A design chart for estimation of horizontal displacement in municipal landfills

Waste Management 29 (2009) 1577–1587

Contents lists available at ScienceDirect

Waste Management

journal homepage: www.elsevier .com/locate /wasman

A design chart for estimation of horizontal displacement in municipal landfills

M.K. Singh *, J.S. Sharma, I.R. FlemingDepartment of Civil and Geological Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon, SK, Canada S7N 5A9

a r t i c l e i n f o

Article history:Accepted 17 October 2008Available online 12 December 2008

0956-053X/$ - see front matter � 2008 Elsevier Ltd. Adoi:10.1016/j.wasman.2008.10.003

* Corresponding author. Tel.: +1 306 966 5359; faxE-mail address: [email protected] (M.K. Singh

a b s t r a c t

This paper describes the development of a design chart for the estimation of maximum horizontal dis-placement within a municipal landfill using the height and the side slope of the landfill. The design chartis based on the results of a finite element parametric study in which the behaviour of the municipal solidwaste (MSW) was modeled using a non-linear elastic hyperbolic model. The model input parameters, i.e.non-linear stiffness, shear strength and unit weight of MSW, were obtained from laboratory testing dataand an extensive stochastic numerical modelling exercise. Non-linear variations of unit weight as well asYoung’s modulus of MSW with depth were incorporated in the finite element analyses. The validity of thedesign chart was assessed using field monitoring results from a large landfill located in Ontario, Canada.

� 2008 Elsevier Ltd. All rights reserved.

1. Introduction

In recent years, there has been an unprecedented global in-crease in urban population. According to a report by the PopulationDivision of the Department of Economic and Social Affairs of theUnited Nations Secretariat (UN, 2006), 47% of the world’s popula-tion lived in large cities at the end of the last century. The reportalso predicts that more than half of the world’s population willbe urban by the year 2010 (UN, 2006). This trend of increasing ur-ban population has resulted in a significant increase in waste pro-duction and has made it necessary for the municipalities to uselandfill space more efficiently. Sanitary landfills are now beingforced to accept greater quantities of municipal solid waste(MSW) per unit area of landfill footprint by increasing landfillheight, employing steeper side slopes, enhancing MSW degrada-tion, or by ‘piggyback’ expansion of existing landfills. Concurrently,there has also been an increase in the use of closed landfills for thegeneration and collection of landfill gas (LFG) from decomposingwaste. As a result, engineered systems for the collection of LFGare being installed in many landfills. Such gas collection systemsalso help to minimize the impact of the landfill on air qualityand to capture emission of greenhouse gases.

These trends of higher and steeper landfills along with theinstallation of gas collection systems have made it challenging toensure both the stability of the landfilled waste mass and the ser-viceability of the installed gas collection infrastructure. It can beargued that the stability of a landfill can be ensured as long asthe landfill is adequately engineered and is monitored regularlyfor significant changes in operating conditions. It is, however, quitedifficult to ensure the serviceability of buried collection pipes, etc.

ll rights reserved.

: +1 306 966 5427.).

A landfill may not fail catastrophically because of increases inheight or because of waste degradation; however, it is always pos-sible for the waste to undergo large lateral deformations, impairingthe function of the gas collection system. It is important, therefore,to be able to estimate the maximum horizontal displacement with-in a landfill in order to mitigate such effects.

This paper presents an easy-to-use design chart for the estima-tion of the maximum expected lateral displacement within a land-fill using the height and the side slope of the landfill. The designchart is developed using results of a finite element parametricstudy in which the behaviour of the municipal solid waste is mod-eled using a non-linear elastic hyperbolic model. The design chartincorporates non-linear variation in unit weight as well as Young’smodulus of MSW with depth. Mechanical properties of MSW usedfor the development of this design chart (i.e., non-linear stiffness,shear strength and unit weight of MSW) were obtained using asubstantial database of laboratory testing data as well as throughstochastic numerical modelling. The validity of the design chartis established using field monitoring results from Brock West land-fill located in Ontario, Canada.

2. Approach

The design chart proposed in this paper is based on the resultsof a series of finite element analyses conducted using a stress–deformation finite element program SIGMA/W, which is a compo-nent of the GeoStudio 2007 suite of software (GSI, 2007). A typicalfinite element analysis involved the simulation of a staged in-crease in the height of a landfill at a given side slope angle. Onlyhalf of the landfill was modeled because of the symmetry alongthe vertical axis. The foundation soil was modeled as a 10-m thicklayer of linear elastic material (Young’s modulus = 20 MPa; Pois-son’s ratio = 0.33). The stress–deformation behaviour of MSW

mailto:[email protected]

http://www.sciencedirect.com/science/journal/0956053X

http://www.elsevier.com/locate/wasman

1578 M.K. Singh et al. / Waste Management 29 (2009) 1577–1587

was modeled using a non-linear elastic hyperbolic (NLEH) model.A brief description of the NLEH model is provided in the nextsection.

The mechanical properties required by the NLEH model(namely shear strength parameters, elastic properties and unitweight) were obtained in two different ways: (a) statistical anal-ysis of data available in the literature as well as data from labora-tory testing of MSW conducted by the authors; and (b) stochasticmodelling of the mechanical behaviour of MSW using ‘unit cell’ fi-nite element simulations. Details of these two methods are pro-vided in the subsequent sections. Non-linear variations withdepth for both Young’s modulus and the unit weight were incor-porated in the finite element analyses. Details of how these vari-ations were obtained are also given in the subsequent sections.

3. Non-linear elastic hyperbolic (NLEH) model

A non-linear elastic hyperbolic (NLEH) model (Kondner, 1963;Duncan and Chang, 1970) is used to model the non-linear deviator-ic stress vs. axial strain response of MSW (Fig. 1). The NLEH modelis deemed appropriate for modelling the stress–deformationbehaviour of MSW because it can simulate decreasing stiffnesswith increasing axial strain as well as increasing initial stiffnesswith increasing confining stress. Detailed formulation of the NLEHmodel can be found in Kondner (1963) and Duncan and Chang(1970), and only a brief summary of the NLEH model is presentedhere.

The stress–strain relationship for the NLEH model can be ex-pressed as

ðr01 � r03Þ ¼ea

1Eiþ eaRf

ðr01�r03Þf

h i ð1Þ

where ðr01 � r03Þ is the deviatoric stress, ea is the axial strain, Ei is theinitial tangent Young’s modulus, ðr01 � r03Þf is the deviatoric stressat failure, and Rf is a factor that relates the deviatoric stress at fail-ure to the ultimate (asymptotic) value of deviatoric stressðr01 � r03Þult as ðr01 � r03Þf ¼ Rf ðr01 � r03Þult . The value of Rf is alwaysless than unity.

