Stability Analysis of Geosynthetic Reinforced MSW Landfill Slopes Considering
Effects of Biodegradation and Extreme Wind Loading
by
Sharmila Pant
A Thesis Submitted to the Faculty of
The College of Engineering and Computer Science
In Partial Fulfillment Of the Requirements
For the Degree of Master of Science
Florida Atlantic University
Boca Raton, Florida
August 2016
Copyright 2016 by Sharmila Pant
ii
ACKNOWLEDGEMENTS
I would like to express my heartfelt gratitude and sincere appreciation to my advisor Dr. Khaled Sobhan for his constant support, guidance, and motivation throughout my MS degree. I am very thankful to Dr. D.V. Reddy for being in my advisory committee. I am deeply indebted to his continuous guidance, vital feedbacks, and suggestions for my research work. To my committee member, Dr. Sudhagar Nagarajan, I very much appreciate your help, support, and valuable comments. I am pleased to have worked with you all.
My earnest thanks to the Department of Civil, Environmental, and Geomatics
Engineering for providing me the opportunity to pursue my masters at Florida Atlantic
University. I would also like to thank the faculty and staffs of Civil Department for their help and support. A big thanks to my friends Mr. Daniel Gonzalez Moya, Mr. Bishow
Nath Shaha, Mr. Nicolo Zaza, and Ms. Nivedita Sairam for making my graduate life memorable. I must thank my officemates, Mr. Denys Purdy and Mr. Raymond Peng for bearing with me. Also, I would like to thank all of my Nepalese friends at the Florida
Atlantic University and United States as well as back in my country Nepal.
Finally, my MS journey would not have been possible without the support of my family. I would like to thank my parents Meghraj Pant and Narmada Pant, my sister
Shamita Pant, my brother Safal Pant, and my very own Vijaya Raj Joshi for their love, care, and support.
iv
ABSTRACT
Author: Sharmila Pant
Title: Stability Analysis of Geosynthetic Reinforced MSW Landfill Slopes Considering Effects of Biodegradation and Extreme Wind Loading
Institution: Florida Atlantic University
Thesis Advisor: Dr. Khaled Sobhan
Degree: Master of Science
Year: 2016
A numerical investigation was conducted to evaluate the geotechnical safety and slope stability of Municipal Solid Waste (MSW) landfills, considering the effects of geosynthetic reinforcements, biodegradation of the waste, and associated changes in material properties, and extreme wind force simulating hurricane conditions. Three different landfill slopes, 1:1, 1:2, and 1:3 having the height of 122m and width of 2134m, were analyzed using Limit Equilibrium Method (SLOPE/W) and Finite Element
Modeling (ANSYS). Techniques developed in this study were used to analyze a case history involving a geogrid reinforced mixed landfill expansion located in Austria. It was found that few years after construction of the landfill, there is a significant decrease in the
FS due to biodegradation. Extreme wind loading was also found to cause a substantial loss in the FS. The geosynthetic reinforcement increased the slope stability and approximately compensated for the damaging effects of biodegradation and wind loading.
