND SURFACE IMPOUNDMENT
PERFORMANCE EVALUATION MANUAL
Contract No. 68-03-2932
Project Officer
Mike H. Roulier
Solid arrct Hazardous Waste Research Division
Municipal EnvironmentaT Research Laboratory
Cincinnati, Ohio 45268
MUNICIPAL ENVIRONMENTAL RESEARCH LAiORATORT
OFFICE OF RESEARCH ANB DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CINCINNATI, OHIO 45268
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DISCLAIMER
This report has been reviewed by the Municipal Environmental Research
Laboratory, U.S. Environmental Protection Aqency, and approved for
publication. Mention of trade names or commercial products does not
constitute endorsement or recommendation for use.
For sale by the Superintendent of Documents, U.S. GoTernment Printing Office. Washington, D.C. 20402
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FOREWORD
The Environmental Protection Agency was created because of increasing
public and governmental concern about the dangers of pollution to the health
and welfare of the American people. Noxious air, foul water, and spoiled land
are tragic testimony to the deterioration of our natural environment. The
complexity of that environment and the interplay of its components require a
concentrated and integrated attack on the problem.
Research and development is the first necessary step in problem solution;
it involves defining the problem, measuring its impact, and searching for
solutions. The Municipal Environmental Research Laboratory develops new and
improved technology and systems to prevent, treat, and manage wastewater and
solid and hazardous waste pollutant discharges from municipal and community
sources; to preserve and treat public drinking water supplies; and to minimize
the adverse economic, social, health, and aesthetic effects of pollution.
This publication is one of the products of that research -- a vital
communications link between the researcher and the user community.
This document describes a method for evaluating designs for landfills and
surface impoundments to predict the amount of liquid collected in leachate
collection systems and the amount seeping through the liner into underlying
soils. The method takes into account the slope, thickness, and permeability
of the soil or clay liner, the thickness and permeability of sand or gravel
drainage layers, and the spacing of pipes in the leachate collection system.
Francis T. Mayo
Director, Municipal Environmental
Research Laboratory
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AUTHOR'S FOREWORD
This evaluation procedures manual updates an identically titled document
published by the U.S. EPA Office of Water and Waste Management in September
1980 as publication No. SW-869. The principal modifications are:
(1) Material referring to partially saturated flow and prediction of time
of first arrival of leachate at the base of the landfill has been moved
to an Appendix. This material was removed from the body because proven
methods are not currently available for measuring the required soil
properties in the laboratory. Readers who are interested in current
research being conducted on this topic are referred to Messuri (1982).
(2) More example problems have been included.
(3) A section has been added that discusses the effects that changes in
design parameters have on the performance of liner/drain systems.
I would like to summarize the philosophy upon which this Evaluation
Procedures Manual is based. The mathematical principles that describe the
transport of liquids through hazardous waste landfills and surface
impoundments are technically complex. Faced with this situation, it is
tempting to circumvent these difficulties by reverting to empiricism or rules
of thumb. I have avoided doing so, however, by using linearized versions of
complicated mathematical equations and by using simplified boundary
conditions. Thus, the evaluator will be able to assess the performance of a
design using algebraic equations.
This approach has three important benefits:
(1) As better analytical techniques are developed, it will be possible to
modify the evaluation procedure in a rational and consistent manner.
Thus, at the design level, acceptable configurations for landfills and
surface impoundments will change gradually rather than abruptly. The
evaluator will not be placed in the awkward position of having to
explain to the engineer 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 the 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. Because
such analytical approaches are compatible with the approach being used
by the the evaluator, the engineer 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
iv
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approach yields an acceptable, and hopefully more economical, design.
(3) The analytical approaches presented in this manual provide a
quantitative basis upon which the evaluator and engineer can discuss
possible modifications so that an unacceptable design configuration can
be transformed into one that is acceptable. This approach avoids the
dilemma that the engineer sometimes faces of (a) being told that a
design violates a rule of thumb criterion, but (b) being given no
guidance on how to modify the design to comply with the intent of the
requirements.
In addition to providing an evaluation procedure, this manual provides
design techniques that can be used by the engineer. 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 to determine the
acceptability of the design. Engineers will be able to approach liquid
routing through landfills and surface impoundments as a discrete analytical
task, and they will be able to substantiate their designs quantitatively.
Chapter 1 describes the purpose of this manual and establishes its
relationship to other U.S. EPA manuals. Chapter 2 describes the physical
attributes of the hazardous waste disposal facilities for which this
evaluation procedure has been developed. Chapter 3 provides the analytical
basis for the evaluation procedure. The fundamental physical and mathematical
principles are presented and the relevant equations are given. Chapter 4
presents the detailed evaluation procedure and serves as a checklist; the
experienced evaluator will use this chapter only. Chapter 5 presents example
evaluations. Chapter 6 contains references, and the Appendix discusses
principles of partially saturated flow.
In conclusion, I hope that this Evaluation Procedures Manual provides a
straightforward, 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, Chris Donaldson, and Susan DeHart.
Charles A. Moore
November 1, 1982
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PREFACE
Subtitle C of the Resource Conservation and Recovery Act (RCRA) requires
the Environmental Protection Agency (EPA) to establish a Federal hazardous
waste management program. This program must ensure that hazardous wastes are
handled safely from generation until final disposition. EPA issued a series
of hazardous waste regulations under Subtitle C of RCRA that is published in
40 Code of Federal Regulations (CFR) 260 through 265 and 122 through 124.
Parts 264 and 265 of 40 CFR contain standards applicable to owners and
operators of all facilities that treat, store, or dispose of hazardous
wastes. Wastes are identified or listed as hazardous under 40 CFR Part 261.
The Part 264 standards are implemented through permits issued by authorized
States or the EPA in accordance with 40 CFR Part 122 and Part 124
regulations. Land treatment, storage, and disposal (LTSD) regulations in 40
CFR Part 264 issued on July 26, 1982, establish performance standards for
hazardous waste landfills, surface impoundments, land treatment units, and
waste piles.
The Environmental Protection Agency is developing three types of documents
for preparers and reviewers of permit applications for hazardous waste LTSD
facilities. These types include RCRA Technical Guidance Documents, Permit
Guidance Manuals, and Technical Resource Documents (TRDs). The RCRA Technical
Guidance Doucments present design and operating specifications or design
evaluation techniques that generally comply with or demonstrate compliance
with the Design and Operating Requirements and the Closure and Post-Closure
Requirements of Part 264. The Permit Guidance Manuals are being developed to
describe the permit application information the Agency seeks and to provide
guidance to applicants and permit writers in addressing the information
requirements. These manuals will include a discussion of each step in the
permitting process, and a description of each set of specifications that must
be considered for inclusion in the permit.
The Technical Resource Documents present state-of-the-art summaries of
technologies and evaluation techniques determined by the Agency to constitute
good engineering designs, practices, and procedures. They support the RCRA
Technical Guidance Documents and Permit Guidance Manuals in certain areas
(i.e., liners, leachate management, closure, covers, water balance) by
describing current technologies and methods for designing hazardous waste
facilities or for evaluating the performance of a facility design. Although
emphasis is given to hazardous waste facilities, the information presented in
these TRDs may be used in designing and operating non-hazardous waste LTSD
facilities as well. Whereas the RCRA Technical Guidance Documents and Permit
Guidance Manuals in certain areas (i.e., liners, leachate management, closure,
covers, water balance) by describing current technologies and methods for
designing hazardous waste facilities or for evaluating the performance of a
facility design. Although emphasis is given to hazardous waste facilities,
the information presented in these TRDs may be used in designing and operating
non-hazardous waste LTSD facilities as well. Whereas the RCRA Technical
Guidance Documents and Permit Guidance Manuals are directly related to the
regulations, the information in these TRDs covers a broader perspective and
should not be used to interpret the requirements of the regulations.
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A previous version of this document dated September 1980 was announced in
the Federal Register for public comment on December 17, 1980. The new edition
incorporates changes as a result of the public comments, and supersedes the
September 1980 version. Comments on this revised publication will be accepted
at any time. The Agency intends to update these TRDs periodically based on
comments received and/or the development of new information. Comments on any
of the current TRDs should be addressed to Docket Clerk, Room S-269(c), Office
of Solid Waste (WH-562), U.S. Environmental Protection Agency, 401 M Street,
S.W., Washington, D.C. 20460. Communications should identify the document by
title and number (e.g., "Landfill and Surface Impoundment Performance
Evaluation, (SW-869).
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ABSTRACT
This technical resource document provides recommended procedures for
evaluating the effectiveness of liquid transmission control systems for
hazardous waste landfill and surface impoundments. The procedures described
allow an evaluator to determine the performance of (1) compacted clay liners
intended to impede the vertical flow of liquids, (2) sand or gravel drainage
layers used to convey liquids laterally into collection systems, (3) slopes on
such liner/drain layers, and (4) spacings of collector drain pipes.
