btp report

Seismic Analysis of Municipal Solid Waste Landfill for Optimum Design of Retaining Structure

Submitted by Akansha Gupta | 2008CE10606

A report of CED 412 – Project Part 2 submitted in partial fulfillment of the requirements

of the degree of Bachelors of Technology

Department of Civil Engineering

Indian Institute of Technology Delhi April, 2012

2"|"C E D $ 4 1 2 $ P r o j e c t $ P a r t $ 2 : $ R e p o r t $$

TABLE OF CONTENTS

1) Abstract

03

2) Introduction

03

3) Motivation for Research

04

4) Research already conducted

04

5) Features of the Present Analysis

06

6) Landfill model Used

07

7) Calculation of ‘Waste Force’

09

8) Parametric Study of the ‘Waste Force’

12

9) Waste Pressure Distribution Calculation (using simplified model)

19

10) Calculation of Seismic Waste Pressure Coefficient

26

11) Stability analysis of berm 30 12) Conclusion

36

APPENDIX A : List of Symbols

APPENDIX B : List of Figures APPENDIX C : References APPENDIX D : MATLAB Code used for the analysis


ABSTRACT

The expansion of existing landfills in the vertical direction is the most economical

alternative to constructing new landfills where the cost of land is prohibitive. One way to do

this capacity expansion is to construct an engineered berm at the toe of the landfill. In the

present research, a pseudo-static limit equilibrium stability analysis is performed for a

typical side-hill type municipal solid waste (MSW) landfill expanded using an engineered

berm. Seismic stability analyses is performed using a simplified version of the three-part

wedge method, including the effect of the solid waste shear strength, for the critical case

when the failure surface passes over the back slope of the berm (over-berm failure). The force

due to the waste mass on the back slope of the berm, FWB was thus calculated. Its distribution

is then plotted against the height of berm. From this waste pressure distribution, the

Seismic Waste Pressure Coefficient, KW is calculated. Also stability analysis of the

engineered berm is done for 4 modes of failure: sliding failure, overturning failure,

eccentricity failure and bearing capacity failure. Then, design charts for the engineered berm

for range of values of various parameters are plotted which can be further used to determine

the optimum dimensions of the engineered berm.

INTRODUCTION

A landfill site (also known as tip, dump or rubbish dump), is a site for the disposal of waste

materials by burial and is the oldest form of waste treatment. Historically, landfills have been

the most common methods of organized waste disposal and remain so in many places around

the world. Municipal solid waste (MSW) landfills are generally hill like structures covering a

large ground surface area with the heights varying from10 m to more than 150.

Rapid urbanization and a rapid growth in population have caused a significant increase in

municipal solid waste (MSW) generation in India in the last few decades. In recent years,

many metropolitan cities in India as well as in other parts of the world, there is great demand

to increase the size and the height of their municipal solid waste (MSW).

! “With three municipal waste landfill sites in Delhi filling up to the brim, there seems

to be no end in sight for the crisis faced by the city. Stating that Delhi produces 9,200

tons of waste every day, and is expected to go up to 19,100 tons by 2024, the MCD

demanded that 1,500 acres of land be made available to cater to the next 20 years. At


present, it has only 150 acres of land at its disposal.”(www.expressindia.com, Nov

2011)

! “With three designated sanitary landfill sites in the Capital having exhausted their

life-span and packed beyond capacity, the Municipal Corporation of Delhi…”

(www.dailypioneer.com, Oct 2011)

The acquisition of a new location and construction of a new landfill at that location may pose

a number of difficulties, especially in urban areas where the cost of land is prohibitive.

Vertical capacity expansion of existing landfills is the most economical alternative to

constructing new landfill. These vertical expansions of landfills offer various advantages in

addition to saving of the huge cost of land. These advantages include optimal use of landfill

area, low cost, less public opposition and easier obtaining of permits.

MOTIVATION FOR RESEARCH

Construction of a retaining structure is required for the vertical capacity expansion of

municipal solid wastes (MSW) landfills as discussed above. The design of the retaining

structure the determination of horizontal stresses (the corresponding force is termed as ‘waste

force’ in this study) exerted by the waste. Some research has been conducted in this regard as

discussed in the next section. However, the data pertaining to waste pressures are very

limited. The magnitude of lateral waste pressures and the factors that influence these lateral

pressures are largely unknown, despite their importance to a broad range of design problems.

The lack of information on MSW lateral waste pressures affects design of landfill structures

and hence landfill stability. An enhanced understanding of waste pressures will enable more

accurate evaluation of landfill stability, providing for safer designs and possibly allowing for

increased capacity at some sites, extending the life of facilities and thus minimizing the need

for new sites.

RESEARCH ALREADY CONDUCTED

To design the waste retaining structure, the lateral waste pressure acting on the retaining

structure should be predicted accurately. As reported by many authors in the literature,

translational failure mechanism can be assumed for the computation waste pressure.

Using the two part wedge translational failure mechanism:


1) Qian et al. (2003) and Qian and Koerner (2004), Qian and Koerner (2007) developed

two part wedge translational failure mechanism for the static stability of MSW

landfills.

2) Savoikar and Choudhury (2010) analysed the seismic stability of typical side-hill

type landfills using a two-part wedge model with both pseudo-static and pseudo-

dynamic approaches.

Using the three part wedge translational failure mechanism:

The two-part wedge method developed by the researchers is not suitable for analyzing the

translational failure of the landfill with retaining wall, and the conventional limit equilibrium

methods are incapable of revealing the effect of the shear strength of solid waste. In this

regard, the following studies have been done using the three-wedge method:

1) Three part wedge method of analysis is reported by Qian and Koerner (2009) for

static stability analysis of expansion of the landfill using an engineered berm.

2) Feng et al. (2010) also reported three-part wedge analysis method which includes the

effects of the solid waste shear strength as well as the retaining wall on the

translational failures of MSW landfills.

3) Choudhury and Savoikar (2011) presented seismic stability analysis of expanded

MSW landfills using pseudo-static limit equilibrium method.


