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COPY FOR yni/R
MEMO ' f^Kv^va x / / / r jTo: OSRR '
From; Dennis P. Gagne, Chis ^5/AklL Technical Support and Sitev
Yoon-Jean Choi, Geotechnical Engineer J ^ L Technical Support and Site Assessment SDMS DOCID 9126
Subject: Alternative Cap Design Guidance Proposed for Unlined, Hazardous Waste Landfills in the EPA Region I
Date: September 30, 1997
The purpose of this technical memorandum is to provide guidance to the designer of a cover or cap system for unlined, hazardous waste landfills (i.e., Superfund landfill sites) in New England. It is also intended to.be a source of technical infonnation for regulatory personnel (e.g., RPMs, RFMs,...) to assist them in evaluating cap designs submitted for approval.
Landfill caps at Superfund sites should meet the RCRA technical requirements contained in 40 CFR 264.310. The regulatory requirements of the above referenced section specify that final covers must be designed and constructed to:
(1) Provide long-term minimization of migration of liquids through the closed landfill.
(2) Function with minimum maintenance.
(3) Promote drainage and minimize erosion or abrasion of the cover. £
(4) Accommodate settling and subsidence so that the cover's integrjtfy^rfSlntained.
(5) Have a permeability less than or equal to permeability of any bottom liner system or natural subsoils present.
The majority of Superfund landfill sites do not have engineered bottom liners. Therefore, following the requirements of 40 CFR 264.310(a)(5), a cap for this type of facility could be designed and constructed with relatively permeable materials. However, though 40 CFR 264.310(a)(5) allows a more permeable design, we believe that more effective long term minimization of rainwater infiltration through the closed landfill would be provided by the cap design recommended in EPA guidance (EPA Technical Guidance Document. Final Covers on Hazardous Waste Landfills and Surface Impoundments; EPAV530-SW-89-047, July 1989). The cap design recommended in this document satisfies the requirements of 40 CFR 264 and 265 Subparts G(closure and post closure), K(surface impoundments) and N(landfills). The EPA recognizes that other cap designs may be acceptable, depending on site specific conditions and a determination by the Agency that the alternative design adequately fulfills the regulatory
OSRR ' Page 2 September 30, 1997
requirements. Such an alternative design is proposed in the following attachment.
The alternative cap design proposed consists of drainage geocomposite, geomembrane and IO"4
cm/sec soil (or geosynthetic clay liner only on top flat areas). An evaluation of this alternative cap using the EPA HELP model shows that it can provide equal or better performance minimizing the infiltration of rainwater (and the resultant leachate generation) than an EPA cap recommended to meet the requirements of RCRA Subtitle C.
Dennis Gagne (617-573-9661) and Yoon-Jean Choi (617-223-5505) of OSRR took the lead in developing this guidance. Please contact them should you need assistance in implementation of the proposed landfill cap design.
ALTERNATIVE CAP DESIGN GUIDANCE PROPOSED FOR UNLLNED1, HAZARDOUS WASTE2 LANDFILLS LN THE EPA REGION I
When designing landfill cap systems, the primary objectives are to 1) limit the infiltration of rainwater to the waste so as to minimize generation of leachate that could possibly escape to ground-water sources, 2) ensure controlled removal of the landfill gas, and 3) provide the foundation for an aesthetic landscape and allow vegetation of the site (or restore the site to the required beneficial afteruse).
I. CAP COMPONENTS
To protect the environment and prevent harm to human health, the EPA Region I recommends that a landfill cap consist of the following (from bottom to top):
1. Base (Leveling) Layer; Forms a base for the capping construction.
• Minimum thickness of fill materials should be 6 inches (15 cm) to establish the rough grading of the cap.
2. Gas Vent Layer (Optional): Based on site-specific basis, the passive gas vent layer (or systems) should be able to control the volume of gas that may be formed during anaerobic decomposition of the waste.
• The gas vent layer should be placed below the low-permeability layer (i.e., geomembrane and low-permeability soil) to facilitate the control and collection of landfill gasses.
• Minimum 12 inches (30 cm) of sand and/or gravel with a permeability greater than 0.01 cm/sec is required to allow free movement of gasses trapped by the low-permeability layer
1 For abandoned landfill sites without a barrier layer at the base
2 Resource Conservation and Recovery Act's (RCRA) Subtitle C regulates hazardous wastes that exhibit one or more of the following characteristics: Ignitability, Corrosivity, Reactivity, or EP Toxicity.
and to protect the structural integrity of the cap from the uplifting forces due to-the gas pressure.
Where gravel or sand (i.e., gas vent layer) is covered by a compacted, low-permeability soil layer, a geosynthetic filter layer may be placed at the interface to separate the two layers.
Geosynthetic materials (e.g., geocomposite) may be substituted for sand or gravel in the gas vent layer if they can provide sufficient gas transmissivity and structural stability under the anticipated field conditions for the projected design life.
The vertical outlet gas vents or pipes for passive systems need to be located at the highest elevation of the gas vent layer to allow maximum evacuation of the gas. In unlined landfills, the gas vent outlets should penetrate to the bottom of the waste or extend to the top of the ground-water to assist in reducing the possibility of gasses migrating laterally.
3. Bottom Low-Permeability Soil Layer: The purpose of this layer is to provide a second level of protection against infiltration in the event that the top low-permeability layer (geomembrane layer) has a leak. The EPA3 recommends a low permeability soil (i.e.. compacted clay) with a permeability of 1 x IO'7 cm/sec or less, but complicating factors such as potential placement problems, desiccation crack development, low shear strength when wet, and borrow source availability, in most cases preclude the use of these materials for landfill covers in EPA Region I. Historical evidence suggests that the identification of a low-permeability soil layer borrow source that has adequate interface friction resistance with the geomembrane, as well as permeability less than 1 x IO'5 cm/sec may not be practical.
The integrity of a compacted clay cap can also be affected, over time, by differential settlement which can disrupt the cap structure and impair its performance. In New England, at least four clay caps constructed in compliance with state closure requirements have experienced extensive damages within compacted clays. Field investigations of existing clay caps have shown in-situ permeabilities in the range of 1 x IO"3 cm/sec to 1 xlO"5 cm/sec instead of 1 x IO'7 cm/sec achieved at the time of installation and required by the design specifications. For the reasons stated in the previous paragraph it appears maintaining the required permeability of 1 x IO"7 cm/sec may not be sustainable except for a short period following its installation. However, based on the HELP model evaluation discussed in Section II: Evaluation of Alternative Caps, locally available silt and sand materials (with a permeability of 1 x 10"4 cm/sec) in combination with a geocomposite drainage layer (with a permeability of 10 cm/sec) and the geomembrane exceeds the hydrologic performance of the EPA-recommended cap design3. In addition, using the locally available material will yield substantial cost savings, remain more impermeable than clays, and could result
3 The EPA Technical Guidance Document: Final Covers on Hazardous Waste Landfills and Surface Impoundments (EPA/530-SW-89-047, July 1989)
in easier construction and greater cap slope stability.
• The soil should be at least 12 inches (30 cm) of compacted, low-permeability materials with a permeability no greater than 1 x IO"4 cm/sec.
• The last lift of the compacted, low-permeability soil layer beneath the geomembrane should contain no stones, larger than Vi inch, that may damage the geomembrane.
• The upper surface of the compacted soil which is in contact with the geomembrane should have a minimum slope of 3 percent after allowance for settlement.
The use of a Geosynthetic Clay Liner4 (GCL) may also be a good alternative to low-permeability soil layer for cover systems due to its very low permeability when fully hydrated. Composite layers consisting of a geomembrane and GCL can be considered the ideal cover system in many conditions such as compliance with total and differential settlement, easy construction and quality control and cost efficiency. However, some aspects of GCL's long-term performance are questionable. These include its vulnerability to puncture and rips," long-term durability to dry/wet and freeze/thaw (e.g., chemical changes of bentonite), aging of the reinforcing fibers, long-term behavior related to the factional characteristics of the interface on steep side slopes and the efficiency of the composite action if GCL incorporates an overlying geotextile. Thus the following should be met if a GCL is used.
• A reinforced geosynthetic clay liner (GCL) may be used on top flat areas with slopes less than or equal to six (Horizontal); one (Vertical) instead of using a compacted, low-permeability soil. The interface friction angle between the GCL and geomembrane can be very low, particularly when the GCL becomes hydrated, so that this material is recommended for use only in relatively flat areas to ensure cap slope stability. All joints should have a minimum overlap of 12 inches (30 cm) to provide a watertight connection and allow a sufficient factor of safety.
4. Top Low-Permeability Layer (Geomembrane: GM): Geomembranes are thin sheets of flexible, relatively impermeable (typical permeability values are in the range of 5 x IO'11 to 5 x IO"14 cm/sec), polymeric materials whose primary function is to act as a fluid (liquid and gas) barrier. They are increasingly used in landfill cover applications due to the fact that the geomembrane plays a primary role in limiting infiltration through the composite cap system.
4 Geosynthetic clay liners (GCLs) used in landfill cap applications are thin (approximately 1/4-inch thick) "blankets" of bentonite sandwiched between woven and non-woven geotextiles
that are needle-punched (ie., reinforced) together. Laboratory permeability test results of GCLs indicate a very low permeability of 1 x 10"8 cm/sec to 5 x IO"9 cm/sec when fully hydrated.
The EPA3 recommends a minimum thickness of 20 mils (0.02 inch or 0.5 mm), but 20 mils may riot be a sufficient thickness for most geomembrane materials. Thicker geomembranes are better able to resist chemical aggression, temperature changes and gradients, stress corrosion and cracking, etc . . . Quality control is of primary importance during installation to guarantee satisfactory long-term performance of geomembranes since maintenance and remediation of the geomembrane is difficult once installed. The minimum thickness of high density polyethylene (HOPE) geomembrane specified in Technical Regulations for Hazardous Waste issued by the German Federal Government is 100 mils (0.1 inch or 2.5 mm) assuming that the waste is thoroughly compacted (or controlled) prior to capping. In this case the stress due to the remaining differential settlement is limited. Where there is a high potential for significant differential settlement, linear low density polyethylene (LLDPE) geomembranes are recommended due to their excellent elongation and flexibility characteristics.
On steep side slopes, the very low friction characteristics of the smooth geomembrane with adjacent layers may cause slope instability. Therefore, textured geomembranes may be needed to increase the cap side slope stability.
• The minimum geomembrane thickness should be 60 mils (0.06 inch or 1.5 mm) for linear low density polyethylene (LLDPE) or equivalently-performing materials, and 80 mils (0.08 inch or 2.0 mm) for high density polyethylene (HDPE) geomembranes based on site-specific conditions such as anticipated differential settlements and long-term durability.
• A textured geomembrane can be used on side slopes to increase cap side slope stability.
5. Drainage Layer: Over the past decade the EPA Region I experienced two Superfund landfill cap failures; one was caused by settlement of the weak subsoil and another by poor drainage systems. Similar occurrence of landfill cap failures (or slides) has been reported 5 6 7 , most failures occurred during, or immediately after, severe storm events. Often the effects of severe storm events over a short period of time (e.g., within a few hours) and resulting seepage forces within the drainage layer were neglected.
Currently the EPA3 recommends that the granular drainage layer for final covers have a minimum
5 Boschuk, J.J., 1991, Landfill Covers; An Engineering Perspective, Geotechnical Fabrics Report, Vol.9, No.2, March, pp. 23-34.
6 Soong, T. and Koerner, R.M., 1997, The Design of Drainage Systems over Geosynthetically Lined Slopes, GRI Report #19, June.
7 Richardson, G.N., 1997, Fundamental Mistakes in Slope Design, Geotechnical Fabric Report, Vol. 15, No.2, March, pp. 15-17.
thickness of 1 foot (30 cm) and a minimum permeability of 0;01 cm/sec. The EPA also recommends use of the HELP model to estimate percolation into the drainage layer and saturated depth over the low-permeability barrier on the basis of a daily precipitation data. Recent studies (Soong and Koemer, 19976, and Thiel and Stewart, 1993 8 ) indicate that the HELP generated percolation values significantly underestimate the hourly interval percolation values (at least 20 times) from severe storm events. Thus the HELP model program, based on a daily precipitation data is not appropriate to evaluate the worst case scenario which may create seepage induced slope instability. GRI's report6 also concluded that "The federal and state minimum permeability values for drainage soils (often taken and used directly in design) of 0.01 cm/sec are too low by a factor of 10, and in some cases 100.".
To prevent the potential for slope failures related to seepage forces, the EPA Region I recommends that a granular drainage layer (e.g., gravel or sandy gravel rather than sand) for landfill cap systems have a minimum thickness of 1 foot (30 cm) and a minimum permeability of 0.1 cm/sec. Properly functioning geocomposite drainage products may be substituted for a gravel drainage layer if equivalent long-term performance can be shown. The geocomposite can provide required flow values, can easily be installed over the geomembrane, and may provide additional puncture protection of the underlying geomembrane. Proper drainage systems; considering other effects such as a slope angle and length,freeze-thaw cycles, etc. . . . ; should be designed to
' reduce the hydraulic head being developed over the geomembrane and increase slope stability
Therefore, the primary function of the drainage layer is to remove excess rainwater, minimize infiltration through the low permeability layer and to enhance the stability of the cover soil on side slopes. The drainage layer can consist of either a geocomposite pr 12 inches (30 cm) of granular materials such as gravel or sandy gravel. It must be designed to facilitate the area's maximum foreseeable rainfall.
• A minimum thickness of 12 inches (30 cm) and a minimum slope of 3 percent, after allowance for settling and subsidence, are required to provide sufficient drainage flow as determined by the site-specific precipitation ratefrom a severe storm event over a short period of time. A 6-hour duration storm6 can be considered as a severe storm event.
• The permeability of drainage material should be no less than 1 x 10"1 cm/sec.
• A gravel drainage layer may necessitate installation of a sufficiently thick non-woven geotextile at the bottom of the layer to protect the geomembrane from being punctured. A granular or geosynthetic filter should be placed directly over the drainage layer to
-minimize the migration offines from overlying topsoil into the drainage layer.
8 Thiel, R.S. and Stewart. M.G., 1993, Geosynthetic Landfill Cover Design Methodology and Construction Experience in the Pacific Northwest, Geosynthetic 93 Conference Proceedings, pp 1131-1144.
A geocomposite drainage layer consisting of two non-woven geotextiles heat-bonded to a drain core should have an equivalent (or required) hydraulic transmissivity9 no less than 3 x IO"4 m2/sec. The top geotextile provides filter and separation functions and the bottom geotextile provides protection to the underlying geomembrane.
The geocomposite drainage layer including the low permeability layer (i.e., geomembrane and low-permeability soil) and the drainage outlet system should be located below the maximum frost depth penetration.
6. Protective Soil Layer: The purpose of the protective soil layer is to provide a soil that is capable of sustaining the vegetative cover through dry periods and protect the underlying drainage arid low permeability layers from frost damage and excessive loads.
7. Topsoil Layer: Below the vegetative cover is top soil which is required to support the vegetative cover. The topsoil layer will consist of a sand-silt-loam mixture to produce good vegetation.
• The final top slopes after allowance for settling and subsidence, should have a slope at least 3 percent to promote surface runoff during storm events while minimizing erosion. A maximum erosion rate of 2.0 tons/acre/year as calculated with the USDA Universal Soil Loss Equation is required.
• Drainage benches (or terraces) should be used to breakup steeply graded slopes of covered landfill sites into less erodible segments. For slopes greater than 10 percent in steepness, the maximum distance between drainage benches should be equal to or less than 100 feet. Benches should also be of sufficient width arid height to withstand a 24-hour, 25-year storm.
9 The equivalent (or required) hydraulic transmissivity can be determined by dividing the allowable hydraulic transmissivity by the design safety factor of 2 to 3. The allowable hydraulic transmissivity can be also determined from the ultimate hydraulic transmissivity data provided by the geocomposite supplier for performance testing (ASTM D4716) of the geosynthetic drainage product (e.g., geocomposite) after applying reduction factors due to long-term creep deformation, clogging effects, etc. . . (Koemer, R.M., 1994, Designing with Geosynthetics, 3rd Edition, Prentice Hall Publication Co., Englewood Cliffs, NJ., pp412-416). If the end product is a heat-bonded geocomposite, transmissivity data should be obtained for a heat-bonded geocomposite, and tested under a soil cover to reflect design drainage performance. The normal compressive load for design should also be at least 2 times higher than the field-anticipated normal pressure and hydraulic gradient be selected representative of the field condition.
It is an important task of environmental geotechnics to establish principles in the design and construction of landfills, in particular with respect to long term safety. The new problems and materials involved in landfill design require new calculation methods to determine settlement, slope stability (both static and dynamic) of capping systems, proper drainage systems, etc . . . There are no satisfactory solutions to all problems which may arise in the day-to-day practice of landfill design and construction. The landfill design should be performed by a qualified geotechnical expert and must consider factors which are important to the construction, operation and closure of the landfill. This discussion is intended to highlight some of the problems and experiences of landfill design and construction to present solutions and approaches which may be beneficial to the designer, construction team, owner or operator of the landfill, and the environment.
IL EVALUATION OF ALTERNATIVE CAPS
The percolation of water through an EPA-recommended cap3 for hazardous waste landfills and a proposed alternative cap, shown in Figure 1, was evaluated with the EPA Hydrologic Evaluation of Landfill Performance (HELP) computer model, Version 3.06 (Schroeder et al., EPA/600/R-94/168, 1994). Although the HELP model may not estimate the hourly peak amount which would cause slope instability over geosynthetically lined slopes, the program may be used to estimate the annual average percolation through the cap components for comparison of designs.
The cap cross sections used for evaluation are as follows:
1. EPA-Recommended Cap3: Bottom 1 x IO"7 cm/sec permeability material (2 feet thick)/upper geomembrane (20 mils thick)/! x IO"2 cm/sec permeability sand (1 foot thick) drainage layer.
2. Alternative Cap: Bottom 1 x IO*4 cm/sec permeability material (1 foot thick)/upper geomembrane layer (60 mils thick)/10 cm/sec permeability geocomposite drainage layer.
Default climatological data for Boston, Massachusetts were used to model the site climate (e.g., annual average precipitation = 43.08 inches . . .) . The cap slope length of 100 feet and side slope of 3 % were also assumed.
The HELP model results on cap performance for various cap sections are summarized in Table 1.