Following Janbu (1963) and Duncan and Chang (1970), the ini-tial tangent Young’s modulus can be considered a function of theeffective confining stress (or minor principle effective stress):

Ei ¼ KPar03Pa

� �n

ð2Þ

where Pa is the atmospheric pressure (equals 101.3 kPa), r03 is theeffective confining stress, K is a modulus number representing thevalue of initial tangent Young’s modulus normalized with atmo-

ult)( 31 σσ ′−′

Axial Strain

Dev

iato

ric S

tres

s

f)( 31 σσ ′−′

fultfR )()( 3131 σσσσ ′−′=′−′iE

Fig. 1. Stress–strain curve for the non-linear elastic hyperbolic (NLEH) model.

spheric pressure (i.e., Ei=Pa) at r03 equals 101.3 kPa and n representsthe rate of change of Ei with r03. The larger the value of n, the morerapidly Ei increases with increasing r03.

The deviatoric stress at failure can be related to the shearstrength parameters – cohesion intercept c0 and angle of shearingresistance /0 – using the Mohr–Coulomb failure criterion:

ðr01 � r03Þf ¼2c0 cos /0 þ 2r03 sin /0

1� sin /0ð3Þ

The tangent Young’s modulus Et for any stress state may then bedetermined by differentiating Eq. (1) with respect to axial strainea and substituting Eqs. (2) and (3) in the resulting equation:

Et ¼ 1� Rf ð1� sin /0Þðr01 � r03Þ2c0 cos /0 þ 2r03 sin /0

� �2

KPar03Pa

� �n

ð4Þ

Eq. (4), which describes the non-linear variation of the tangentYoung’s modulus with deviatoric stress (or axial strain) for a NLEHmodel using the five input parameters: K, n, c0, /0 and Rf , is used inthe finite element analyses conducted for the development of thedesign chart.

4. Mechanical properties of MSW

Modelling the mechanical behaviour of MSW using the NLEHmodel requires five input parameters (K, n, c0, /0 and Rf ) for thecomplete description of its stress–strain behaviour. Additionally,the unit weight of MSW ðcÞ is required to determine the verticaland horizontal effective stress profiles within the landfill.

Lower- and upper-bound values of parameters K, n and Rf wereobtained from statistical analysis of these parameters estimatedfrom triaxial stress–strain data available in the literature as wellas data obtained from extensive laboratory testing of MSW carriedout by the authors using large samples of MSW taken from two dif-ferent landfills in Canada (Singh et al., submitted for publication-a).Lower- and upper-bound values of parameters c0 and /0 were ob-tained from the results of stochastic modelling of the mechanicalbehaviour of MSW using ‘unit cell’ finite element analyses as wellas statistical analysis of data available in the literature. The profilesof unit weight vs. depth corresponding to low, typical and high val-ues of unit weight were obtained using data available in the pub-lished literature.

4.1. Estimation of Young’s modulus

Using large-scale tests on MSW, the Young’s modulus of MSWhas been found to increase with depth and increasing confiningstress (Beaven and Powrie, 1995; Castelli and Maugeri, 2008; Singhand Fleming, 2008). Accordingly, a power function first proposedby Janbu (1963) for a wide range of geomaterials ranging fromplastic clays to soft rocks and given by Eq. (5) is used to capturethe stress dependence of Young’s modulus of MSW:

E ¼ KPar03Pa

� �n

ð5Þ

Eq. (2), which relates initial tangent Young’s modulus Ei to the effec-tive confining stress, is simply a special case of Eq. (5). It is worthmentioning here that municipal waste was likely not a materialconsidered by Janbu (1963) when proposing Eq. (5). A practicaladvantage in using this formulation is that it is coded into somestress–deformation finite element software such as SIGMA/W(GSI, 2007). Eq. (5) implies that as r03 approaches 0, Ei should alsoapproach 0; this is consistent with the authors’ laboratory compres-sion cell testing data (Singh and Fleming, submitted for publication)and data from a large-scale compression cell in the UK (Beaven andPowrie, 1995) as shown in Fig. 2.

0

50

100

150

200

0 500 1000 1500 2000 2500 3000

Effective constrained Modulus(kPa)

Ver

tical

Eff

ectiv

e st

ress

(kP

a)

Singh & Fleming (2008)

Singh & Fleming



Beaven & Powrie(1995)

Fig. 2. Modulus of MSW from large compression cell.

Table 1Summary of hyperbolic model parameters K, n and Rf for MSW estimated fromlaboratory test results (after Singh et al., submitted for publication-a).

Reference study Estimatedhyperbolicparameters

n K Rfa

Vilar and Carvalho (2004) CD 0.83 29 0.70CU 1.05 28 0.91

Machado et al. (2002) 1.26 25 0.72Caicedo et al. (2002) 0.31 68 0.90Jessberger and Kockel (1993) 0.39 42 0.33Kockel (1995) 0.76 55 0.55Grisolia et al. (1995) 0.61 12 0.53

Authors study using samples from Spadina landfill,Saskatoon, Canada

R 0.65 34 0.68I 0.53 75 0.87LC 0.56 44 0.86

Authors study using samples from Brock West landfill,Ontario, Canada

R 0.87 93 0.92I 1.12 58 0.82

Mean 0.75 47 0.73Standard deviation 0.29 24 0.18Standard error of mean 0.08 7 0.05

Using confidence level of 90% for the mean of the hyperbolic parametersUpper confidence limit 0.88 58 0.82Lower confidence limit 0.61 36 0.64

Note: R, recompacted; I, intact; LC, statically compacted in compression cell.a Average value from a series of tests for each study.

M.K. Singh et al. / Waste Management 29 (2009) 1577–1587 1579

Unlike soils, MSW shows significant variability in terms ofcomposition and undergoes chemical and biological degradationwith time. It is likely, therefore, that Young’s modulus of MSWmay also depend on the composition and the state of degradationof MSW; however, no evidence has been found in published liter-ature in support of this hypothesis. Hence, in the present study,the Young’s modulus of MSW is assumed to vary only with theeffective confining stress according to Eq. (5). It is also assumedthat the effective confining stress can be estimated from the effec-tive vertical stress r0v and the at-rest coefficient of earth pressureK0 using:

r03 ¼ K0r0v ð6Þ

Substitution of Eq. (6) into Eq. (5) results in:

E ¼ KPaK0r0v

Pa

� �n

ð7Þ

K0 was obtained from one-dimensional compression tests onMSW samples using a 400-mm diameter dual-purpose landfillbioreactor and compression cell (LCC) capable of measuringchanges in horizontal stress. Further details of the LCC and theestimation of K0 from measured changes in horizontal stresscan be found in Singh and Fleming (2008). A constant value ofK0 equal to 0.40 was used in the finite element analyses, corre-sponding to a value of 0.29 for the Poisson’s ratio of MSW andconsistent with published values of K0 (e.g., Landva et al., 2000)and m0 (e.g., Matasovic and Kavazanjian, 1998; Dixon et al.,1999; Kavazanjian, 2006) for MSW.