FEATURES OF THE PRESENT ANALYSIS The following are the key features of the present analysis:

1) Pseudo-static limit equilibrium translational failure analysis

2) Inclusion of seismic forces through the vertical and horizontal seismic coefficients

3) The retaining structure used in this study is an engineered berm.

4) A three-wedge model used by Savorikar and Choudhury (2011) for seismic stability

with over-berm failure condition is used which is later on simplified to plot design

charts.

5) In the case of over-berm failure, the waste mass slides over the back slope of the

berm. Thus, the failure plane is predetermined.

Some important assumptions made in the analysis are:

1. Cohesion of waste and liner material has been taken into account.

2. The inter-wedge forces active at the interface of block and passive wedge and at the

active and passive wedge interface are assumed to be inclined at angles ω1 and ω2 to

the horizontal, respectively, and act at one-third height from the base of the

interface. For the equilibrium of the entire waste mass, the factor of safety at those

interfaces is assumed to be higher than the factor of safety of the entire waste mass,

and the factor of safety is assumed to be constant over the entire failure plane.

3. To meet the waste shear strength failure criteria, the average shear stress at the

interface between the active and the passive wedges and between the passive and the

block wedge should be less than the average shear strength of the waste at these

interfaces

4. The water table is considered to be well below the base of the landfill.


LANDFILL MODEL USED (Initially used) The landfill model used in the present analysis and the various forces including the pseudo-

static forces acting on these wedges under over-berm failure condition is shown in figure 6.1

and figure 6.2((a),(b) and (c)). A list of the notation used herein in given in APPENDIX A.

Figure 6.1 Schematic Diagram of the Landfill Model used

Figure 6.2(a) Pseduo-Static Limit Equilibrium Analysis of Active Wedge


Figure 6.2(b) Pseduo-Static Limit Equilibrium Analysis of Passive Wedge

Figure 6.2(c) Pseduo-Static Limit Equilibrium Analysis of Block Wedge


CALCULATION OF WASTE FORCE

Frictional forces acting below the active (FA), passive (FP) and the block (FB) wedges can be

evaluated as shown below:

!!!! =!!!"+ !!

!"#!!!" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(!)

!! =!!!"+ !!

!"#!!!" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(!)

!! =!!!"+ !!

!"#!!!" !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(!)

Furthermore, the inter-wedge forces acting at the interface between the active and the passive

wedge (FvPA and FvAP) and the passive and the block wedge (FvPB and FvBP) are:

!!"# =!!"!"!

+ !!"!!"#!!"!"!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(!)

!!"# =!!"!"!

+ !!"#!"#!!"!"!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(!)

!!"# =!!"!"!

+ !!!"!"#!!"!"!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(!)

!!"# =!!"!"!

+ !!"#!"#!!"!"!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(!)

For simplification, the following relations were used !"#!!"!"!

=!!"!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(!) !!"!"!

= !!"!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(!)

!!"!"!

= !!"!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(!")

The equations (4) and (7) can be written as:

!!"# = !!" + !!"#.!!"!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(!!) !!"# = !!" + !!!".!!"!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(!") !!"# = !!" + !!"#.!!"!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(!") !!"# = !!" + !!"#.!!"!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(!")


ACTIVE WEDGE

Considering the equilibrium of forces acting on the active wedge, equating the sum of all the

vertical forces acting on the active wedge to zero yields:

!!. !"#$+ !!.!! + !!. !"#$+ !!"# =!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(!")

Substituting Equations (1) and (11) into Equation (15) yields

!! !"#$+ !"#!!!"#$!" =!! −

!!!"#$!" − !!!! − !!" − !!"#!!"!!!!!!!!(!")

Equating the sum of all horizontal forces acting on the active wedge to zero, one can obtain

!!!! − !!"# − !!!"#$+ !!!"#$ = !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(!")

Substituting Equation (1) into Equation (17), one can obtain the value of RA as below:

!!!! − !!"# −!!!"#$!" + !! !"#$− !"#!!

!"#$!" = !!!!!!!!!!!!!!!!!!!!!!(!")

Using equation (18) and (16), one can find RhAP and RA.

PASSIVE WEDGE

Similarly considering the equilibrium of forces acting on the passive wedge and equation the

sum of all the vertical forces acting on the passive wedge to zero gives

!!!"#$+ !!!! + !!!"#$− !!"# + !!"# =!!!!!!!!!!!!!!!!!!!!!!!!!!(!")

Substituting Equation (2), (5) and (7) into (19) yields

!! !"#$+ !"#!!!"#$!"

=!! − !!" − !!"#!!" − !!!"#$!" − !!!! + !!" + !!"#!!"!!!!!!!!!!(!")

Similarly, equating the sum all horizontal forces acting on the passive wedge to zero gives

!!!! − !!"# + !!"# − !!!"#$+ !!!"#$ = !!!!!!!!!!!!!!!!!!!!!!!!!!!(!")

Substituting Equation (2) into Equation (21), one can obtain:

!!!! − !!"# + !!"# −!!!"#$!" + !! !"#$− !"#!!!"#$!" = !!!!!!!!!!!(!!)


Simultaneously solving Equation (20) and (22), we can get RP and RHpb.

BLOCK WEDGE

Considering the equilibrium of forces acting on the block wedge, equating the sum of all

vertical forces acting on the block wedge to zero yields:

!!!"#$+ !!!! =!! + !!!"#$+ !!"# (23)

Substituting Equations (3) and (6) into Equation (23), one can obtain

!! !"#$− !"!" !"#!!!" + !!!! − !!!"#$

!" =!! + !!" + !!"#!!" (24)

Similarly, equating the sum of all the horizontal forces acting on the block wedge to zero

yields:

!!"# + !!!! = !!!"!"+ !!!"#$ (25)

Submitting Equation (3) into Equation (25), one can obtain

!!"# + !!!! = !!!"#$!" + !!(!"#$+ !"#!!!"#$

!" ) (26)

Simultaneously solving Equation (24) and (26), we can get RB. Using Equation (3), we can

find FB. Hence, we can find the ‘waste force’, FWB on the back slope of the berm as,

!!" = !!! + !!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(!")