Table. 1 - Summary of Average Annual Percolation and Cap Efficiency Predicted by the HELP Model for Various Cap Sections
Cap Section Annual Percolation Cap Efficiency* (Inches) (%)
99.9976 EPA-recommended Cap 0.00101
Alternative Cap 0.00017 99.9996
Single Geomembrane Cap** 0.46407 98.9227
* Cap efficiency is defined as the sum of the percentage of percolation lost to runoff, evapotranspiration, and lateral drainage, and changes in the water storage system.
** Single geomembrarie cap without a bottom low-permeability soil layer [i.e., geomembrane layer (60 mils thick)/10 cm/sec permeability geocomposite drainage layer] for comparison.
This evaluation indicates that the proposed alternative cap allows less average annual percolation (or leakage) through the low-permeability layer than the EPA-recommended cap section3. Even the single geomembrane has a cap efficiency higher than 98.9%. This is primarily due to the fact that the relatively impermeable geomembrane (with a permeability of about 4 x IO"13 cm/sec) plays a, primary role in limiting infiltration through the composite cap system. In addition, the use of a high-permeability geocomposite (about 10 cm/sec) instead of the sand drainage materials (with a permeability of 0.01 cm/sec) enhances the removal of water which infiltrates through the cover soil layer to an exit drain, so that the potential for infiltration through a geomembrane can be effectively minimized. Because the geocomposite drainage layer offers this and other benefits, including easier and faster construction, the geocomposite drainage layer is proposed for use in the cap.
In summary, the proposed alternative cap provides equal or better performance in minimizing annual percolation and any resulting leachate generation from the landfill into ground water compared with a cap system based on the EPA-recommended cap design guidance3 for hazardous waste landfills.
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FIG. 1 LANDFILL CAP DESIGN
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Geosynthetic Research Institute DREXFJ. 33rd & Lancaster Walk Rush Building - West Wing U N I V E R S I T Y
Philadelphia, PA 19104 TEL 215 895-2343 FAX 215 895-1437
FOR GSI/GRI MEMBER ORGANIZATIONS
ONLY!
. A SA,
THE DESIGN OF DRAINAGE SYSTEMS OVER GEOSYNTHET1CALLY LINED SLOPES
by
Te-Yang Soong, Ph.D. Research Engineer
and
Robert M. Koerner, Ph.D. Director and Professor
Geosynthetic Research Institute Drexel University
West Wing - Rush Building Philadelphia, PA 19104
• f GRI Report #19
JUNE 17,1997
The Design of Drainage Systems Over GeosyntheticaUy Lined Slopes
Table of Contents
Page
Abstract i
Acknowledgments iii
1.0 Introduction 1
2.0 Background 3
2.1 Seepage Induced Slides 3 2.2 Storm Event Characteristics 7 2.3 Types of Drainage Systems 10
2.3.1 Natural Soils 10 2.3.2 Geosynthetics 13 2.3.3 Long-Term Effects 18
3.0 Water Balance Analyses 20
3.1 Basic Concepts 20 3.2 Calculation Options 23
3.2.1 Manual Method for Monthly Averages 23 3.2.2 Computer Method for Daily Averages 24
3.2.2.1 Design Profile 27 3.2.2.2 Default Properties 31
3.2.2.3 Method of Solution 31
3.2.3 Manual Method for Hourly Averages 32
3.3 Comparison of Results 34
4.0 Drainage Layer Considerations 38
4.1 Patterns of Seepage Buildup in Cover Soils 38 4.2 Drainage Layer Capacity {DLQ 40
4.3 Parallel Submergence Ratio (PSR) 41
5.0 Slope Stability Analysis Incorporating Seepage Forces 43
6.0 Behavior of Selected Cross Sections 47
6.1 General Slope Configurations and Dimensions 47 6.2 Leachate Collection Systems 49 6.3 Final Cover Systems Over Drainage Soils 51 6.4 Final Cover Systems Over Geosynthetic Drains 54
i
7.0 Parametric Evaluations
7.1 Leachate Collection Systems 7.2 Final Cover Systems Over Drainage Soils 7.3 Final Cover Systems Over Geosynthetic Drains
8.0 Summary
8.1 Water Balance Analysis Critique 8.2 Slope Stability Analysis Comments 8.3 Drainage Layer Capacity (DLC) Comments
8.4 Parametric Study Implications
9.0 Recommendations
10.0 References
57
57 64 71
77
78 79 80 81
84
87
'1
« •
• >
• <
* •
n :• i
-. <
Abstract
Upon investigating eight recent seepage induced slides of leachate collection and final
cover systems, it was felt that many designs underestimate the site-specific required flux (lateral
flow rate) value. Rather than rely on the HELP model, an hourly-interval procedure for
calculating the required flux is presented. It is based on a severe storm event and subsequent
water balance analysis over a 6 hour period. The various types of natural and geosynthetic
drainage materials are presented and assessed in light of the 25 to 40 times higher required flux-
values from such storm events.
The design methodology used to incorporate the site-specific required flux and the
material specific allowable flux-values into a slope stability analysis is developed and illustrated.
Example problems and a parametric study are presented. Based on the results, the
recommendations of the report are as follows:
• The site-specific precipitation rate should be based on a severe storm event basis,
particularly for the final covers of landfills.
• Permeability of natural soils and geosynthetic drains must be significantly increased
over those currently used in practice.
• Well graded and poorly graded gravels, and possibly sandy gravels, are the obvious
choice for natural soils.
• Higher flow rate geosynthetic drains than are currently used, e.g., triaxial geonets and
composite sheet drains, are necessary to meet the higher flux requirements.
• The length of slope should probably be limited to 30 m, unless the site is in an arid
region. The cumulative effect of long slopes was seen to be a major cause of seepage
induced slope instability.
• The drainage outlet at the toe of the slope must have the greatest capacity of any part
of the drainage system. Some design scenarios are offered.
- i
Using the method proposed herein, the eight seepage induced jslides"were back calculated '
to estimate the site specific precipitation values. They were quite high for leachate collection
layers, 14 to 44 mm/hour, except for one with very low permeability soil. For the final cover i
system slides, the precipitation values were remarkably low, i.e., 0.38 to 1.34 mm/hour. Clearly, ' ]
the permeability of the drainage layer soil was far too low, i.e., 0.01 cm/sec. Interestingly, this is
the regulatory minimum value in federal and many state regulations. * *
It is hoped that the report stimulates an increased awareness in the possibility of seepage _.1
induced slope instability. While instability of the leachate collection layer before waste is placed
is often not a critical issue (the slope can often be repaired by on-site personnel), instability of
final covers is a serious issue. Such instability could occur many years after closure of a facility,
when the expense of repair is a very contentious issue. Such seepage induced instability *$*
situations can be avoided by the type of conservative drainage design presented herein.
- i i
Acknowledgments
This study was funded through general membership fees of the organizations in the
Geosynthetic Institute consortium. We are grateful for their generosity and support. The
organizations are as follows; along with the primary contact person within that organization or
company. Members of the GSI Board of Directors (BOD) are identified accordingly.
GSE Lining Systems, Inc. (William W. Walling)
RUST Environmental and Infrastructure, Inc. (John Rohr/Anthony W. Eim)
U.S. Environmental Protection Agency (David A. Carson)
Polyfelt GmbH (Gemot Mannsbart/Gerhard Werner)
Browning-Ferris Industries (Charles Rivette/Dan Spikula [BOD])
Monsanto Company (Roy L. Hood)
E. I. duPont de Nemours & Co., Inc. (John L. Guglielmetti/Ronald J. Winkler)
Federal Highway Administration (Albert F. DiMiUio/Jerry A. DiMaggio)
Golder Associates, Inc. (Leo K. Overmann [BOD]/Mark E. Case)
Tensar Earth Technologies, Inc. (Peter J. Vanderzee/Donald G. Bright/Mark H. Wayne)
National Seal Co. (Gary Kolbasuk [BOD]/George Zagorski)
Poly-Flex, Inc. (James Nobert/George Yazdani)
Akzo Nobel Geosynthetics Co. (Wim Voskamp/Joseph Luna)
Phillips Petroleum Co. (Rex L. Bobsein)
GeoSyntec Consultants Inc. (Jean-Pierre Giroud)
- i i i
NOVA Chemicals Ltd. (Nolan Edmunds)
Tenax, S.p.A. (Pietro Rimoldi [BOD]/Aigen Zhao)
Amoco Fabrics and Fibers Co. (Gary Willibey)
U.S. Bureau of Reclamation (Alice I. Comer)
EMCON (Donald E. Hullings/Mark A. Swyka)
Montell USA, Inc (B. Alam Shah)
TC Mirafi, Inc. (Thomas Stephens/Dean Sandri)
CETCO (Richard W. Carriker)
Huesker, Inc (Thomas G. Collins)
Solvay Polymers (Philip M. Dunaway)
Naue-Fasertechnik GmbH (Georg Heerten/Kent von Maubeuge)
Synthetic Industries, Inc. (Marc S. Theisen/Deron N. Austin)
STS Consultants Ltd. (Cynthia Bonczkiewicz/Mark D. Sieracke)
Mobil Chemical Co. (Frank A. Nagy)
BBA Nonwovens, Inc. (William M. Hawkins/Ian R. Clough)
NTH Consultants, Ltd. (Jerome C. Neyer/Robert Sabanas)
Netlon, Ltd. (Richard A. Austin)
TRI/Environmental, Inc. (Sam R. Allen [BOD]/Richard Thomas)
- I V
GeoSystems Consultants (Craig R. Calabria)
U.S. Army Corps of Engineers (David L. Jaros [BOD])
Chevron Chemical Co. (Pamela L. Maeger [BOD])
Serrot Corp. (Robert A. Otto/Bill Torres BOD])
Lockheed Martin Energy Systems (Syed B. Ahmed/Sidney B. Garland)
Union Chemical Lab (ITRI) (Yen-Jung Hu)
Haley and Aldrich, Inc (Richard P. Stulgis)
Westinghouse-Savannah River (Michael Hasek)
Woodward-Clyde Consultants (Pedro C. Repetto/John C. Volk)
S. D. Enterprise Co., Ltd. (David Eakin)
PPG Industries, Inc. (N. (Raghu) Raghupathi)
Solmax Geosynthetiques (Robert (Bob) Denis)
EnviroSource Treatment & Disposal Services, Inc. (Patrick M. McNamara)
Strata Systems, Inc (John N. Paulson[BOD])
CARPI, Inc. (Alberto M. Scuero)
Rumpke Waste Service, Inc (Bruce Schmucker)
Civil & Environmental Consultants, Inc (Richard J. Kenter)
Agru Americas, Inc (Paul W. Barker/Peter Riegl)
-v
THE DESIGN OF DRAINAGE SYSTEMS OVER> GEOSYNTHETICALLY LINED SLOPES
The previous report in this series, GRI Report #18 dated December 9, 1996, presented
numerous analyses involving the stability of cover soils overlying geomembrane lined slopes. In
so doing, the report highlighted the precarious nature of several situations. For example,
equipment loads and seismic forces can be critical, as can be multi-geosynthetic lined slopes.
Nowhere, however, was stability more adversely effected than when seepage forces were
involved. Paradoxically, this is one situation that can be completely avoided by use of proper
drainage materials, either natural drainage soils or geosynthetic drains. Yet, slopes continue to
fail due to seepage induced slope instability. This report focuses completely on the issue of
proper drainage layer design and the subsequent analysis of the slope*s factor of safety for soils
located above geosynmetically lined slopes wim the hope that seepage-related slides can be
avoided in the future.
1.0 INTRODUCTION
For most geosynmetically lined slope applications like landfill Uners and the final covers
of closed landfills and waste piles, a geomembrane {GM), geosynthetic clay liner {GCL), or
compacted clay liner (CCL) is used as a hydraulic barrier. Furthermore, the liner is directly
oriented in the direction of the critical potential sliding plane. While this is unfortunate from a
stability perspective, it does allow for a tractable solution of the problem in a relatively
straightforward manner. The solution used by numerous researchers is a linear failure plane
oriented along the direction of the slope angle, of finite length and of constant thickness e.g.,
Giroud and Beech (1989), Koemer and Hwu (1991), McKelvey and Deutsch (1991), Thiel and
Stewart (1993), Bordeau, et al (1993), Soong and Koemer (1996), and others. In each case, the
analysis uses limit equilibrium concepts where the destabilizing actions involved (gravity, live
loads, etc.) create driving forces, and the shearing resistance of the materials at the critical
interface provides the resisting force. This assumes that the shearing resistance of the critical
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interface is less than the shearing resistance of the soil itself,-whicfi is, usually the case with
geosyntheticaUy lined slopes. In terms of a factor of safety (FS), this concept is expressed as
follows: _ Resisting Force
Driving Forces
When the FS is less than 1.0, the slope fails by sliding along the critical interface. When the FS
is greater than 1.0, stability is suggested with the higher the value, the greater the stability. For
temporary slopes, FS-values are typically 1.2 to 1.4. For permanent slopes, the FS-value should '
be at least equal to 1.5. Liu, et al (1997) give greater insight in this regard.
A critical issue, and one which has not seen much attention [the exceptions being Thiel
and Stewart (1993), Soong and Koemer (1996) and Richardson (1997)] is the negative influence
of seepage forces within the drainage layer and/or cover soil above the geosynmetically lined
interface. The tacit assumption of most designers appears to be that the cover soil' can readily
handle the required drainage, or that a drainage layer (often regulatory suggested insofar as
thickness and permeability) will be adequate. Unfortunately, neither assumption is accurate and
seepage-mobilized slope instability has all too frequently occurred.
This report focuses completely on the issue of the design of adequate drainage systems so
as to prevent seepage-mobilized slope instability. The report will present background
information, water balance analyses, drainage layer considerations (using both natural soils and
geosynthetic drainage materials), slope stability analysis, behavior of selected cross-sections,
parametric evaluations, related discussion, summary and recommendations.
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2.0 BACKGROUND x
This section of the report describes eight recent seepage induced slides known to the
writers. It also presents the possible magnitude of heavy rainstorm events and the idiosyncrasies
of various drainage systems.
2.1 Seepage Induced Slides
The occurrence of seepage induced instability was originally day lighted by Boschuk
(1991) and actually challenged in a field trial reported by Giroud, et al. (1990). Yet, such
incidents still occur and appear to have occurred more frequently in the intervening years. Figure
1 illustrates four case histories of slides occurring in the leachate collection soils above a
geomembrane liner before waste was placed in the respective landfills. Figure 2 illustrates an
additional four case histories of slides occurring in the drainage and cover soils above barrier
layers after waste was placed in the respective landfills, i.e., final cover situations. While all four
cases in the latter category involved compacted clay liners, the situations would probably have
been similar with geosynmetic liners. A brief description of each slide follows, and then all eight
are compared and contrasted in Table 1.
Case #1 occurred in 1992 with a 25 mm average diameter leachate collection stone
underlain by a needle punched nonwoven protection geotextile sliding on a stationary smooth
HDPE geomembrane. The geotextile failed at the top of the slope carrying it and the stone above
into the base of the landfill. The slope was 3(H)-to-l(V) and a number of successive slides
occurred during several heavy rainfalls. The stone was AASHTO #57 quarried limestone.
Case 2 occurred in 1993 with a 37 mm average diameter leachate collection stone placed
directly on a smooth HDPE geomembrane. The stone slid on the surface of the stationary
geomembrane down to the toe of the landfill. The slope was approximately 3(H)-to-l(V) and the
slide occurred immediately after a heavy rainfall. The stone was a very coarse AASHTO #3
quarried material.
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GT
Case #1 - GT failure Case #2 - Stone slide n
...V 450 rt*° ;J
GM
Case #3 - GM failure Case #4 - GT failure
Figure 1 - Various seepage involved slides of leachate collection systems in landfill liner systems
f S
i
m i i
•i i.
GravelN>N'
Case #7 - Soil/sand slide Case #8 - Soil/sand slide
1 Figure 2 - Various seepage involved slides offinal cover systems above solid waste landfills
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Table 1 - Recent Slope Instability Case Histories Involving Seepage Forces
No. Upper Lower Slope Inclination Cover Soil Approx. Slope Approx. Time after Cause of Interface Interface ( Hor.: Vert.) Thickness, (mm) Length, (m) Construction, (yr) Seepage Force
(a) Slides of leachate collection layers before waste placement
1 NW-NP-GT HDPE-GM 3 : 1 450 45 1 2 fines in stone
2 Stone HDPE-GM 3 : 1 450 30 3 4 fines in stone
3 VFPE-GM NW-NP-GT 2.5: 1 300 20 0.2-0.5 low initial permeability
4 NW-NP-GT PVC-GM 4 : 1 450 90 (3 benches of 30 m each)
1 2 ice wedge at toe of slope
(b) Slide of final cover/drainage layers after waste placement
5 Silty sand CCL 2.5: I 750 40 2 3 no drainage layer
6 Sand CCL 3 : 1 600 + 300 50 5 6 low initial sand permeability
7
8
Sand
Sand
CCL
CCL
3 : 1
2.5: I
750 + 300
600 + 200
45
90 (2 benches of 45 m each)
5
4
6
5
fines clogging ' gravel around pipe
fines clogging GT around pipe
Notes: GTGMCCL
= Geotextile = Geomembrane = compacted clay liner
NW-NPHDPEVFPEPVC
= Nonwoven needle punched = High density polyethylene = Very flexible polyethylene
= Polyvinyl chloride
Case #3 occurred in 1994 with a sand leachate collection material and VFPE H
geomembrane sliding on a stationary needle punched nonwoven geotextile. The slope was
approximately 2.5(H)-to-l(V) and the slide occurred during a relatively .light rainfall. The
geomembrane failed along the crest of the slope for a distance of approximately 30 m with its
upper end remaining in the anchor trench.
Case #4 occurred in 1995 with a 25 mm average diameter quarried leachate collection
stone underlain by a needle punched nonwoven protection geotextile sliding on a geomembrane.
The difference between it and Case 1 was that the geomembrane was PVC, the slope was 4(H)
to-l(V) and the toe blockage was via a frozen ice wedge with sun-melted seepage forces being
mobilized upslope. Approximately 3 ha of geomembrane was exposed after the geotextile and *
stone slid down to the toe of the landfill.
Case *5 occurred in 1995 with 750 mm of silty sand (k = 0.001 cm/s) cover soil sliding on
a compacted clay liner (CCL) during a storm event The slide was relatively small and localized.
The slope was 2.5(H)-to-l(V).
Case #6 occurred in 1996 with 900 mm of sand drainage layer (k = 0.01 cm/s) and cover
soil sliding on a CCL immediately after a storm event. At least four localized slides occurred.
The slope was 3(H)-to-l(V).