The mathematical principles that describe the transport of liquids
through hazardous waste, landfills and surface impoundments are technically
complex. Faced with this situation, it is tempting to circumvent these
difficulties by reverting to empiricism or rules of thumb. In this manual,
however, this has been avoided by using linearized versions of complicated
mathematical equations and by using simplified boundary conditions. Thus, the
evaluator is able to assess the performance of a design using algebraic
equations.
vi 11
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TABLE OF CONTENTS
Page
1. INTRODUCTION 1
1.1 Purpose 1
1.2 Relationship to Other Manuals 1
2. DESIGN CONFIGURATIONS 4
2.1 Functional Characteristics of Design Modules 4
2.2 Categorizing Functions of Design Modules 7
2.3 Definition of Units to be Included in the
Liquid Transmission Control System 8
2.4 Liquid Diversion Interfaces 8
2.5 Constructing Liquid Routing Diagrams 9
3. ANALYTICAL METHODS 11
3.1 Introduction 11
3.2 Analysis of Sand and Gravel Drain Layers 12
3.2.1 Calculating the Maximum Height to which
Leachate Rises in a Drain Layer 12
3.2.2 Comments on the Height of Rise 15
3.3 Analysis of Flow through Saturated Clay Liners 17
3.3.1 Calculating Vertical Seepage Quantites
through a Liner 17
3.3.2 Comments on Steady State Seepage Quantites 19
3.4 Efficiency of a Liner/Drain Module 20
3.4.1 Calculating the Efficiency 20
3.4.2 Comments on the Efficiency of
Liner/Drain Modules 27
3.5 Efficiencies for Multiple Liner/Drain Modules 34
3.5.1 Calculating the Efficiency 34
3.5.2 Comments on the Cumulative Efficiency
of Liner/Drain Systems 38
4. PROCEDURES FOR EVALUATING PROPOSED DESIGNS 39
4.1 Evaluating Hazardous Waste Landfills 39
4.1.1 Operating Conditions 39
4.1.2 Quantifying the Performance of a Landfill Design 39
4.1.3 Information Required to Use the Evaluation Procedure 40
4.1.4 Evaluation Procedure for Landfill Designs 42
4.2 Evaluating Hazardous Waste Surface Impoundments 46
4.2.1 Operating Conditions 46
4.2.2 Quantifying the Performance of a Surface
Impoundment Design 46
4.2.3 Information Required to Use the Evaluation Procedure 47
4.2.4 Evaluation Procedure for Surface Impoundment Designs 47
IX
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5. EXAMPLE EVALUATIONS 48
5.1 Evaluation of a Landfill 48
5.2 Evaluation of a Lagoon 62
6. REFERENCES 64
APPENDIX. Principles of Partially Saturated Flow 66
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LIST OF FIGURES
Figure Title Paqe
1 Relationship of this manual to other manuals in the series. 3
2 Cross section of landfill showing typical containment cells. 5
3 Detailed views of modules constituting landfill
cross section of figure 2. 6
4 Liquid routing diagram showing intended functions
of components of leachate containment system. 10
5 Geometry assumed for bounding solution for effectiveness
of sand drains. 13
6 Relationship between hmax/L and tan a for various values of ks/e. 16
7 Geometry for calculating efficiency of liner/drain systems
using method proposed by Wong (1977). 21
8 Geometry for calculating efficiency of liner/drain systems.
(after Wong, 1977) 23
9 Diagram for computing efficiency of liner/drain systems.
(after Wong, 1977) 23
10 Efficiency and effectiveness as a function of liquid
impingement rate for designs A and B. 30
11 Effectiveness as a function of impingement rate for
designs Al, A2, Bl, B2. 31
12 Seepage rate versus impingement rate with maximum
potential steady state seepage rate superimposed. 31
13 Effect of varying a, d, and L on liner/drain
module effectiveness. 33
14 Cross section of landfill showing liquid transmission
control system and liquid routing diagram. 35
15 Information required to use the evaluation procedure. 41
16 Diagram of the evaluation procedure. 44
17 Excerpt from plans for proposed landfill. 49
18 Excerpts from specifications for proposed landfill. 50
19 Liquid routing diagram for proposed landfill. 50
20 Efficiency of first liner/drain module as a
function of impingement rate. 55
21 Efficiency of bottom liner/drain module as a
function of impingement rate. 59
22 Excerpt from plans of proposed lagoon. 63
23 Excerpt from specifications for proposed lagoon. 63
24 Liquid routing diagram for proposed lagoon. 63
25 Simplified microscopic view of wetting interface
in a partially saturated soil. 67
26 Macroscopic view of wetting interface in a partially
saturated soil. 67
XI
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LIST OF TABLES
Table Title Page
1 Parameter values for modules A and B. 28
2 Values used for parameter studies. 28
3 Equations used in evaluation procedure. 45
4 Site precipitation and percolation data. 51
5 Efficiencies for various impingement rates. 54
XII
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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 entering the environment. 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 evaluator to determine how the design
will function. It is the responsbility of the design engineer to propose an
adequate design initially. The procedures described herein should allow an
evaluator to determine the performance of:
(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/drain systems, and
(4) spacings of collector drain pipes.
1.2 Relationship to Other Manuals
As shown in figure 1, this procedures manual relates to four other
manuals in the following ways:
(1) SW-868, titled Hydrologic Simulation on Solid Waste Disposal Sites
(Perrier and Gibson, 1982) and prepared by the U.S. Army Corps of
Engineers, Waterways Experiment Station, provides the analytical basis
for determining the partitioning of rainfall into surface runoff and
infiltration. The water that infiltrates is, in turn, partitioned into
that which returns to the atmosphere through evapotranspiration, 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 landfill. 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.
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(2) SW-168, titled Use of the Water Balance Method for Predicting Leachate
Generation from Solid Waste Disposal Sites (Perm, Hanley and DeGeare,
1975), provides an alternative source for determining the quantity of
liquid percolating through the cover. The method presented in this
manual is based upon the principles developed by Thornthwaite and
Mather (1955 and 1957).
(3) SW-870, titled Lining of Waste Impoundment and Disposal Facilities
(Matrecon, Inc., 1980), relates to the present manual in that the
outflow quantities to collector drain pipes from sand and gravel
drainage layers determined according to procedures described in the
present manual become input quantities to section 5.6 of SW-870.
(4) SW-871, titled Hazardous Waste Leachate Management Manual (Monsanto
Research, 1980), uses the outflow quantities to collector drain pipes
determined in the present manual as an indirect input.
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2. 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 transport of liquids through simple modular configurations.
With these analytical procedures at their disposal, evaluators can then
interconnect several modules to represent the specific configuration being
evaluated.
Figure 2 shows a hypothetical landfill cross section including final
cover, waste cells, intermediate or daily cover, and a liner/drain system
resting on undisturbed ground. Three separate modules can be delineated as
follows:
(1) final cover with adjacent waste cells beneath,
(2) intermediate cover with adjacent waste cells above and below, and
(3) liner/drain system consisting from bottom to top of underlying
undisturbed ground, clay liner, sand drain layer, and overlying waste
cell.
2.1 Functional Characteristics of Design Modules
The modules shown in figure 2 will be examined in some detail to
delineate the functional characteristics of each. This examination forms the
basis for abstracting the physical characteristics to be included in the
analytical techniques to be presented. The configuration described here is
hypothetical only and does not necessarily constitute a recommended design.
The final cover shown in figure 2 is redrawn in more detail in figure 3a.
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 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 layer to provide a horizontal
pathway along which liquid collected on the clay liner can be
transmitted to collector drain pipes for diversion away from the
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final cover
intermediate cover
waste cell
drain
synthetic membrane
undisturbed soil
Figure 2 - Cross section of landfill showing typical containment cells.
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clay liner
und if f erent i a ted
leveling layer
waste
native soi
(a) detail of cover
waste
intermediate cover
waste
(b) detail of intermediate cover
waste
sand drain
drain
synthetic liner
(c) detail of drain and liner system
Figure 3 - Detailed views of modules constituting
landfill cross section of figure 2.
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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 drain pipes and
subsequent diversion away from or recirculation through the landfill.
The intermediate cover is drawn in more detail in figure 3b. 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 liner/drain module is drawn in more detail in figure 3c.
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
downward movement of liquids into the native soil,
(3) a high permeability sand or gravel drain layer whose purpose is to
provide a horizontal pathway along which liquid that collects on the
synthetic liner can be transmitted to the collector drain pipes for
diversion away from the landfill, and
(4) the overlying waste.
2.2 Categorizing Functions of Design Units
The various layers described above perform differing functions with
respect to the transmission of liquid through the landfill. The low
permeability layers, such as the clay liner in the final cover and the
synthetic membrane in the bottom liner, are included to retard the rate of
vertical flow of liquids. The high permeability layers, such as the sand or
gravel drain in the liner/drain module, are included to encourage the flow of
leachate toward the collector drain pipes. Some layers, for example the
topsoil, are included because they are able to reduce the quantity of liquid
available for leachate formation due to their evapotranspiration properties.
Finally, some layers serve functions not primarily concerned with their
ability to control transmission of liquids. These include the
undifferentiated leveling layer, the waste, and the intermediate cover.
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2.3 Definition of Units to be Included in the
Liquid Transmission Control System
The above observations form the basis for an important axiom in
evaluating the adequacy of containment in a hazardous waste surface
impoundment:
Certain units within the design are included primarily to control
liquid transmission. These units should be clearly delineated and
their intended functions described by the designer in the design
documents.
In preparing the facility plans the designer should:
(1) specifically designate those units that are intended to control liquid
transmission;
(2) describe how each unit will function to achieve this control;
(3) quantitatively assess the control capabilities of each unit in a
rational manner; and
(4) demonstrate that each unit can be reasonably expected to serve this
function when constructed according to the specifications given in the
design.
Units for which the designer has not provided this information should be
considered only to provide a safety margin above the basic control
requirements and should not be taken into consideration in evaluating the
adequacy of the system to meet minimum control requirements.
2.4 Liquid Diversion Interfaces
From figure 3 it is evident that many of the units that serve to control
liquid transmission occur as modules consisting 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,
subsequently to be conducted from the site. Examples 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.
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2.5 Constructing Liquid Routing Diagrams
Figure 4 shows a liquid routing diagram that both describes the several
units comprising a landfill, and clearly designates by the letters LTC those
modules 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
transmissibility units and which serve to divert flow direction from vertical
to horizontal are designated by the symbol DI for Diversion Interface. This
suggests the first step in the evaluation procedure:
If the designer has not already done so, construct a liquid routing
diagram for the landfill. Using the symbol LTC, designate the units
that are considered to be part of the liquid transmission control
system. Determine the location of diversion interfaces and label
them DI. Use arrows to show the liquid transmission control mechan-
isms. If the designer has provided such a diagram, the evaluator
should confirm that it represents an appropriate diagram for use in
evaluating the proposed design.
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evapotranspiration (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 4 - Liquid routing diagram showing intended functions
of components of leachate containment system.
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3. ANALYTICAL METHODS
3.1 Introduction
Many landfill designs incorporate one or more liner/drain modules to
limit the quantity of leachate that reaches the environment underlying the
landfill. Modules located above the waste serve to intercept water before it
can become contaminated, whereas modules located below the waste collect the
leachate for treatment or for recirculation through the landfill.
The liner/drain system is one of the principal elements of hazardous
waste landfills over which there can be a high degree of control during
construction. The liner/drain system is constructed of select material and is
emplaced using construction techniques that can be carefully supervised.
Moreover, the finished liner/drain system can be inspected. Therefore, in
designing and evaluating liner/drain systems, the engineer can use relatively
exact analytical techniques and be assured that the design can be implemented
in the field.