Values of K, n and Rf were obtained from laboratory testing ofMSW conducted by the authors as well as laboratory testing datafrom published literature (Singh et al., submitted for publication-a). The authors’ laboratory testing program comprised triaxial test-ing of large-diameter samples of intact as well as recompactedMSW samples. Published triaxial test data were extracted fromJessberger and Kockel (1993), Kockel (1995), Grisolia et al.(1995), Machado et al. (2002), Caicedo et al. (2002) and Vilar andCarvalho (2004) by digitization of their deviatoric stress vs. axialstrain curves. Eq. (4) was then used for the analysis of data fromtriaxial tests in order to obtain K, n and Rf values. More than 50individual triaxial compression tests representing 12 different testseries were evaluated using this approach. The values estimatedfor the parameters K, n and Rf are presented in Table 1. Upperand lower limits on the mean values of K, n and Rf at 90% confi-dence level are also shown in Table 1. Further details regarding thistesting and analysis can be found in Singh and Fleming (2008). Theestimated values of K, n and K0 were used in Eq. (7) to establish a

lower and upper-bound of typical modulus profile with depth forMSW.

4.2. Estimation of unit weight

The unit weight of MSW is a function of the effective confiningstress, which increases as the height of the landfill is increased.This increase in unit weight with increasing landfill height mayhave a significant effect on the stress–deformation behaviour ofMSW because it influences the stress distribution within the wastebody. It is important, therefore, to account for the variation of unitweight with depth in order to obtain accurate estimates of themaximum lateral deformation within a landfill.

Published data on the in situ unit weight of MSW show consid-erable scatter from one site to another. Higher values of unitweight are generally associated with landfills having a greater pro-portion of daily or interim cover soil and landfills with highermoisture content (Zekkos et al., 2006); however, information oncover soil content and moisture content is often not reported in

0

10

20

30

40

50

5 10 15 20

z(m)

γ (kN/m 3)

Low

Typical

High

Unit Weight of MSW

iγ

(kN/m3 )

α(m

4/kN)

β(m

3/kN)

Low 5 2 0.1 Typical 10 3 0.2

High 15.5 6 0.9

[after Zekkos et al., 2006]

0

10

20

30

40

50

z(m)

(kN/m 3)(kN/m 3)

Low

Typical

High

Low 5 2 0.1 Typical 10 3 0.2

High 15.5 6 0.9

[after Zekkos et al., 2006]

Fig. 3. Range of values of unit weight profiles used in the development of the designchart.

Table 2Summary and statistical analysis results of shear strength parameters for MSW estimated

Reference Shear strength parameters Met

c0 (kPa) /0 (�)

Cowland et al. (1993) 10 25 BackCaicedo et al. (2002) 67 23 LargEdincliler et al. (1996) 27 42 DSEid et al. (2000) 25 35 LargGabr and Valero (1995) 17 34 SmaGrisolia et al. (1995) 2–3 15–20 LargGrisolia et al. (1995) 10 30–40 LargHarris et al. (2006) 9–14 20–29 DSS,Houston et al. (1995) 5 33–35 LargJessberger and Kockel (1995) 0 31–49 BothKavazanjian (1995) 24 0 For nKavazanjian (1995) 0 30 For nLandva and Clark (1986) 10–23 24–42 DS oLandva and Clark (1990) 0–23 24–41 DSMahler and De Lamare Netto (2003) 2.5–4 21–36 DSMazzucato et al. (1999) 43 31 LargPelkey et al. (2001) 0 26–29 LargSiegel et al. (1990) 0 39–53 DS. AStoll (1971) 0 24–42 SmaVilar and Carvalho (2002) 39.2 29 At nVilar and Carvalho (2002) 60.7 23 SatuWithiam et al. (1995) 10 30 LargZekkos et al. (2007) 36–41 TriaxZwanenburg et al. (2007) 35–37 LargSingh et al. (submitted for publication-b) 0–8.4 35–47 LargSingh et al. (submitted for publication-a) 16–36 21–41 Larg

Mean 16 31Standard deviation 18 9Standard error of mean 3 2Upper confidence limit 22 34Lower confidence limit 11 29

Note: DS, direct shear test; CU, consolidated undrained triaxial test; I, intact; R, recomp


published literature and this could be one of the reasons for thescatter in the reported unit weight values. It is worth noting thatregardless of the scatter in reported unit weight values, the trendof unit weight values increasing with depth has been observedconsistently (Zekkos et al., 2006).

Published data on the unit weight of MSW from various Amer-ican landfills, such as the OII landfill (Kavazanjian et al., 1999) andthe Tri-Cities landfill (Zekkos et al., 2006) indicate a non-linearrelationship between the unit weight and the effective confiningstress. Profiles of unit weight vs. depth suggested by Kavazanjian(1995) and later revised by Kavazanjian (1999) have been cited fre-quently in the literature. Zekkos et al. (2006) have proposed ahyperbolic relationship between the unit weight and the depth ofthe landfill represented by the following equation:

c ¼ ci þz

aþ bzð8Þ

where ci is the near-surface in-place unit weight (in kN/m3), z is thedepth (in m), and a (in m4/kN) and b (in m3/kN) are hyperboliccurve-fitting parameters. Parameter a represents the near-surfacerate of increase of unit weight with depth; its value typically lies be-tween 0 and 10. Parameter b is the inverse of the difference be-tween the maximum (asymptotic) unit weight of MSW and ci; itsvalue typically lies between 0 and 1.

Based on the compaction effort and the amount of daily coversoil present within a landfill, Zekkos et al. (2006) have recom-mended three sets of ci, a and b values corresponding to low, typ-ical and high values of unit weight (Fig. 3). These three sets of ci, aand b values were used in this study as input for the finite elementanalyses. Using the unit weight vs. depth profiles shown in Fig. 3, aunit weight value corresponding to the overburden stress at fullheight of the landfill was assigned at mid-height of each layer of

from published literature.

hod of estimation

analysis of deep trench cut in wastee DS, pressure phicometer

e DS and back analysis of failed slopesll CU triaxial (values at 20% axial strain)e triaxial (at 10–15% axial strain)e triaxial (at 10–15% axial strain)DS, large CU triax

e DS on undisturbed sampleslarge and small triaxialormal stress up to 30 kPaormal stress more than 30 kPa

n waste from various Canadian landfills

e DSe DSt 10% shear displacement; c0 assumed zero

ll triaxialatural water content (20% strain)rated sample (20% strain)e DS

for confining pressure of 200 kPae triaxiale triaxial (I and R from Brock West landfill)e triaxial from Spadina landfill (I, R and statically compacted and degraded in LCC)

acted; LCC, dual-purpose landfill compression cell and bioreactor.