Case #7 also occurred in 1996 under very similar circumstances to Case 6, except
exhuming the gravel around the toe drain showed the gravel to be highly contaminated with fines f A
which migrated through the cover soil and/or sand. A number of localized slides occurred at this
site. The slope was 3(H)-to-l(V). '
Case #8 also occurred in 1996 under very similar circumstances to Case 7 except the >
geotextile filter surrounding the prefabricated toe drain pipe was excessively clogged with fines ,_j
from the cover soil and/or sand. There were a number of small localized slides at this site. This
is the so-called "socked pipe" design which is known to be problematic in other situations, e.g., '
in leachate collection filters beneath the waste mass, Koemer G. R. et al (1993). The slope was
2.5(H)-to-l(V).
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2.2 Storm Event Characteristics "
In seven of the eight cases of seepage induced slides just described, the occurrence was
during, or immediately after, rain storm events. Unfortunately, the exact storm magnitudes were
not recorded. It is assumed, however, mat localized short-term seepage forces created enough of
an additional driving force to decrease the FS-value to less than 1.0 and thereby result in the
slope's instability. The other case. Case #4, of an ice wedge at the toe of the slope and seepage
forces due to thawing at the top of the slope is certainly a plausible situation depending on site
specific climatic conditions. However, this case is somewhat unique and is somewhat outside of
me main thrust of this report. Clearly its teaching, however, is that toe blockage of any type
must be avoided in order to have a free up-gradient drainage system without mobilizing seepage
forces.
It should be obvious that rain storms are not well-behaved, uniform events. Figure 3
illustrates just how random a short-term storm event can be. The peaks occur over extremely
short time periods, i.e., minutes, and can reach dramatic rates. In light of this behavior, a slope
will undoubtedly be most susceptible during periods of high rainfall and particularly during or
immediately after the highest rainfall rate. In this regard, a seepage-related slope stability
analyses should be analyzed as a severe storm event and the drainage system designed
accordingly. This is not unlike all types of engineering design when considering live load
circumstances, e.g., snow loads, seismic loads, equipment loads, etc.
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; j
Time (in hours)
Figure 3 - Precipitation time-rate data for an extreme storm in Oklahoma on May 27, 1987, as measured by the National Storm Service Laboratory. Values are for a 2- by 2-km area, after Maidment (1993).
Ideally, one would like to select a design storm for which there is no risk of exceedance.
This concept, however, is most troublesome and hydrologists even argue about me existence of
an upper limit. More practical, and accepted in the design of spillways for dams, is the concept
of the probable maximum precipitation (PMP). This term is defined by the World 'A
Meteorological Organization as:
"theoretically the greatest depth of precipitation for a given duration that is physically possible over a given size storm area at a particular geographical location at a certain time of the year."
Four critical issues are related to the above definition: storm duration, storm intensity, l i
orientation (slope) effects and infiltration into the cover soil. For the first two issues. Table 2 is
available for the selected cases in the United States. It is seen that extremely high rates can occur
over small, localized areas. For the second two issues, one must proceed on the basis of site
specific material properties and an appropriate water balance analysis.
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Table 2 - Maximum observed rainfall amount, area and duration data for selected locations in the United States
[Table values are for average rainfall in millimeters, after the World Meteorological Organization (1986).)
Duration, hour
Area 6 12 18 24 36 v 48 72
26 km2 627* 757" 922' 983' 1062' 1095' 1148'
260 km2 498" 668e 826' 894' 963' 988' 1031'
520 km2 455" 65C 798' 869s 932' 958' 996'
1300 km2 391" 625' 754' 831' 889' 914' 947'
2600 km2 340" 574' 696' 767' 836' 856' 886'
5200 km2 284" 450" 572' 63C 693' 721' 754'
13000 km2 206" 282" 358" 394' 475' 526' 62C
26000 km2 145" 201j 257k 307k 384' 442' 541'
52000 km2 102" 152j 201k 244k 295' 351' 447'
130000 km2 64m 107° 135V 160k 201k 25 lr 335r
260000 km2 43m 64m 89" 109" 152p 170" 226"
Storm Date Location of Center Remark a July] L7-18 1942 Smethport PA b Sept. 8-10 1921 Thrall TX e Sept. 3-7 1950 Yankeetown FL Hurricane i June 27-July 1 1899 Heame TX k Mar. 13-15 1929 Elba AL
q July 5-10 1916 Bonifay FL Hurricane n Apr. 15-18 1900 Eutaw AL m May 22-26 1908 Chattanooga OK o Nov. 19-22 1934 Millry AL h June 27-July 4 1936 Bebe TX
j Apr. 12-16 1927 Jefferson Parish LA r Sept. 19-24 1967 Cibolo Ck. TX Hurricane
P Sept. 29-Oct. 3 1929 Vernon FL Hurricane
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For the cases of sliding of cover soils as described previously, it appears to the authors { i
that a 6-hour duration storm event falls acceptably close to the concept of a PMP event, i.e., a 6
hour duration storm can be considered as a severe storm event and, arguably, a worst-case event. i
Local weather conditions would prevail and the nearest meteorological station would be the : ] i
logical source of the hour-by-hour precipitation data. As far as the infiltration into the cover soil
calculated via a water balance analysis, one is immediately drawn to the use of the U.S. EPA
computer model entitled Hydrologic Evaluation of Landfill Performance (HELP). Clearly, the
methodology of this model is beyond reproach. At issue, however, is the periodicity of i
monitoring the infiltration (hence drainage) quantity and some of the assumptions generally used rj
by designers. The HELP-model proceeds on me basis of a daily monitoring of precipitation. As
will be seen, this significantly underestimates the drainage quantities which must be efficiently j
removed in the site specific cross-section on the basis of hourly monitoring. Monthly, daily and
hourly monitoring examples will be illustrated later in this report so as to illustrate the
significance of this issue.
23 Types of Drainage Systems
The traditional material used for the drainage of liquids has been naturally occurring
granular soils, e.g., sands and gravels. Beginning in the mid-1980's, geosynthetic drainage J
materials emerged. First geonets and later different types of drainage geocomposites. Each type, %%
under me collective name "geosynthetic drains", will be described in this section. ^ • - • ^
; :v
23.1 Natural Soils H
The drainage capacity of natural soils is usually analyzed using Darcy's formula:
q = kiA (2)
where q = flow rate (through or within the soil),
k = coefficient of permeability (the term used herein but more properly, the
hydraulic conductivity),
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/ = hydraulic gradient, and . '
A = cross sectional area perpendicular to flow.
Critical in the above formulation is the value of "k" for which many relationships exist.
Formulas range from the empirical Hazen relationship;
£(cm / sec) = CdlQ (3)
where C = constant ranging from 0.4 to 1.2,
d10 = 10% finer particle size (mm),
to the more complex Kozeny-Carman equation:
* = — I T {1 + eT*~3
J] — (4) l I n' p
J where k0 = slope factor (=2.5),
T = tortuosity (factor (=1.4),
S0 = wetted surface per unit volume of particles,
e = void ratio,
yp = unit weight of the permeating liquid,
)i = viscosity of the permeating liquid.
All formulas of this type indicate that particle size and gradation play the major role insofar'as
drainage of granular soils is concerned. Typical values of permeability for granular soils are
provided in Table 3.
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Table 3 - Typical values of permeability for granular soils.
Type of Soil USCS* Range ot "k"-values Classification (cm/sec)
clean, poorly graded gravel GP 5 - 20 clean, well graded gravel GW 1 - 10 clean, poorly graded sand SP 0.5 - 5 clean, well graded sand SW 0.2 - 2 mixed, poorly graded sandy gravel SP -GP 0.1 - 2 mixed, well graded sandy gravel SW - GW 0.01 - 0.5 mixed, poorly graded gravely sand GP -SP 0.005 - 0.05 mixed, well graded gravely sand GW -SW 0.001 - 0.01 silty gravels ML-GP, ML-GW, 0.0005 - 0.01 silty sands ML-SPorML-SW 0.0001 - 0.005 Unified Soil Classification System
Of course, the use of estimated or typical values as presented in Table 3 is for illustrative
purposes only and should never be used for final design. Testing by ASTM D2434 is necessary
in this regard. Upon obtaining the value of "it" for the candidate drainage soil, it must be
compared to the site-specific required value to arrive at a factor of safety. Alternatively, "k" can
be used to calculate a flow rate, q, and used in a similar manner, for example:
_ fallow FS = (5) Kreq'd
or, °a^o w PS = (6) Qreq'd
where FS = factor of safety,
= allowable permeability,
qallow = allowable flow rate (using Darcy's formula),
Kreq'd = required permeability, and
qreq-d = required flow rate (using Darcy's formula).
Depending on the drainage soil that is being used, a filter may also be necessary, e.g.,
when using GP or GW gravel in the final cover above the barrier layer, and perhaps witii other
coarse granular soils as well. Insofar as soil filters are concerned, the material will typically be a
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well-graded sand with particle sizes intermediate between the overlying protection or cover soil,
and the underlying drainage soil. The following filtration criteria for sand filters are from the
U.S. Army Corps of Engineers (1948).
To prevent piping: dl5 (filter) A . .
^ — < 4 to 5, and ^85(cover soil)
d\ 5 (drainage soil)
- -— > 4 to 5, and
< 4 t o 5 (7) ^(filter)
To maintain permeability: diS (filter)
t3 A _, _ ,
^5(cover soil)
«i15 (drainage soil) > 4 t o 5 (8)
d15(fflter)
The devalues refer to the size of particle at which 85% by dry weight of the particles are
smaller. Similarly, dis refers to the size of particle below which 15% by dry weight is smaller.
23.2 Geosynthetics
Geosynthetic drains are always composites in that the drainage core transmitting the flow
must be protected by a geotextile which acts as both a filter and a separator with respect to the
overlying soil. There are many types of drainage cores that are available:
• Biaxial extruded geonets
• Triaxial extruded geonets
• Stiff 3-D entangled webs
• Vacuum formed cuspated sheets
• Extruded columns or nubbed sheets
The design of a geonet, or other type of drainage core is straightforward. It results in the
quantification of a flow rate factor of safety as follows:
FS = ^ ^ - (9) <ireq'd
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where FS = factor of safety, '
qaUow = allowable flow rate as obtained from laboratory testing, and
qreq-d - required flow rate as obtained from design requirements of the actual
system.
The allowable flow rate comes from in-plane (transmissivity) laboratory testing of the
geosynthetic drainage product under consideration. Options in this regard are ASTM D4716 and
ISO/DIS 12958. The test setup must simulate the actual field svstem as closely as possible. If it
does not model the field system accurately, then adjustments to the laboratory value must be
made. This is generally the case. Thus, the laboratory generated flow rate is often an ultimate
(or index) value which must be reduced before use in design; that is,
Qallow < aul t (10)
One way of doing this is to ascribe reduction factors' on each of the items not simulated in the
laboratory test. This can be accommodated as follows:
1 (11) fallow ~ Inlt R F m x RFCR x RF C C * RFB C
Alternatively, if all of the reduction factors are grouped together:
(12) fallow - Quit URF.
where qaUow allowable flow rate to be used for final design purposes,
quit flow rate determined from a short-term transmissivity test between
solid plates, e.g., see the index data of Figure 4 which was generated
according to ASTM D4716,
'The term "reduction factor" is synonymous with the term "partial factor of safety" which has been used in past literature. This newer definition leaves me traditional term "factor-of-safety" to be uniquely associated with uncertainties in the design process.
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10 -2 • I I I • i i i i i i
Sheet Drain "N" - Index Normal stress = 100 kPa Sheet Drain T - Index
Sheet Drain "M" - Index -3 •Geonet - triaxial - Index
Geonet - biaxial - Index Sheet Drain "E" - Index Geonet (biaxial) - composite NP-NW-GT (1500 g/nV^)
C3 NP-NW-GT (1000 g/rtv^)
10"°
< E
10"= 5
LL
10"
io- i * i . l . m I Jkmm, ImmK I «
-2 10 10 10
Hydraulic gradient
(a) Variation of hydraulic gradient with normal stress constant
10" • Sheet Drain "E" - Index 1 — Sheet Drain T • Index
— - o — Sheet Drain "N" - Index — • • - - Sheet drain "M" - Index
10" — Q — Geonet - triaxial - Index — • — Geonet - biaxial - Index
o — -A- - - Geonet (biaxial) - composite cs * — NW-NP-GT (1500 g/nV^)
— » — NW-NP-GT (1000 g/m*2) t 10" CD
2 S o
LL
10 " :
1CV
100 200 300 400 500
Normal stress (kPa)
(b) Variation of normal stress with hydraulic gradient constant
Figure 4 - Flow rate behavior of various geosynthetic drainage materials and composites compared to the drainage capability of geotextiles and geonets.
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RF!N = reduction factor for elastic deformation, or intrusion, of the adjacent
geotextile into the drainage core space,
RFCR = reduction factor for creep deformation of the drainage core and/or
adjacent geotextile into the drainage core space,
RFCc = reduction factor for chemical clogging and/or precipitation of
chemicals in the drainage core space,
RFBr = reduction factor for biological clogging in the drainage core space,
and
URF = product of all relevant reduction factors for the site specific
conditions.
Additional reduction factors, such as core overlap flow restriction, temperature effects and liquid
turbidity, might also be considered. If needed, they can be included on a site-specific basis. On
the other hand, if the test has included the particular item, the reduction factor would appear in
the foregoing formulation as a value of unity. Details of the design and guidelines for the
various reduction factors are given in Koemer (1997).
As noted previously, a geotextile must cover the geonet or drainage core and its primary
function will be to serve as a filter. In so doing, the geotextile must allow the liquid to pass
without mobilizing upstream pore water pressure and, simultaneously, must retain the upstream
soil so that up-gradient piping and down-gradient clogging of the geonet or drainage core do not
occur. Thus the design is a two-step process; first, openness for permeability (or permittivity)
and second, tightness for soil retention (via the geotextile's apparent opening size).
Geotextile permeability is the first part of a geotextile filter design. A factor of safety is
formulated using permittivity, which is the permeability divided by the geotextile's thickness, as
follows:
F S =Vallow. (13) Vnq'd
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V = — • (14)
where
\ff= permittivity
kn = cross-plane permeability coefficient, and
t = thickness at a specified normal pressure.
The testing for geotextile permittivity follows similar lines as used for testing soil permeability.
The method is standardized as ASTM D4491 and ISO/DIS 11058. Alternatively, some designers
prefer to work directiy with permeability and require the geotextile's permeability to be some
multiple of the adjacent soil's permeability (e.g., 1.0 to 10.0, or higher).
The second part of a geotextile's filter design is focused on adequate upstream soil
retention. There are many approaches toward a soil retention design, most of which use some
characteristic of the upstream soil particle size and then compares it to the 95% opening size of
the geotextile (i.e., defined as O95 of the geotextile). The test method used in the United States to
determine this value is called the apparent opening size (AOS) test, designated as ASTM D4751.
"AOS" is defined as the approximate largest soil particle that would effectively pass through the
geotextile. In Canada and Europe, the test method is called filtration opening size (FOS) and is
accomplished by hydrodynamic sieving. One variation is designated as ISO/DIS 12956. Wet
sieving is felt by the writers to be the preferred method.
The simplest of the design methods examines the percentage of soil passing the No. 200
sieve, which has openings of 0.074 mm.
1. For soil with < 50% passing the No. 200 sieve: 09 5 < 0.59 mm (i.e., AOS of the fabric
> No. 30 sieve)
2. For soil with > 50% passing the No. 200 sieve: 09 5 < 0.30 mm (i.e., AOS of the fabric
> No. 50 sieve)
Alternatively, a series of direct comparisons of geotextile opening size (O95, O50, or 015) can be
made to a specific soil particle size to be retained (dgo, dgs, dso, or di5). The numeric value
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depends on the geotextile type, soil type, flow regime, etc. For example, Carroll (1983)
recommends the following widely used relationship.
0 9 5 <{2or3)d S 5 (15)
where 09 5 - the 95% opening size of the geotextile (in mm), and
d85 = soil particle size (in mm) for which 85% of the soil particle is finer.
More detailed procedures, for both static and dynamic flow are available, see Luettich, et al.
(1992). Details of the design and example problems are given in Koemer (1997).
23.3 Long-Term Effects
All too often when designing natural soil or geosynthetic drainage systems the focus is on
the as-received materials. While this may be appropriate for temporary slopes, it is not
appropriate for permanent situations like the drainage layer of final covers above closed landfills.
The overriding long-term effect on drainage systems is the potential for fine particle
migration and contamination of the drainage and/or filter materials. As seen in the case histories
presented in Table 1, seepage induced slides have occurred in gravel soils having 25 to 38 mm
average particle sizes. While these coarse drainage gravels may have appeared initially
acceptable, it must be remembered that quarried stone always contains fines and furthermore
with the weaker mineral types, e.g., limestone, many fracture surfaces exist to generate even
more fines. Furthermore, the filter (if one is present) may allow fines from overlying soils to
pass into the underlying drain. Over time and successive rain events, fines from various sources
migrate down through the thickness of the drainage layer and can then further migrate
downgradient. Obviously, the permeability of the stone (which always appears clean and porous
on its surface) decreases over time. The potential clogging mechanisms can be modeled in the
laboratory, but to the writers' knowledge long-term drainage tests of soils are rarely conducted
and have never (?) been reported in the open literature.
In a similar manner, long-term clogging can also negatively influence geosynthetic
drainage systems; both the drainage core and the geotextile filter. Focus in geosynthetic drainage
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systems has been on the geotextile due to its relatively small openings in'comparison to the
drainage core of geocomposites and geonets. Three candidate tests aimed at an assessment of
long-term geotextile clogging are available. They are the following:
• Long-Term How (LTF) test via GRIGT-1.
• Gradient Ratio (GR) test via ASTM D 5101.
• Hydraulic Conductivity Ratio (HCR) test via ASTM D 5084.
Of these tests, the hydraulic conductivity ratio test is preferred by the authors since it can model
the field situation under closely simulated conditions. The test is performed using a flexible wall
soil permeameter of the type mat is readily available in most soil testing laboratories, e.g., ASTM
D5084.
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3.0 WATER BALANCE ANALYSES '
The potential pathways for water movement on and through a soil cover system are
summarized in Figure 5. Two separate cross sections (both of which are utilized throughout this
report) are distinguished. Figure 5(a) illustrates the uniform drainage layer configuration typical
of leachate collection systems located beneath the waste mass (before the waste is placed). The
four slides illustrated in Figure 1 are of this type. Figure 5(b) illustrates the layered soil
configuration of final covers above the waste mass. The four slides illustrated in Figure 2 are of
this type.