This chapter presents the equations that quantify leachate flow in
individual liner/drain modules and in systems composed of multiple modules:
(1) Section 3.2 presents the equations used to calculate the maximum height
of rise of leachate in a sand or gravel drain layer. The drain layer
must be thick enough so that mounding liquid does not overtop it,
thereby risking further contamination through additional contact with
the waste.
(2) Section 3.3 presents the equations used to calculate the quantity of
leachate flowing through compacted clay liners after they have become
saturated. These equations determine how much leachate seeps through
the liner to impinge on underlying liner/drain modules or to migrate
into the underlying hydrogeologic regime.
(3) Section 3.4 presents the equations used to calculate the efficiency of
liner/drain modules. These equations quantify the proportion of
leachate that is diverted to horizontal flow, later to be collected,
and the proportion that continues to seep downward.
These equations serve as the basis for the evaluation procedures to be
presented in Chapter 4.
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3.2 Analysis of Sand and Gravel Drain Layers
3.2.1 Calculating the Maximum Height to which Leachate Rises in a Drain Layer
Because of viscous resistance to horizontal flow, leachate tends to mound
up in sand or gravel drain layers. This mounding could be great enough to
cause the leachate to overtop the drain layer, resulting in the leachate
becoming further contaminated. It is important to make certain that the
thickness of the sand or gravel drain layer is greater than the anticipated
height of mounding of the leachate.
The height of the mound does not increase without limit; rather, for a
particular configuration of drain layer and for a given steady state
impingement rate, leachate mounds to a certain maximum height. Figure 5 shows
the conditions assumed for calculating the height of mounding in sand and
gravel drain layers. Figure 5a shows a drain layer of thickness d (m)
overlying a low permeability liner. The module slopes symmetrically at an
angle a (exaggerated in this drawing) down to drain pipes spaced a distance
L (m) apart. The saturated permeability of the drain layer is ksj (m/sec),
and its porosity is n. Liquid impinges upon the module at a rate of e
(m/sec). The source of this liquid could be rainfall, recirculated leachate,
or liquid generated by the waste itself.
In the limiting case of a = 0 (shown in figure 5b), the shape of the
water mound that accumulates in the drain layer is given by Harr (1962) as:
(D
For a horizontal module, the maximum value of h occurs at x = L/2 and is given
by:
max
(2)
As an example, consider a flat module having drain pipes placed 30 m
(approximately 100 feet) apart in a sand having ksi = lx!0~3 cm/sec and
n = 0.5. Assume an annual rainfall of 100 cm/yr (39 in/yr) equally
12
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L i J * _» I * * *
Figure 5 - Geometry assumed for bounding solution for
effectiveness of sand drains.
13
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distributed in time so that e = 3.2x10-6 cm/sec. Thus from equation (2):
30m
max ~ 2(0.5)
/ 3.2x10"*
\ IxlO"3
2xlO"6 cm sec \ 1/2
= 1.7 m
sec cm
The high value for hmax obtained in this example demonstrates that
designing an open-topped, flat-bottomed landfill is impractical. Returning to
figure 5a, it can be seen that putting the drain module on a slope a not equal
to zero tends to accelerate the flow of water toward the collector pipes.
Figure 5c shows the accumulation profile. It is very much like that of figure
5b, except that hmax does not occur at x = L/2. The configuration with a not
equal to zero has some convenient properties when compared with a equal to
zero. The obvious one is that the hydraulic gradient toward the drain pipe is
higher. Another significant 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 zero;
whereas, the drainage time for a equal to zero is infinitely long.
As shown in figure 5c, there is a value for hmax
expression similar to equation (2):
that is given by an
max
+ tan a - tan a
(3)
For the example presented above, but with a = 10° rather than zero, we
can use equation (3) to give:
max
3,2xlO"6 cm sec . tan2(10)V/2 . tan(10)
1x10" sec cm
= 0.26 m
Thus, placing the module at this incline reduces the height of mounding by a
factor of 6.5.
14
-------
3.2.2 Comments on the Height of Rise
Figure 6 presents hmax/L as a function of a for several values of
The graph holds for all values of a because equation (3) reduces to equation
(2) for a = 0. It can be seen that for higher e/ksj ratios, increasing the
slope of the liner reduces hmax significantly. For lower e/ksi ratios,
increasing the slope of the liner has some effect on hmax for small a;
however, further increases in a produce little additional benefit.
Equations (2) and (3) were derived on the assumption that saturated Darcy
flow occurs within the drain layer. This presumes that the wetted volume of
soil is large relative to the diameter of the soil particles. The hmax to
grain diameter ratio should be perhaps 10 or more for the equations to be
valid. For example, if 1 inch gravel is being used for the drain layer, and
equation (2) or equation (3) predicts hmax =0.5 inch, the value of hmax is
not likely to be valid.
These equations also assume that the liner/drain module is constructed as
a perfectly flat plane oriented at an angle a to the horizontal. In practice
there will be undulations in the surface of the compacted clay liner that can
provide an opportunity for ponding to occur over relatively short distances to
relatively shallow depths. This is not likely to affect hmax appreciably;
however, it may significantly affect the calculations to be performed in
section 3.4. Thus, when evaluating the slope on a liner/drain module, the
designer and evaluator should not rely on extremely shallow slopes functioning
in accordance with the equations presented.
Both equations (2) and (3) include the soil porosity, n, in the
relationship. The reason for this is as follows. Impingement rates are given
in units of meters per second based upon the assumption that the depth of
accumulation is measured by a device such as a rain gage. However, when one
meter of water is introduced into a sand or gravel layer, the water can only
occupy the soil voids. It cannot occupy the volume devoted to the soil
solids. Thus, one meter of water will mound to a height equal to the
impingement quantity divided by the soil porosity; hence, the division by n.
Finally, the analytical solution represented by equation (3) was obtained
by neglecting a small differential term that would tend to reduce the value
determined for hmax. The error involved is relatively small, and it is on the
conservative side (i.e. use of equation (3) will result in drain layers being
designed somewhat thicker than necessary). McBean et al. (1982) present a
numerical method that approximates the exact solution for the case of a sloped
liner/drain module.
15
-------
'max
Ml^Mft
L
0.10
0.08
0.06
0.04
0.02
0.1
0.2
to n«x
.0001
0.3
0.4
Figure 6 - Relationship between hmax/L and tan a for various
values of ks/e.
16
-------
3.3 Analysis of Flow through Saturated Clay Liners
3.3.1 Calculating Vertical Seepage Quantities through a Liner
After the clay liner has become saturated, gravitational forces dominate
the flow process. The total quantity, Q, of liquid passing through the clay
liner in time, At, is given by:
.dh_(A)At
s2 dz
where
kS2 = the saturated hydraulic conductivity of the clay liner,
more commonly referred to as the Darcy coefficient
of permeability,
dh = the change in total hydraulic head,
dz = distance over which the head change occurs, and
A = cross sectional area through which flow occurs.
The quantity of liquid seeping through the liner, e, per unit
cross-sectional area and per unit time can be determined by setting A and At
in equation (4) equal to 1.0. Thus, for a saturated liner of thickness, d,
with no leachate standing on top (dh/dz = 1.0), the seepage quantity from
equation (4) becomes:
e = ke9 (5)
As an example, consider a saturated liner constructed of a clay having
kS2 = IxlO-? cm/sec. We can use equation (5) to calculate the monthly
quantity of leachate seeping through this liner:
e = 2678400 sec
17
-------
An upper bound for the seepage quantity in a liner/drain module would be
the case where liquid mounds within the drain layer to a depth hmax. In this
case equation (4) becomes:
e = ( d + hmax 1 k , (6)
As an example, consider a two foot thick clay liner having ks2 = lxlO~7 cm/sec
and hmax =1.3 feet. Equation (6), in combination with the previous example
problem result, gives:
e = 9 ' I (0.268) = 0.442 cm/mo
In evaluating surface impoundments, the hydraulic gradient is augmented
by the liquid ponded within the lagoon. In this case, the flow quantity is
given by:
+ H
where
H = depth of liquid in the lagoon.
For example, consider a lagoon impounding liquid to a depth of 10 feet. It
has a two foot thick clay liner with ks2 = 1x10-7 cm/sec. Equation (7) gives:
= I-2 +210 )
(0.268 cm/mo) = 1.61 cm/mo
18
-------
3.3.2 Comments on Steady State Seepage Quantities
The equations presented in section 3.3.1 cannot be used to calculate the
velocity with which liquid moves through the liner. Neither can they be used
to predict the velocity with which a pollutant is carried through the liner by
the liquid. This is because the flow process occurs by liquid moving randomly
through a multitude of pores, each varying in size, orientation, and
tortuosity. The actual flow velocity is a microscopic characteristic, varying
greatly from location to location. Moreover, physico-chemical forces of
attraction such as Van der Waal's forces and ion hydration cause a significant
portion of the liquid to be relatively securely retained by the soil
particles. This causes the remainder of the liquid to flow in even smaller
channels and at even higher velocities.
In short, the Darcy coefficient of permeability, ks2, used in equations
(4) through (7) is a macroscopic parameter calculated by measuring the
quantity of liquid flowing through a soil sample in a given period of time.
That quantity (ks2) can, in turn, only be used to calculate the quantity of
liquid that will pass through the same soil in a given period of time. Any
attempt to use the coefficient of permeability to speculate about flow
velocities or pollutant transport velocities at the microscopic level will be
conceptually and numerically incorrect.
It is also erroneous to attempt to predict the time required for leachate
to appear at the bottom of a clay liner wetting up for the first time using
calculations based only on the saturated coefficient of permeability, ks2-
The reason for this is that Darcy flow assumes that the gravitational
potential is the only force tending to move liquid through the soil. As
explained in the Appendix, flow through partially saturated soil occurs both
as a result of the gravitational potential and capillary potential. During
initial wetting up, the capillary potential can greatly exceed the
gravitational potential in the soil. Thus, the flow process during initial
wetting up usually occurs much faster than the gravity-induced Darcy flow that
governs the process after the clay liner has become saturated.
19
-------
3.4 Efficiency of a Liner/Drain Module
The efficiency of a liner/drain module is a quantitative measure of the
proportion of liquid that moves along the drain layer to be collected by the
collector drain pipes, relative to the proportion that seeps through the
liner. For liner/drain modules located above the waste, a highly efficient
module means that very little water seeps downward into the waste where it may
become contaminated. For liner/drain modules located below the waste, a
highly efficient module means that most of the leachate is collected for
treatment or recirculation.