Table 3Elastic and shear strength properties and relative proportions of MSW constituent groups used in stochastic modelling.

Group Property Constituents Range (% byweight)

Elastic parameters Shear strength parameters

E0 (MPa) m0 c0 (kPa) /0 (�)

A Rigid and incompressible Metals, glass, wood, ceramic 5–17 75–110 0.26–0.49 20–30 33–39B Soil-like material Demolition waste, cover soil, ash 6–25 10–20 0.25–0.33 0 25–30C Degradable and compressible Food, yard and animal waste 16–43 0.5–0.7 0.05–0.15 2–7 25–30D Reinforcing and tensile

elementsPaper, cardboard, flexible and rigidplastics, tires

16–60 1.5–3 0.28–0.32 4–8 22–28


MSW. This approach has also been suggested by Penman et al.(1971) for the estimation of deformations in heterogeneousembankments.

4.3. Estimation of shear strength parameters

The values of shear strength parameters c0 and /0 were esti-mated using statistical analysis of data obtained from large triaxialtests on intact and recompacted MSW samples (150 and 200 mmdiameter) conducted by the authors, along with data from pub-lished studies on laboratory and field testing of MSW. The esti-mated values of c0 and /0 are presented in Table 2. Upper andlower confidence limits on the mean value of c0 and /0 at 90% con-fidence level are also shown in Table 2. Shear strength parameterswere also estimated from stochastic modelling. The purpose ofconducting stochastic modelling was to justify the use of an ‘equiv-alent’ homogeneous material model (NLEH model) as an analogueto multi-component system for simulating the overall bulk stress–deformation behaviour of MSW. A brief overview of stochasticmodelling work carried out by the authors is provided in followingsection.

Determination of c0 and /0 using stochastic numerical modellingwas a three-step process. The first step involved characterization ofMSW into four major constituent groups based on their similarityin influencing the overall mechanical behaviour of MSW. Accord-ingly, four major constituent groups were identified with eachgroup containing material with similar mechanical properties. Ta-

1

(x 0.001)

0 200 400.0

0.2

0.4

0.6

0.8

1.0

Rigid & incompressible

Soil-likecomponents

Tensile components not providing reinforcement

Top horizontal downward vert

Bottom horizontal boundary(fixed in y-direction)

Inside vertical boundary(fixed in x-direction)

y

1

(x 0.001)

0 200 400.0

0.2

0.4

0.6

0.8

1.0

Rigid & incompressible

Soil-likecomponents

Tensile components not providing reinforcement

Top horizontal downward vert

Bottom horizontal boundary(fixed in y-direction)

Inside vertical boundary(fixed in x-direction)

y

Fig. 4. A typical finite element ‘unit cell’ mesh used

ble 3 lists the assigned material properties to each constituentgroup. It was noted that not all constituents classified under GroupD provide reinforcing effect; therefore, the Group D constituentswere further classified into two subgroups: (a) those providingreinforcing effect such as plastics, corrugated boards, textiles, tiresand rubber; and (b) those not providing any reinforcing effect suchas newspaper and constituents smaller than 40 mm.

The second step was the stochastic modelling of the stress–deformation behaviour of MSW, which involved conducting planestrain finite element ‘unit cell’ simulations of drained shearing ofMSW and using the Monte Carlo method for random allocationof various parameters such as the material properties, the relativeproportion and the positioning of each constituent element ofMSW. A typical finite element ‘unit cell’ mesh (shown in Fig. 4) rep-resented a MSW sample of 1.0 m width and 2.0 m height. Axes ofsymmetry were used to reduce the size of the finite element mesh.Each finite element in a ‘unit cell’ mesh was 8-noded square with9-point integration scheme. In addition to the 8-noded square ele-ments, linear elastic bar elements were used to model those con-stituents classified under Group D that are capable of providingreinforcing effect. Since only square finite elements were used inall the finite element meshes, it was not possible to model the var-iation in shape and orientation of the individual constituents. MSWin these finite element simulations was modelled as an elastic–per-fectly plastic material with Mohr–Coulomb failure criterion.

Four random variables were defined as: (i) proportions of indi-vidual constituent groups; (ii) elastic properties of the individual

0 600

Bar elements representing tensile components providing reinforcement

Compressiblecomponents

boundary (prescribed ical displacement)

Outside vertical boundary[constant normal stress (cell pressure)]

x0 600

Bar elements representing tensile components providing reinforcement

Compressiblecomponents

boundary (prescribed ical displacement)

Outside vertical boundary[constant normal stress (cell pressure)]

x

in the stochastic modelling of MSW behavior.

Table 5Range of hyperbolic model input parameters used in the development of the designchart.

Parameter K n Rf c0 (kPa) /0 (�)


constituent groups; (iii) shear strength properties of the individualconstituent groups; and (iv) relative positioning of the individualconstituent groups within MSW matrix. The Monte Carlo methodwas used for generating the random variables. For example, a pro-portion was randomly selected for each group (from their respec-tive distribution shown in Table 3) using the Monte Carlomethod such that the total percentage proportion of all four groupsadded up to 100%. Random variations in relative positioning of theconstituent groups were then achieved by manipulating the mate-rial properties of individual finite elements. Such manipulationwas accomplished by editing SIGMA/W input files, which haveXML-compatible structure.

The third step involved the extraction of c0 and /0 values fromthe results of each set of three simulations conducted at 100 kPa,200 and 300 kPa effective cell pressures. The stress paths leadingup to the tult-point for each of the three effective cell pressureswere plotted and a Mohr–Coulomb failure line was fitted throughthe points. The values of cohesion intercept c0 and angle of friction/0 were obtained from the slope and the intercept of the fittedMohr–Coulomb failure line. Further details about stochasticnumerical modelling and estimation of shear strength parameterscan be found in Singh et al. (2007).

0

50

100

150

200

250

300

0.0 0.5 1.0

Axial Strain (x

Dev

iato

ric

Str

ess

(kP

a)

Finite E

Fitted H

Effecti

0

50

100

150

200

250

300

0.0 0.5 1.0

Axial Strain (x

evia

tori

c S

tres

s (k

Pa)

Finite E

Fitted H

Finite E

Fitted H

Effecti

Fig. 5. Method of estimation of tult by extrapolatin

Table 4Summary and statistical analysis results of shear strength parameters for MSWestimated from stochastic modelling.