The input of water into the cross-section is the site specific precipitation as described in
section 2.2. Some of the precipitation moves directly across the surface of the soil as runoff.
The remainder infiltrates into the soil. Part of the infiltration will escape back into the
atmosphere via evapotranspiration, some is stored in the remaining air voids of the soil, and the
remainder is called percolation where its vertical movement is eventually prevented by the
barrier layer (GM, CCL or GCL). The vertical percolation accumulated over the length of the
slope becomes the required lateral drainage or "flux". The maximum flux-value at the toe of the
slope is used for the design of the drainage layer. Thus, within the cover soil(s), water can be
returned to the atmosphere via evapotranspiration, stored within soil voids, drained laterally or
leak through the barrier layer. To conserve mass, the quantity of water that flows into the cover
must equal the quantity of water that flows out of the cover, plus the change in amount of water
stored within the cover. This principle of conservation of mass is the basis for the term water
balance analysis. Three alternate calculation procedures will be described after some basics are
presented.
3.1 Basic Concepts
Working from the definitions given in Figure 5, each term will be explained in the
context of the two types of cross sections that are illustrated.
- 2 0
Precipitation (P)
t ^ t u u i m , Surface Runoff fSfl;
Infiltration (I) -* A, —-IDrainage layer (Sand or gravel) A Actual Evapotranspiration (AET) ^ ^ ^ A £ —
Percolation (PERC) T ^ <3
• • • ^ -A - 4 i * drainage (FLUX) Hydraulic barrier layer
(a) Cross section of typical leachate collection drainage systems
Precipitation (P)
tttt in u m i Surface Runoff (SR)
Cover soil Actual Evapotranspiration (AET)
Change in water stored 4
in cover soil (AWS) &.-•
Percolation (PERC)j}. Drainage layer j (Natural soil or< geosynthetics) l
Lateral drainage fFLt/X} Hydraulic barrier layer
(b) Cross section of typical final cover systems
Figure 5 - Pathways of water movement through soil systems typical of leachate collection and final covers.
- 2 1
As described in section 2.2, the precipitation (P) that we will focus upon is the hourly
storm event over a 6-hour period. This will be seen to be very intense in comparison to daily or
monthly monitoring of precipitation on the basis of the flux that is generated.
The infiltration (7) into the cover soil is minimized by increasing the surface runoff (R).
For the cross sections we are considering, the runoff is relatively high since slope angles where
instability occurs are usually greater than 14 deg. which is 4(H)-to-l(V). Of course, high surface
runoff can easily lead to surface soil erosion but this consideration is not addressed in this report,
see Koemer and Daniel (1997) for details in this regard. The infiltration is also influenced by the
type of surface soil. For example, a coarse drainage gravel as shown in Figure 5a will accept
significantly more infiltration and less runoff than will a fine grained soil as shown in Figure 5b.
Water that enters the cover soil as infiltration flows downward by gravitational forces.
However, capillary action tends to retain water in the soil. Sto age of water in soil, coupled with
removal of water by e vapotranspiration, are important mechanisms in limiting the percolation of
water through the cover soils. Much of the water that falls on the soil surface infiltrates into the
soil and is returned to the atmosphere over time by plants through evapotranspiration.
Unfortunately, for very intense storms, the actual evapotranspiration (AET) is very limited due to
the short time periods considered.
An important major retarding mechanism toward high percolation values is the water
storage capacity of soils (WS). For dry, or partially saturated soils, infiltrating water will simply
fill the available space in the :r-'I voids. For sporadic and relatively mild rain events, the
retardation of percolation by water storage is a major factor in limiting percolation through the
system. When the voids in the cover soils are at field capacity or are fully saturated, however,
there is no additional storage capacity and the infiltrating water all passes through the system as
percolation in accordance with Darcy's formula. When the soils involved have high k-values the
quantities can be quite large. Cover soils at field capacity, or fully saturated, are the likely case
for the extreme storm events which are focused upon in this report.
-22
4
The vertical percolation (PERC) value itself (in units of .rnm/hour) is based on a
horizontal unit area, thus its units are mm/hour-m . It would continue downward except for the
underlying hydraulic barrier. lu diis report we make the assumption that there is "zero leakage"
through the hydraulic barrier layer (GM, GCL and/or CCL) beneath the drainage layer. This is
done for the following reasons:
1. For slopes of 4(H)-to-l(V), and greater, the value will be quite small, e.g., roofs of
homes at these angles (generally) do not leak.
2. The velocity of flow will be quite high for the short duration and intense storm events
considered herein further minimizing leakage rates.
3. The no leakage assumption gives rise to conservative estimates of percolation.
4. We have no idea what value to assume for leakage and would much prefer to assume
good CQC and CQA of the barrier system with no leakage.
Finally, whatever value of percolation arrives at the drainage layer, it translates completely into
lateral drainage, or flux (FLUX). The flux accumulates as it flows on top of the hydraulic barrier
to a maximum value at the toe of the slope. Thus, the flux is at a maximum at the toe of the
slope and the drainage system is designed on the basis of this value. It is a worst case scenario
assumption and is recommended for design so as to avoid seepage related slope instability
problems.
3.2 Calculation Options
There are many possible calculation options for percolation and we have selected three of
them; manually for peak monthly averages, computer modeling for peak daily averages, and
manually for peak hourly averages. Each will be explained.
3.2.1 Manual Method for Monthly Averages
A water balance analysis can be performed on a monthly average basis. The procedure
can be performed manually as proposed by Dr. D. E. Daniel of the University of Illinois-Urbana,
-23
however, it is highly amenable to use of a computer spread sheet to facilitate the actual
computations. Three publications provide the basis of Daniel's procedure; Thomthwaite and
Mather (1957), Fenn, et al. (1975), and Kmet (1982).
A table or spread sheet should be set up with twelve columns estabUshed for the twelve
months of the year. In a progressive sequence of steps, an additional twelve rows (from A
through P) are developed for each of the twelve months of the year. Table 4 gives an overview
of the information needed and the respective calculations to eventually arrive at a percolation
value (PERQ passing through the cross-section arriving at the drainage layer. The flow units are
in "mm/month" over a square meter of horizontal surface. Table 5 gives an illustration of this
procedure for a final cover system as shown in Figure 5b. Details of the procedure are found in
Koemer and Daniel (1997). The target value in Table 5 is the maximum monthly value of
"PERC", i.e., the required percolation value which is used to design the drainage system. Note
that the value in this example is 8.54 mm/month in the month of January and thereafter the
evapotranspiration has eliminated all of the infiltration resulting in zero percolation for the rest of
the year.
3.2.2 Computer Method for Daily Averages
Nearly all water balance analyses performed in the United States are conducted using the
computer program "HELP" (Hydraulic Evaluation of Landfill Performance). The HELP
program was written by Dr. P. R. Schroeder of the U.S. Army Corps of Engineers, Waterways
Experiment Station under sponsorship of the U.S. EPA. The program, which has been
periodically updated, is.available in the public domain. At the time of this writing, the latest
version is Version 3.0 and is available by purchasing "The Hydraulic Evaluation of Landfill
Performance Model, Engineering Documentation for Version 3", EPA/600/R-94/168b, from the
National Technical Information Service in Springfield, Virginia. A user's manual is supplied
with a diskette mat contains the program, which is written in FORTRAN for use on a personal
computer.
- 2 4
Table 4 - Manual Procedure for "PERC Calculation, Based on Monthly Average Rainfall Values, see Table 5 for Example
Row A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Value average monthly temperature
monthly heat index
unadjusted daily potential evapotranspiration
monthly duration of sunlight
potential evapotranspiration
mean monthly precipitation
runoff coefficient
runoff
infiltration
infiltration minus potential evapotranspiration
accumulated water loss
water stored
change in water storage
actual evapotranspiration
percolation (PERC)
check of calculations
Units °C
mm/mo.
—
mm/mo.
mm/mo.
—
mm/mo.
mm/mo.
mm/mo.
mm/mo.
mm/mo.
mm/mo.
mm/mo.
mm/mo.
mm/mo.
Comment or Calculation local weather station data
calculated value needed to determine evapotranspiration
calculated value using data from Row A & Row B
values taken from published tables
multiply Row C by Row D
local weather station data
estimated value, but guidance is available
multiply Row F by Row G
subtract Row H from Row F
subtract Row E from Row I
sum of negative values in Row J
calculated value having many details
difference in monthly water storage from Row L data
comparison to potential evapotranspiration
comparison to determine if percolation occurs (or not) and to what amount
validation of water balance calculations
- 2 5
Table 5 - Illustration of the water balance analysis in a typical final cover system using the manual method for monthly averages.
Row January Feburary March April May June July Auguit September October Toltl
Avq monthly Temp, *C ne 2 9 3 29 2
«eoH/haalfrici9>(fH.l ' 2 . 6 4 $ _fcffl i3.ea • I4.S4 t*.*L ma M M
8.78 JJZ_ * i *
Unadjusted deny potential
(UPET). mnVrno
044 0 7 2 139 246 355 ? « 5 110
, ' D ' P0»»lbla rftonlhly'clurallon;" \ *7i(kk V ? ? ?v ..*.
/32,4, 93 4 t ' 051 36 342 -1309 2 9 4 ' 817 ' / • :
t2H A
I ro
I
Poterrtta) evapotranspiration
(Ptm. mrnAnq
ftraeteltallon (PrrnhVWb.*
Runoff Coefficient (RC1
MHffi^
1192
.HO?-7
040
- u M 8 & i *
18.80
040
43.02
040
- m
8033
••w:
•fflier
•sfraW
i z a l
27.492
17782
1&Z2_
A
16820
ipc' j
• 40.052 •
" 100 M' j
0 40
$6232 i
• " ' M . 7
0 40
'-1'* 95 g "
>«so
JIM
!£{££
•12M8Zr
•4 J
r j « K
ia.5
Infiltration (IN). mm/mo
«(*£ 4*,%." l>PET.mnVmo: I*?*'
(880
o.gf
(gOO
•ffiftf •
6884
•?tff • ,-W>if7 .-</*#:.
2583
'If2,19...
8008
•mm...
8035
•7445 •mo... '
57 30
m i
18.79
•tut.. I '!•'
Sag
Accumulated water loss
mm/mo. *SHW
0.00
116.50 :•''
0.00
118.60'^
•27.02
' .!w'Ml
•38.71 •98.92
-"' 6989" ^ • 4i.eo r .
•368.98
gQ,ee...
-47/.or
45.S6 • 40.96V-' • • • > ; » ' i
"119.W ' t lBW-:?--::*..
' -•;#>
if Change In waler storage
(CVYS1. mm/mo.
Aoliial,«wp«raMplratloo _; >4 •'**f?
0.00
, 18.80%
•25.18
• % ,
•12.04
"77.33 ,k'
•27.79 •10.95
; 38,58'
14.70
,48.38 , ' ;4W'.S5 • ' /
•20.40
j • f i & i : 'f.\ • v-; .
OOO
In:' Yhit.f7 «3»
?p"?.
Percolation (PERC). mm/mo. iiii.&i1i*i'Sf , \ *>
ftCKl.'mnVnK); - : ' :
8.S4
3 4 . ' ( » r 4
0.01
t54; 4«fr- '
0.00
i'2eS0/i
0.00
•;iu:4oJ
0.00
U M ooo 0.00
4Z72
0.00
100.13 | (00.58 |
0.00
95.71 •
-52.31
" " 9 5 . M
0.00
f 4 ^ I OPS
The computer program employs the same principles as the methooVof manual analysis
described in section 3.2.1, but HELP uses a daily (rather than monthly) time internal and
employs sophisticated algorithms for many of the computations. The model accepts weather,
soil, and geometric data. It then uses solution techniques that account for the effects of surface
storage, snowmelt, runoff, infiltration, evapotranspiration, vegetative growth, storage of soil
moisture, lateral drainage of water in drainage layers, leachate recirculation, vertical percolation
of soil water, and leakage through hydraulic barriers (GM, GCL, CCL or composite liners).
Engineering documentation of HELP is provided by Schroeder et al. (1994). We will not
attempt to repeat the documentation here. Instead, we will provide an overview of HELP'S
capability and discuss the key technical components of the model. The HELP program contains
a number of default values for soil and other parameters, which can prove to be helpful even for
manual analyses.
3.2.2.1 Design Profile
A schematic view of the profile that HELP was designed to simulate is shown in Figure
6. The profile is divided into three subprofiles (cover, waste and bottom liner system) to
simulate a landfill. For purposes of this report, attention is focused on me cover.
The layers that are analyzed with HELP are categorized by the hydraulic function that
they perform. Four types of layers are available, as summarized in Table 6.
(a) Vertical Percolation Layer
A vertical percolation layer is any layer permitting vertical movement of water
(downward due to gravity or upward due to evapotranspiration) within it, and not serving as a
lateral drainage layer. Examples of layers that are treated as a vertical percolation layers are top
soil, protection soil, gas collection layer, foundation soil, and waste.
- 2 7
Precipitation
Evapotranspiration
-Vegitafon 4
o. (D lateral drainage layer a. Lateral drainage CO
3 (from cover) o CO o
Geomembrane liner £ 3 CO
.o 0 Barrier soil layer Percolation O
Vertical percolation (D Waste layer
CL .Q 3 CO •a CD c C - . o o <D (|) Lateral drainage layer Sand E
CO fc <D Lateral drainage CD CD C CO (leachate collection) j @ Lateral drainage net E ~ >. o '
Io .
Sand Leakage i »
Geomembrane liner CD - \ Lateral drainage _C
® Lateral drainage layer (leachate detection) CD EQ. XI CD — 3 (0 *
CO C L
CO
T3 fcO O
® Barrier soil laye: 1'
Percolation • (leakage)
Figure 6 - Elevation view of a typical solid waste landfill
-28
Table 6 - Four Types of Layers Allowed in the HELP.Program
Type of Layer Hydraulic Characteristics Vertical Percolation Layer Flow in this layer is strictly vertical (downward due to gravity or
upward due to evapotranspiration). Hydraulic conductivity (permeability) at saturation is typically in the range of IO"3 to IO"6
cm/sec.
Lateral Drainage Layer This layer promotes lateral drainage to collection systems, e.g., drains at the perimeter of the cover. Hydraulic conductivity (permeability) can vary greatly. (This layer is the focus of the present report). The underlying layer is normally a barrier consisting of some type of liner.
Barrier Soil Liner Barrier soil liners are low-permeability soils; a compacted clay liner (CCL) with a permeability of IO"6 to IO7 cm/sec or a geosynthetic clay liner (GCL) with a permeability of lf>8 to IO9
cm/sec.
Geomembrane Geomembranes can be of many types. In the HELP program, they are assumed to permit leakage via vapor diffusion, manufacturing flaws (pinholes), and installation defects (e.g., flaws).
The method of calculating the downward movement of water in the unsaturated vertical
percolation layer is approximate. More rig us analytic techniques are available that more
carefully compute hydraulic gradients and consider vapor and thermal transport mechanisms.
However, computer codes that account for unsaturated flow more rigorously tend to be difficult
to use because of their complexity and, therefore, are rarely employed for water balance
analyses. Nevertheless, HELP is not considered a particularly accurate simulation program for
covers that are located in arid areas, where the subdeties of unsaturated moisture movement can
dominate the water balance.
(b) Lateral Drainage Layer
Lateral drainage layers may consist of granular soils or geosynthetic materials. Vertical
drainage in a lateral drainage layer is modeled in the same manner as a vertical percolation layer.
However, lateral flow in the saturated zone at the base of the lateral drainage layer is allowed.
- 2 9
Unconfined lateral flow in the drainage layer is modeled usirfg Darcy's formula,
assuming continuity and employing the Depuit-Forcheimer assumptions (seepage parallel to the
slope of the layer and hydraulic gradient proportional to the slope of the underlying barrier
layer). The algorithm used by HELP is reasonably rigorous and accurate. The accuracy with
which the permeability value of the lateral drainage is determined, not the method of analysis,
limits the overall accuracy of the calculations.
(c) Low-Permeability Soil Barrier Layer
Compacted clay liners (CCLs) and geosynthetic clay liners (GCLs) are frequently used as
hydraulic barrier layers. The soil is assumed to be saturated, i.e., to have no capacity to store
water without drainage occurring. Leakage through the CCL or GCL is assumed to occur
whenever there is a head of water on top of the barrier.
When the soil liner is located near to the surface of the cover and there is no
geomembrane overlying the clay, the low-permeability soil layer will probably desiccate at
times, invalidating the assumption of continuous saturation. To model this process, the low-
permeability soil layer can be treated as a vertical percolation layer. Also, clay liners are not
completely saturated with water at the time of construction, so the liners must first absorb some
nominal amount of water before drainage is initiated.
(d) Geomembrane Layer
Geomembranes are widely and routinely used in well engineered covers and liners
beneath the waste. Geomembranes can be extremely effective hydraulic barriers and can
withstand many of the forces (e.g., differential settlement and freeze/thaw or wet/dry cycles) that
are destructive to clay liners.
The HELP program assumes that liquids can leak through geomembranes by three
mechanisms: (1) vapor diffusion through the intact geomembrane; (2) leakage through
manufacturing defects (pinholes); and (3) leakage through construction defects (mainly flaws in
seams). The equations are complex and involve a number of possible cases. The reader is
referred to Schroeder, et al. (1994) for details.
- 3 0
3.2.2.2 Default Properties '
One of the useful aspects of the HELP model is that it contains default parameters for
various soil and waste properties based upon data available for more than a thousand soils.
Default properties are available for low-density, moderate-density and high-density soils.
Information is also available on default waste characteristics, on saturated hydraulic conductivity
(permeability) of wastes, and on default material characteristics for various geosynthetic
materials. In addition to the manual which documents the HELP program, these default tables
are reproduced in Koemer and Daniel (1997).
3.2.23 Method of Solution
The HELP program models both surface processes and subsurface processes. The
surface processes include snowmelt, interception of rainfall by vegetation, surface runoff, and
evaporation of water. The subsurface processes modeled are evaporation of water from the soil,
transpiration of water by plants, vertical percolation of water through unsaturated soil, lateral
drainage in drainage layers, and leakage of water through clay barrier soils, geomembranes, or
composite liners. Daily infiltration of water into the surface of the cover is determined indirectly
from a surface water balance. Each day, infiltration is assumed to equal the sum of rainfall and
snowmelt, minus the sum of runoff, surface storage (e.g., on the surfaces of plants), and surface
evaporation (e.g., evaporation of water stored on the surfaces of plants).