3.4.1 Calculating the Efficiency
Wong (1977) proposed an approximate technique for quantifying the
efficiency of a liner/drain module based upon saturated Darcy flow in both the
drain layer and the clay liner. Figure 7 describes the geometry assumed in
Wong's calculations.
The approach postulates that at some initial time, a rectangular slug of
liquid is placed upon the saturated liner to a depth h0. The liquid flows
both horizontally along the slope of the module and vertically into the clay
liner. The fraction of liquid moving into the collector drain pipes at time,
t, is given by:
-5-. = i - 4- (8)
s_ t, v '
and the fraction of liquid seeping into the clay liner at that instant is
given by:
h / rf \ -Ct/t1 H
TT- = I 1 + T - )e l - T 0 < t < t, (9)
TT I h cos a J h cos a - - 1
20
-------
Figure 7 - Geometry for calculating efficiency of liner/drain
systems using method proposed by Wong (1977).
21
-------
where
sn a
and
cot a (11)
and
s = length of saturated volume at time, t (cm)
h = thickness of saturated volume at time, t (cm)
s0 = initial length of saturated volume (cm) = L/2cos(a)
h0 = initial thickness of saturated volume (cm) = (impingement quantity)/n
n = soil porosity
ksi = saturated permeability of the material above clay liner (cm/sec)
ks2 = saturated permeability of the clay liner (cm/sec)
a = slope of angle of the module (degrees)
d = thickness of the clay liner (cm).
Figure 8 shows the geometry at some time, t.
If the module is allowed to drain completely, its efficiency can be
determined using figure 9, which graphs h/h0 versus s/s0 and t/tj. Equations
(8) and (9) can be solved parametrically in t/tj to yield the line shown on
figure 9. The line is actually a curve; however, for practical liner/drain
configurations it can be approximated as a straight line. In figure 9 the
efficiency of the module is given by the area labeled E. This area is most
easily determined by calculating the value of h/h0 when t/tj = 1.0 (or s/s0 =
0). This parameter, called N, can be obtained by solving equation (9) with
t/tj = 1.0:
22
-------
Figure 8 - Geometry for calculating efficiency of
liner/drain systems, (after Wong, 1977)
1.0
h/h.
s/s0
1.0
1.0
t/t,
Figure 9 - Diagram for computing efficiency of
liner/drain systems, (after Wong, 1977)
23
-------
The value of N can be either positive or negative; however, most efficient
designs will have N _> 0. The efficiency, E, is given by either
E = -~- for N >. 0 (I3a)
or
E = 97Tirr for N 1 0 (13b)
Thus the efficiency varies from 0 to 1.0.
The following procedure is used to calculate the quantity of liquid
collected in the drain pipes and the quantity of liquid seeping through the
clay liner at the end of one month. First, calculate tj using equation (10).
Next, solve for N1 using t = one month:
. \ -Ct/t, .
+ d 1 e l - d (14)
h cos a le h cos a { '
Then calculate an efficiency at the end of one month using equations analogous
to equations (13a) and (13b):
1-111 for N' > 0 (15a)
E' - 2(1*N.} for N' <0 (15b)
24
-------
Thus, the quantity of liquid flowing to the collector drain pipes per meter of
liner/drain module in cubic meters during the month is:
Qd=E'hoson (16)
The quantity of liquid seeping through the clay liner and impinging below is:
e = (1 - E1) ho n (17)
As an example of the above calculations, consider a module having a 30 cm
thick compacted clay liner with ks2 = l.OxlO-7 cm/sec, overlain by a gravel
layer having ksj = lxlO~3 cm/sec. The entire module slopes at 17.6 ft/100 ft,
and the spacing between drain pipes is 30 m. Assume that in the month in
question 1.25 cm of liquid impinges on a sand drain layer having a porosity of
0.5.
a = 10° (17.6 ft/100 ft)
= IxlO'3 cm/sec
kS2 = IxlO-? cm/sec
d = 30 cm = 0.3 m
n = 0.5
h0 = 1.25/0.5 = 2.5 cm
S0 = L/2cos(a) = 30 m/2cos(10) = 1523 cm
From equation (11):
C = - cm sec cot(1Q) = Q>()288
2 x 0.3 m cos(10) 1x10 sec cm
From equation (12):
. . . 0.3 m \ -0.0288 0.3 m n
N = I l'° + 0.025m cos(10) j e ' 0.025 m cos(10) - °'
25
-------
From equation (13):
=0.813
Thus 81.3% of the liquid is ultimately diverted to the drain pipes.
To determine the quantity of liquid flowing to the collector drain pipes
and the quantity impinging below, begin by calculating the value of tj as
given by equation (10):
, 30 m sec 100 cm mo , 07 mn
t = * . = 3.27 mo
1 2 cos(10) x lxlO"J cm sin(10) m 2678400 sec
Then, from equation (14), determine N':
0.3 m \ -0.0288(1/3.27)
0.025 m cos(10) / e
= 0.88
0.025 m cos(10)
Next, put this value of N1 into equation (15a) to give:
11 n o o
I \J m OO « A «
i- * »r n QZL
L. "~ n U» j1-*
26
-------
Finally, the quantity of liquid flowing to the collector drain pipes at the
end of one month per meter of drain pipe is given by equation (16) to be:
0.94 x 2.5 cm 30 cm 0.5 m n ,Q 3,,
2 cos(lO) 100 cm = °«18 m /mo/m
The quantity of liquid seeping through the clay liner during the month is
given by equation (17) to be:
e = (1.0 - 0.94) 2.5 cm (0.5) = 0.075 cm/mo
3.4.2 Comments on the Efficiency of Liner/Drain Modules
This section examines the interrelationships among the parameters
affecting a liquid transmission control module's performance. The objective
is to determine which parameters can be most practically adjusted to achieve
satisfactory system performance. The parameters to be examined include:
the impingement rate on the liner/drain module (e-j),
the slope of the module (a),
the thickness of the clay liner (d),
the spacing between collector drain pipes (L),
the saturated coefficient of permeability of the sand
or gravel drain layer (ksi), and
the saturated coefficient of permeability of the clay liner (ks2).
To show these interrelationships, we will consider two contrasting
designs. For the particular site under consideration, liner/drain module A
will be shown to perform efficiently, whereas liner/drain module B performs
inefficiently. Table 1 compares the design characteristics for these two
modules.
Selecting a value for the impingement rate, e-j, on the liner is a
complicated process because this quantity is highly dependent upon geographic
location, season of the year, and position of the liner/drain module within
the landfill. The U.S. EPA Municipal Environmental Research Laboratory in
Cincinnati used the computer programs described in SW-868 to provide
hydrologic information for a typical landfill cover configuration used at six
sites representing a range of climatic conditions for the continental United
States. Seepage quantities varying from zero to perhaps 0.5 inch/month
(4.9x10-' cm/sec) could be expected through a well designed and well
27
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Table 1 - Parameter values for modules A and B.
PARAMETER MODULE A VALUE MODULE B VALUE
L 2286 cm = 75 ft 3810 cm = 125 ft
d 152 cm = 5 ft 61 cm = 2 ft
a 10 degrees 5 degrees
ksi IxlO-3 cm/sec IxlO"3 cm/sec
ks2 IxlO'7 cm/sec IxlO-6 cm/sec
ksi/ks2 lxlO'4
Table 2 - Values used for parameter studies.
FIGURE a d L
13a 5 to 10 degrees 106.5 cm 3048 cm
13b 7.5 degrees 61 to 152 cm 3048 cm
13c 7.5 degrees 106.5 cm 2286 to 3810 cm
28
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maintained cover. Moreover, during landfilling and prior to construction of
the cover, the liner/drain module could be subjected to direct rainfall
amounting to 15 inches/month (1.5x10-5 cm/sec) or more.
Because the rainfall amounts vary so much, it is not practical to select
a single value for e-j. Rather, the performance of the liquid transmission
control system should be evaluated by using a range of values appropriate to
the particular site and design.
For purposes of this discusssion we will examine the performance of
liner/drain modules A and B using impingement rates varying from zero to
1x10-5 cm/sec (10.2 inches/month). Figure lOa plots efficiency, E, versus
impingement rate, e-j, for these modules; figure lOb plots the seepage
quantity, es, through the clay liner versus impingement quantity, ej, for the
same modules.
For both designs, as the impingement rate approaches zero, the efficiency
also approaches zero. This is an algebraic consequence of equations (8)
through (13) and will be the case for any design, good or poor. However, note
that design A shows a substantial increase in efficiency over the relevant
range of impingement rates; whereas design B shows a disappointingly small
increase in efficiency as impingement rate increases. If a particular
liner/drain module has a low efficiency, it may be poorly designed.
Conversely, it may be quite well designed, but have a low impingement rate --
perhaps due to other well designed liner/drain modules or a good cover
overlying it. Thus, low efficiency should not be used as the sole basis for
rejecting a liner/drain design.
Figure lOb shows that both modules allow very little seepage for low
impingement rates. However, as impingement rate increases, design A quickly
reaches a low asymptotic value above which the steady state seepage quantity
never rises. Conversely, design B does not exhibit an apparent upper limit
over the range of impingement rates examined. Rather, design B stays
dangerously close to the 45 degree line representing zero efficiency; that
is, most of the liquid that impinges on the module continues seeping downward
through the liner.
In conclusion, a well designed liner/drain module not only performs well
under the conditions that could be reasonably anticipated in the landfill, but
also exhibits increasing efficiency if the actual amount of impinging liquid
exceeds the expected amount.
We now examine what makes design A function better than design B. Figure
lla shows two designs that have module A's design features of high slope,
thick clay liner, and close spacing between drain pipes. Design Al has a
ks2/ksi ratio of IxlO"4, while design A2 has a ks2/ksi ratio of lxlO~3.
Clearly, module Al performs significantly better than module A2. A similar
conclusion can be drawn from figure lib, which shows two designs that have
module B's design features of low slope, thin clay liner, and long spacing
between drain pipes. Design Bl has ks2/ksi equal to lxlO~4, whereas design B2
has a kS2/ksi ratio of 1x10-3.