Shear strength parameter

c0 (kPa) /0 (�)

Estimated mean value 16.4 33Weighed mean value 3.2 26.1Standard deviation 8 5Standard error of mean 1 1Upper confidence limita 18 34Lower confidence limita 14 32

a Using confidence level of 90% for mean.

The mean values of ‘equivalent’ shear strength parameters c0

and /0 estimated using stochastic modelling are presented in Table4. For comparison, weighted mean values of c0 and /0 are also pre-sented in Table 4. These weighted mean values were obtained bymultiplying the values of c0 and /0 for each constituent group bythe proportion of that constituent group.

Statistical analysis of stochastic modelling results confirmedthat the values of c0 and /0 were normally distributed. Upper andlower confidence limits on the mean values of c0 and /0 at 90% con-fidence level are also shown in Table 4. It can be seen from Table 4that the mean values of c0 and /0 obtained from stochastic model-ling are higher than their weighted values. This could be attributedto the interlocking of waste components in the matrix, resulting inhigher overall shear strength. It should be pointed out that suchinterlocking is likely influenced by the variations in shape of thewaste components, which was not modelled in the present study.

1.5 2.0

100 %)

lement Simulation Results

yperbolic Stress-Strain Curve

tult = 109.5 kPa

tult = 207 kPa

tult = 270 kPa

ve Cell Pressure = 300 kPa

200 kPa

100 kPa

1.5 2.0

100 %)





tult = 109.5 kPa

tult = 207 kPa

tult = 270 kPa

ve Cell Pressure = 300 kPa

200 kPa

100 kPa

g numerical results using hyperbolic curves.

Table 6Range of parameters used in the parametric study for the development of the designchart.

Parameter Range

Height (m) 20, 3.0, 4.0, 5.0, 60Side slope (coth) 20, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0Unit weight Low, typical, high

Note: h – inclination of side slope with horizontal.

Upper confidence limita 58 0.88 0.82 22 34Lower confidence limita 36 0.61 0.64 11 29

a Using confidence level of 90% for the mean.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 20 40 60 80

maxhδ(m)

H (m)

3)cot( =θ

]88.0;36[ == nK

]61.0;58[ == nK

0.0

0.1

0.2

0.3

0.4

0.5

0.6

1 2 3 4 5 6

maxhδ(m)

)cot(θ

]88.0;36[ == nK

]61.0;58[ == nK

m40=H

a b

Fig. 6. Effect of (a) height of the landfill H, and (b) horizontal stretch of the side slope of the landfill cotðhÞ on maximum horizontal displacement dhmax.


As such, further work is required to confirm the increase in shearstrength of MSW due to interlocking effect.

Results from stochastic modelling and comparison of data pre-sented in Tables 2 and 4 reveal some important observations. It isinteresting to note that while individual constituent groups weremodeled using an elastic–perfectly plastic constitutive modeland, therefore, had well-defined yield (failure) points, the overallstress–strain behaviour as shown in Fig. 5 did not exhibit a well-

Table 7Magnitudes of maximum horizontal displacement for various combinations ofparameters K, n and Rf (H = 20 m; cotðhÞ ¼ 4).

n K Rf dhmax (m)

0.61 36 0.64 0.0820.61 36 0.82 0.082

0.61 58 0.64 0.0600.61 58 0.82 0.060

0.88 58 0.82 0.0730.88 58 0.64 0.073

0.88 36 0.64 0.1130.88 36 0.82 0.113

0

500

1000

1500

2000

0 0.1 0.2

tE(kPa)

aε

cot(m;20[ =H

n K0.61 360.61 360.61 580.61 580.88 580.88 580.88 360.88 36

0

500

1000

1500

2000

0 0.1 0.2

tE(kPa)

tE(kPa)

aε

cot(m;20[ =H

n K0.61 360.61 360.61 580.61 580.88 580.88 580.88 360.88 36

Fig. 7. Effect of combinations of parameters K , n and Rf on maximum hori

defined yield point and resembled the stress–strain response of aNLEH model.

The mean values of c0 and /0 from real test data (Table 2) arequite close to mean values of c0 and /0 from stochastic modelling(Table 4), although the values of c0 and /0 from real test data showgreater deviation from the mean values. This deviation could bebecause of differences in testing protocols, sample type, unitweight, waste composition and age and interpretation of results.Furthermore, the upper and lower confidence limits of c0 and /0

from stochastic modelling lie within the upper and lower confi-dence limits from real test data. These findings suggest that a mul-ti-component composite material may be modeled as an‘‘equivalent” homogeneous material exhibiting a non-linear hyper-bolic stress–strain behaviour and, therefore, validate the use of aNLEH model to simulate the overall or ‘equivalent’ stress–strainbehaviour of MSW.

4.4. Range of material properties of MSW for the development ofdesign chart

The range of material properties, obtained from the analysespresented above and bound by the lower and upper confidencelimits at 90% confidence level, are presented in Table 5 and usedin the development of design chart.

0.3 0.4

Lowest maxhδ

]4) =θ

kPa103 =′σ

fR maxhδ (m)

0.64 0.082 0.82 0.082 0.64 0.060 0.82 0.060 0.82 0.073 0.64 0.073 0.64 0.113 0.82 0.113

Highest maxhδ

0.3 0.4

Lowest maxhδLowest maxhδ

]4) =θ

kPa103 =′σ

fR maxhδ (m)

0.64 0.082 0.82 0.082 0.64 0.060 0.82 0.060 0.82 0.073 0.64 0.073 0.64 0.113 0.82 0.113

Highest maxhδHighest maxhδ

zontal displacement dhmax for effective confining stress r03 < 100 kPa.


5. Parametric study

5.1. Methodology

The parametric study involved conducting finite element simu-lations of landfill at five different heights, seven different sideslopes, and three different unit weight profiles as presented in Ta-ble 6. Each simulation was done using both the lower- and theupper-bound values of the five input parameters: K, n, c0, /0 andRf given in Table 5. A total of 210 finite element simulations wereconducted. For all the simulations, the bottom width of the landfillwas kept constant and the foundation soil was modeled using a 10-m thick layer of linear elastic material ðE0 ¼ 20 MPa; m0 ¼ 0:33Þ.The results of these simulations are presented in the next sectionin terms of the effect of each parameter on the value of maximumhorizontal displacement ðdhmaxÞ within the landfill.

0

0.1

0.2

0.3

0.4

0 5 10 15 20

maxhδ(m)

iγ (kN/m3)

3)cot( m; 40 == θH

]88.0 ;36[ == nK

]61.0 ;58[ == nK

0

0.1

0.2

0.3

0.4

0 5 10 15 20

maxhδ(m)

maxhδ(m)

iγ (kN/m3)iγ (kN/m3)

3)cot( m; 40 == θH

]88.0 ;36[ == nK

]61.0 ;58[ == nK

Fig. 8. Effect of unit weight (represented by near-surface unit weight ci) onmaximum horizontal displacement.