The daily surface water accounting procedure used in HELP is as follows. Snowfall and
rainfall are added to the surface snow storage, if present, and then snowmelt plus excess storage
of rainfall is computed. The total outflow from the snow cover is then treated as rainfall in the
absence of a snow cover for the purpose of computing runoff. A rainfall-runoff relationship is
used to calculate runoff. Surface evaporation is then computed, but surface evaporation is not
allowed to exceed the sum of surface snow storage and intercepted rainfall. The snowmelt and
rainfall that does not run off or evaporate is assumed to infiltrate into the landfill. Computed
infiltration in excess of the storage and drainage capacity of the soil is routed back to the surface
and is added to the runoff or held as surface storage.
- 3 1
The subsurface processes modeled by HELP are as follows. The fi&t subsurface process
considered is evaporation of water from the soil. Next, transpiration of water from the
evaporative zone by plants is computed. Other processes are modeled using a rime seep varying
from 30 minutes to 6 hours. For vertical percolation layers, a water balance is performed on each
layer to determine the water content of the material. Hydraulic conductivity is computed from
the water content, and then the amount of gravity drainage (if any) is determined. For lateral
drainage layers, a water balance is used to determine whether the drainage layer is saturated at
any point, and if so, lateral drainage is computed for that portion of the layer that is saturated.
Vertical percolation is assumed to occur in the lateral drainage layer above the zone of saturation.
The same equations employed for analyzing gravity drainage in vertical percolation layers are
used to analyze vertical flow above the saturated zone in lateral drainage layers. Soil barrier
layers are assumed to be continuously saturated and, therefore, no water balance is performed for
them. Leakage is computed from the hydraulic properties of the drainage layer and the amount
of head acting on the barrier layer. Leakage through geomembranes is computed from vapor
diffusion, leakage through pinholes, and leakage through installation defects.
The HELP program allows the user to select the number of years to simulate as well as
the output frequency. The user may use a maximum of 100 years of simulation provided the
weather are available for that many years. The user may also select any, all or none of the
available output options - namely, daily, monthly or annual output. Note that daily output is the
shortest time-interval available using the HELP program. Of the resulting output information,
the peak daily percolation (PERC peak daily, in units of mm/day) into the drainage layer within the
cover soil system is the target value for this report. This value will be used to calculate the value
of flux which is then used to design the drainage system.
3.2.3 Manual Method for Hourly Averages
Under the hypothesis that seepage induced slope instability occurs in periods consisting
of hourly intervals, and recognition that the minimum time-internal from HELP is days, a manual
method to calculate hourly averages is presented. Obviously, it requires hourly precipitation
- 3 2
data. Based on the basic concepts of water balance analysis shown in Figure 5, the following
relationships hold:
P = I + SR (16)
and * I = PERC + AET + AWS . (17)
where P = probable maximum (hourly) precipitation
/ = infiltration
SR - surface runoff
PERC = percolation
AET - actual evapotranspiration AWS = change in water stored in cover soil
= (field capacity) - (actual water content)
Under the assumptions that the immediate time before the PMP event has been a period
of regular rainfall, the actual evapotranspiration is negligible for a intense rainfall over a short
period of time (e.g., a few hours), and the cover soil is zi field capacity before the storm reaches
its highest intensity (i.e., there is only nominal excess water storage capacity available at the
time), the infiltration results directly in percolation, i.e., / = PERC. Therefore, the following
relationships result:
P = PERC + SR (18)
orPERC = P-SR
but SR = P(RC) (19)
where "RC " equals the runoff coefficient
thus PERC = P ( \ - R Q (20)
Note mat Equation (20) is valid only when the cover soil is sufficiently permeable so that
the amount of water which does not runoff [i.e., P( 1 - RQ] can percolate through the cover soil
into the drainage layer. When the cover soil is not permeable enough to handle such amount of
-33
water, the difference will occur as sheet flow over the ground surface. The amount is governed
by the permeability of the cover soil (k cover son). Thiel and Stewart (1993) showed that the
percolation into the drainage layer, under such a situation, should be determined as;
. PERC = kcoversoil; when Pf 1 - RC) > kcoversoil (21a)
otherwise: PERC = as calculated; when P( 1 - RC) <k cover sou (21b)
3.3 Comparison of Results
The following example is used to demonstrate the dramatic differences between the three
calculation options just presented; namely, monthly, daily and hourly averages.
Example: A landfill is to be built in Thrall, Texas (60 kilometers northeast of Austin). The site is
a 200 m by 200 m square, i.e., it is 4 hectares. The side slopes of the leachate collection layer in
the liner system, as well as the final cover, have slope inclinations of 3(H)-to-l(V). The runoff
coefficients for the leachate collection layer is 0.18 and for the cover soil is 0.4. Calculate the
percolation (PERC) and flux (FLUX) values of the leachate collection layer in the side slope liner
system (figure "a" following) and the final cover system (figure b" following) for slope lengths
of 10, 30, 60 and 100 m on the basis of monthly precipitation (per Section 3.2.1), daily
precipitation (per section 3.2.2), and hourly precipitation (per section 3.2.3). The soil
permeability values are default values suggested in the HELP manual.
- 3 4
T 450 mm 50 m
1 Geomembrane
(a) Leachate collection system
Geomembrane
(b) Final cover system
Solution: Each of the three calculation options presented in the previous section were used to
obtain the percolation (i.e., "PERC") and the results were multiplied by the
respective slope lengths using a unit width to obtain the respective values of flow
rates (i.e., "FLUX"). The results are summarized in Table 7.
-35
Table 7 - Results of the example problem using various time interval options of water balance analyses to obtain PERC and varying slope lengths to obtain FLUX.
Time Type Internal PERC FLUX (m3/hr)
for (mm/hr) Calculations L = 1 0 m L = 30m L = 60m L = 1 0 0 m
(a) leachate monthly 0.046 l 4.4 x 10-4 1.3 x 10-3 * 2.6 x IO-3 4.4 x IO"3
collection daily varies 0.025 0.079 0.16 0.28
system hourly Oo.l 3 0.65 1.9 3.9 6.5
(b) final monthly 0.011 * l . l x l ( H 3.3 x IO-4 6.6 x 10-4 l . lx lO- 3
cover daily varies2 0.013 0.041 0.088 0.14
system hourly 49.93 0.50 1.5 3.0 5.0 Note: 1. Via spread sheets as shown in Table 5, using the average monthly temperature, duration of sunlight and
precipitation data from Austin, Texas. 2. Via the HELP model using evapotranspiration , synthetic temperature and solar radiation data from
Austin, Texas and historical precipitation data (1974-1978) from San Antonio, Texas. The PERC and FLUX-values vary since the HELP model takes the slope length into consideration when calculating the amount of runoff.
3. Using the 6-hour rainfall data recorded at Thrall, Texas over an area of 260 km2 (see Table-2) and Equations 20 and 21.
For the above example, the values of FLUX for the various slope lengths can be put into a
comparison format by assuming that the HELP model gives the conventionally used values for
design purposes. Thus the HELP generated FLiTX-values will be assigned a value of 100% (or
1.0), and the monthly and hourly values compared accordingly. As seen in Table 8, it is readily
apparent that the precipitation time interval plays a dominate role in the calculations. Usiug
monthly intervals, the FLC/X-values vastly underestimate the HELP generated values (~ 60 to
120 times), whereas the hourly interval FLUX-values vastly overpredict the HELP generated
values (= 25 to 40 times). In the writers' opinion, it is the hourly interval calculations that result
in flux-values which create seepage induced slope instability and calculations using this time
interval should be used in the design of drainage layers for applications as described in this
report. This will be the approach taken in the remainder of the report. At the outset, however, it
should be stated that drainage systems designed as just noted (i.e., on an hourly interval basis
-36
with the worst case assumptions stated in section 3.2.3) will require significantly greater
hydraulic capacity than the comparable drainage systems designed using the HELP model.
Table 8 - Comparison of FLUX-values for different calculation options normalized to the conventionally used HELP generated values.
Slope length (m) Type Calculation option
10 30 60 100
(a) monthly 0.018 0.016 0.016 0.016
leachate
collection daily (HELP) 1.0 1.0 1.0 1.0
system hourly 26.0 24.0 24.4 23.2
(b) final monthly 0.008 0.008 0.008 0.008
cover daily (HELP) 1.0 1.0 1.0 1.0
system hourly 38.5 36.6 34.1 35.7
-37
4.0 DRAINAGE LAYER CONSIDERATIONS '
As long as there is percolation into the drainage layer beyond its field capacity, there will
be water flowing within the slope's drainage system. When the drainage layer is capable of
handling this flow rate, which is generally the assumption made in the design stage, seepage will
occur in the drainage layer only. Giroud and Houlihan (1995) describe the situation for both
steady state and transient flow conditions. They caution that the drainage layer must be able to
accommodate the required flow rate. However, when the flow rate is too large to be handled by
the drainage layer and/or its toe drain, seepage will buildup above the drainage layer into the
overlying cover soil or even flow above grade as an addition to runoff. Such seepage in the
drainage layer or overlying cover soil could build up in a horizontal or a parallel manner, or as a
combination of both. Since water tends to uplift soil particles due to a buoyancy effects and
seepage tends to drag particles in the direction of flow, such seepage forces lead to a decrease in
the slope's factor of safety and can easily result in seepage induced sliding.
From the above discussion, two issues are significant in conducting the design of the
drainage layer above a lined slope: the flow (phreatic surface; orientation and the depth of
submergence. Both issues are discussed in this section.
4.1 Patterns of Seepage Buildup in Cover Soils
Consider a cover soil of uniform thickness placed directly above a geomembrane or other
barrier material at a slope angle of "p"' as shown in Figure 7. Two discrete zones are illustrated;
a small passive wedge at the toe of the slope resisting a long, thin active wedge extending the
length of the slope. Only one type of soil is placed directly against the geomembrane and it is
cohesionless, i.e., typical of a leachate collection layer or a drainage layer in a final cover. For
the case of a drainage layer in a final cover, the profile can also consist of different soil materials
placed in parallel layers. In this case, the drainage soil would be granular and placed directly
above the geomembrane and then a locally available finer grained soil (including topsoil) would
-38
be placed above the drainage layer. Other soil properties, soil-to-geomembrane friction angle
and the dimensions of the considered profile are shown in Figure 7.
Note should be made in Figure 7 of two possible phreatic surface orientations. This is
necessary because seepage can be built-up in two different ways: horizontal or parallel to the
slope. Thus, orientation is quantified as a horizontal submergence ratio (HSR), or a parallel
submergence ratio (PSR). As to the depth of submergence, it is a function of the amount of
infiltration, the permeability of the drainage layer and the drainage layer capacity. The
dimensional definitions of both ratios are given in Figure 7.
Cover soil: 7, <t> Interface friction angle: 5
Active Wedge
Geomembrane 1
Passive H Wedge
HSR=^f H
P S R = h w
Figure 7 - Cross-section of cover soil on a geomembrane with different seepage buildup patterns.
Of the two seepage orientation possibilities shown in Figure 7, it is felt that extremely
low permeabilities at the toe of slope will result in a horizontal seepage buildup, Soong and
Koemer (1996). This would typify cases where toe blockage occurs due to fines migrating
downgradient over time, or due to ice buildup at the toe of the slope as the up-gradient drainage
layer thaws producing seepage pressure. However, in most steady-state situations, it is generally
assumed that water flows parallel to the slope, e.g., Giroud et al. (1995), Thiel and Stewart
-39
(1993). This would likely occur when the drainage system is underdesigned from the outset. In
a separate study, however, it has been shown that different seepage orientations, under the same
submergence ratio, make little difference in the resulting slope stability factor of safety values,
Soong and Koemer (1996). Furthermore, a specific amount of percolation results in a unique
submergence ratio regardless of the seepage orientation assumption, i.e., HSR = PSR, since the
total submerged volume of soil remains the same. Based on the above reasons, only the parallel
seepage orientation will be considered in this report.
4.2 Drainage Layer Capacity (DLC)
The rate of percolation per unit area (in units of m /hour) coming through a given cross
section, assuming no leakage through the underlying hydraulic barrier layer (which is a
conservative assumption), is determined as follows:
FLUX r e q d =^-xL{cosj5)xw (22)
where PERC = the rate of percolation in units of mrn/hr [see Equations 20 and 21],
L = length of drainage slope, m
/? = slope angle,
w = 1.0 = unit width of drainage slope, m
When designing the drainage layer in a soil covered slope, the following concept of drainage
layer capacity should be evaluated:
FLUXal l0WDLC = (23) FLUXreqd
where DLC = drainage layer capacity
FLUXaiion = allowable flow rate of the drainage layer per unit width of slope,
FLUXnq'd = actual flow rate per unit width of slope.
-40
It is good design practice and is generally required by regulatory agencies that the drainage layer
capacity cannot be exceeded, i.e., DLC > 1.0. That is, complete saturation of the drainage layer
should not be allowed at any time.
4.3 Parallel Submergence Ratio (PSR)
In a cover soil slope stability analysis, it is necessary to determine the depth of
submergence in the cross section so as to quantify the value of parallel submergence ratio (PSR).
The value of PSR can then be used in the slope stability analysis and ultimately results in a factor
of safety (FS) regarding slope stability. The following procedure can be used to calculate the
parallel submergence ratio (PSR). The typical cover system configuration of Figure 5b and
dimensions are illustrated in Figure 8. Note that the analysis also applies for full thickness
drainage layers typical of leachate collection layers beneath the waste material as shown in
Figure 5a.
hc.s.
/=s/n(ten"1(-£-)) 100
= sinfi
Figure 8 - Typical cover system configuration and dimensions used to calculate parallel submergence ratio
The average head buildup (havg) above the barrier layer can then be determined as
follows:
- 4 1
When hmg < hd, i.e., DLC > 1.0 (and the average phreatic surface level is within the
drainage layer).
_(FLUXreqd/3600) "•avg
kd x i (24)
When hmg > hd, i.e., DLC < 1.0 (the average phreatic surface level is within the cover
soil layer),.
FLUXreqd 13600 = / x [ kcs. {havg-hd) + kdhd ] ^ ( 2 5 )
where FLUXreqd - required flux, m /hr - .
kcs. - permeability of cover soil, m/sec /
kd - permeability of drainage soil, m/sec
lavg. = average head buildup above the geomembrane, m, and
= thickness of the drainage layer, m.
_ \ 3600 xi j h m g — kcs. (26)
Finally, the parallel submergence ratio, "PSR", can be calculated as follows:
PSR = — ^ — (27) n + ndc.s
The parallel submergence ratio is then used in the slope stability analysis as the mechanism to
incorporate seepage forces into the calculation. Note that the above aiscussion has been focused
on natural drainage materials. However, the procedure is also applicable to geosynthetic
drainage composites, providing the thickness and the equivalent permeability of the drainage
geocomposite under the site specific normal pressure and hydraulic gradient is known.
- 4 2
5.0 S L O P E S T A B I L I T Y ANALYSIS I N C O R P O R A T I N G S E E P A G E F O R C E S
F igure 9 shows the free body diagrams of both the active and passive wedges assuming
parallel seepage bui ldup result ing in a parallel submergence ratio (PSR). As noted previously, it
follows the same concept as does horizontal seepage bui ldup. The symbols used are defined
below.
WA = total weight of the active wedge
WP = total weight of the passive wedge
(Area) 'A = area of the active wedge below the free water surface
(Area) "A = area of the active wedge above the free water surface
(Area)p = area of the passive wedge
Ysafd = saturated unit weight of the cover soil
Ydry = dry unit weight of the cover soil
fw = unit weight of water
h = thickness of the cover soil
H = vertical height of the slope measured from the toe
h w = (PSR) (h) = height of the free water surface measured from the geomembrane
PSR = parallel submergence ratio
j3 = s lope angle
Uh = resultant of the pore pressures acting on the interwedge surfaces
U„ = resultant of the pore pressures acting perpendicular to the slope
Uv = resultant of the vertical pore pressures acting on the passive wedge
NA = effective force normal to the failure plane of the active wedge
N P - effective force normal to the failure plane of the passive wedge
<p = cover soil friction angle
5 = interface friction angle between cover soil and geomembrane
EA = interwedge force acting on the active wedge from the passive wedge
Ep = interwedge force acting on the passive wedge from the active wedge
- 4 3
(a) Active
y»hncosp
(b) Passive wedge
Figure 9 - Free body diagrams of cover soil with parallel seepage buildup
- 4 4
FS = factor of safety against instability ^ x
The expression for finding the factor of safety in the case of seepage buildup parallel in
the cover soil is obtained as follows, see Soong and Koemer (1996) for details.
_„ b + ^ b 2 - 4 a c F S = (28)
2a
where a = WA («Hp)(owP) - Uh (c<w2p) + Uh
b = -WAi[sin2^j{tan^) + Uh{sin$)(cos$){tan$) - NA{cos >){tanZ) - [WP - Uv){tan$)
c = NA{sm$){tanS){tan$)
in which ydry(h-.hwpHco$-{h + hw)] + ysa t .d(hwpHcos$-hw)
WA = —— (29) s inlp
Uh = y w M (30)
NA = WA («wP) + Uh (5mP) -U n (31)
_yw{hw){cosV){2Hcos?,-hw) Un (32) ~ ^ p
_ydry (h 2 -K 2 ) + ysafd(hw2)
P sin2$
Uv = Uh{cot$) (34)
Utilizing the above equations, the cover soil stability of geosynthetically lined slopes
with the incorporation of seepage forces, can be evaluated. A spread sheet containing the
required calculations was developed and is shown as Figure 10. The required input data is
shown in shaded boxes. It will be used in the next section of this report to examine the behavior
of typical cross-sections and then, in the following section, to conduct a parametric evaluation of
a number of relevant variables.