29
-------
E (»)
0.9 In/mo
0.6
0.5
i
0.4
(cm/sec x 10J)
0.3
0.2
O.I
design A
0 0.1 0.2 0.3
0.4 0.3 0.6
i, (cm/sec x 105>
10 In/mo
zero percent
efficiency line
0.7 0.8 0.9 1.0
Figure 10 - Efficiency and effectiveness as a function of
liquid impingement rate for designs A and B.
30
-------
(cm/sec x 10
(cm/sac x 105)
0 0.1 0.2 0.3 0.4 0.9 0.6 0.7 0.8 0.9 1.0
x 109>
Figure 11 - Effectiveness as a function of impingement rate
for designs Al, A2, Bl, B2.
s2
Figure 12 - Seepage rate versus impingement rate with maximum
potential steady state seepage rate superimposed.
31
-------
These comparisons demonstrate that the ratio of the permeabilities of the
drain layer to the clay liner strongly affects the efficiency of the
liner/drain module.
Nevertheless, the reader is cautioned against concluding that specifying
the ks2/ksi ratio alone will insure an adequate design: The above
calculations are based on theories (expressed in equations (8) through (13))
that assume saturated Darcy flow. This means that the quantity of liquid
present must substantially fill the pore space in the soil mass. This, in
turn, implies that the size of the largest particle in the drain layer must be
considerably smaller than the mounded liquid depth as expressed, for example,
by nmax* ln the extreme, a kS2/ksi ratio of 1x10-4 could be achieved by
having a boulder drain layer overlying a sand liner. This clearly would
neither constitute an acceptable design, nor would it constitute a module
within which the flow approximates the assumptions used in the theories.
To avoid such situations, we need to use the analytical tools provided by
equations (5) and (6). These equations predict the maximum potential steady
state seepage quantity based upon the coefficient of permeability of the clay
liner, ksp. Assuming for the moment that hmax is relatively small, we can use
equation (5) which predicts that the maximum potential steady state seepage
quantity through the clay liner is equal to ks2. Thus, we can superimpose the
value of ks2 on the es axis of the ei versus es plot of figure lOb (redrawn as
figure 12). If the asymptote approached by the e^ versus es relationship for
a particular liner/drain module lies well below the kS2 line, and if the kS2
line is acceptably low, then the liner/drain module performs effectively.
Finally, we examine the influence of varying liner/drain slope, a , clay
liner thickness, d, and collector drain spacing, L, on liner/drain module
effectiveness. For this evaluation, ksj = lxlO~3 cm/sec, ks2 = 1x10"' cm/sec
and e-j = 5x10"^ cm/sec for all cases. The combinations of a, d, and L
evaluated are summarized in Table 2, and the results are presented in figure
13.
It can be seen that both a and L have a measurable influence on the
effectiveness of the liner/drain module. Clearly, they should be considered
when optimizing a design. However, their effect is not nearly as great as the
effect of the kS2/ksi ratio. It is also apparent that the clay liner
thickness, d, has no influence on the effectiveness of the module, provided
that there is no liquid standing on the liner.
The analytical techniques that were presented in this section are based
on the work of Wong (1977). Other methods for determining efficiencies have
been presented by Lentz (1981) and by Skaggs (1982). Lentz's method has the
advantage of being able to incorporate multiple sequential applications of
liquid slugs onto the liner. However, his method presumes that liquid is
always in contact with the clay liner along its entire length. Moreover, his
method does not explicitly incorporate the thickness of the clay liner into
the calculations. Skaggs's method involves a computer program to implement
numerical solutions.
32
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(cm/sacxIO )
5.0
-------
3.5 Efficiencies for Multiple Liner/Drain Modules
3.5.1 Calculating the Efficiency
By incorporating multiple liner/drain modules into a landfill, it is
possible to greatly increase the efficiency of leachate containment. When a
system incorporating multiple modules is used, it is necessary to evaluate not
only the efficiency of each individual liner/drain module, but also to
evaluate the cumulative efficiency of the system composed of the several
liner/drain modules. The analytical techniques presented in section 3.4.1 for
determining the efficiency of a single liner/drain module are extended in this
section to analyze multiple modules.
Figure 14 presents a liquid routing diagram for a landfill containing
multiple liner/drain modules and defines the following seepage rates (cm/sec)
to be used in subsequent definitions and calculations:
e c = precipitation rate (18)
e n = seepage rate through the cover as determined (19)
sO
from hydrologic simulation (SW-868)
e., = impingement rate on module 1, usually taken (20)
equal to e Q under the assumption of plug flow
e . = seepage rate through the clay liner of module 1 (21)
e.? = impingement rate on the bottom control module (22)
e ? = seepage rate impinging on the regime underlying (23)
s the landfill
34
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atmosphere
cover
vast*
cell
Intermediate
transmission
control unit
vast*
call
bottom
transmission
control unit
region under
landfill to b*
protected fro*
contamination
evapo-
transplratlon
precipitation
vegetation
topso11
compacted
cover sol I
SO
liquid flowing to collector drains
and drain layer
col lector drain
clay liner
"si
12
flowing to collector drains
sand drain layer
coI lector drain
clay liner
native sol I
Figure 14 - Cross section of landfill showing liquid transmission
control system and liquid routing diagram.
35
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We can define the efficiencies of the individual liner/drain modules as
follows:
e
E0 = -- - for the cover (24)
prec
" esl
for the intermediate transmission (25)
il control module
ei2 ' es2
E = - - - for the bottom control module (26)
* ei2
We also define the following cumulative efficiencies for segments of the
design composed of more than one liner/drain module:
- e ,
EQ1 = ~ for cover plus the intermediate (27)
prec transmission control module
p P
orec s2
Egg =t for cover plus the intermediate (28)
prec and bottom transmission control
modules
E = E-_ where ET is the total efficiency (29)
of the transmission control system
Here the subscripts (Egn for example) indicate that the efficiency is the
cumulative efficiency for all layers above and including the nth layer. This
approach can, of course, be extended to accommodate any desired number of
liner/drain modules.
As an example of a calculation for multiple liner/drain systems, consider
a landfill consisting of a cover, an intermediate liner/drain module, and a
bottom liner/drain module. Suppose that the amount of precipitation impinging
per month on the the landfill is 5.0 cm. Analysis following the techniques
36
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described in SW-868 showed that 0.78 cm of liquid seeped through the cover.
An analysis using the techniques described in section 3.4.1 showed that 0.50
cm of liquid seeped through the intermediate liner/drain module. A similar
analysis showed that 0.20 cm of liquid seeped through the bottom liner/drain
module.
According to the definitions presented above,
e = 5.0 cm
prec
e = 0.78 cm
e ^ = 0.50 cm
e 2 = 0.20 cm
The following efficiencies can be calculated for the individual modules:
-° - °-78
o 5o
= °'78- °-50
l 0.78
,0.50 - 0.20
50
ne,
60'0%
The cumulative efficiencies are:
F - 5-0 - 0.5 _ Qfw
Eoi To 90%
c c 5.0 - 0.2 QM
E02 = ET = ^0 = 96%
37
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3.5.2 Comments on the Cumulative Efficiency of Liner/Drain Systems
It is important to use the cumulative efficiency to evaluate the
containment capability of liner/drain systems. As pointed out in section
3.4.2, a liner/drain module can be inefficient either because it is poorly
designed or because it has very little liquid impinging upon it. It would not
be appropriate to penalize low efficiency in a liner/drain module that is well
designed, but that has very little liquid impinging upon it. Using the
cumulative efficiency overcomes this difficulty. Thus, even though additional
liner/drain modules may display low individual efficiencies, they will
contribute significantly to the cumulative efficiency of the entire system.
It is important to make certain that the liner/drain modules displaying
low efficiencies when subjected to low impingement rates also display higher
efficiencies with increasing impingement rates. Such modules will contribute
a margin of safety to the design because they could respond efficiently to
unanticipated increases in impingement rates.
38
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4. PROCEDURES FOR EVALUATING PROPOSED DESIGNS
This chapter presents two evaluation procedures. Section 4.1 describes a
procedure for evaluating hazardous waste landfills; section 4.2 describes a
procedure for evaluating hazardous waste surface impoundments.
4.1 Evaluating Hazardous Waste Landfills
4.1.1 Operating Conditions
This evaluation procedure has been prepared with the assumption that the
operating conditions for the hazardous waste landfill meet the basic
requirements of good engineering design. For example, it is presumed that:
(1) surface water 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 relieved
so that the hydrostatic head in the artesian aquifer lies below the
base of the landfill;
(6) water on the site has been controlled during the construction of the
landfill; and
(7) the designs proposed for the components of the landfill form a properly
functioning system.
4.1.2 Quantifying the Performance of a Landfill Design
A well designed hazardous waste landfill contains a liquid transmission
control system that consists of a cover and one or more liner/drain modules.
These modules collectively must accomplish the following:
(1) They must assure that liquid does not mound up so high in the drain
layer that it overtops the layer, thus coming into contact with waste
39
-------
where it can become further contaminated. To quantify this, perform
the computations described in section 3.2 to determine the height of
mounding for liquid in each drain layer.
(2) They must maximize the amount of contaminated liquid diverted to and
collected by drain pipes. To quantify this, perform the computations
described in section 3.4 to determine the efficiency of the liner/drain
module comprising each liquid diversion interface.
(3) They must minimize the amount of liquid seeping through the landfill
and impinging on the underlying environment. To quantify this, perform
the computations described in section 3.3 to determine an upper bound
to the seepage quantity through each clay liner.
The following two sections present an evaluation procedure that implements the
considerations listed above using the analytical procedures developed in
Chapter 3.
4.1.3 Information Required to Use the Evaluation Procedure
Figure 15 shows the input required to use the evaluation procedure. The
sources of input are as follows:
(1) The plans developed by the designer supply the typical cross sections
needed for step (1). These cross sections are used both to construct
the liquid routing diagrams for step (2) and to locate the liquid
diversion modules for step (3). The designer may have provided liquid
routing diagrams as part of the plans and specifications and may also
have delineated the liquid diversion modules.
(2) Area precipitation records provide the maximum monthly precipitation
used in steps (4), (5), (7), and (12).
(3) The Hydrologic Simulation on Solid Waste Disposal manual (SW-868)
provides input to step (5) amount of liquid impinging on first
module. This quantity is available on a daily basis as the quantity,
Q. We recommend expressing these values on a monthly average basis.
Alternatively, monthly percolation can be determined using SW-168
(Water Balance Method of Fenn, Hanley, and DeGeare (1975)) or other
infiltration models.