v Stability Analysis of Geosynthetic Reinforced MSW Landfill Slopes Considering
Effects of Biodegradation and Extreme Wind Loading
LIST OF FIGURES ...... xi
LIST OF TABLES ...... xvii
LIST OF ACRONYMS ...... xix
NOTATION ...... xx
Chapter 1: Introduction ...... 1
1.1 Problem Statement ...... 1
1.2 Motivation and Significance ...... 2
1.3 Impact of Climate Change on Waste Management ...... 3
1.4 Technical Background...... 4
1.4.1 Definition of Landfill ...... 5
1.4.2 Types of Landfills ...... 5
1.4.3 Design of Landfill ...... 7
1.4.4 Slope Stability Analysis ...... 9
1.4.5 Mohr-Coulomb Failure Theory...... 12
1.4.6 Finite Element Method ...... 14
vi 1.4.7 Geosynthetics in Landfill Applications ...... 15
1.4.8 Biodegradation of the waste...... 16
1.4.9 Wind load ...... 17
1.5 Scope and Limitations ...... 18
1.6 Objectives ...... 19
1.7 Thesis Organization...... 20
Chapter 2: Literature Review...... 22
2.1 Slope Instability...... 22
2.2 Geotechnics of Landfill ...... 23
2.3 Interaction between Soil and Geogrid ...... 26
2.4 Finite Element Analysis of Landfills ...... 30
2.5 Wind on slopes ...... 33
Chapter 3: Material Properties ...... 37
3.1 Landfill Geometry ...... 37
3.2 Unit Weight ...... 38
3.3 Shear Strength and Friction Angle ...... 39
3.4 Initial Void Ratio and Poisson’s Ratio ...... 40
3.5 Compressibility Parameters ...... 41
3.6 Elastic Modulus ...... 43
3.7 Geotechnical Properties after Biodegradation...... 44
vii Chapter 4: Research Methodology ...... 49
4.1 Approach ...... 49
4.1.1 Local Factor of Safety ...... 51
4.1.2 Global Factor of Safety ...... 52
4.2 Analysis without Geogrids ...... 53
4.2.1 Slope Stability Analysis with SLOPE/W Program ...... 53
4.2.2 Slope Stability Analysis with Finite Element Method ...... 55
4.3 Analysis with Geogrids ...... 62
4.3.1 Vertical Spacing and Length of Geogrids ...... 62
4.3.2 Slope Stability Analysis using SLOPE/W Program ...... 66
4.3.3 Slope Stability Analysis using Finite Element Modeling ...... 67
Chapter 5: Data Analysis, Results, and Discussions ...... 73
5.1 Data Analysis ...... 73
5.2 Analysis without geogrids ...... 73
5.2.1 With and Without Biodegradation ...... 73
5.2.2 Effect of Extreme Wind loading ...... 79
5.3 Results for the analysis with geogrids ...... 82
5.3.1 With and Without Biodegradation ...... 83
5.3.2 Effects of Extreme Wind loading ...... 89
5.4 Result Summary ...... 91
viii 5.4.1 Effects of Geosynthetics ...... 92
5.4.2 Effects of Biodegradation ...... 92
5.4.3 Effects of Extreme Wind Loading ...... 93
Chapter 6: Case Study ...... 95
6.1 Background ...... 95
6.2 Unreinforced Case ...... 96
6.2.1 Slope Stability Analysis with SLOPE/W ...... 96
6.2.2 Slope Stability Analysis with Finite Element Method ...... 97
6.3 Reinforced Case ...... 100
6.3.1 Slope Stability Analysis with SLOPE/W ...... 100
6.3.2 Slope Stability Analysis with Finite Element Method ...... 101
6.4 Data Analysis and Results ...... 101
6.4.1 Unreinforced Case ...... 101
6.4.2 Reinforced Case ...... 103
6.5 Result Summary ...... 104
Chapter 7: Conclusions and Recommendations ...... 105
7.1 Conclusions ...... 105
7.2 Recommendations for Future Work ...... 105
7.3 Final Remarks ...... 106
Chapter 8: Appendices ...... 107
ix 8.1 Appendix A: Calculation of pullout resistance of reinforcement for
SLOPE/W ...... 107
8.2 Appendix B: Results from SLOPE/W ...... 115
8.3 Appendix C: Sample Calculation of Geogrid forces ...... 118
8.4 Appendix D: Sample Calculation in ANSYS ...... 121
8.5 Appendix E: Calculation for Rule of Mixtures ...... 123
Chapter 9: References ...... 128
x LIST OF FIGURES
Figure 1.1 MSW Generation in United States (1960-2013), Data Source: USEPA ...... 2