-45
Calculation ot DLC and PSR
Calculation o( FS Acllve Wedge:
W A = 655 kN(a) Active wedgeHHWHHI U . = 56.45 kN U , = 0.1973 kN N A = 579.04 kN
fics. VIkcs && USL
tinp slrtfloosP
. < • > ' . Passive Wedpe: W , = 65.053 kN
t ' 1 *t Ut '*. '1 ' i '1 *'. *i ' t ' i * U , = 0.7912 kN . • ' . • ' • • ' . • ' . • ' • ' ' ' ; ' ; ' ; ' ; ' . " '
hd
Fs^'b+lb'-^iss
where a = 153.8
L » 30.0 i / = 0.2419 b = 275.1 /} = 14.0 deg. L(cosp*) = 29.11 c = 32.7
x = 7.26 m DLC 1.488
ho* = 1000 mm ft e» = 1.0 m PSR 0.154 FS- 1.661 /) tf or f oa =t 300.0 mm h . or t o, = 0.30 m FS 1.661
h c, + h , = 1.30 m
m
T^T r.h.oos/)^ ) l
* M = I^OE^M;: cm/s k c» = 1.0E-0S m/s
k , orkoa « 1.00E-01 cm/s * , or k „ , = 1.0E-03 m/s (b) Passive wedge
/* P = 10.00 mm/hr P(RC)= 4.0 mm/hr
nc = 0.4 Actual runoff * 4.00 mm/hr thickness of cover soil = h = /.30 P£flC = 6.00 mm/tir length of slope measured along Ihe geomembrane = L = 30
FLUX „ * = 0.175 mVhr soil slope angle beneath the geomembrane = p = 14.0 0.24 (rad.) Note: It only one soil layer above GM, FLUX **, = 0.26128 m'/hr DLC « 1.4980 vertical height of the slope measured from the toe = H = 7.3
treat H asIhe drainage layer. parallel submergence ratio = PSR = 0.154 depth of Ihe water surface measured Irom the geomembrane = h . - 0.20
F L U X M = 4.BSE-05 m'/sec dry unit weight ol Ihe cover soil = y n = ;18.6 kN/m'
h „ = 0.20 saturated unit weight of Ihe cover soil = r „ =[i21.6 kN/m* PSR - 0.154 unit weight of water = y , = 9.89.811 kN/m"
friction angle ol Ihe cover soil = <. = 30.0 0.52 (rad.) Interface friction angle between cover soil and geomembrane = 6 •• 22.0 0.38 (rad.)
Nolejnumbers In boxes are required input data)
numbers In Italics are calculated values ConslnJded by Te-Yang Soong
Figure 10 - Cover soil stability analysis worksheet incorporating seepage forces with parallel seepage buildup
6.0 BEHAVIOR OF SELECTED CROSS SECTIONS
In this section, several cross sections typical of leachate collection systems and
final cover systems will be analyzed. These were the two general categories of the different
failures described in Table 1 and illustrated in Figure 2.
6.1 General Slope Configurations and Dimensions
So as to minimize the large number of variables that are possible, the general
configuration shown in Figure 11a will be used. It consists of a geomembrane lined slope which
is either 30 m long at a 3(H)-to-l(V) slope, or 100 m long at a 4(H)-to-l(V) slope. These are
commonly seen geometric choices by designers of both leachate collection systems and final
cover soil systems. To keep the number of variables at a minimum, a single type of cover soil is
used having the following properties:
j d r y =18kN/m3
Ysafd = 21 kN/m3
0 =30 deg. (soil-to-soil)
c = 0
5 =22 deg. (soil-to-geosynthetics)
In order to typify a leachate collection system which will eventually be covered by waste,
the drainage soil will be constant in its thickness and uncovered, see Figure 1 lb. For final cover
systems, a drainage layer will be incorporated between the underlying geomembrane and the
overlying cover soil. The drainage layer will be considered as being either natural soil (Figure
l ie ) or a geocomposite drain (Figure lid). Thus, three separate cases will be analyzed; each
having two geometric lengths and slope angles. Note that in all cases the precipitation is
calculated on an hourly basis as described in Chapter 3 and uses the assumptions stated therein.
- 4 7
yd,y=18kWn3
y«M=21 krirn3
> = 30°
see details below c = 0 kPa critical 5 = 22°
(a) General configuration and dimensions
critical interface: soil-to-GM
(b) Leachate collection system
5-mm G/V k = 10 cm/sec critical interface:
drainage soil-to-GM 5;tlfl^W^| critical interface: cover soil-to-GT
GM
(c) Cover system over drainage soil (d) Cover system over geosynthetic drain
Figure 11 - General configuration and specific dimensions of slopes to be analyzed.
- 4 8
6.2 Leachate Collection Systems -r.
Using the general slope configuration shown in Figure Ua, along with the details shown
in Figure 1 lb, an analysis for leachate collection soil stability was undertaken per the concepts
developed in Chapters 3, 4 and 5. The homogeneous drainage layer is 450 mm thick and has a
permeability of 0.3 cm/sec. This permeability was selected because it is the default value
suggested in the HELP manual. A relatively low runoff coefficient of 0.18 is used since the soil
is granular (sand or gravel) ?nd will accept a large portion of the precipitation. The stability
analysis has been performed for two separate geometric slopes:
• 100 m long slope at 4(H)-to-l(V)
• 30 m long slope at 3(H)-to-l(V)
The precipitation has been systematically varied between 5 mm/hr and 100 mm/hr. The results
are presented in Figure 12 for drainage layer capacity (DLC), the resulting parallel submergence
ratio (PSR), and the resulting slope's factor of safety (FS) against instability. The following
trends can be observed.
• Only for relatively low values of precipitation, e.g., less than 5 mm/hr, is the DLC
high, giving a low PSR and a FS-value greater than 1.2 for both slopes evaluated.
Note that this relatively low value of factor of safety may be acceptable since the
situation is temporary and stability will be established when waste is placed in the
landfill.
• For precipitation values between approximately 15 and 65 mm/hr for the two slopes
analyzed, the DLC drops below 1.0, the PSR is rapidly increasing and the FS-value is
less than 1.0.
• The above trends, in PSR and FS values are very abrupt and they result in a
discontinuity in the PSR and FS response curves when the DLC values drop lower than
1.0.
-49
y<#y=18kNUn3
y«f<,= 21 kUrn3
= 30°
O
l \
J t t 1
* * 1
'
ii
I
i
i c = 0 kPa o
cd critical 5 = 22° a.
ca
3 \\\\ I V\\ i
2 •VHUo-1 f \A
CD >. _m L = 3 0 m '
CD O ) co _c ca
•j
V4(H)-tO-1(V).
> ' " " " I ^ ^
* . i — '
0 - ^ "- —I 1 r— •
\ 1 i 1 1 !
o
1 0 -
~T 1•
• 4>
4>
/
critical interface: -to-GM
OR. i " j 4(H)-to-1(V), / L = 1 0 0 m
* •
c CD O) CD
E
0 6 -/
///
'/
, N ^ A
\ i
3(1 l ) - IO-l(V), L = 30m
1
1
i
a 0 4 -4>
/ ' ! ! i 2 4 *
ca a.
0 2 -\ , . -1 .' 1 1
;
;';
j
' !
0 . 0 1
i , i •
. ' i
' ! i
3(H)-tc-1(V), L = 30m
^ r
80 100 40 60
Precipitation (mm/hr.)
Figure 12 - Results of leachate collection system example problem
- 5 0
• The physical significance of the DLC decreasing to a value pf 1.0, and continuing to
values less than 1.0, is that water has filled the layer and will begin to flow on the
surface of the leachate collection layer and add to the naturally occurring runoff.
• For the two geometric cross sections analyzed, the 100 m long 4(H)-to-l(V) slope
reaches full drainage capacity sooner than the 30 m long 3(H)-to-l(V) slope, thus the
FS-value is less than 1.0 at lower intensity precipitation storms.
• The reason for the above is more related to the length of slope than to its slope angle,
since the require flux is cumulative over the length of slope. Long slope lengths will
be seen to be very challenging in this regard.
63 Final Cover Systems Over Drainage Soils
Using the general slope configuration shown in Figure 11a, along with the details shown
in Figure 1 Ic, an analysis for stability was undertaken per the concepts developed in Chapters 3,
4 and 5. The cover soil is 1000 mm thick and has a permeability of 0.0017 cm/sec. This
permeability is the default value of "SM" soils (commonly used for cover soils) suggested in the
HELP manual. A relatively high runoff coefficient of 0.40 is used since the soil is fine grained
and is probably somewhat cohesive. The underlying soil drainage layer is 300 mm thick and has
a permeability of 0.1 cm/sec. This value of permeability is 10-times greater than the HELP
manual's default value of "SP" soils and is used because the default value of 0.01 cm/sec always
results in FS-values less than 1.0. The stability analysis has been performed for two separate
geometric cases:
• 100 m long slope at 4(H)-to-l(V)
• 30 m long slope at 3(H)-to-l(V)
The precipitation has been systematically varied between 5 mm/hr and 100 mm/hr. The results
are presented in Figure 13 for drainage layer capacity (DLC), the resulting parallel submergence
ratio (PSR), and the resulting slope's factor of safety (FS) against instability. The following
trends can be observed:
- 5 1
'I y«y=18kMrn3
r«ftf = 21 kNin3
= 30° c = 0 kPa
critical 5 = 22°
critical interface: drainage soil-to-GM
^ j• 4
O c!
ca 3 • a. co I\\
2
I\ 1 CD \ \ 3<HHc-1(V), O l 1 co \ \ L = 30m |
1 \
0 - . | r- 1 ' '
i n. i :
I 0 8 a
<D O C
o 0 6 DI CD
E
0 4
1« 02
0 . 0
1.8
V 1 4(H)-to-1(V), / L=100m j
1
i
/ ^/*
3(H)-to-1(V). L = 30 m
i
i i i
i
i i i i
_ j ,',
//'" i1 1 1 1 1 1 1 — , —
u.
1.6
1.4
. \
A 4(H)-to-1C L=100m V
f).
*
o t> .* li
1.2
1.0
•
" \ 3(H)-to-1(V
\ L = 30 m i
1 X ! !
0.8
0.6 20
\%
i
40 — • —
,
i
i i
60 — < —
80 100
Precipitation (mm/hr.)
Figure 13 - Results of cover system over drainage soil example problem
-52
• Only for relatively low, values of precipitation, i.e., less than 5 mm/hr for the 100 m
long 4(H)-tp-l(V) slope and less than 20 mm/hr for the 30 m long 3(H)-to-l(V) slope,
is the DLC high, giving low PSR values and FS values greater than 1.0.
• Furthermore, a FS greater than 1.5, which is recommended for permanent slopes, only
occurs for the 100 m long 4(H)-to-l(V) slope at a precipitation value of less than 5
mm/hr.
• Water abruptly fills the drainage layer beyond this precipitation value rapidly
decreasing the FS-value to less than 1.0.
• For the 30 m long 3(H)-to-l(V) slope between precipitation values of 5 and 20 mm/hr,
the DLC falls to a value of 1.0. This increases the PSR and decreases the FS -value to
1.2. Water has completely filled the drainage layer at this point.
• As precipitation increases beyond 20 mm/hr for the 30 m long 3(H)-to-l(V) slope, the
DLC becomes less than 1.0, the PSR increases rapidly to a value of 1.0 and the FS-
values becomes less than 1.0.
• The above trends in PSR and FS values are very abrupt and result in discontinuities in
the PSR and FS response curves when the DLC values drop lower than 1.0.
• When the DLC is less than 1.0, which occurs for both geometric slopes above 20
mm/hr, the phreatic surface rises above the drainage layer into the cover soil. This is
clearly unacceptable insofar as slope stability is concerned. [Had the drainage layer
permeability been used as 0.01 cm/sec, which is the U.S. EPA minimum technology
guidance value and also the HELP default value, the FS-value would never have been
acceptable.]
• For these two geometric considerations, the 100 m long 4(H)-to-l(V) slope is more
sensitive to intense rain storms than is the 30 m long 3(H)-to-l(V) slope due to the
cumulative nature of required flux value over the longer length of slope.
- 5 3
6.4 Final Cover Systems Over Geosynthetic Drains . '
Using the general slope configuration shown in Figure 11a, along with the details shown
in Figure lid, an analysis for stability was undertaken per llie concepts developed in Chapters 3,
4 and 5. The cover soil is 1000 mm thick and has a permeability of 0.0017 cm/sec. This
permeability is the default value suggested in the HELP manual for "SM" soils, which are
commonly used for cover soils. A relatively high runoff coefficient of 0.40 is used since the soil
is fine grained and probably somewhat cohesive. The underlying geosynthetic drainage layer is
5.0 mm thick and has a permeability of 10 cm/sec. This value is not available as a default value
in the HELP manual and must be evaluated for tie candidate geosynthetic drainage material as
illustrated in Figure 4. The stability analysis has been performed for two separate cases:
• 100 m long slope at 4(H)-to-l(V)
• 30 m long slope at 3(H)-to-l(V)
The precipitation has been systematically varied between 5 mm/hr and 100 mm/hr. The results
are presented in Figure 14 for drainage layer capacity (DLC), the resulting parallel submergence
ratio (PSR), and the resulting slope's factor of safety (FS) against instability. The following
trends can be observed:
• Only for relatively low values of precipitation, i.e., less than 10 mm/hr for the 100 m
long 4(H)-to-l(V) slope and 30 mm/hr for the 30 m long 3(H)-to-l(V) slope, is the
DLC high, giving a near zero PSR value and FS -values of 1.6 and 1.3, respectively.
• At the above precipitation limits the PSR response curves go from near zero to 1.0 very
quickly because the geosynthetic drains are quite thin with respect to soil drainage
layers and they fill very rapidly.
• At the above precipitation limits, the FS-values drop rapidly to values less than 1.0.
• When the DLC is less than 1.0, the phreatic surface rises above the geocomposite
drainage layer into the cover soil. This is clearly unacceptable insofar as slope stability
is concerned.
-54
ydysismrrr3
r**rd = 21 kWn3
0 = 30° o = 0 kPa O
critical 8 = 22° Q
a Q . CO u a >.
S cc D) CO
c <o
1 1
i n. tt 8 o"
0 8 -* \
41.1-1)
L = 100 m
5-mm GN k = 10 cm/sec
c CD
s> 0 6
^ 3(H)-tO-1(V),L = 30 m
!
cntical interface: cover soii-to-GT
CD
E a <o
2 0 4 i
i
CD 0.
0.2
0.0 r J 1 i •
~1 1 6 1 4(H)-to-1(V), I L=100m
U. 1 4 r • - - - • - - - I
"5 '• 3(h )-fo-1(V),
30 m 1 2
o l !
1 0 1 1 l ! lL
)
11
0 8-1
i
1
0.6 1 — | r — l
20 40 60 80 100
Precipitation (mm/hr.)
Figure 14 - Results of cover system over geosynthetic drain example problem
-55
• For these two slopes, the 100 m long 4(H)-to-l(V) slope is somewhat more sensitive to
intense rain storms than is the 30 m long 3(H)-to-l(V) slope since the required flux is
cumulative over the relatively long slope length.
-56
7.0 PARAMETRIC EVALUATIONS . x
Based on discontinuous trends in drainage layer capacity (DLC), parallel submergence
ratio (PSR) and factor of safety (FS) in the previous section for only two slope conditions, it
should be obvious that the selection of variables for illustrative purposes is very sensitive and
quite subjective. Rather than select specific conditions, it is perhaps instructive to conduct a
parametric evaluation on a range of variables. This section presents this type of parametric
variation for the three profiles shown in Figures lib, c and d. It includes variation of
precipitation between 5 and 100 mm/hr, as well as variation in other selected variables.
7.1 Leachate Collection Systems
Using the general slope configuration shown in Figure 11a, along with details shown in
Figure 1 lb, a parametric evaluation of leachate collection systems was undertaken per Table 16.
Table 16 - Conditions Evaluated for Leachate Collection Systems
Parameter Evaluated Conditions (in addition to precipitation) P kd.s. hd.s. L p
(mm/hr.) (cm/sec) (mm) (m) (deg.)
Permeability of drainage soil, kd.s. 5-100 10-M01 1000 100 14.0
Thickness of drainage soil, hd.s 5-100 10-1 300-2000 100 14.0
Length of slope, L 5-100 10-1 1000 10-300 14.0
Slope angle, p 5-100 10-1 1000 100 2.9-40.0
Values held constant for all iterations are as follows:
'dry = 18 kN/m3
= 21 kN/m3 ''m'd
<t> = 30 deg. (soil-to-soil)
6 = 22 deg. (soil-to-geomembrane)
RC = 0.18
-57
The response for the first variation in permeability of leachate collection sou" between 0.001 and
10 cm/sec is given in Figure 15. The results are striking.
• With a permeability of leachate collection drainage soil equal, or less, than 0.05
cm/sec, the FS-values for all precipitation values, even as low as 5 mm/hr, are always
less than one, signifying instability.
• Paradoxically, a permeability of 0.01 cm/sec drainage soil is the value noted in U.S.
EPA regulations as being minimum technology guidance. As expected, this value is
used widely. Here it is seen that such low permeability drainage soil will always lead
to seepage induced slope instability under the conditions assumed herein.
• Depending on the precipitation intensity, FS-values of 1.5 require drainage soil it-
values of 0.3 to 6.0 cm/sec.
• Referring back to Table 3, this value of permeability can only be achieved using "GP"
or "GW" gravels, and possibly "SP" sand. However, the poorly graded gravels and
sands are often unstable, leaving only well graded gravel as being the candidate
material for leachate collection layers of the type being analyzed.
• The above gravel is typical of AASHTO #1, #3 or #5. In general, AASHTO #57 must
be screened of its fines to meet such a permeability requirement.
• Of course, with such coarse sized gravel the underlying geomembrane must be
protected using a thick needle punched nonwoven geotextile, or equivalent, see
Koemer, etal. (1996).
• Furthermore, the issue of placing waste directly on the surface of the gravel versus
using a geotextile filter, must be carefully considered, see Koemer, G. R. et al. (1993).
The second variation in the leachate collection system profile varied the thickness of the
drainage layer between 300 and 2000 mm. The response curves are given in Figure 16. At a
constant drainage layer permeability value of 0.1 cm/sec, essentially all of the resulting FS-
values are less than 1.5. It should be noted that the minimum technology guidance of the U.S.
-58
Pecipitation varies
Tnjj_mjj
-tff* - k vanes "• \ . T
•»vg
Permeability of drainage soil (cm/sec.)
Figure 15 - Parametric study of leachate coUection system: permeability variation
-59
1 m
o
o co Q . CD O
CD >. CD
S o
Pedpitation varies
vanes t - Drainage soil
k = 0.1 cm/sec TZ.Z7.Z _ _
i tvg I o
CD o c CD D5
CD E x> CD
1 CO 0.
£ XI
s «0 CD CL (0
05 CO CO CO
Sr CO
"CD
500 1000 1500 2000
Thickness of drainage soil (mm)
Figure 16 - Parametric study of leachate collection system: thickness variation
-60
EPA regulations is an order of magnitude lower, i.e., 0.01 cm/sec, which (if analyzed) would
produce proportionally even lower FS-values.
The third variation in the leachate collection system profile varied the slope length
between 10 and 300 m. The response curves are given in Figure 17. -With a constant drainage
layer permeability value of 0.1 cm/sec, the F5-values are only acceptable for slope lengths
between 10 and 50 m, for precipitation values between 100 and 5 mm/hr, respectively. In such
cases, the storm intensity is a significant factor and therefore, careful selection of the design
storm is necessary.