(4) The plans and specifications must also provide the following additional
information for each liner/drain module:
(a) the thickness of the sand or gravel drain layer, to be used in step
(6),
(b) the soil porosity, n, to be used in steps (6), (7), and (8),
(c) the thickness, d, of the clay liner, to be used in steps (7) and
40
-------
(d) the coefficient of permeability, ksj, for the sand or gravel drain
layer, to be used in steps (6) and
;1. r<
(7).
(e) the coefficient of permeability, ks2, for the saturated clay liner,
to be used in steps (7) and (9),
(f) the slope, a, of the clay liner, to be used in steps (6) and (7),
and'
(g) the length, s0, from the high point of the liner to the drain, to
be used in steps (7) and (8).
INFORMATION
SOURCE
I percolation through the cover V < >
typical cross sections for
constructing Liquid Routing
Diagrams
SW-868, SW-168 or other
infiltration model
-frj plans and specifications |
geometry and material properties
for liner/drain modules
-frf plans and specifications \
Figure 15 - Information required to use the evaluation procedure.
41
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4.1.4 Evaluation Procedure for Landfill Designs
Figure 16 diagrams the evaluation procedure and designates the criteria
that should be used to assess the acceptability of a design. Table 3
summarizes the equations used. The procedure is as follows:
(1) From the design drawings, select a typical cross section through the
landfill. If the vertical profile through the landfill differs from
place to place, more than one cross section will require evaluation.
(2) Construct a liquid routing diagram, similar to that shown in figure 4,
to track the course of the liquid as it moves through the cross
section.
(3) On the liquid routing diagram, designate each liquid diversion
interface consisting of low permeability liners overlain by high
permeability drain layers.
(4) Examine the precipitation record for the landfill vicinity. Select the
maximum monthly precipitation.
(5) Determine the maximum monthly percolation through the cover as
predicted by the techniques presented in SW-868, SW-168, or other
infiltration models. This amount of liquid plus any liquid introduced
by the waste itself or by recirculated leachate is taken to be the
amount of liquid impinging upon the first module.
(6) Using either equation (3) or figure 6, plus the impingement quantity
determined in step (5), calculate hmax for the uppermost liner/drain
module. Determine whether hmax is less than the design thickness of
the drain layer. If not, change the design of the cover or the
thickness of the drain layer so that hmax is less than the drain layer
thickness.
(7) Using equations (11) through (13), calculate the efficiency of the
liner/drain module for impingement rates, e-j, ranging from zero to a
maximum value determined by the maximum monthly precipitation quantity
from step (4). Be sure to evaluate the case where ej is equal to the
anticipated impingement rate determined in step (5) above. Using this
information assess the performance of the liner/drain module based on
the following criteria:
(a) Evaluate the efficiency of the module at the anticipated
impingement rate as determined in step (5) above. If the
efficiency is above 75%, the design is acceptable.
(b) If the efficiency is below 75%, do not categorically reject the
design. Rather, determine whether low efficiency results from
poor design or from a low impingement rate on the module. To do
this, evaluate the way in which the efficiency increases with
increasing impingement rates up to the maximum monthly
precipitation rate determined in step (4) above. If the asymptote
42
-------
at high values of e-j is above 90%, more effort on this aspect of
the design is not warranted. If the value is below 90%, further
improvement in the design should be considered.
(8) Using equations (10), (11), (14), (15) and (17), determine the
anticipated monthly seepage quantity, es, through the liner. When
calculating E', use a value of h0 based upon the anticipated monthly
impingement quantity from step (5). If this is the bottom liner/drain
module, determine whether the hydrogeologic environment underlying the
landfill is capable of assimilating this seepage quantity.
(9) Using equation (5), determine the hypothetical monthly seepage
quantity corresponding to a constantly wet liner, but with no mounding
of liquid.
(10) Using equation (6), determine the hypothetical monthly seepage
quantity corresponding to a liner with liquid constantly mounded to a
height equivalent to hmax as determined in step (6).
(11) Repeat steps (6) through (10) above for each successive liner/drain
module included in the liquid routing diagram. Use step (4)
precipitation rates where called for; however, when step (5) liquid
impingement values are called for, use the anticipated monthly seepage
quantity as calculated in step (8) for the module immediately
overlying the one being analyzed. In step (7) include hypothetical
seepage quantities, as determined in steps (9) and (10), when
evaluating the response of the module to seepage rates in excess of
the anticipated seepage rate determined in step (8).
(12) If the liner/drain module being evaluated is the bottom one in the
system, use equations (28) and (29) to calculate the cumulative
efficiency for the module being analyzed plus all overlying modules
and the landfill cover. If the cumulative efficiency exceeds 90%, the
system as a whole performs adequately.
43
-------
CALCULATIONS
1
select typical cross sect I on (s)
EVALUATIONS
construct Liquid Routing Diagram
Isolate Liquid Diversion Interfaces
examine precipitation record and
select maximum monthly precipitation
determine amount of liquid
Imlnglng on the module
calculate hma)
calculate the module's efficiency
for a range of Impingement rates
calculate the anticipated monthly
seepage quantity through the liner
I
calculate the hypothetical seepage
quantity through the liner assuming
a constantly wet liner but with no
mounding of I Iquld
10
calculate the hypothetical seepage
quantity through the liner assuming
mounding of liquid to a height h
max
In the drain layer
Is this the
bottom
Iner/draln
module?
12
calculate the cumulative efficiency
for the bottom module plus overlying
modules and cover
assess the adequacy of the
drain layer design
assess the adequacy of the
IIner/draln module design
if this Is the bottom
liner/drain module, determine
whether the environment
underlying the landfill Is
capable of assimilating this
seepage quantity
assess the cumulative
efficiency of the system
Figure 16 - Diagram of the evaluation procedure.
44
-------
Table 3 - Equations used in evaluation procedure.
EQUATION
EQUATION STEP{S) IN
NUMBER WHICH USED
w * Ar ta"z
N /I + d ^ "C
V ho cos a 1
E = 1 * N for N>0
1
*1 " ksl sin a
a - tan a (3)
(ID
d /i ->\
ho cos a (1Z)
(13a)
(13b)
(10)
(. \ -Ct/t, ,
, d \ 1 a M/n
E' = * g N' for N'>0
f ' fnr M1 ^ 0
e = (1 - E') % n
e = ks2
e-/ d + hmax\ k
I d / ^
,. eprec " es2
02 Vec
ET = En9
hQ cos a v '
(15a)
(15b)
(17)
(5)
(6)
(28)
(29)
(6)
(7),(i
(7)
(7)
(7)
(8)
(8)
(8)
(8)
(8)
(9)
(10)
(12)
(12)
45
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4.2 Evaluating Hazardous Waste Surface Impoundments
4.2.1 Operating Conditions
This evaluation procedure has been prepared with the assumption that the
operating conditions for the hazardous waste surface impoundment meet the
basic requirements of good engineering design. For example, it is presumed
that:
(1) surface water has been intercepted and directed from the site;
(2) synthetic liners have been properly installed so that their integrity
is assured for their design life;
(3) ground water flowing laterally into the surface impoundment has been
intercepted or otherwise diverted around the site;
(4) artesian pressures in strata underlying the surface impoundment have
been relieved so that the hydrostatic head in the artesian aquifer lies
below the base of the surface impoundment;
(5) inlet and outlet structures have been designed and rate of flow
controlled to eliminate scour of liners;
(6) freeboard design and slope protection result in no detrimental wave
action; and
(7) the designs proposed for the components of the surface impoundment form
a properly functioning system.
4.2.2 Quantifying the Performance of a Surface Impoundment Design
A well designed hazardous waste surface impoundment contains a bottom
liner that minimizes the amount of liquid seeping to the underlying
environment. To quantify this, perform a computation described in section 3.3
to determine an upper bound to the seepage quantity through the clay liner.
The next two sections present an evaluation procedure based upon this
computation.
46
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4.2.3 Information Required to Use the Evaluation Procedure
The plans and specifications must provide the following information
required to use this evaluation procedure:
(1) typical cross sections,
(2) the thickness, d, of the clay liner,
(3) the coefficient of permeability, ks2, for the saturated clay liner, and
(4) the depth, H, of liquid in the lagoon.
4.2.4 Evaluation Procedure for Surface Impoundment Designs
The procedure is as follows:
(1) From the design drawings, select a typical cross section through the
surface impoundment. If the vertical profile through the lagoon
differs from place to place, more than one cross section will require
evaluation.
(2) Construct a liquid routing diagram to track the course of the liquid as
it moves through the cross section.
(3) Using equation (7), determine the anticipated monthly seepage quantity,
es, through the liner. Determine whether the hydrogeologic environment
underlying the lagoon is capable of assimilating this seepage quantity.
47
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5. EXAMPLE EVALUATIONS
This chapter contains numerical examples to illustrate the use of the
evaluation procedure. Section 5.1 presents the evaluation of a hazardous
waste landfill, while section 5.2 presents the evaluation of a hazardous waste
lagoon.
5.1 Evaluation of a Landfill
The example hazardous waste landfill is to be located in a region where
the ground water must be protected from contamination. Figures 17 and 18
contain excerpts from the plans and specifications respectively. The solution
procedure follows that recommended in Chapter 4. The steps referred to in the
calculations correspond to the steps of the recommended procedure.
Step 1. Select a typical cross section.
The plans give one typical cross section as shown in figure 17.
Step 2. Construct a liquid routing diagram.
Excerpt 1 from the specifications, as shown in figure 18, describes the
leachate control system and provides the basis for constructing the liquid
routing diagram. The modules that are considered to be part of the leachate
control system are the vegetated cover, the intermediate liner/drain module,
and the bottom liner/drain module. The intermediate cover is not included
because the designer provided too little information about its construction to
allow the evaluator to analyze its effects. The liquid routing diagram is
shown in figure 19.
Step 3. Designate the liquid diversion interfaces.
There are two modules containing liquid diversion interfaces: the inter-
mediate liner/drain module and the bottom liner/drain module.
48
-------
4)1 slopes
waste
vegetated
soil cover
Intermediate
cover
intermediate
sand drain layer
and clay 1 Iner
hazardous waste
bottom sand
drain layer
and clay Uner
native soil
Figure 17 - Excerpt from plans for proposed landfill.