Figure 1.2 MSW Management in United States, 2013 (Source: USEPA)...... 3
Figure 1.3 Type of slip surfaces in the slopes ...... 9
Figure 1.4 Bishop's Modified Method showing slip surface & weight slices ...... 11
Figure 1.5 Stress vs Strain showing Mohr-Coulomb failure Envelope ...... 13
Figure 1.6 Stress-Strain Diagram showing Pole Method...... 13
Figure 1.7 Different Types of Geogrids (Uniaxial, Biaxial, and Triaxial) ...... 15
Figure 1.8 Application of wind load on slopes ...... 18
Figure 2.1 Cohesion and Friction angle values, Landva & Clark (1990) ...... 24
Figure 2.2 Cohesion and Friction angle values, Landva & Clark (1990) ...... 24
Figure 2.3 Cohesion vs Friction angle, Singh & Murphy (1990) ...... 25
Figure 2.4 Mohr's circle of Stress for reinforced and unreinforced soil, Zhong-Chun
& Feng, 2002 ...... 28
Figure 2.5 Inclusion length vs safety factor, Wu et al (2002) ...... 29
Figure 2.6 Factor of Safety vs Tensile Strength of Geogrid, Wulandari & Tjandra
(2006) ...... 30
Figure 2.7 Triangular Elements with 15 nodes used in slope stability, Hossain &
Haque (2009) ...... 31
Figure 2.8 Factor of Safety for different phases of decomposition and different slopes, Hossain & Haque (2009) ...... 33
xi Figure 2.9 Wind Phenomenon on buildings showing pressure and suction ...... 34
Figure 2.10 Flow and Pressure Characteristics of Wind on Pyramidal Structures,
Ikhwan & Ruck (2004) ...... 34
Figure 2.11 Stream line of a flow over a building model - Vertical view & Pressure
Distribution, Mendis et al (2011) ...... 35
Figure 2.12 Drag Coefficient vs Wind Direction for different slope angles of pyramid, Ikhwan & Ruck (2004) ...... 36
Figure 2.13 Drag coefficient vs Base angle at different angles of wind directions,
Ikhwan & Ruck (2004) ...... 36
Figure 3.1 Layout of the landfill for 1:1 slope ...... 37
Figure 3.2 Initial Void Ratio vs Compression Index, Mohammed & Stephen (1995) ..... 41
Figure 3.3 Initial Void Ratio vs Secondary Compression Index, Mohammed &
Stephen (1995) ...... 42
Figure 3.4 Different layers of soil and its properties ...... 44
Figure 3.5 Relation between Cohesion, Friction Angle and Degree of
Decomposition, Reddy et al (2015) ...... 45
Figure 3.6 Compression Ratio vs Degree of Decomposition ...... 46
Figure 3.7 Unit weight vs Time (Fei and Zekkos, 2008) ...... 47
Figure 3.8 Different layers of landfill with soil properties after degradation ...... 48
Figure 4.1 Flowchart showing the procedures followed in the research ...... 50
Figure 4.2 Mohr's Failure Criterion (Huang and Yamasaki, 1993) ...... 51
Figure 4.3 SLOPE/W Model for 1:2 slope with different layer properties without geogrids ...... 54
xii Figure 4.4 PLANE 183 element with 8 nodes & 6 nodes ...... 56
Figure 4.5 ANSYS Model for Slope of 1:1 ...... 58
Figure 4.6 Ultimate Design Speed for Risk Category III and IV Buildings and Other
Structures (ASCE 7-10) ...... 60
Figure 4.7 Slope of 1:1 without geogrids and wind load ...... 61
Figure 4.8 Example showing the centroids and the slip surface obtained from centroids ...... 62
Figure 4.9 Jewell's Chart (1991) ...... 64
Figure 4.10 Geogrid Layers for Landfill Slope of 1:1 ...... 65
Figure 4.11 Geogrid Layers for Landfill Slope of 1:2 ...... 65
Figure 4.12 Geogrid Layers for Landfill Slope of 1:3 ...... 66
Figure 4.13 SLOPE/W Model for 1:2 slope with different layer properties with geogrids ...... 67
Figure 4.14 Calculation of Nodal Forces ...... 68
Figure 4.15 Nodes created to apply the geogrid forces for the slope of 1:1 ...... 68
Figure 4.16 Geogrid forces applied in ANSYS for the slope of 1:1 ...... 69
Figure 4.17 Schematic Layout of the Geogrids as Composite Layers ...... 70
Figure 4.18 Geogrid layers according to Rule of Mixtures ...... 71