0.04

0.1

0.16

0.2

2

0.28

0.

Dis50 100 150 200 250 300

Ele

vatio

n

15

25

35

45

55

65

75

85

95

105

115

h 0.04

0.1

0.16

0.2

2

0.28

0.

Dis50 100 150 200 250 300

Ele

vatio

n

15

25

35

45

55

65

75

85

95

105

115

h

Fig. 9. Spatial distribution of dhmax for a typi

6. Results

6.1. Effect of height and side slope on lateral deformation

The effect of height of the landfill H on the lateral deformationðdhmaxÞ was studied by conducting five simulations with same sideslope but different H values. The effect of the side slope of the land-fill cotðhÞ on dhmax was studied by conducting seven simulationswith the same H but with different cotðhÞ values. The results arepresented in Fig. 6. As seen from Fig. 6a, increasing the height ofthe landfill resulted in an increase in dhmax. Also, the rate of in-crease of dhmax with respect to H was greater for higher landfills,which can be attributed to reduction in stiffness with increasingdeviatoric stress. A landfill with a gentler side slope (i.e., highercotðhÞ) results in a lower dhmax as seen from Fig. 6b. This is an ex-pected result since gentler side slopes have higher stiffness be-cause of lower deviatoric stresses.

6.2. Effect of mechanical properties of MSW

6.2.1. Effect of K, n and Rf

Table 7 lists the values of maximum horizontal displacementdhmax for eight different combinations of lower- and upper-boundvalues of parameters K, n and Rf (H = 20 m; cotðhÞ ¼ 4 for the land-fill). It is evident from Table 7 that Rf has no effect on the magni-tude of maximum horizontal displacement. One explanation forthis could be that at full height, the stress state of the entire landfillis sufficiently far from failure. It is also worth noting that the low-est value of dhmax is obtained for the combination of an upper-bound value of K and a lower-bound value of n, whereas the high-est value of dhmax is obtained for the combination of lower-boundvalue of K and an upper-bound value of n. This result may appearto be counter-intuitive because the highest values of dhmax shouldcorrespond to lower-bound values of both K and n and vice versa;however, the result makes perfect sense when examined in thelight of the magnitude of effective confining stress r03. It was notedfrom the results of the finite element analyses that the magnitudeof r03 at the location of maximum horizontal displacement withinthe landfill was between 10 and 60 kPa (depending on the heightof the landfill). At values of r03 less then 100 kPa, it is the combina-tion of lower-bound K and upper-bound n that gives the lowest va-

0.34

4

tance350 400 450 500 550 600

m48

5.2

h 0.34

4

tance350 400 450 500 550 600

m48

5.2

h

cal values of H = 60 m and 4H:1V slope.

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50

R2 = 0.991]88.0 ;36[ == nK

R2 = 0.998]61.0 ;58[ == nK

maxhδ(m)

)cot(θH

(m)

High compaction effort and soil content

Fig. 10. Results of the parametric study plotted in dhmax � H=ffiffiffiffiffiffiffiffiffiffiffiffifficotðhÞ

p� �space (all

analyses with high density).


lue of Young’s modulus and, therefore, the highest value of dhmax

(Fig. 7).

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50

maxhδ(m)

)cot(θH

(m)

Low compaction effort and soil content

Upper Bound

Lower Bound

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50

maxhδ(m)

maxhδ(m)

)cot(θH

(m)

Low compaction effort and soil content

Upper Bound

Lower Bound

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50

maxhδ(m)

)cot(θH

(m)


Upper Bound

Lower Bound

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50

maxhδ(m)

maxhδ(m)

)cot(θH

(m)


Upper Bound

Lower Bound

Fig. 11. Design chart for the estimation of m

6.2.2. Effect of c0 and /0

Values of c0 and /0 appear to have no effect on the magnitude ofdhmax. The magnitude of dhmax obtained from simulations usinglower-bound values of c0 and /0 was the same as that obtainedfrom simulations using upper-bound values of c0 and /0, whichindicated that at full height, the stress state within the landfill issufficiently far from failure. It was decided, therefore, to use thelower-bound values of c0 and /0 for all simulations.

6.2.3. Effect of unit weightFig. 8 shows the variation of dhmax with near-surface in-place

unit weight ci for a 40-m high landfill with 3H to 1V side slopesfor the two combinations of K and n that yield the highest and low-est values of Young’s modulus. It can be seen from Fig. 8 that dhmax

increases as ci increases; however, the rate of increase of dhmax

with respect to ci is smaller for higher values of ci. An increase inunit weight results in an increase in overburden stress, resultingin more horizontal displacement; however, an increase in overbur-den stress also results in an increase in effective confinement,resulting in higher stiffness and a reduction in horizontal displace-ment. Consequently, the rate of increase in dhmax with respect to ci

drops at higher values of ci.

6.2.4. Spatial distribution of dhmax

Fig. 9 shows the spatial distribution of dhmax for a typical landfillheight of 60 m and with a side slope of 4H:1V. The contours of hor-

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50

maxhδ(m)

)cot(θH

(m)

Typical compaction effort and soil content

Upper Bound

Lower Bound

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50

maxhδ(m)

maxhδ(m)

)cot(θH

(m)

Typical compaction effort and soil content

Upper Bound

Lower Bound

Compaction effort and soil amount

iγ

(kN/m3)

α (m4/kN)

β (m3/kN)

Low 5 2 0.1 Typical 10 3 0.2

High 15.5 6 0.9 [after Zekkos et al., 2006]

θ

)cot(θ

1H

Compaction effort and soil amount

iγ

(kN/m3)

α (m4/kN)

β (m3/kN)

Low 5 2 0.1 Typical 10 3 0.2

High 15.5 6 0.9 [after Zekkos et al., 2006]

θ

)cot(θ

1H

θ

)cot(θ

1H

θ

)cot(θ

1H

aximum horizontal displacement dhmax.


izontal displacement shown in Fig. 9 are for a typical unit weight of10 kN/m3 and upper-bound of input parameters (Table 5). Forother combinations of these variables (Tables 5 and 6), the locationof dhmax did not show significant variation and was found to be lo-cated between h=2:5 and h=3 of the total height (h). Similarly, thehorizontal distance of dhmax was observed to vary from 40 to 55 mfrom the sloping surface.