As discussed a number of times in Section 6.0 for the two example slopes of 30 m and
100m lengths, the longer slopes with cumulatively increasing required flux values are generally
troublesome. If long slope lengths are necessary, it is suggested that they be segmented by
berms and that the drainage be removed at each berm level. An illustration will be given later.
The fourth variation in the leachate collection system profile varied the slope angle
between 2.9 and 40 deg. The response curves are given in Figure 18. With a constant
permeability 0.1 cm/sec, it is seen that only relatively flat slopes are stable, e.g., less than
approximately 10 deg. which is approximately 5(H)-to-l(V). The storm intensity is only
nominally a factor, the major constituent being the permeability of the drainage layer as noted
earlier in this section.
- 6 1
1 m
O c!
CO Q . CO o CD >. a CD o ca
.c
T EE
Pedpitation varies
H t t m t t
' ' Drainage soil ^- ,
'«vg g
1.0
0.8
•
•100/50
/ / /
/
1 i
CD O c CD ra 0.6
• / 10 /
/
i5 2 a0.
0.4
0.2
• '
• '/
/ /
/ .
5mm/h '
0.0 r- i • •
£ XI o « CD C L O IB
ca
CD
J?
Length of slope (m)
Figure 17 - Parametric study of leachate collection system: slope length variation
-62
1 m
cs a ca o
CB C D
co
Pedpitation varies
HHIIIH
| %:-'-r^,2"'DrainagesoiI-£S?^^
• J i ' ; : ; ^k=^ .1 j^sec ! ' - ; ^ ;2 ; i *
lav? I JO
2 CD o c CD
E> CD
E XI 3 CO
1.0
0.8
0.6
0.4
•
•
\
\
5 mm/hr.
10
50 and 100 mm/hr.
\ 25
ca 0.2
•
i
^ " ^ - - - - - ^ i
•
0.0 •
e i\
1
11 1
Xt S <o CD C L
St CO
T
•
ca ra <o 2
•
— - ^ " ' 5
•) 1
10
**-—.~^_25,50 and 100 mm/hr.
o. 10 20
,
i
r
30
•
40
Slope angle, /J (deg.)
Figure 18 - Parametric study of leachate collection system: slope angle variation
- 6 3
7.2 Final Cover Systems Over Drainage Soils . ^
Using the general slope configuration shown in Figure 11a, along with details shown in
Figure lie, a parametric evaluation of cover systems over drainage soils was undertaken per
Table 17.
Table 17 - Conditions Evaluated for Cover Systems Over Drainage Soils
Parameter Evaluated Conditions (in addition to precipitatior) P kds. Kc.s L 3
(mm/hr.) (cm/sec) (cm/sec) (m) (deg.)
Permeability of drainage soil, kj s 5-100 10-2-101 IO"3 100 •14.0
Permeability of cover soil, kc.s 5-100 io-1 10-5-10-1 100 14.0
Length of slope, L 5-100 io-1 10-3 10-300 14.0
Slope angle, 3 5-100 io-1 10-3 100 2.9-40.0
Values held constant for all iterations are as follows:
•dry = 18 kN/m3
= 21 kN/m3 •sat 'd
<t> = 30 deg. (soil-to-soil)
s = 22 deg. (soil-to-geomembrane)
3» RC = 0.4 it i
= 1000mm leaver soil
tdrainage soil = 300 mm
The response for the first variation of drainage soil permeability between 0.01 and 10 cm/sec is
given in Figure 19. As with the leachate collection system described in section 7.1, the results
are striking.
• Drainage soil permeabilities less than 0.1 cm/sec result in DLC-values less than 1.0
(i.e., the drainage layer is at full capacity), producing PSR-values equal to 1.0 and the
FS-values are always less than 1.0.
- 6 4
Pedpitatkm varies
I l l l l l i U .•Cover soil
'.\- •• vk = o"fJ01 em/seV s&tkk
•••••••v««p««'"^« ••••••«••••• ••••^•^•V*Ef fft- Drainage soil, k varies y ;E
n "
Permeability of drainage soil (cm/sec.)
Figure 19 - Parametric study of cover system over drainage soil: permeability (drainage soil) variation
- 6 5
• The FS-values are less than 1.0 even for the 5 mm/hr precipitation-, which is the lowest
value analyzed.
• As precipitation increases, the permeability of the drainage layer must also increase for
suitable FS-values. For example, for a factor of safety of 1.5:
• A 5 mm/hr precipitation storm requires k > 0.12 cm/sec
• A 10 mm/hr precipitation storm requires k > 0.22 cm/sec
• A 25 mm/hr precipitation storm requires k > 0.55 cm/sec
• A 50 mm/hr precipitation storm requires k> 1.3 cm/sec
• A 100 mm/hr precipitation storm requires it > 1.5 cm/sec
• The implication of the above is that coarse sand or gravel must be used as discussed in
section 7.1.
• Alternatively, the permeability of the cover soil could be reduced thereby allowing less
percolation through this layer. (This alternative is treated in the next section.) Of
course, this strategy will add to the runoff value and potentially create erosion of the
cover soil, but this issue not treated in this report.
The second variation in the cover soil over drainage soil profile varied the permeability of
the cover soil between 10"5 and 10"1 cm/sec. The response curves are given in Figure 20. The
curves are somewhat challenging to interpret.
At cover soil permeability values less than 7 x 10-5 cm/sec, the FS-values can be quite
reasonable. This permeability is sufficiently low that the underlying drainage layer (k = 0.1
cm/sec) can handle the relatively low percolation and its subsequent flux requirement. Similarly,
at very high cover soil permeability values of greater than 0.05 cm/sec, the FS-values can also be
acceptable but only for light precipitation, i.e., less than 5 mm/hr. In this case there is drainage
within the cover soil which adds to the capability of the drainage layer. When the permeability
of cover soil increases to 0.1 cm/sec, the entire profile becomes a homogeneous drainage layer.
For cover soil permeability ranges between 7 x 10'5 and 5 x IO"2 cm/sec, however, unacceptable
FS-values result under all precipitation conditions. Unfortunately, this is a very common
-66
X
1 m
Pedpitation varies
iili.iii.ii Cr; :;/.;
J,,Cover soil :*%X''T£t£$%
E ^Drainage soil, fc= 0.1 cm/se<s
X
co Q. co u
CD O l
. 00 C
(0
i 5 mm/hr. 50 100
V\ - 10
" i 25 -LU-I > . ' . ' . . . . , j
i t v g o
CD O
c CD EP CD
E XI
_CD
s co
e Xt eg to CD CL O
c co O) CO
£ co co
"? k . ,2 o £
Permeability of cover soil (cm/sec)
Figure 20 - Parametric smdy of cover system over drainage soil: permeability (cover soil) variation
-67
• i
permeability range for cover soil materials which are usually on-site borrow soils. If only such
cover soils were available, the design strategy would be to increase the drainage layer capacity or
shorten the slope length with benches.
The third variation in the cover soil drainage soil profile varied the length of slope from
10 to 300 m. The response curves are given in Figure 21. Here it is seen that slope lengths of
less than 80 m can be acceptable depending on the magnitude of precipitation. The higher the
precipitation, the shorter the slope must be in order to result in an acceptable FS-value, for
example:
I • For 5 mm/hr precipitation, the slope can be up to 80 m in length. j
• For 10 mm/hr precipitation, the slope can be up to 45 m in length. ,
• For 25 mm/hr precipitation, the slope can be up to 20 m in length.
• For greater than 25 mm/hr precipitation, the slope must be less than 20 m in
length.
The fourth variation in the cover soil over drainage soil profile varied the slope angle
from 2.9 to 40 degrees. The response curves are given in Figure 22. Note that the FS-values are
unacceptable for all cases except very shallow slope angles, e.g., less than 10 degrees (i.e., less
than 5(H)-to-l(V)). The reason for this response is (a) the poorly selected permeability value of i cover soil (held constant at 0.001 cm/sec) which is in the unacceptable mid-range in Figure 20, B
and (b) the unacceptably low value of drainage soil permeability (held constant at 0.1 cm/sec), • 7 "
recall Figure 19. f
-68
1 m
- J
Q
co a
CD >> S CD O CO
E f E o
Pedpttation varies
ntnjuj ICover soil ->^1|*2;~,-.
• • • • J I • • _•• „•• • • • • J • • • • _ • • • • J
>l'Drainage soil, *r= 0.1 cm/sootf
' J V V I S5 S co o c CD
P
0.8
1.0
0.6
50 and 100 mm/hr
/
25
10
1
1 1 1
XI 3 » 0.4
• 5 mm /hr. 1
a 0.2 i
^ ^ >
0.0
1.8
& 1 < I r
£ 1.6
I fa CD
a ta to _c ca cs a 2 " CD
"2
o 1.4
1.2
1.0
£ -all
0.8
50— i 1
100 1 j
150 1 j
200 1 1
250 1 —
300
Length of cover soil, L (m)
Figure 21 - Parametric study of cover system over drainage soil: slope length variation
-69
1 m
Pedpitation varies
iiKLiiiii '*' i ; V' : Cover soil'"''"?; V -,"M'
;/•, •'*• = 0.001 cm/sec T T
•»vg lVlV.V.V.V.V.V.V.V.V.V.V.V,V E •s'Drainage soil,fc= 0.1 cm/seas' • j . j - . j . j - „-• j . f . j . ? . _-• ^ . _-• ? . ! . iS;>i>iV,s»S"V»%«v1v,1s«s»s»1v
O 3
oCD >. _g CD
ffCO
c 2 Q
_3 2 CD O c CD ra
XI 3 (0
2 CO
Q .
£
XI
« CD C L O
CO ra co
o
£
3.0
2.5
2.0
1.5 5 mm/hr.
1-0 y S ^ ^ 1 0
0.5
0.0
1.2
.
0.8
-.
1
1
—•
1
- - 2 5 | SO
1 1
25, 50 and 100 mm/hr.
0.6 10
0.4 5 mm/hr.
0.2
0.0
5
1 1 1 — 1
Slope angle, jS (deg.)
Figure 22 - Parametric study of cover system over drainage soil: slope angle variation
- 7 0
73 Final Cover Systems Over Geosynthetic Drains -c
Using the slope configuration shown in Figure 11 a, along with details shown in Figure
1 Id, a parametric evaluation of cover systems over geosynthetic drains was undertaken per Table
18.
Table 18 - Conditions Evaluated for Cover Soil Systems Over Geosynthetic Drains
Parameter Evaluated Conditions (in addition to precipitation) P kcs kcs L p hc.s k}s
_mm/hr.__ (cm/sec) (cm/sec) (m) (deg) (mm) (mm)
Rainfall intensity, P 1-100 0.6GS1 io-3 100 14.0 1000 5.5GS1
Permeability of cover soil, k<. s 60 10GS2 lO-S-lO1 100 14.0 1000 5.5GS2
Length of slope, L 60 12GS3 io-3 10-300 14.0 1000 i4 0 GS3
Slope angle, (5 60 io-3 100 2.9-40.0 1000
Values held constant for all iterations are as follows:
'dry = 18 kN/m3
y = 21 kN/m3
'sad
<t> = 30 deg. (soil-to-soil)
s = 22 deg. (soil-to-geocomposite)
RC = 0.4
tcover soil = 1000 mm
kcover soil = 0.001 cm/sec
GS1 = GT/GN/GT composite*
GS2 = plate/GN/plate*
GS3 = sheet drain geocomposite*
*A11 geosynthetic drains were evaluated at 25 kPa normal stress and reduced by a cumulative reduction factor of 5.0.
- 7 1
The response for the first variation of precipitation intensity between 1 and 100 mm/hr is
given in Figure 23. The response shows that only storm events of less than approximately 30
mm/hr can be handled by the GS3 drain and approximately 8 mm/hr for the GS2 drain. The GS1
drain is unacceptable under all conditions.
The second variation in the cover soil over geosynthetic drain profile varied the
permeability of the cover soil from IO"5 to lO^1 cm/sec. The rainfall intensity was held constant
at 60 mm/hr. The response curves are given in Figure 24. Here it is seen that both GS2 and GS3
geocomposite drains result in acceptable FS-values when the permeability of the cover soil is less f i
than 1.5 x IO-4 cm/sec and 4.5 x IO*4 cm/sec, respectively. At these relatively low values of
cover soil permeability the percolation values are sufficiently low that the required flux can be
handled. The GS1 geocomposite is not acceptable at any cover soil permeability value.
The third variation in the cover soil over geosynthetic drain profile varied the length of
slope from 10 to 300 m. The rainfall intensity was held constant at 60 mm/hr. The response
curves are given in Figure 25. The cover soil permeability was held constant at 0.001 cm/sec.
The curves indicate that the FS-values are only acceptable for the GS2 and GS3 geocomposites at
slope lengths of 15 m and 40 m, respectively. Again, the GS1 drain is never acceptable under
these conditions.
The fourth variation in the cover soil over geosynthetic drain profile varied the slope
angle between 2.9 and 40 degrees. The rainfall intensity was held constant at 60 mm/hr. The
response curves are given in Figure 26. Again, the cover soil permeability was held at 0.001
cm/sec. The resulting F5-values are only acceptable at relative shallow slope angles, e.g., less
than 9 deg., i.e., approximately 5(H)-to-l(V). All three geosynthetic drains give similar response
up to this slope angle. The behavior is dominated by the slope angle, but steeper slopes could be
accommodated by cover soil permeability values lower than 0.001 cm/sec (allowing for less
percolation) or higher capacity geosynthetic drains (allowing for greater flux capacity).
- 7 2
11 m
O 6 , ' • : |
] 1
EE o o o
P varies
y \ u w w w g Cover soil ^5-^" '•<' k = 0 001 cm/sec . '
co a co o CD >. .2 CD a ca _: 2 a
4
?
0-
1.2
1.0
\ I 6S3 \ \\ V
GS2 \
r •
GST GS1 and GS2
i
V
•
1
j
1
, 1 ! GS1,GS2andGS3
tGS
T
','dSr X
X~)00<"X X >< X"X~
^ • Geosynthetic drain, Vas
i
'ny
5
c CD ra t— CD E XI D
_D
"2 CD
Q .
=
0.8
0.6
0.4
0.2
0.0
G & GS3
1
J
1
i 1 i
1
|
1 i
-072. 1 : • i • 1 •
1.8
j c ca o> a
<9
tXI Sto CD
a. I
1.6
1.4
1.2
G K
"1 1 GS3
\
1
1 I
1
S 1.0 !
1 ! 1
0.8
GS1 GS1 an 6GS2 \
'
GS1. GS2andGS3
| i 60 80 100
Rainfall intensity, P (mm/hr.)
Figure 23 - Parametric study of cover system over geosynthetic drain: rainfall intensity variation
-73
1 m
O \ T .
!
P = 60 mm/hr.
UHUHUt ' ; • ; / ' ^ ' J^ t^^ ' ^ i ^A^ip*M'^i^if, '_-'^-3:
CD >> _C0
CD ra CO c CD
Q
• \ \
\ GS2
\ \
^ ^ G S I
\ 2 -
\ \v\ i • i
1 i i
i 1 1 I I i j 1—<—i 1 1 i n
/ ' O Cover soil,* varies } / ' : ] {
1.0. esr GSIand GS2 GS1,GS2andGS3
Uvy 0.8
tes
T X X ^ X X X X X X X
—• Geosynthetic drain, kss
* 2 o u c CD E? CD
E XI 0)
s CO a.
0.6
0.4
0.2
0.0 GS2andGS3
GS2 GS3
GS3
•02 i 1111 | 1—i— • i 1111 | 1—i—i i 111
1.8.
e •£XI
S CD Q .
£to _c CO ra cs
.2
1.6
1.4
1.2
GS2andGS3 GS3
GS2 GS3
oo 1.0
GS1 GSIand GS2 GS1.GS2andGS3
0.8 10
i i i I ' i ' i u r
io "* i i i " i i r i i
10 | i -i i I T H I J •"T- f
10 -2
n i r n
10
Permeability ot cover soil (cm/sec)
Figure 24 - Parametric study of cover system over geosynthetic drain: permeability (cover soil) variation
-74
• V
1 m
O Q
1 *5 •
P = 60 mm/hr.
UHUHIH
o co o. co
CD >. a CD ra co _c <s
1 0
0 5 -
\ \
V\ \ GS2
^GSI
GS3
j
i
I
i — •
m
Cover soil K " * . k = 0001 cm/sec •*•".,*ks^
1.2
1.0
• GS2 GS1, GS2andGS3
'GS x " > c R Y ^ x x x x "*" CZ • Geosynthetic drain, kas
cc
g o"
c CD
ra
XI • D
0)
2 CO
£
0.8
0.6
0.4
0.2
CS2 G£ !3
j
1
1 i
i
i
1
GS3
-0.2 T • r— ' 1 1 1 •
2.0
e 1.8.
GS3
X) CO
CD a Ct <o
£
1.6
1-4 GS2
GS3
1.2
o o 1.0
GS2 GS1.GS2andGS3
0.8 - r 50 100
— I —
150 200 — I — 250 300
Length of cover soil, L (mm)
Figure 25 - Parametric study of cover system over geosynthetic drain: slope length variation
- 7 5
1.6
1.4 • i
i y
1.2 • , i s •
1.0 UbJ
0.8
•
0.6
•
0.4
., - / .^^.»**^ 0.2
0.0 C— 1 i " 1 • i —
GSr
\ 2
1.0 GSf, GS2andGS3
I i GS1 and 6S2
i i
0.8 1 _ !
• j
0.6
0.4 i l GS3
• 0.2
• GS3
0.0
-0.2 •i
1 1 i
1 1 1 1
1 m
CO Q . CC O
5 o CD ra co _c
P= 60 mm/hr.
( U I I U I I H Cover soil
'•''. k = 0.001 cm/sec
fe - i f ; , # " •
T
M xx^xxxxxxxT J?
f— Geosynthetic drain, kas
fiavg
2; co o c 03
CD)
CD
E X)
« "CD
CO CL
£
CO CD Q .
.o (0 to _c co ra <S
O co u.
Slope angle, 0 (deg.)