(NOTE: In the MATLAB Code given in APPENDIX D, the equation number used in this

section has been marked alongside the corresponding part of the code)


PARAMETRIC STUDY OF THE ‘WASTE FORCE’

! For the parametric study of the waste force, only one parameter was taken to be

variable. The rest were assigned a constant value (taken from Choudhury and

Savorikar (2011)) as given in the graphs below.

! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"! = !"

This condition gives the upper bound or the maximum value of factor of safety. Also,

the effect of waste shear strength is included in the analysis.

Variation with depth of waste mass at back slope

Figure 8.1: Waste force exerted on the back slope of the berm, FWB (N) versus depth of waste

mass at back slope, H (m) for different values of kh. As the depth increases, weight of the

waste mass increases and hence the forces exerted on the berm also increases. The rate of

increase increases with the value of kh.(Constants used: HT=10 m; BT=150 m; cA=5 kNm-2;

cP=15 kNm-2; cB=12 kNm-2;cSW=8kNm-2; δA=15°; δB=18°; δP=20°; β=18.43°; θ=1.1°;

ξ=14.03°; γSW=10.5kNm-2; ϕSW=30°;γB=20 kNm-2; ε=10°; L=250 m; FS=2; kv=0.5kh).

kh=0.1$

kh=0.2$

kh=0.3$

kh=0.4$


NOTE: The value of H has to be constrained to the following constraint due to geometric

compatibility. !!!"#$+ !! !"#$ < ! < !!

!!"#$+

!!"#$ + ! !"#$

Variation with cohesion of waste mass

Figure 8.2: Waste force exerted on the back slope of the berm, FWB (N) versus cohesion of

solid waste, cSW (Nm-2). As the cohesion values increases, inter-wedge forces increase and

hence the force on the berm back slope also increases. The increase in the magnitude of

waste force is not that much when compared with other graphs (FWB increases by 120 kN for

an increase in cSW of 10 kNm-2 while it increases by around 6 MN for a change of 10 m in the

depth of waste mass at back slope, H). This fact is also shown in Figure 8.3 given below.

(Constants used: HT=10 m; H=70 m; BT=150 m; cA=5 kNm-2; cP=15 kNm-2; cB=12 kNm-2;

δA=15°; δB=18°; δP=20°; β=18.43°; θ=1.1°; ξ=14.03°; γSW=10.5kNm-2; ϕSW=30°;γB=20

kNm-2; ε=10°; L=250 m; FS=2; kh=0.1; kv=0.5kh).


Figure 8.3: Waste force exerted on the back slope of the berm, FWB (N) versus cohesion of

solid waste, cSW (Nm-2) for different values of kh. As already mentioned above, the value of

waste of waste force does not change much with the cohesion value, when compared with

other graphs. Hence, change in cohesion of waste mass may not be a governing factor in the

stability analysis as its effect will be subdued by the effect of other factors. (Constants used:

HT=10 m; H=70 m; BT=150 m; cA=5 kNm-2; cP=15 kNm-2; cB=12 kNm-2; δA=15°; δB=18°;

δP=20°; β=18.43°; θ=1.1°; ξ=14.03°; γSW=10.5kNm-2; ϕSW=30°;γB=20 kNm-2; ε=10°;

L=250 m; FS=2; kv=0.5kh).

kh=0.1$

kh=0.2$


Variation with horizontal seismic coefficient of acceleration

Figure 8.4: Waste force exerted on the back slope of the berm, FWB (N) versus horizontal

seismic acceleration coefficient, kh for different values of H. The force exerted on the back

slope of the berm increases with increase in kh as the seismic component of force increases.

Also, the rate of increase of force also increases with increase in H. This is expected

following the trend form Figure 8.1.(Constants used: HT=10 m; BT=150 m; cA=5 kNm-2;

cP=15 kNm-2; cB=12 kNm-2; δA=15°; δB=18°; δP=20°; β=18.43°; θ=1.1°; ξ=14.03°;

γSW=10.5kNm-2; ϕSW=30°;γB=20 kNm-2; ε=10°; L=250 m; FS=2; kv=0.5kh).

H=60$m$

H=70$m$

H=80$m$


Variation with density of waste mass

Figure 8.5: Waste force exerted on the back slope of the berm, FWB (N) versus density of

waste mass, γSW (Nm-3) for different values of kh. The force exerted on the back slope of the

berm increases with increase in γSW as the weight of the waste mass and hence the active,

passive and block wedge increases. Also, the rate of increase of force also increases with

increase in kh. This is expected following the trend form Figure 8.4.(Constants used: HT=10

m; BT=150 m; H=70m; cA=5 kNm-2; cP=15 kNm-2; cB=12 kNm-2; δA=15°; δB=18°; δP=20°;

β=18.43°; θ=1.1°; ξ=14.03°; ϕSW=30°;γB=20 kNm-2; ε=10°; L=250 m; FS=2; kv=0.5kh).

kh=0.1$

kh=0.2$

kh=0.3$

kh=0.4$


Variation with internal friction angle of waste mass

Figure 8.6: Waste force exerted on the back slope of the berm, FWB (N) versus internal

friction angle of waste mass, ϕSW (°) for different values of kh. The force exerted on the back

slope of the berm increases with increase in ϕSW. Also, the rate of increase of force also

increases with increase in kh. This is expected following the trend form Figure 8.4.(Constants

used: HT=10 m; BT=150 m; H=70m; cA=5 kNm-2; cP=15 kNm-2; cB=12 kNm-2; δA=15°;

δB=18°; δP=20°; β=18.43°; θ=1.1°; ξ=14.03°; γSW=105 kNm-2; γB=20 kNm-2; ε=10°; L=250

m; FS=2; kv=0.5kh).

kh=0.1$

kh=0.2$

kh=0.3$


Summary till now As much data is not available about waste pressures, this study is very useful because it

attempts to quantify the waste force for various paraments of the landfill model. It not only

bring forth the trends the the waste force follows but also gives the exact values of the waste

force which may be used to design the engineered berm. Generic curves can be plotted by

using the techniques used in the present research which may be used in any set of conditions.