7. Design chart

7.1. Presentation

It was shown in Fig. 6 that dhmax increases as the height of thelandfill H is increased and decreases as the side slope of the landfilldecreases (i.e., increasing cotðhÞ). Regression analysis of dhmax vs. Hand dhmax vs. cotðhÞ results revealed that dhmax is directly propor-tional to H and inversely proportional to the square root of cotðhÞWhen the results of finite element analyses are plotted in termsof dhmax and the ratio H=

ffiffiffiffiffiffiffiffiffiffiffiffifficotðhÞ

p, they appear to plot on two un-

ique curves corresponding to the upper-bound and lower-boundcombinations of parameters K and n as shown in Fig. 10.

The goodness of fit for the two curves was excellent as indicatedby R2 values very close to 1. It was decided, therefore, to presentthe design chart in terms of three sets of upper-bound and low-er-bound dhmax vs. H=

ffiffiffiffiffiffiffiffiffiffiffiffifficotðhÞ

pcurves (one set each for low, typical

and high unit weights) as shown in Fig. 11. For each curve shown inFig. 11, the R2 value was greater than or equal to 0.99. The pro-posed design chart is easy-to-use and results in quick estimatesof the lowest and highest values of the maximum horizontal dis-placement expected in a landfill of height H and horizontal stretchof side slope cotðhÞ.

7.2. Validation

The validity of the proposed design chart can be establishedusing records of the height of the landfill and its maximum hori-zontal displacement; however, such records are rarely kept and itis very difficult to find these in published literature. The authors

Fig. 12. A distorted gas lateral located on the south slope of the Brock West landfill,Ontario.

have been involved with continuous monitoring of horizontal dis-placements at the Brock West landfill in Ontario, Canada. Themonitoring of horizontal displacements of the south slope of thelandfill began in 2004 after it was noticed that a few of the gaslaterals were severely distorted (Fig. 12).

Although horizontal displacement of the south slope was occur-ring prior to 2004, there are no documented records of these dis-placements. Data from four inclinometers installed on the southslope showed an increase in horizontal displacement from0.04 m in October 2004 to 0.23 m in September 2006. Using the de-sign chart, the expected range of maximum horizontal displace-ment at Brock West landfill (H = 60 m; cotðhÞ ¼ 4; typical unitweight) is 0.28–0.44 m. Given that, the horizontal displacementsare on-going at this landfill; this range of maximum horizontal dis-placement estimated using the proposed design chart is quitereasonable.

8. Conclusions

In this paper, an easy-to-use design chart for the estimation ofmaximum horizontal displacement within a landfill using only theheight and the horizontal stretch of the side slope of the landfillhas been presented. The design chart was developed using resultsof a finite element parametric study in which the behaviour of themunicipal solid waste was modelled using a non-linear elastichyperbolic model. The development of the design chart took intoaccount non-linear variation in unit weight as well as Young’smodulus of MSW with depth. Mechanical properties of MSW usedin the development of the design chart, i.e., non-linear stiffness,shear strength and unit weight of MSW, were obtained using sta-tistical analysis of laboratory testing data as well as using stochas-tic numerical modelling. For each mechanical property, upper andlower confidence limits at 90% confidence level were used toestablish the range of expected maximum horizontal displace-ment. The range of maximum horizontal displacement estimatedusing the proposed design chart were reasonably close to mea-sured maximum horizontal displacement at the Brock West land-fill site in Ontario, Canada. The design chart is easy-to-use andprovides landfill engineers with quick estimates of maximum hor-izontal displacements within a landfill, which are crucial forensuring satisfactory functioning of ancillary services such asthe gas collection system.

References

Beaven, R.P., Powrie, W., 1995. Hydrogeological and geotechnical properties ofrefuse using a large scale compression cell. In: Proceedings of the FifthInternational Waste Management and Landfill Symposium, Sardinia, pp. 745–760.

Caicedo, B., Yamin, L., Giraldo, E., Coronado, O., 2002. Geomechanical properties ofmunicipal solid waste in Dona Juana sanitary landfill. In: Proceedings of theFourth International Congress on Environmental Geotechnics, vol. 1, Brazil, pp.177–182.

Castelli, F., Maugeri, M., 2008. Experimental analysis of waste compressibility.Geotechnical Special Publication, ASCE 177, 208–215.

Cowland, J.W., Tang, K.Y., Gabay, J., 1993. Density and strength properties of HongKong refuse. In: Proceedings of the Fourth International Waste Managementand Landfill Symposium, Sardinia, pp. 1433–1446.

Dixon, N., Jones, D.R.V., Whittle, R.W., 1999. Mechanical properties of householdwaste: in situ assessment using pressuremeter. In: Proceedings of the SeventhInternational Waste Management and Landfill Symposium, Sardinia, pp. 453–460.

Duncan, J.M., Chang, C.Y., 1970. Nonlinear analysis of stress and strain in soils.Journal of the Soil Mechanics and Foundation Engineering Division, ASCE 96(SM5), 1629–1653.

Edincliler, A., Benson, C.H., Edil, T.B., 1996. Shear strength of municipal solidwaste. Interim Report – Year 1, Environmental Geotechnics Report 96-2,Department of Civil and Environmental Engineering, University ofWisconsin, Madison.

Eid, H.T., Stark, T.D., Evans, W.D., Sherry, P.E., 2000. Municipal solid waste slopefailure. I: Waste and foundation soil properties. Journal of Geotechnical andGeoenvironmental Engineering, ASCE 126 (5), 397–407.


GSI, 2007. SIGMA/W, 2007 Stress–deformation analysis software. Geo-SlopeInternational (GSI). <http://www.geo-slope.com/products/sigmaw2007.aspx>(accessed on April 4, 2008).

Gabr, M.A., Valero, S.N., 1995. Geotechnical properties of municipal solid waste.Geotechnical Testing Journal, ASTM 18 (2), 241–251.

Grisolia, M., Napoleoni, Q., Tancredi, G., 1995. Contribution to a technicalclassification of MSW. In: Proceedings of the Fifth International WasteManagement and Landfill Symposium, Sardinia, pp. 703–710.

Harris, J.M., Shafer, A.L., DeGroff, L., Hater, G.R., Gabr, M., et al., 2006. Shear strengthof degraded reconstituted municipal solid waste. Geotechnical Testing Journal,ASTM 29 (2), 1–8.

Houston, W.N., Houston, S.L., Liu, J.W., Elsayed, A., Sanders, C.O., 1995. In situ testingmethods for dynamic properties of MSW landfills. Geotechnical SpecialPublication, ASCE 54, 73–82.

Janbu, N., 1963. Soil compressibility as determined by odeometer and triaxial tests.In: Proceedings of the Third European Conference on Soil Mechanics, vol. 1,Wiesbaden, Germany, pp. 19–25.

Jessberger, H.L., Kockel, R., 1993. Determination and assessment of the mechanicalproperties of waste materials. In: Proceedings of the Fourth International WasteManagement and Landfill Symposium, Sardinia, pp. 1383–1392.