Figure 26 - Parametric study of cover system over geosynthetic drain: slope angle variation
-76
8.0 SUMMARY
Presented in section 2.1 was information on the recent occurrence of four seepage
induced slides of leachate collection systems and an additional four seepage induced slides of
final cover systems. All occurred during, or immediately after, relatively large storm events (the
one exception was by rapid thawing of frozen drainage soil above a still-frozen outlet drain at the
toe of the slope). While the exact nature of these storm events are unknown, an idea of their
magnitude can be gained by back calculating the various situations. Knowing the dimensions of
the slopes and an approximation of the permeability of the soil(s) involved, the design
methodology used herein (using an incipient failure FS-value of 1.0) has been followed resulting
in the data of Table 19. Here it is seen that the precipitation values for the leachate collection
systems was probably quite high, i.e., up to 44 mm/hour. Conversely, precipitation values for the
final cover systems were apparently quite low, i.e., between 0.38 and 1.34 mm/hour. The latter
are far from extraordinary events and the very low values of drainage soil permeability played
strongly into the cause of the instability.
Table 19 - Back Calculated Precipitation Rates to Achieve Slope Instability for the Case Histories Presented in Table 1.
No. Assumed Assumed Precipitation at permeability of permeability of incipient sliding
cover soil, drainage soil, (i.e.,FS=1.0), kc,s, (cm/sec) kd (cm/sec) Pcritical (mm/hr)
(a) Slides of leachate collection layers before waste placement 1 none 0.25 14 2 none 0.50 44 3 none 0.05 1.0 4 none 0.25 35
(b) Slides of final cover/drainage layers after waste placement 5 0.01 0.01 0.42 6 0.0001 0.01 1.20 7 0.0001 0.01 1.34 8 0.0001 0.01 0.38
Note: Values are calculated based on the following assumed constants: Dry unit weight of soils, y = 18.0 kN/m3
Saturated unit weight of soils, y^d = 21.0 kN/m3
Friction angle of soils, $ = 30 deg. Critical interface friction angle, 5 = 22 deg. Runoff coefficient, RC = 0.18 for Type (a) slides and 0.40 for Type (b) slides
- 7 7
To the writers, the occurrence of such a large number of recent slides is an unacceptable
situation. It appears that seepage forces are being considerably underestimated by the design
community in view of the very low permeability drainage soils used in "conventional" design.
Both required flux quantities Gateral flow rates) and drainage system capacities are involved..
8.1 Water Balance Analysis Critique
The occurrence of eight seepage induced cover soil slides (there are probably others not
known to the writers) lead directly toward mounting a challenge to the manner in which required .
drainage quantities are calculated. Agreed upon is the necessity of using a water balance analysis
to obtain a required value of percolation through the cover soil and into the drainage layer. This
value of percolation over an unit area, is then used to calculate a flux-value (lateral flow rate)
which accumulates within the drainage layer reaching a maximum value at the toe of the slope.
The maximum flux-value is the required value to use in designing the drainage layer capacity.
Not agreed upon is the customary manner of obtaining the percolation-value, hence the required
flux is effected accordingly. Typically used in this regard is the computer program entitled
Hydrologic Evaluation of Landfill Performance (HELP).
It is felt that HELP model is an excellent program for its originally intended use; namely,
to estimate the leachate quantities at the base of a landfill. The gravitational flow process
through the landfilled waste material is long and slow. The daily monitoring used in the program
is an excellent model. HELP should continue to be used to estimate leachate quantities, as well
as the hydraulic head on the liner system. However, for short time period intense storms,
through relatively thin and often high permeability soils, HELP monitoring on a daily interval is
not recommended. The resulting percolation values are too low, resulting in very low required
flux values and an underdesigned drainage system capacity.
Recommended and illustrated in this report is to obtain the required percolation and flux
values from an hourly monitoring of a short time intensive storm, e.g., a six-hour storm event.
Using this type of design scenario for leachate collection layers (before waste is placed) or final
- 7 8
cover soil systems (after waste is placed), the following assumptions regarding the mechanisms
of the water balance process are felt to be appropriate:
• Evapotranspiration is negligible during such a short time interval.
• The soils are at field capacity before the most intense part of the storm arrives, thus
water storage is negligible.
• The barrier system (GM, CCL, GCL) beneath the drainage layer has no appreciable
leakage, at least at the slope angles focused upon in dealing with slope stability issues.
Using the above assumptions, the local site-specific precipitation falling on the leachate
collection layer or final cover soil system will be initially bifurcated into runoff and infiltration.
The runoff is controlled by die surface soil (or vegetation) and the slope angle. The remainder of
the precipitation results in water infiltration into the soil. The value of infiltration results directly
in the percolation coming to the drainage layer. It is controlled by Darcian flow according to the
soil's permeability. This value of vertical flow, in turn, produces the flux-value in the drain
which accumulates over the slope length and is the required design value for selecting the
drainage material's type, permeability and thickness.
Design in the manner just described results in flux-values that are 25 to 40 times greater
than do designs based on HELP modeling. Furthermore, it appears that minimum technology
guidance in many federal and state regulations are based on, or substantiated by, HELP
modeling. Such a process results in values of required permeability of 0.01 cm/sec, and even as
low as 0.001 cm/sec by some state regulatory agencies, which are orders of magnitude lower
than values suggested in this report. It is felt by the authors that this situation is the fundamental
reason that seepage induced slides are frequently occurring.
8.2 Slope Stability Analysis Comments
Once the phreatic surface is established within the specific cross section (i.e., its flow
orientation and its depth of submergence), the mechanisms of the calculation procedure are quite
straightforward. [The details were not presented completely in this report since the full
-79
t '
procedure is available elsewhere, see Soong and Koemer (1996)]. .The procedure uses limit
equilibrium on a finite slope length of given slope angle and cover soil properties. The flow
orientation can be of two types:
• Horizontal submergence ratio (HSR), produced by toe blockage at the downgradient
end of the drainage system. ,
• Parallel submergence ratio (PSR), produced by inadequate initial permeability of the
drainage layer, or gradual clogging of the drainage layer over time.
The PSR assumption was used in this report. (The two assumptions are equivalent for an equal • '.
amount of saturated drainage soil.) The depth of submergence results directly from the water
balance analysis just described. §
83 Drainage Layer Capacity (DLC) Comments at
Using flux values obtained from an hourly-interval water balance analysis, one can size
the drainage layer accordingly. Using either natural soils or geosynthetic drains it is essential
that the drainage layer capacity is never exceeded. Equation 23 expresses the concept.
DLC = FLUX*»™ > 1.0 (23) rmx r e q d
Once the DLC decreases to a value of 1.0, the submergence ratio increases to a value of 1,0 and i
the slope's factor of safety falls precipitously, generally less than 1.0.
;i Thus, it is readily seen in the above equation that if the required flux is 25 to 40 times I•
higher than that used in past practice, the allowable flux must be similarly increased over that
used in past practice.
When using natural soils as drainage materials, the parametric study presented in this
report indicated that only gravel soils (possibly, sandy gravels) could accommodate such flow
rates. Clearly, the minimum technology guidance permeability value noted in most federal and
state EPA regulations of 0.01 cm/sec is much too low. From the data generated herein, drainage
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soil permeability values in the range of 0.12 to 1.5 cm/sec are necessary to maintain FS-values of
1.5.
When using geosynthetic drains, the same allowable drainage requirements must also be
applied. Thus the typical biaxial geonets, with a large amount of geotextile intrusion, cannot
handle very intense storms. The maximum precipitation storm that can be handled being
approximately 10 mm/hr. For geocomposite sheet drains, and (possibly) triaxial geonets with
closely spaced covering ribs to minimize intrusion, the maximum precipitation that can be
accommodated is approximately 30 mm/hr. Other geometric considerations than those addressed
herein will obviously modify these values.
It should also be noted that the allowable flux values used to calculate the DLC-values is
the long-term allowable flux. Long-term is, of course, relative to the site-specific situation. For
leachate collection layers, the time is directly related to waste placement in the landfill or cell.
This could be months or even a few years for a small landfill. For final covers, however, the
necessary time frame is extremely long. Clearly, equilibrium of the entire cover system (topsoil,
cover soil, filter, drainage soil and toe drain) must be estabUshed or else the permeability of the
drainage layer will decrease over time leading to decreased allowable flux and the possibility of
seepage induced slope instability. Long-term allowable flux is a most serious consideration.
8.4 Parametric-Study Implications
Section 7.0, and to a somewhat lesser extent, section 6.0, presented a parametric
sensitivity analysis on a number of variables insofar as the resulting DLC, PSR and FS-values
were concerned. In approximate order of influence, some summary comments follow:
• The necessity of high permeability drainage layers cannot be over emphasized. Figures
15,19 and 24 all show the need for high permeability to result in reasonable FS-values.
The minimum permeability resulting from the parameters used herein was 0.3 cm/sec,
and values of 6.0 cm/sec were required in some cases.
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• The precipitation rate, which was varied from 5 to 100. mm/hr., was equally as
significant as permeability. As noted in section 2.2, the selection of this key variable is
not easy but other designers have precisely the same dilemma, e.g.. geotechnical
engineers in estimating spillway capacity, transportation engineers in estimating culvert
capacity, hydrauhc engineers in designing retention basins.
• The length of slope is very important. Since the required flux is cumulative over the
length of the slope, the longer slopes need progressively larger capacity drainage
systems. Slope lengths should be restricted, and 30 m seems to be an upper length for
which a number of drainage designs can be still accommodated. Long slopes become
progressively more difficult to accommodate high flux-values and should be segmented
by benches as shown in Figure 27.
• Slope angle was evaluated and it was seen to be very low for adequate FS-values for the
parameters selected. Clearly, slopes greater than 10 degrees can be safely designed, but
they must have adequate drainage layer capacity and relatively short lengths.
• Cover soil permeability (above the drainage layer) was seen to be interesting in that the
range of 7 x 10"5 to 5 x 10"2 cm/sec was most troublesome insofar as unacceptable low
FS-values were concerned. Lower than 7 x 10-5 cm/sec the percolation rate through the
cover soils are too small to create problems, and higher than 5 x IO-2 cm/sec the cover
soils are drainable in themselves and contribute to the drainage layer in accommodating
the required flux-values. Unfortunately, cover soils in the permeability range between
7 x IO-5 to 5 x IO"2 cm/sec are very common.
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Natural soil or
Geosynthetic drain
Geomembrane
i»>"* '
Figure 27 - Method of segmenting long slopes using benches and daylighting the flux from each segment into drainage ditches.
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9.0 RECOMMENDATIONS '
It is hoped the results of this study change some long-standing assumptions and
perspectives regarding seepage design in assessing slope instability.
First, and foremost, is the recognition that seepage induced slope instability has occurred
often and that its timing is during, or immediately after, intense storm events. This suggests that
hourly-interval tracking of precipitation is necessary for use in the water balance analysis used to
obtain the required flux (or drainage rate) value. The HELP program, based on daily-intervals is
not appropriate as il is currently configured. Furthermore, and related to any type of water
balance analysis whatever is its time interval, is that worst case assumptions should be made.
For example, evapotranspiration, soil water storage and leakage through barrier layers are all
negligible (if not zero) for short interval, high intensity storms, on relatively steep slopes with
soils having high drainage rates. There are precisely the conditions where seepage induced slope
instability occurs.
Second, (and certainly related to the high values of required flux), is that allowable flux
values of the drainage system must be increased tremendously over current practice. The federal
and state minimum permeability values for drainage soils (often taken and used directly in
design) of 0.01 cm/sec are too low by a factor of 10, and in some cases 100. However, the use of
higher permeability requirements has profound implications. Natural soil drainage materials can
only be gravel and even then the fines can be troublesome. The use of coarse clean gravel
requires the underlying geomembrane to be suitably protected against puncture. Further, serious
consideration must be given to filter design with respect to overlying fine-grained soils or solid
waste. Both are serious design considerations. Geosynthetic drainage materials (geonets and
geocomposites) are often not capable of conducting such high required flux-values. Needed in
this regard are triaxial geonets or geocomposite cores, protected by a geotextile filter/separator
with minimum intrusion into the core spaces.
Third, is that most of the focus of this report has been on the drainage layer but, in reality,
the drainage layer is part of the larger drainage system. In this regard, too little attention has
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been paid to the drainage layer outlet at the toe of the slope. It must be freecof excess blockage
by fines, as well as physical blockage by ice formations, equipment ramps, access roads, etc.
Each toe situation is unique, but the sketches of Figure 28 give some schemes which might be
considered. Each shows a gradually increasing drainage layer permeability as the required flux
becomes greater in moving from the crest to the toe of slope. Alternatively, a natural soil
drainage layer can be augmented by a geosynthetic drainage layer as greater capacity is needed
towards the toe of the slope. At the toe, the drainage capability must be at its maximum.
Geotextile filters should be placed as far away from the drainage pipes as possible. The pipe
itself may have to be increased in diameter as it conveys water to the ultimate off-site outlet.
Increasing the drainage capacity of the toe, as with the upgradient drainage layer is
clearly within the design community's capability. It remains to see if we are up to the challenge
(and the expenses0involved to the owner community) to accomplish the task.
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frost depth ~~i (if applicable) f
frost depth ~~X (if applicable) y
Geotextile filter wrapped around stone (typical)
Drainage material
Geomembrane
Transition material (higher transmissivity)
(a) Extremely large stone-toe drain
Geotextile filter wrapped around stone (typical)
Geomembrane
(b) Large perforated pipes surrounded by large stones
(c) Daylighting of drainage stone into a drainage channel in non-freezing climates
QNote: only feasible if sediments that run off the surface of the cover do not excessively clog the toe drainage material.)
Figure 28 - Various designs allowing for free drainage at the toe of slopes, after Soong and Koemer,j(J996).
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10.0 REFERENCES . '
Bordeau, P.L., Ludlow, SJ. and Simpson, B.E. (1993), "Stability of Soil Covered Geosynthetic Lined Slopes: A Parametric Study," Geosynthetics '93 Conference Proceedings, IFAI Publ., St. Paul, MN, pp. 1511-1521.
Boschuk, J.J. (1991), "Landfill Covers: An Engineering Perspective," Geotechnical Fabrics Report, Vol. 9, No. 2, March, IFAI, St. Paul, MN, pp. 23-34.
Carroll, R.G., Jr., "GeotextileFilter Criteria", TRR 916, Engineering Fabrics in Transportation Construction, Washington, DC, pp.46-53.
Daniel, D.E. (1997), Geoenvironmental Engineering Class Notes.
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Giroud, J.P. and Beech, J.F. (1989), "Stability of Soil Layers on Geosynthetic Lining Systems," Geosynthetics '89 Conference Proceedings, IFAI, St. Paul, MN, pp. 35-46.
Giroud, J. P., Swan, R. H., Jr., Richer, P. J. and Spooner, P. R. (1990), "Geosynthetic Landfill Cap: Laboratory and Field Tests, Design and Construction," Proc. Geotextiles, Geomembranes and Related Products, G. den Hoedt, Ed., Balkema, Rotterdam, pp. 493-498.
Giroud, J.P., Bachus, R.C. and Bonaparte, R. (1995), "Influence of Water Flow on the Stability of Geosynthetic-Soil Layered Systems on Slopes", Geosynthetics International, Vol. 2, No. 6, pp. 1149-1180.
Giroud, J. P. and Houlihan, M. F. (1995), "Design of Leachate Collection Layers," Proc. Sardinia '95, CISA, Cagliari, Italy, pp. 613-640.
Kmet, P. (1982), "EPA's 1995 Water Balance Method - Its Use and Limitations," Wisconsin Department of Natural Resources, Madison, WI.
Koemer, G.R., Koemer, R.M. and Martin, J.P. (1993), "Design of Landfill Leachate-Collection Filters", J. of Geotechnical Engineering, Vol. 120, No. 10, pp. 1792-1803.
Koemer, R.M. and Hwu, B.-L. (1991), "Stability and Tension Considerations Regarding Cover Soils on Geomembrane Lined Slopes," Jour. Geotextiles and Geomembranes, Vol. 10, No. 4, pp. 335-355.
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Koemer, R.M and Daniel, D.E. (1997') Final Covers for Solid Waste Landfills and Abandoned Dumps. ASCE Press, New York, NY.
Koemer, R.M., Wilson-Fahmy, R.F. and Narejo, D. (1996), "Puncture Protection of Geomembranes Part UI: Examples", Geosynthetics International, Vol. 3, No. 5, pp. 655-676.
Liu, C.N., Gilbert, R.B., Thiel, R.S. and Wright, S.G. (1997), "What is an Appropriate Factor of Safety for Landfill Cover Slopes," Geosynthetics '97 Conference Proceedings, IFAI Publ., St. Paul, MN, pp. 481-496.
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Luettich, S.M., Giroud, J.P. and Bachus, R.C. (1992), "Geotextile Filter Design Guide", Jour, of Geotextiles and Geomembranes, Vol. 11, No. 4-6, pp. 19-34.
Maidment, D.R., Ed. (1993), Handbook of Hydrology. McGraw-Hill Publ. Co., New York, NY.
McKelvey, J.A. and Deutsch, W.L. (1991). "The Effect of Equipment Loading and Tapered Cover Soil Layers on Geosynthetic Lined Landfill Slopes." Proceedings of the 14th Annual Madison Waste Conference, Madison, WI, University of Wisconsin, pp. 395-411.
Richardson, G.N. (1997) "Fundamental Mistakes in Slope Design", Geotechnical Fabrics Report, Vol. 15, No. 2, IFAI, St. Paul, MN, pp. 15-17.
Schroeder, P.R., Dizier, T.S., Zappi, P.A., McEnroe, B.M., Sjostrom, J.W., and Peyton, R.L. (1994), "The Hydrologic Evaluation of Landfill Performance (HELP) Model: Engineering Documentation for Version 3," EPA/600/R-94/168b, U.S. Environmental Protection Agency, Risk Reduction Engineering Laboratory, Cincinnati, OH, 116 pgs.
Soong, T.-Y. and Koemer, R.M. (1996), "Seepage Induced Slope Instability," Jour, of Geotextiles and Geomembranes, Vol. 14, Nos. 7/8, pp. 425-445.
Thiel, R.S. and Stewart, M.G. (1993), "Geosynthetic Landfill Cover Design Methodology and Construction Experience in the Pacific Northwest," Geosynthetics '93 Conference Proceedings, IFAI, St. Paul, MN, pp. 1131-1144.
Thomthwaite, C.W., and Mather, J.R. (1955), "The Water Balance," Drexel Institute of Technology, Publications in Climatology, Vol. 8, No. 1, Philadelphia.
U.S. Army Corps of Engineers (1948), "Laboratory Investigation of Filters for Enid and Grenada Dams," U.S. Army Waterways Experiment Station, Vicksburg, Miss., Technical Memorandum No. 3-245.
World Meteorological Organization (1986), " Manual for Estimation of Probable Maximum Precipitation," Operational Hydrology Report 1, WMO No. 332, 2nd Ed., Secretariat of the World Meteorological Organization, Geneva, Switzerland.
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