49
-------
-excerpt 1-
CONTROL OF LEACHATE
Leachate will be controlled by
vegetated final cover, by an inter-
mediate sand drain layer underlain
by a compacted clay layer, and 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 2-
LABORATORY TESTS ON SAND
Laboratory permeability tests
were performed on the sand compacted
to the field density and then
saturated. The coefficient of
permeability was found to be lxlO~3
cm/sec.
Laboratory permeability tests
were performed on the clay compacted
at 2% above optimum moisture content
to field density. After saturation,
the coefficient of permeability was
found to be 1x10-7 cm/sec.
Figure 18 - Excerpts from specifications for proposed landfill.
(LTC)
(LTC)
Figure 19 - Liquid routing diagram for proposed landfill
-------
Step 4. Examine the precipitation record.
Table 4 shows the monthly precipitation record for the region. The month
showing the maximum precipitation is March, with 12.21 cm of precipitation;
thus,
e c = 12.21 cm/mo = 4.56x10" cm/sec
Table 4 - Site precipitation and percolation data.
MONTH PRECIPITATION (cm) PERCOLATION (cm)
January 0 0
February 0 0
March 12.21 1.83
April 6.48 3.25
May 9.47 2.51
June 10.60 0.05
July 9.27 0
August 9.04 0
September 8.56 0
October 5.18 0.61
November 1.70 1.60
December 0 0
Annual 72.51 9.85
51
-------
Step 5. Determine the maximum monthly percolation through the cover.
This example uses the water balance method described in SW-168. Table 4
shows the resulting values for monthly percolation. The maximum monthly
percolation is 3.25 cm in April. Note that the month showing the maximum
percolation is one month later than the month showing the maximum
precipitation. This lag reflects the time required for water to flow through
the cover. Assuming no generation of liquid by the waste and assuming no
recirculation of leachate, we obtain:
e = 3.25 cm/mo = 1.21xlO~6 cm/sec
Step 6. Calculate hmax and compare with drain layer thickness.
From equation (3):
, 30 m
n
max ~ 2(0.5)
1.21xlO-6 cm sec + tan2(5>n) \ 1/2 . tan(5.71)
lxlO~ sec cm /
= 0.176 m = 17.6 cm
Because 17.6 cm is less than the design thickness of 30 cm, the leachate will
not overtop the drain layer. Thus, the design is adequate in this respect.
52
-------
Step 7. Calculate the efficiency of the first module.
The value of C is not a function of impingement rate. Therefore, the
same value is used for all calculations in this step. C can be calculated
from equation (11):
C = JL lxl0"7 cm sec cot(5.71)
2 x 0.3 m cos(5.71) lxlO~ sec cm
= 5.025xlO"2
We now calculate the efficiency of the module for a range of values for
impingement rate. For the first calculation, use the anticipated monthly
impingement rate of 3.25 cm/mo from step (5). Assuming a porosity of 0.5,
calculate h0:
3 25
h = n*c = 6.50 cm
o 0.5
Putting the above values for C and h0 into equation (12) gives:
30 cm \ -5.025xlO"2 30 cm
N = ' X 6.50 cm cos(5.71) / e " 6.50 cm cos(5.71)
= 0.724
From equation (13a):
+ 0.724
53
-------
A second calculation based on the maximum monthly precipitation quantity
of 12.21 cm from step (4) gives:
h ,12'21 74 M rm
h = n c= 24.42 cm
o 0.5
The resulting value for E is 94.5%.
Table 5 presents the efficiency of the module for the above values of
impingement rate as well as for some additional values. This allows us to
plot efficiency versus impingement rate as shown in figure 20.
Table 5 - Efficiencies for various impingement rates.
e(cm/mo) h
0.5 1.0 32.6
1.0 2.0 60.6
2.0 4.0 79.1
3.0 6.0 85.2
3.25 6.5 86.2
4.0 8.0 88.3
5.0 10.0 90.2
7.0 14.0 92.3
10.0 20.0 93.8
12.0 24.0 94.5
12.21 24.42 94.5
Step 7a. Evaluate the efficiency at the anticipated impingement rate.
At the anticipated impingement rate of 1.21xlO~6 cm/sec (h0 = 6.50 cm),
the efficiency exceeds the limiting value of 75%; therefore, the module
performs adequately in this respect.
54
-------
E (*>
100
80
60
40
20
4 6 8 10
e (cm/mo)
12
Figure 20 - Efficiency of first liner/drain module
as a function of impingement rate.
55
-------
Step 8. Calculate the anticipated monthly seepage quantity through the
clay liner.
The anticipated monthly seepage quantity through the clay liner is
calculated using equations (10), (11), (14), (15) and (17). Equation (10)
gi ves:
+ 30 m sec 100 cm mo ,- cc
t, = = = b.ob mo
2 cos(5.71) x lxlO"J cm sin(5.71) m 2678400 sec
Equation (11) previously gave C = 5.025xlO~2. Equation (14) then gives:
l , 30 cm |_-5.025xlQ"2ri/5.66^
6.50 cm cos(5.71)/e
30 cm
6.50 cm cos (5. 71)
= 0.95
From equation (15a) we obtain the efficiency at the end of one month:
E. =_ =97.5%
From equation (17) we obtain the amount of liquid seeping through the clay
liner:
esl = ^ " °-975)(6.50 cm)(0.5) = 0.08 cm
56
-------
Step 9. Determine the hypothetical monthly seepage quantity for a constantly
wet liner, but with no mounding.
From equation (5) the seepage quantity is found to be:
e - 1X10"7 ^2678400 sec = ^ cm/mo
Step 10. Determine the hypothetical monthly seepage quantity assuming liquid
constantly mounded to a height, hmax, on the liner.
Using hmax = 17.6 cm from step (6) and also using equation (6):
_/30 + 17.
= V~30
6\ IxlO-7 cm 2678400 sec = 0.425 cm/mo
sec mo
Step 11. Repeat steps (6) through (10) for the next liner/drain module,
Note that this module also happens to be the bottom module.
Step 6. Calculate hmax and compare with drain layer thickness.
o
e = ei2 = esl = 0.08 cm/mo = 2.99xlO~ cm/sec
30 m
/ 2.99X10-8 cm sec + tin2(5.71)) 1/2 . tan(5.71)
\ 1x10 sec cm /
'max 2(0.5)
= 0.0045 m = 0.45 cm
Because 0.45 cm is less than the design thickness of 30 cm, the leachate will
not overtop the drain layer. Thus, the design is adequate in this respect.
57
-------
Step 7. Calculate the efficiency of this module.
Because this module happens to have the same design parameters as the
overlying module, the calculations previously performed in step (7) above can
be used to evaluate the present module. It is necessary, however, to
calculate the efficiency for this module's anticipated impingement rate of
0.08 cm/mo.
Step 7a. Evaluate the efficiency at the anticipated impingement rate.
ho = = °'16 cm
Using equations (11) through (13) as in the previous step (7), we obtain:
E = 5.4%
The efficiency of 5.4% is well below the limiting value of 75%.
Therefore, we proceed to step (7b) to determine whether low efficiency results
from poor design or simply from low impingement rates on the liner.
Step 7b. Evaluate the efficiency at high impingement rates.
Figure 20, which plots E versus e-j for the previous step (7) also happens
to apply to this step (7). Figure 21 duplicates figure 20 and also shows the
efficiencies at additional impingement rates. In particular, it is also
useful to calculate the efficiencies for the impingement rates associated with
a constantly wet liner with no mounding of liquid (e = 0.268 cm/mo) and for
mounding to a height hmax (e = 0.425 cm/mo). These give efficiencies of 17.8%
and 27.9% respectively. Figure 21 shows that the liner/drain module is,
indeed, a well designed one despite its low efficiency at the anticipated
impingement rate. This decision was made based on the observation that as the
impingement rate approaches the maximum monthly precipitation rate of
12.21 cm/mo from step (4), the efficiency increases to 94.5%. Because this
exceeds the limiting value of 90%, this aspect of the design is adequate.
58
-------
100
80
60
40
20
468
e (cm/mo)
10
12
Figure 21 - Efficiency of bottom liner/drain module
as a function of impingement rate.
59
-------
Step 8. Calculate the anticipated monthly seepage quantity through the
clay liner.
The anticipated monthly seepage rate through the clay liner is calculated
using equations (10), (11), (14), (15), and (17). Equation (10) gives
tj = 5.66 mo, as in the case of the overlying liner/drain module. C also
retains its previous value of -5.025xlO~2. Thus, equation (14) gives:
-.x~2
0.16 cm cos(5
30 cm \ -5.025x10*^(1/5.66)
.71) ) 6
30 cm
0.16 cm cos(5.71)
= -0.67
From equation (15b) we obtain the efficiency at the end of one month:
E' = 2(1 - (-0.67)) = 29'9%
From equation (17) we obtain the amount of liquid seeping through the clay
liner:
es2 = (1 - 0.299)(0.16 cm)(0.5) = 0.056 cm
Because this is the bottom liner/drain module, the value of 652 = 0.056 cm/mo
represents the quantity of leachate released to the environment. This
quantity should be compared with the quantity that the environment is capable
of assimilating.
60
-------
Step 9. Determine the hypothetical monthly seepage quantity for a constantly
wet liner, but with no mounding.
From equation (5):
e = 2678400 sec
Step 10. Determine the hypothetical monthly seepage quantity assuming liquid
constantly mounded to a height, hmax, on the liner.
From equation (6):
/ ^n + n 45 \
= 1 3p 1(0.268) = 0.272 cm/mo
V /
Because this module is the bottom liner/drain, we now proceed to step
(12).
Step 12. Calculate the cumulative efficiency.
From equations (28) and (29):
c 6prec " 6s2 12.21 - 0.056
02 - LT - epre(. - 12.21 -
Because 99.5% exceeds the limiting value of 90% for total system efficiency,
this liquid transmission control system performs adequately.
61
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5.2 Evaluation of a Lagoon
The example hazardous waste lagoon is to be located in a region where the
ground water must be protected from contamination. Figures 22 and 23 contain
excerpts from the plans and specifications respectively. The solution
procedure follows that recommended in Chapter 4. The steps referred to in the
calculations correspond to the steps of the recommended procedure.