Figure 4.19 Slope of 1:1 with geogrids and wind load ...... 72
Figure 5.1 SLOPE/W result for Unreinforced Slope 1:1 without Biodegradation ...... 74
Figure 5.2 SLOPE/W result for Unreinforced Slope 1:1 with Biodegradation ...... 74
Figure 5.3 SLOPE/W result for Unreinforced Slope 1:2 without Biodegradation ...... 75
Figure 5.4 SLOPE/W result for Unreinforced Slope 1:2 with Biodegradation ...... 75
xiii Figure 5.5 Local FS and Critical Slip Surface for Unreinforced Slope 1:1 using the
Centroid Method without geogrids (a) Without Biodegradation (b) With
Biodegradation ...... 76
Figure 5.6 Local FS and Critical Slip Surface for Unreinforced Slope 1:2 using the
Centroid Method without geogrids (a) Without Biodegradation (b) With
Biodegradation ...... 77
Figure 5.7 FS for the slopes without geogrids & without Biodegradation ...... 79
Figure 5.8 FS for the slopes without geogrids & with Biodegradation ...... 79
Figure 5.9 Local FS and Critical Slip Surface for extreme wind loading for
Unreinforced Slope 1:1 using the Centroid Method without geogrids (a) Windward side (b) Leeward side ...... 81
Figure 5.10 FS for the slopes without geogrids & with wind loads on windward and leeward side ...... 82
Figure 5.11 SLOPE/W result for Geogrid Reinforced slope 1:1 without
Biodegradation ...... 84
Figure 5.12 SLOPE/W result for Geogrid Reinforced slope 1:1 with Biodegradation .... 84
Figure 5.13 SLOPE/W result for Geogrid Reinforced slope 1:2 without
Biodegradation ...... 84
Figure 5.14 SLOPE/W result for Geogrid Reinforced slope 1:2 with Biodegradation .... 84
Figure 5.15 Local FS and Critical Slip Surface for Reinforced Slope 1:1 using the
Centroid Method without geogrids (a) Without Biodegradation (b) With
Biodegradation ...... 86
xiv Figure 5.16 Local FS and Critical Slip Surface for Reinforced Slope 1:2 using the
Centroid Method without geogrids (a) Without Biodegradation (b) With
Biodegradation ...... 87
Figure 5.17 FS for the slopes with geogrids & without Biodegradation ...... 88
Figure 5.18 FS for the slopes with geogrids & with Biodegradation ...... 89
Figure 5.19 Local FS and Critical Slip Surface for extreme wind loading for
Reinforced Slope 1:1 using the Centroid Method without geogrids (a) Windward side
(b) Leeward side ...... 90
Figure 5.20 FS for the slopes with geogrids & with wind loads on windward and leeward side ...... 91
Figure 5.21 FS of the Landfill Without and With Geogrids ...... 92
Figure 5.22 FS of the Landfill Without and With Geogrids after biodegradation ...... 93
Figure 5.23 FS of the Landfill Without and With Geogrids after extreme wind loading for the windward side...... 94
Figure 5.24 FS of the Landfill Without and With Geogrids after extreme wind loading for the leeward side ...... 94
Figure 6.1 Model used for slope stability analyses (Alexiew et al., 2015) ...... 95
Figure 6.2 Unreinforced Model used in SLOPE/W program with different layers ...... 97
Figure 6.3 ANSYS® Model for the case history with different layers ...... 99
Figure 6.4 ANSYS® Model showing the elements used for the case history ...... 99
Figure 6.5 Reinforced Slope from Case History (Alexiew et al, 2015) ...... 100
Figure 6.6 Reinforced Model used in SLOPE/W program with different layers ...... 101
xv Figure 6.7 Result from SLOPE/W showing critical slip surface and Global FS for unreinforced case ...... 102
Figure 6.8 Result from ANSYS® showing location of centroids and Slip Surface from Centroid Method for Unreinforced case ...... 102
Figure 6.9 Result from SLOPE/W showing critical slip surface and Global FS for
Reinforced case ...... 103
Figure 6.10 Result from ANSYS® showing location of centroids and Slip Surface from Centroid Method for Reinforced case ...... 103