In the present study, from the graphs shown in the previous section, we can conclude that:

1. As the depth of the waste mass increases, the force exerted on the berm increases.

2. As the cohesion values increases, the force on the berm back slope also increases but

the increase is not that significant when compared with other factors.

3. The force exerted on the back slope of the berm increases with increase in kh.

4. The force exerted on the back slope of the berm increases with increase in γSW

5. The force exerted on the back slope of the berm increases with increase in ϕSW


WASTE PRESSURE DISTRIBUTION CALCULATION (Simplified Model Used + Horizontal Method of Slices) Figure"9."1"

$Figure"9."2


The waste force distribution on the back slope of the berm is calculated using horizontal method of slices, as follows: $

For Part (1), from the horizontal equilibrium,

!!!! + !!sin! − !!!"#$ − !! = 0

From the vertical equilibrium,

!!!! −!! + !!cos! + !!!"#$ + !! = 0

!! =!!!" + !!

!"#!!"!"

!! =!!!" + !!

!"#!!!"

!! = ! − !! !"#$!%!!

!! = ! + !!!"#$ !!"

Solving these equations gives us the values of !! and !!.

Dividing the waste mass behind the back slope of the berm into N thin slices, each of thickness ∆!,

! = !!∆!

For any nth slice,

Figure"9."3"


!! = ! + !! − ! − 1 ∆! !"#$

!!!! = ! + !! − ! ∆! !"#$

!!" = 0.5(!! + !!!!)∆!!!"

From horizontal equilibrium,

!!! − !! + !!!! − !!!!" + !!"!"#$ − !!!!"#$ = 0

From vertical equilibrium,

−!!" − !! + !!!! + !!!!" −!!" + !!"!"#$ − !!!!"#$ = 0

!!!! =!!"(!!!)!" + !!!!

!"#!!"!"

!!" =!!"!" + !!!

!"#!!!"

!!" =!!"!" + !!!

!!"!!!"

!!"(!!!) = [!!!!]!!"

!!" = ∆! !!

!!" = ∆! !"#$!%!!

For the force between liner and slice (lower side of last slice),

!!!! =!!!" + !!!!

!"#!!!"

!! = !!!

By the moment equilibrium of the slice about the point S,

0.5!!!! − (0.5∆!)!! − 0.5∆! !!!! − !!!! 0.5!!!! +!!" 1− !! 0.25 !! + !!!!− !!"!"#$ + !!!!"#$ 0.5 !! + !!!! = 0

From these equations, we can calculate the value of !!! and !!", which when plotted against the height along the back slope of the berm gives the force distribution.

For the forthcoming force distribution plots, the constant values are HB=80m; BT=150m; L=250m; BT=150 m; δA=15°; δP=20°; β=18.43°;γB=25 kNm-2; FS=2.


Calculation of Seismic Waste Pressure Coefficient, Kw

!! = !!/(0.5!!"!!)

where !! is the total force acting on the back slope of the berm due to the waste mass. !! can be calculated by integrating the force distribution obtained in the last section over the height of the berm.

To$calculate$the$Seismic$Active$Earth$Pressure$Coefficient,$we$use$the$expression$of$

MononobeMOkabe$analysis,$$

!!" =!"#!(! − ! − !)

!"#$!!"#!!!cos!(! + ! + !) 1+ sin ! + ! sin!(! − ! − !)cos ! + ! + ! cos!(! − !)

!$

where,$ϕ$–$β$≥$ψ$$and$! = !"#!! !!!!!!

$

kh$=$horizontal$seismic$acceleration$coefficient$

kv$=$vertical$seismic$acceleration$coefficient$

δ$=$friction$angle$between$the$berm$wall$and$the$soil$on$the$back$slope$

θ$=$0°$(for$our$geometry)$

β$=$slope$of$soil$surface$from$horizontal$

ϕ$=$internal$friction$angle$of$soil$mass$

$

$


$

$


$


Stability analysis of the berm

The measure of stability against external modes of failure is defined as the ratio of resisting to driving forces (or moments in case of overturning), as in the design of conventional gravity wall structures.

!! = 0.5!!!!!!"#$!!!"

!! = !! − !!!"#$ !!! !!!"

(i) Limit state function for siding failure mode:

For stability against the sliding failure mode along the base of the berm, sum of horizontal resisting forces must be more than sum of horizontal driving forces. The factor of safety against sliding is given by,

!"!"# =!!!!= !"#$!!

!

! = !! +!! 1− !! − !!

where, !! is the total vertical force exerted by the waste on the berm at the interface between the two

! = !! + !!(!! +!!)

(ii) Limit state function for overturning failure mode:

For stability against overturning failure about the toe, the resisting moment of the wall should be more than the overturning moment. The factor of safety against overturning is estimated as,

!"!" =!!!!

!! =!! 1− !! 0.5 !! − !!!"#$ + !!!"#$ +!! 1− !! !!!!"#$! − !!!!

!! = !!!! 0.5!! + !!!!!!3 + !!!!"#

where !!!"# = point of action of force exerted by the waste on the back slope of the berm (can be found out by integrating the distribution and dividing it by the total force)


(iii) Limit state function for eccentricity failure mode:

FWHA (2001) reported that for the stability in the eccentricity failure mode, the eccentricity should be less than one sixth of the base width of the berm. But due to relaxation in seismic conditions, this has been increases to one-fourth of the base of the berm.

!"! =(!! !/!4)

!

where the eccentricity e of the resultant force on the base can be calculated as follows,

! = !!2 − !! − !!

!