Jessberger, H.L., Syllwasschy, O., Kockel, R., 1995. Investigation of waste body-behavior and waste structure interaction. In: Proceedings of the FifthInternational Waste Management and Landfill Symposium, Sardinia.

Kavazanjian, E., 2006. Waste mechanics: recent findings and unanswered questions.Geotechnical Special Publication, ASCE 148, 34–54.

Kavazanjian, E., 1999. Seismic design of solid waste containment facilities. In:Proceedings of the Eighth Canadian Conference on Earthquake Engineering,Vancouver, pp. 51–89.

Kavazanjian, E., 1995. Evaluation of MSW properties for seismic analysis.Geotechnical Special Publication, ASCE 46, 1126–1141.

Kavazanjian, E., Matasovic, N., Bachus, R.C., 1999. Large diameter static and cycliclaboratory testing of municipal solid waste. In: Proceedings of the SeventhInternational Waste Management and Landfill Symposium, Sardinia.

Kockel, R., 1995. Scherfestigkeit von Mischabfall im Hinblick auf die Standsicherheitvon Deponien (Shear Strength of Municipal Solid Waste from the Point-of-Viewof Stability of Landfills). Ph.D. Thesis, Mitteilungen Heft 133, Leichtweib-Institutfur Wasserbau, Technische Universitat Braunschweig.

Kondner, R.L., 1963. Hyperbolic stress–strain response: cohesive soils. Journal of theSoil Mechanics and Foundation Division, ASCE 89 (SM1), 115–141.

Landva, A.O., Clark, J.I., 1986. Geotechnical testing of wastefills. In: Proceedings ofthe 39th Canadian Geotechnical Conference, Ottawa, pp. 371–385.

Landva, A.O., Clark, J.I., 1990. Geotechnics of MSW fills. In: Landva, A., Knowles, G.D.(Eds.), Geotechnics of MSW Fills – Theory and Practice. ASTM STP 1070, pp. 86–103.

Landva, A.O., Valsangkar, A.J., Pelkey, S.G., 2000. Lateral earth pressure at rest andcompressibility of municipal solid waste. Canadian Geotechnical Journal 37,1157–1165.

Machado, S.L., Carvalho, M.F., Vilar, O.M., 2002. Constitutive model for municipalsolid waste. Journal of Geotechnical and Geoenvironmental Engineering, ASCE128 (11), 940–951.

Mahler, C.F., De Lamare Netto, A., 2003. Shear resistance of mechanical biologicalpre-treated domestic urban waste. In: Proceedings of the Ninth InternationalWaste Management and Landfill Symposium, Sardinia (on CD Rom).

Matasovic, N., Kavazanjian, E., 1998. Cyclic characterization of OII landfill solidwaste. Journal of Geotechnical and Geoenvironmental Engineering, ASCE 124(3), 197–210.

Mazzucato, A., Simonini, P., Colombo, S., 1999. Analysis of block slide in a MSWlandfill. In: Proceedings of the Seventh International Waste management andLandfill Symposium, Sardinia.

Pelkey, S.A., Valsangkar, A.J., Landva, A., 2001. Shear displacement dependentstrength of municipal solid waste and its major constituents. GeotechnicalTesting Journal, ASTM 24 (4), 381–390.

Penman, A.D.M., Burland, J.B., Charles, J.A., 1971. Observed and predicteddeformations in a large embankment dam during construction. Proceedings ofthe Institution of Civil Engineers 49, 1–21.

Siegel, R.A., Robertson, R.J., Anderson, D.G., 1990. Slope stability investigation at alandfill in Southern California. In: Landva, A., Knowles, G.D. (Eds.), Geotechnicsof Waste Fills – Theory and Practice. ASTM STP 1070, pp. 259–284.

Singh, M.K., Fleming, I.R., 2008. Estimation of the mechanical properties of MSWduring degradation in a laboratory compression cell. Geotechnical SpecialPublication, ASCE 177, 200–207.

Singh, M.K., Fleming, I.R., submitted for publication. Evolution of compressibilitybehaviour of municipal solid waste during degradation. Journal of Geotechnicaland Geoenvironmental Engineering, ASCE.

Singh, M.K., Fleming, I.R., Sharma, J.S., submitted for publication-a. Application of anonlinear stress–strain model to municipal solid waste. Géotechnique.

Singh, M.K., Sharma, J.S., Fleming, I.R., submitted for publication-b. Shear strengthtesting of intact and recompacted samples of municipal solid waste. CanadianGeotechnical Journal.

Singh, M.K., Fleming, I.R., Sharma, J.S., 2007. Estimation of mechanical properties ofmunicipal solid waste using stochastic modelling. In: Proceedings of the 11thInternational Waste Management and Landfill Symposium, Sardinia (on CDRom).

Stoll, O.W., 1971. Mechanical properties of milled refuse. In: ASCE National WaterResources Engineering Meeting, Phoenix, Arizona, pp. 11–15.

UN, 2006. World Population Prospects: The 2004 Revision and WorldUrbanization Prospects: The 2005 Revision. Report by Population Divisionof the Department of Economic and Social Affairs of the United NationsSecretariat.

Vilar, O.M., Carvalho, M.F., 2002. Shear strength properties of municipal solid waste.In: Proceedings of the Fourth International Conference on EnvironmentalGeotechnics, Lisse, The Netherlands, pp. 59–64.

Vilar, O.M., Carvalho, M.F., 2004. Mechanical properties of municipal solid waste.Journal of Testing and Evaluation, ASTM 32 (6), 1–12.

Withiam, J.L., Tarvin, P.A., Bushell, T.D., Snow, R.E., German, H.W., 1995.Geotechnical Special Publication, ASCE 46, 1005–1019.

Zekkos, D.P., Bray, J.D., Kavazanjian, E., Matasovic, N., Rathje, E.M., et al., 2006. Unitweight of municipal solid waste. Journal of Geotechnical and GeoenvironmentalEngineering, ASCE 132 (10), 1250–1261.

Zekkos, D., Bray J.D., Riemer, M., Kavazanjian, E. Athanasopoulos, G.A., 2007.Response of municipal solid waste from tri-cities landfill in triaxialcompression. In: Proceedings of the Eleventh Waste Management and LandfillSymposium, Sardinia (on CD Rom).

Zwanenburg, C., Knoeff, J.G., Hounjet, M.W.A., 2007. Geotechnical characterizationof waste. In: Proceedings of the 11th International Waste Management andLandfill Symposium, Sardinia (on CD Rom).

http://www.geo-slope.com/products/sigmaw2007.aspx

A design chart for estimation of horizontal displacement in municipal landfills

Documents

Transcript of A design chart for estimation of horizontal displacement in municipal landfills