Step 1. Select a typical cross section.
The plans give one typical cross section as shown in figure 22.
Step 2. Construct a liquid routing diagram.
The excerpt from the plans reproduced in figure 22 forms the basis for
constructing the liquid routing diagram. The leachate control system consists
of one module, the compacted clay liner. The liquid routing diagram is shown
in figure 24.
Step 3. Calculate the anticipated monthly seepage quantity through the
clay liner.
The anticipated monthly seepage quantity through the clay liner is
calculated using equation (7):
75 + 200 \ 1.25xlO"5 cm 1 mo 2678400 sec 199 Q ,mrt
e = 75 ~ = 122'8 Cm/m°
This is the quantity of leachate that must be assimilated by the underlying
hydrogeologic regime.
62
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liquid waste
compacted clay liner
native soil
T
2 m
75 cm
Figure 22 - Excerpt from plans of proposed lagoon.
-excerpt 1-
CONTROL OF LEACHATE
Leachate will be controlled by a
clay liner. The clay will be
compacted at 2% above optimum water
content and to 95% of standard
Proctor density.
-excerpt 2-
LABORATORY TESTS ON CLAY
Laboratory permeability tests
were performed on the clay compacted
at 2% above optimum water content
and at field density. After
saturation, the coefficient of
permeability was found to be
1.25xlO-5 cm/sec.
Figure 23 - Excerpt from specifications for proposed lagoon,
liquid
compacted
clay
I
I
native i
soil
Figure 24 - Liquid routing diagram for proposed lagoon.
63
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6. REFERENCES
Crank, John. 1975. The Mathematics of Diffusion. Clarendon Press. Oxford.
414pp.
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 Disposal Management Programs, SW-168, U.S. Environmental
Protection Agency, Cincinnati, Ohio.
Green, W. Herbert, and G. A. Ampt. 1911. Studies on Soil Physics, 1. The
Flow of Air and Water Through Soils. Journal of Agricultural Science.
Harr, Milton E. 1962. Groundwater and Seepage. McGraw-Hill, New York, 315
PP.
Klute, Arnold. 1952. A Numerical Method for Solving the Flow Equation for
Water in Unsaturated Materials. Soil Science. 73:105-116.
Lentz, John J. 1981. Apportionment of Net Recharge in Landfill Covering
Layer Into Separate Components of Vertical Leakage and Horizontal
Seepage, Water Resources Research. 17(4):1231-1234.
Matrecon, Inc. 1980. Lining of Waste Impoundment and Disposal Facilities.
SW-870. Municipal Environmental Research Laboratory. U.S. Environmental
Protection Agency. Cincinnati. Ohio, and Office of Water and Waste
Management. U.S. Environmental Protection Agency. Washington. D.C.
McBean, Edward A., Ronald Poland, Frank A. Rovers, and Anthony J. Crutcher.
1982. Leachate Collection Design for Containment Landfills. Journal of
the Environmental Engineering Division, ASCE, 108(EE1):204-209.
Mein, Russell G. and Curtis L. Larson. 1973. Modeling Infiltration during a
Steady Rain. Water Resources Research. 9(2): 384-394.
Messuri, Joseph A. 1982. Predicting Appearance of Leachate Under Clay
Liners. M.S. Thesis. The Ohio State University.
Monsanto Research. 1980. Hazardous Waste Leachate Management Manual.
SW-871. Municipal Environmental Research Laboratory. U.S. Environmental
Protection Agency. Cincinnati. Ohio, and Office of Water and Waste
Management. U.S. Environmental Protection Agency. Washington. D.C.
Perrier, Eugene R. , and Anthony C. Gibson. 1982. Hydrologic Simulation on
Solid Waste Disposal Sites. SW-868. Municipal Environmental Research
Laboratory. U.S. Environmental Protection Agency. Cincinnati. O.H.
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and Office of Water and Waste Management. U.S. Environmental Protection
Agency. Washington. D.C.
Philip, J. R. 1969. Theory of Infiltration. Advances in Hydroscience.
5:215-305.
Skaggs.\i982. , Develop 2-D Subsurface Drainage System Evaluation Model for
Hazardous Waste Disposal Facilities. Interagency Agreement AD96F2A140.
U.S. Army Corps of Engineers, Waterways Experiment Station.
Smith, Roger E. 1972. The Infiltration Envelope: Results from a Theoretical
Infiltrometer. Journal of Hydrology. 17:1-21.
Thornthwaite, C. W. and J. R. Mather. 1955. The Water Balance. Publications
in Climatology, Laboratory of Climatology. 8(1):9-86.
Thornthwaite, C. W. and J. R. Mather. 1957. Instructions and Tables for
Computing Potential Evapotranspiration and the Water Balance.
Publications in Climatology, Laboratory of Climatology. 10(3):185-311.
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Landfill Site. Water Resources Research. 13(2):404-410.
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APPENDIX
Principles of Partially Saturated Flow
The evaluation procedure presented in this manual does not incorporate
the time to first appearance of leachate for a particular design. The
engineer may, however, wish to determine this parameter as a part of the
design procedure. Messuri (1982) reports recent research on methods designed
to assist engineers in determining the laboratory parameters required to
perform these predictions.
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 nature of the
micropores that exist in clay soils, water moves not only by gravitational
forces, but also by capillary forces that tend to draw the liquid into the
soil. The smaller the pore radius, the larger the capillary attraction force.
Thus, soils with a high clay content will have very small micropores and
therefore very large capillary attraction forces. As the grain size of the
soil increases, the capillary attraction forces decrease; thus silty soils
have lower capillary action than clays. Sandy soils have such large
micropores that capillary attraction forces can reasonably be neglected, as we
in fact did in section 3.2.
The rest of this section presents a non-mathematical discussion of the
physical factors affecting the time to first appearance of leachate at the
base of a compacted clay liner.
When liners are emplaced, they are usually compacted at or slightly
wetter than optimum water content. The optimum water content is defined to be
that water content at which, for a given compaction procedure, the maximum
amount of soil particles could be packed into a given volume. Soil compacted
at optimum water content exhibits desirable properties such as high strength
and stiffness while still maintaining reasonably non-brittle behavior. While
the optimum water content originally meant optimum with respect to a soil's
performance as a highway subgrade, the same water content also imparts optimum
behavior in many other situations. For reasons beyond the scope of this
discussion, it is best to compact landfill liners somewhat wet of optimum
water content. In any case, any practical compaction water content for soil
liners will result in the soil being partially saturated. That is, the voids
in the soil mass will be partly filled with liquid and partly filled with air.
If additional water is introduced, say, at the surface of a clay liner
constructed of partially saturated soils, the liner will imbibe this water at
a relatively rapid rate. The physical reason for this is shown in figure 25.
The isolated water packets labeled B represent the water placed in the soil
upon compaction. The water labeled A is the new water moving into the soil
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Figure 25 - Simplified microscopic view of wetting interface
in a partially saturated soil.
\
Figure 26 - Macroscopic view of wetting interface in a
partially saturated soil.
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from above. Level C is termed the wetting interface, and moves downward
through the soil.
The forces causing the wetting interface to move are two. First, there
is the gravitational potential due to the weight of the water above the
wetting interface forcing the water into the soil'. Second, there is the
capillary potential produced by surface tension of the menisci forming the
wetting interface (point D).
The gravitational force causing flow will always be directed vertically
downward. However, this is not necessarily the case for the capillary
potential because that is neither caused by nor related to gravity. In
general, the capillary potential will be directed perpendicular to the wetting
interface. It always tends to pull the wetting interface into new regions of
partially saturated soil. For example, if the clay liner had been wet-up from
the bottom rather than from the top, the capillary potential would tend to
draw the water up into the liner against the gravitational forces tending to
force the water down. In the former case, both the gravitational and
capillary potentials cause the water to move downward through the soil. In
the latter case, the potentials counteract each other. Thus infiltration from
top to bottom occurs more rapidly than infiltration from bottom to top.
The situation depicted in figure 25 is oversimplified in that it implies
that the wetting interface, C, appears as a precisely defined line. In fact,
as shown in figure 26 drawn at a larger scale, this interface is distributed
over a finite region E-F. The graph to the right of the figure shows how the
water content varies with depth. Above point E the water content equals that
of the saturated soil, es. Below point F the water content equals the initial
compaction water content, e-j. Between points E and F the water content varies
smoothly between es ande-j.
Without going into the mathematical details, we will now rationalize why
the analytical treatment of partially saturated flow is complex. In the
extreme case of a soil mass that is fully saturated, there are no capillary
fringes, and flow is caused entirely by the gravitational potential. Flow in
this case is rather easily treated using Darcy's law, which states that the
flow velocity is linearly related to change in gravitational potential per
unit distance. A constant of proportionality, called the saturation
coefficient of permeability (or just coefficient of permeability), quantifies
the flow rate for any particular soil. For situations where there is no
ponding on the liner, the change in gravitational potential per unit distance
is unity; therefore, the flow rate is numerically equal to the coefficient of
permeability.
Flow in partially saturated soils is more complicated. Reference to
figure 26 shows that in the region above point E (where the soil is saturated)
there are no capillaries, therefore flow is simply saturated Darcian. In the
region E-F, capillary forces greatly affect the flow process. However, even
within this region the capillary forces vary with position. The longer
saturated strings such as those marked A on figure 26, are moving into the
smallest of soil pores, and thus the capillary forces are quite high.
Conversely, near location E, the water is moving into larger pores and the
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capillary forces are not as great.
In this situation it becomes difficult to characterize the soil's ability
to transmit water because this ability is related to the water content at the
particular point being considered. In the region where the soil is saturated
(above point E), the saturated coefficient of permeability characterizes flow
in the entire region. However, where the water content varies (region E-F),
the partially saturated coefficient of permeability governs. Between points E
and F the soil is quite non-homogeneous with respect to moisture content, and
thus, with respect to coefficient of permeability.
In calculating the flow through such a partially saturated soil mass, it
is necessary to address the variability of permeability with position by
mathematically integrating over the entire depth. During this integration
process, the variability in the coefficient of permeability can be accounted
for in a relatively direct manner.
The problem is further complicated, however, because the interface
region, E-F, is not stationary, but rather, moves downward with time. Thus
the integration process must be carried out not only in space (throughout the
depth of the soil), but also in time. This double integration complicates the
mathematics somewhat.
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