(iv) Limit state function for bearing failure mode:

The bearing capacity refers to the ability of a foundation soil to support the structure. Meyerhof distribution (FWHA 2001) assumes that eccentric loading results in uniform distribution of pressure over a reduced area at the base of the berm. This area is defined by a width equal to the base of the berm minus twice the eccentricity. The factor of safety against bearing capacity can be estimated as,

!"! =!!!!

where,

!! = !!!!!!!"!!" + 0.5!!(! − 2!)!!!!"!!"

!! =!

! − 2!

where qe is the effective stress at the level of the bottom of the foundation (it is zero in the present case as height of the soil at the toe side of the berm =0.0), Fqd , Fγd are the depth factors, Fqi , Fγi are the load inclination factors and Nq , Nγ are the bearing capacity factors.

Expressions for these factors as reported in (Das 1990) are

!! = !"!!(45+ !!2 )e!"#$!!

!! = 2 !! + 1 !"#!!

!!" = 1− !°90!


!!" = 1− !°!!

!

!!" = 1 for no soil at the toe side of the wall

!° = !"#!! !!

Substituting in the expression for qu,

!! = !0.5!!(! − 2!)!!!!"

$

$

Using$the$expressions$for$Factor$of$safety,$design$charts$for$the$berm$have$been$plotted$as$

follows$

$

$

$

$


CONCLUSION If a design engineer wants to find the optimum value of ratio of base width to height of berm, he can do so from the above charts for the given conditions. (If conditions are different, different graphs need to be plotted for those values) For example, if we take safety margin for various safety factors as follows (75% of the static condition): FSsli = 1.125 ; FSe =1 ; FSb = 1.875 ; FSot = 1.875 And the conditions be kv 0.0kh

H 80 m

kh 0.1

c 10 kN/m2

δB 16°

ϕSW 28°

So the minimum ratio will be 1.52 (from sliding), 0.92 (from bearing capacity), 1.06 (from eccentricity), 1.19 (from overturning). We see that the critical ratio is 1.52. Since height of berm is 30m, so base width =1.52 × 30 = 45.6 ≈ 46 m Hence the berm geometry will be as follows


APPENDIX A (List of Symbols)

BT top width of waste mass (m) CA,CB,CP cohesive force between liner components beneath active, block ,and

passive wedges (kN m-2) CAP cohesive force at interface between active and passive wedges (kN) CPB cohesive force at interface between passive and block wedges (kN) CSW cohesive force of waste material(kN) cSW cohesion of solid waste (kN m-2) DB top width of berm (m)

RhAP normal force from active wedge acting on passive wedge(kN) RhBP normal force from the block wedge acting on the passive wedge(kN) RhPA normal force from passive wedge acting on the active wedge(kN) RhPB normal force from passive wedge acting on the block wedge(kN) FvAP frictional force acting on the side of the passive wedge next to active

wedge(kN) FvBP frictional force acting on the side of the passive wedge next to block

wedge(kN) FvPA frictional force acting on the side of the active wedge next to passive

wedge(kN) FvPB frictional force acting on the side of the block wedge next to passive

wedge(kN) FA,FB,FP frictional force acting on the bottom of the active, block and passive

wedges(kN) FS factor of safety of entire waste mass

FSv factor of safety at the interface between two wedges G acceleration due to gravity(m s-2) H depth of waste mass at back slope (m)

HB height of berm (m) HT height of waste mass above back slope (m) kh horizontal seismic acceleration coefficient kv vertical seismic acceleration coefficient L horizontal distance between toe of back slope and toe of berm (m)

mSW, nAP, nPB constants used in the present analysis MSW municipal solid waste

RA, RB, RP normal force acting on the bottom of the active, block and the passive wedges (kN)

WA, WB, WP weight of the active, block and passive wedges (kN) ω1, ω2 angles of inclination of inter-wedge forces with the horizontal (°) α, β, θ angles of back slope of berm ,back slope of waste mass, and the

landfill cell subgrade, measured from horizontal (°) δA, δB, δP interface friction angles of liner components beneath the active, block

and passive wedges (°) ε, ξ angle of the front slope of the waste mass, the landfill cover slope, and

the front slope of berm, measured from horizontal (°) γSW unit weight of waste (kN/m3) ϕSW internal friction angle of solid waste (°)


APPENDIX B

List of figures

Figure 6.1 Schematic Diagram of the landfill model used showing over-the-berm

failure

Figure 6.2(a) Pseduo-Static Limit Equilibrium Analysis of Active Wedge

Figure 6.2(b) Pseduo-Static Limit Equilibrium Analysis of Passive Wedge

Figure 6.2(c) Pseduo-Static Limit Equilibrium Analysis of Block Wedge

Figure 8.1 Waste force exerted on the back slope of the berm, FWB (N) versus depth

of waste mass at back slope, H (m) for different values of kh

Figure 8.2 Waste force exerted on the back slope of the berm, FWB (N) versus

cohesion of solid waste, cSW (kNm-2)


cohesion of solid waste, cSW (kNm-2) for different values of kh


horizontal seismic acceleration coefficient, kh (kNm-2) for different values

of H

Figure 8.5 Waste force exerted on the back slope of the berm, FWB (N) versus density

of waste mass, γSW (Nm-3) for different values of kh


internal friction angle of waste mass, ϕSW (°) for different values of kh

Figure 9.1 Simplified Model for calculation of waste force distribution at the back

slope of the berm

Figure 9.2 Break up of the waste into two parts, one above the top edge of the berm

and one below, and break up of the part below into slices in accordance

with horizontal method of slices

Figure 9.3 Free body diagram of a single slice


APPENDIX C References

Choudhury, D., and Savoikar, P. (2011). “Seismic stability analysis of expanded MSW

landfills using pseudo-static limit equilibrium method.” Waste Management & Research,

29(2),135–145.

Feng, S. J., Chen, Y. M., and Gao, L. Y., Gao, G. Y. (2010). “Translational failure analysis of

landfill with retaining wall along the underlying liner system.” Environmental Earth Science,

60, 21–34.

Qian, X., Koerner, R. M., and Gra, D. H. (2003). “Translational failure analysis of landfills.”

Journal of Geotechnical and Geoenvironmental Engineering ASCE, 129(6), 506–519

Qian, X., and Koerner, R. M. (2009). “Stability analysis when using an engineered berm to

increase landfill space.” Journal of Geotechnical and Geoenvironmental Engineering, 135,

1082–1091.

Savoikar, P. and Choudhury, D. (2010). “Effect of cohesion and fill amplification on seismic

stability of municipal solid waste landfills using limit equilibrium method.” Waste

Management & Research, 28, 1096–1113.

www.expressindia.com (Nov 2011). “Come clean on landfill sites, High Court tells DDA”

http://www.expressindia.com/latest-news/come-clean-on-landfill-sites-high-court-tells-

dda/874702/

www.dailypioneer.com (Oct 2011). “In 2014, MCD to achieve zero garbage pile-up goal”

http://www.dailypioneer.com/pioneer-news/city/16388-in-2014-mcd-to-achieve-zero-

garbage-pile-up-goal.html

Das, B. M. (1999). Principles of Foundation Engineering, 4th Ed., Publishing Workflow System Publication, Pacific Grove, CA, USA.

FWHA (2001). Mechanically Stabilised Earth Walls and Reinforced Soil Slopes: Design and Construction Guidelines. Publication FWHA NH1-00-43. Federal Highway Administration and National Highway Institute, Washington, DC, USA.

Basha, B. M. and Babu, G. L. S. (2009). “Seismic reliability assessment of external stability of reinforced soil walls using pseudo-dynamic method.” Geosynthetics International, 2009, 16, No. 3, 197-215.


APPENDIX D

Parametric study of force on the back slope of berm deltaB=pi/10; deltaA=15*pi/180; deltaP=pi/9; cb=12000; ca=5000; cp=15000; BT=150; H1=64:82; HT=10; beta=18.43*pi/180; theta=1.1*pi/180; eta=14.03*pi/180; gammaSW=10500; cSW=8000; phiSW=pi/6; gammaB=20000; kh=0.1; kv=0.5*kh; epsilon=pi/18; L=250; FS=2; i=1; for H=64:82; x=H*cot(beta)-HT*cot(eta)-BT; y=(HT*cot(epsilon))-x; z=y*tan(epsilon); AreaA=0.5*H*H*cot(beta)+0.5*HT*HT*cot(eta)+BT*HT+0.5*(z+HT)*x; WA=gammaSW*AreaA; CAP=cSW*(H+z); CA=ca*H*csc(beta); nAP=CAP/FS; Equation (9) mSW=tan(phiSW)/FS; Equation (8) syms RA RhAP; eqnA1=RA*(cos(beta)+(tan(deltaA)*sin(beta)/FS))-WA+(CA*sin(beta)/FS)+kv*WA+nAP+RhAP*mSW; Equation (16) eqnA2=kh*WA-RhAP-(CA*cos(beta)/FS)+RA*(sin(beta)-(tan(deltaA)*cos(beta)/FS)); Equation (18) AnsA=solve(eqnA1,eqnA2); RA1=double(AnsA.RA); RhAP1=double(AnsA.RhAP); syms RhBP RP; lamda=H+z-L*tan(epsilon); p=L*L*0.5*(tan(theta)+tan(epsilon))+lamda*L; WP=gammaSW*p; CP=L*sec(theta)*cp; CBP=(lamda+L*tan(theta))*cSW;


nBP=CBP/FS; Equation (10) eqnp1=RP*(cos(theta)+tan(deltaP)*sin(theta)/FS)-WP+nBP+RhBP*mSW+CP*sin(theta)/FS+kv*WP-nAP-RhAP1*mSW; Equation (20) eqnp2=kh*WP-RhBP+RhAP1-CP*cos(theta)/FS+RP*(sin(theta)-tan(deltaP)*cos(theta)/FS); Equation (22) g=solve(eqnp1,eqnp2); RhBP1=double(g.RhBP); RP1=double(g.RP); syms alpha var1 b HB WB RB; eqnB1=(lamda+L*tan(theta))/(tan(epsilon)+tan(alpha))-var1; eqnB2=b-0.5*var1*var1*(tan(epsilon)+tan(alpha)); eqnB3=HB-var1*tan(alpha); eqnB4=WB-gammaSW*b; eqnB5=RB*(cos(alpha)-(sin(alpha)*tan(deltaB)/FS))+kv*WB-(cb*HB*csc(alpha))*(sin(alpha)/FS)-WB-nBP-RhBP1*mSW; Equation (24) eqnB6=RhBP1+kh*WB-(cb*HB*csc(alpha))*cos(alpha)/FS-RB*(sin(alpha)+tan(deltaB)*cos(alpha)/FS); Equation (26) solution=solve(eqnB1,eqnB2,eqnB3,eqnB4,eqnB5,eqnB6); RB1=double(solution.RB(1)); FB1=(CBP+RB1*tan(deltaB))/FS; Equation (3) Force1(i)=(RB1^2+FB1^2)^0.5; Equation (27) i=i+1; end plot(H1,Force1)

CODE FOR CALCULATION OF FACTOR OF SAFETY

deltaB=16*pi/180; deltaA=15*pi/180; deltaP=pi/6; cb=12000; ca=5000; cp=15000; BT=150; H=80; HB=30; L=250; FS=2; beta=atan(80/150); height=(HB-0.25):-0.5:0.25; gammaSW=10500; cSW=8000; phiSW=24*pi/180; gammaB=25000; kh=0.1; kv=0.6*kh;


CA=(H-HB)*csc(beta)*ca; CW=(L+HB*cot(beta))*cSW; W1=(0.5*L*(H-HB)*gammaSW)+(0.5*(BT+HB*cot(beta))*(H-HB)*gammaSW); syms F1 R1 RA FA; eqn1=kh*W1+RA*sin(beta)-FA*cos(beta)-F1; eqn2=kv*W1-W1+RA*cos(beta)+FA*sin(beta)+R1; eqn3=F1-CW/FS-R1*tan(phiSW)/FS; eqn4=FA-CA/FS-RA*tan(deltaA)/FS; solution=solve(eqn1,eqn2,eqn3,eqn4); F1_val=double(solution.F1); R1_val=double(solution.R1); array_Ftop(1)=F1_val; array_Rtop(1)=R1_val; diff_H=0.5; N=HB/diff_H; for i=1:N L1=L+(HB-(i-1)*diff_H)*cot(beta); L2=L+(HB-i*diff_H)*cot(beta); Ws(i)=(L*diff_H+(2*HB-(2*i-1)*diff_H)*cot(beta)*diff_H*0.5)*gammaSW; Fn=array_Ftop(i); Rn=array_Rtop(i); Cswn=cSW*(L+(HB-(i-1)*diff_H)*cot(beta)); Cswnn=cSW*(L+(HB-i*diff_H)*cot(beta)); cBP=diff_H*cb; cAn=diff_H*csc(beta)*ca; syms BVn BHn Fnn Rnn LHn LVn; eqns1=BHn-Fn+Fnn-kh*Ws(i)+LVn*sin(beta)-LHn*cos(beta); eqns2=-BVn-Rn+Rnn+kv*Ws(i)-Ws(i)+LVn*cos(beta)+LHn*sin(beta); eqns3=Fnn-Cswnn/FS-Rnn*tan(phiSW)/FS; eqns4=BVn-cBP/FS-BHn*tan(deltaB)/FS; eqns5=LVn-cAn/FS-LHn*tan(deltaA)/FS; eqns6=Rn*0.5*L1-(Fn+Fnn)*0.5*diff_H-Rnn*0.5*L2+Ws(i)*(1-kv)*(0.25*(L1+L2))-(LVn*cos(beta)+LHn*sin(beta))*(0.5*(L1+L2)); solution_slice=solve(eqns1,eqns2,eqns3,eqns4,eqns5,eqns6); array_Ftop(i+1)=double(solution_slice.Fnn); array_Rtop(i+1)=double(solution_slice.Rnn); Force_bermV(i)=double(solution_slice.BVn); Force_bermH(i)=double(solution_slice.BHn); Force_berm(i)=((Force_bermV(i)^2)+(Force_bermH(i)^2))^0.5; if i==N syms BVn BHn Fnn Rnn LHn LVn; eqns1=BHn-Fn+Fnn-kh*Ws(i)+LVn*sin(beta)-LHn*cos(beta); eqns2=-BVn-Rn+Rnn+kv*Ws(i)-Ws(i)+LVn*cos(beta)+LHn*sin(beta); eqns3=Fnn-(L*cp)/FS-(Rnn*tan(deltaP))/FS; eqns4=BVn-cBP/FS-BHn*tan(deltaP)/FS; eqns5=LVn-cAn/FS-LHn*tan(deltaA)/FS;


eqns6=Rn*0.5*L1-(Fn+Fnn)*0.5*diff_H-Rnn*0.5*L2+Ws(i)*(1-kv)*(0.25*(L1+L2))-(LVn*cos(beta)+LHn*sin(beta))*(0.5*(L1+L2)); solution_slice2=solve(eqns1,eqns2,eqns3,eqns4,eqns5,eqns6); Force_linerV=double(solution_slice2.BVn); Force_linerH=double(solution_slice2.BHn); Force_diffV=-Force_linerV+Force_bermV(i); Force_diffH=-Force_linerH+Force_bermH(i); end end delta_berm=30*pi/180; RT=sum(Force_bermV); FT=sum(Force_bermH); Rl=Force_diffV; Fl=Force_diffH; j=1; sum1=0; for i=(HB-0.25):-0.5:0.25 sum1=Force_bermH(j)*i+sum1; j=j+1; end point_of_action=sum1/FT; j=1; BbyH1=0.8:0.01:1.7; lamda=45*pi/180; for BbyH=0.8:0.01:1.7 Db=BbyH*HB; Wb1=HB*HB*cot(lamda)*0.5*gammaB; Wb2=(Db-HB*cot(lamda))*HB*gammaB; summV=(Wb1+Wb2)*(1-kv)-RT+Rl; numerator=summV*tan(delta_berm); summH=FT-Fl+kh*(Wb1+Wb2); FS_sliding(j)=numerator/summH; mom_resisting=(Wb2*(1-kv)*(0.5*(Db-HB*cot(lamda))+HB*cot(lamda)))+(Wb1*(1-kv)*(2*HB*cot(lamda)/3))+Rl*Db+(Fl*diff_H*0.5); mom_overturning=(kh*Wb2*HB*0.5)+(kh*Wb1*HB/3)+FT*point_of_action+RT*Db; FS_overturning(j)=mom_resisting/mom_overturning; eccen=(Db*0.5)-((mom_resisting-mom_overturning)/summV); FS_ecc(j)=Db/(4*eccen); psi_bc=atan(summH/summV); phi_berm=1.5*delta_berm; F_gammai=(1-(psi_bc/phi_berm))^2; Nq=((tan(pi*0.25+0.5*phi_berm))^2)*(exp(pi*tan(phi_berm))); Ngamma=2*(Nq+1)*tan(phi_berm); qu=0.5*gammaB*(Db-2*eccen)*Ngamma*F_gammai;


sigma_v=summV/(Db-2*eccen); FS_bearcap(j)=qu/sigma_v; j=j+1; end plot(BbyH1,FS_sliding,BbyH1,FS_overturning,BbyH1,FS_ecc)

CODE FOR CALCULATION OF KW

deltaB=16*pi/180; deltaA=15*pi/180; deltaP=pi/9; cb=10000; ca=5000; cp=15000; BT=150; H=80; HB=30; L=250; FS=2; beta=atan(80/150); height=29.75:-0.5:0.25; gammaSW=10500; cSW=8000; phiSW=24*pi/180; gammaB=20000; j=1; for kh=0.1:0.005:0.3; kv=0.1*kh; CA=(H-HB)*csc(beta)*ca; CW=(L+HB*cot(beta))*cSW; W1=(0.5*L*(H-HB)*gammaSW)+(0.5*(BT+HB*cot(beta))*(H-HB)*gammaSW); syms F1 R1 RA FA; eqn1=kh*W1+RA*sin(beta)-FA*cos(beta)-F1; eqn2=kv*W1-W1+RA*cos(beta)+FA*sin(beta)+R1; eqn3=F1-CW/FS-R1*tan(phiSW)/FS; eqn4=FA-CA/FS-RA*tan(deltaA)/FS; solution=solve(eqn1,eqn2,eqn3,eqn4); F1_val=double(solution.F1); R1_val=double(solution.R1);


array_Ftop(1)=F1_val; array_Rtop(1)=R1_val; diff_H=0.5; N=HB/diff_H; for i=1:N L1=L+(HB-(i-1)*diff_H)*cot(beta); L2=L+(HB-i*diff_H)*cot(beta); Ws(i)=(L*diff_H+(2*HB-(2*i-1)*diff_H)*cot(beta)*diff_H*0.5)*gammaSW; Fn=array_Ftop(i); Rn=array_Rtop(i); Cswn=cSW*(L+(HB-(i-1)*diff_H)*cot(beta)); Cswnn=cSW*(L+(HB-i*diff_H)*cot(beta)); cBP=diff_H*cb; cAn=diff_H*csc(beta)*ca; syms BVn BHn Fnn Rnn LHn LVn; eqns1=BHn-Fn+Fnn-kh*Ws(i)+LVn*sin(beta)-LHn*cos(beta); eqns2=-BVn-Rn+Rnn+kv*Ws(i)-Ws(i)+LVn*cos(beta)+LHn*sin(beta); eqns3=Fnn-Cswnn/FS-Rnn*tan(phiSW)/FS; eqns4=BVn-cBP/FS-BHn*tan(deltaB)/FS; eqns5=LVn-cAn/FS-LHn*tan(deltaA)/FS; eqns6=Rn*0.5*L1-(Fn+Fnn)*0.5*diff_H-Rnn*0.5*L2+Ws(i)*(1-kv)*(0.25*(L1+L2))-(LVn*cos(beta)+LHn*sin(beta))*(0.5*(L1+L2)); solution_slice=solve(eqns1,eqns2,eqns3,eqns4,eqns5,eqns6); array_Ftop(i+1)=double(solution_slice.Fnn); array_Rtop(i+1)=double(solution_slice.Rnn); Force_bermV(i)=double(solution_slice.BVn); Force_bermH(i)=double(solution_slice.BHn); Force_berm(i)=((Force_bermV(i)^2)+(Force_bermH(i)^2))^0.5; end force_total=sum(Force_berm); Kw(j)=force_total/(0.5*gammaSW*H*H); kh_range(j)=kh; j=j+1; end plot(kh_range,Kw)

CODE FOR CALCULATION OF FORCE DISTRIBUTION

deltaB=16*pi/180; deltaA=15*pi/180; deltaP=pi/9;


cb=10000; ca=5000; cp=15000; BT=150; H=100; HB=30; L=250; FS=2; beta=atan(80/150); height=29.75:-0.5:0.25; gammaSW=10500; cSW=8000; phiSW=24*pi/180; gammaB=20000; kh=0.1; kv=0.2*kh; CA=(H-HB)*csc(beta)*ca; CW=(L+HB*cot(beta))*cSW; W1=(0.5*L*(H-HB)*gammaSW)+(0.5*(BT+HB*cot(beta))*(H-HB)*gammaSW); syms F1 R1 RA FA; eqn1=kh*W1+RA*sin(beta)-FA*cos(beta)-F1; eqn2=kv*W1-W1+RA*cos(beta)+FA*sin(beta)+R1; eqn3=F1-CW/FS-R1*tan(phiSW)/FS; eqn4=FA-CA/FS-RA*tan(deltaA)/FS; solution=solve(eqn1,eqn2,eqn3,eqn4); F1_val=double(solution.F1); R1_val=double(solution.R1); array_Ftop(1)=F1_val; array_Rtop(1)=R1_val; diff_H=0.5; N=HB/diff_H; for i=1:N L1=L+(HB-(i-1)*diff_H)*cot(beta); L2=L+(HB-i*diff_H)*cot(beta); Ws(i)=(L*diff_H+(2*HB-(2*i-1)*diff_H)*cot(beta)*diff_H*0.5)*gammaSW; Fn=array_Ftop(i); Rn=array_Rtop(i); Cswn=cSW*(L+(HB-(i-1)*diff_H)*cot(beta));


Cswnn=cSW*(L+(HB-i*diff_H)*cot(beta)); cBP=diff_H*cb; cAn=diff_H*csc(beta)*ca; syms BVn BHn Fnn Rnn LHn LVn; eqns1=BHn-Fn+Fnn-kh*Ws(i)+LVn*sin(beta)-LHn*cos(beta); eqns2=-BVn-Rn+Rnn+kv*Ws(i)-Ws(i)+LVn*cos(beta)+LHn*sin(beta); eqns3=Fnn-Cswnn/FS-Rnn*tan(phiSW)/FS; eqns4=BVn-cBP/FS-BHn*tan(deltaB)/FS; eqns5=LVn-cAn/FS-LHn*tan(deltaA)/FS; eqns6=Rn*0.5*L1-(Fn+Fnn)*0.5*diff_H-Rnn*0.5*L2+Ws(i)*(1-kv)*(0.25*(L1+L2))-(LVn*cos(beta)+LHn*sin(beta))*(0.5*(L1+L2)); solution_slice=solve(eqns1,eqns2,eqns3,eqns4,eqns5,eqns6); array_Ftop(i+1)=double(solution_slice.Fnn); array_Rtop(i+1)=double(solution_slice.Rnn); Force_bermV(i)=double(solution_slice.BVn); Force_bermH(i)=double(solution_slice.BHn); Force_berm(i)=((Force_bermV(i)^2)+(Force_bermH(i)^2))^0.5; end plot(Force_berm,height)