Figure 6.11 Comparison of results with and without Geogrids ...... 104
xvi LIST OF TABLES
Table 1.1 Factor of Safety by various methods (Das and Sobhan, 2007) ...... 10
Table 1.2 Risk Category of Buildings and Other Structures (ASCE 7-10) ...... 18
Table 2.1 Case histories showing factor of safety for 2D & 3D models (Koerner &
Soong, 2000) ...... 23
Table 2.2 Factor of Safety for different slope angles, Jones et al (1997) ...... 25
Table 2.3 Phases of decomposition at different stages, Hossain & Haque (2009) ...... 32
Table 2.4 Material properties at different phases of decomposition, Hossain & Haque
(2009) ...... 32
Table 3.1 Unit Weight Parameters, Zekkos et al (2006) ...... 38
Table 3.2 Cohesion and Friction angles, Jones et al (1997) ...... 39
Table 3.3 Material Properties at different heights ...... 41
Table 3.4 Cce and Cα Parameters ...... 42
Table 3.5 Elastic Modulus of soil at different depths ...... 44
Table 3.6 Unit weight and Dry Unit Weight of the layers after Biodegradation ...... 47
Table 3.7 Elastic Modulus of the different layers of Landfill after Biodegradation ...... 48
Table 4.1 Calculation of Wind Forces for different slopes ...... 60
Table 4.2 Elastic Modulus of the composite layer ...... 70
Table 5.1 Factor of safety obtained from FEM and SLOPE/W without geogrids ...... 74
Table 5.2 Factor of Safety from FEM for the effect of extreme wind loading for unreinforced case ...... 80
xvii Table 5.3 Factor of safety obtained from FEM and SLOPE/W with geogrids ...... 83
Table 5.4 Factor of Safety from FEM for the effect of extreme wind loading for reinforced case ...... 89
Table 6.1Material Properties used in the landfill model ...... 96
Table 6.2 Unit weight and Maximum Dry Density for Case Study ...... 97
Table 6.3 Void Ratio, Constrained and Young's Modulus of Landfill Materials ...... 98
Table 6.4 FS for the landfill with and without Geogrids ...... 104
xviii LIST OF ACRONYMS
FEM Finite Element Method
MSW Municipal Solid Waste
ANSYS Analysis of Systems
FOS/ FS Factor of Safety
GDP Gross Domestic Product
WRI World Resources Institute
USEPA United States of Environmental Protection Agency
FDOT Florida Department of Transportation
HDPE High Density Polyethylene
xix NOTATION
Angle of Friction, ϕ Secondary Compression Index, Cα Angle of Slice, θ Shear Strength, S
Coefficient of Consolidation, cv Shear Strength on the failure plane Coefficient of Friction, µ Shear Stress, τ
Compression index, Cc Shear Stress in the X-Y Plane, τxy
Constrained Modulus, D Shear Stress on the failure plane, τf
Depth, z Strain in the X direction, ϵx
Density, ρ Strain in the Y direction, ϵy Elastic Modulus, E Stress, σ
Factor of Safety, FS Stress in the X direction, σx
Frictional Force, Ff Stress in the Y direction, σy Height, H Unit Weight, γ
Interface Friction Angle, δ Unit weight of water, γw ’ Normal Stress, σN Vertical Effective Stress, σv
Poisson’s Ratio, υ Vertical Spacing of geogrids, Sv Porosity, n Void Ratio, e
Primary Compression Index, Ccϵ Speed of the wind, V
Pullout Force of Geogrids, fds Drag coefficient, cd
Required Tensile Strength of Geogrids, Treqd Initial Void Ratio, e0
Specific Gravity, Gs Wind Pressure, P
Dry unit weight, γd Earth Pressure coefficient, K
xx Chapter 1: Introduction
1.1 Problem Statement
Disposal of solid waste has always been a burning problem, which will continue to grow with the upsurge of population, high concentration of the population in urban areas, industrial development, changes in eating habits, and the widespread use of disposable containers and packages. So, there is a requisite to get a sustainable solution which will lead to healthy, resilient, and pollution free environment.
There is a need of more space for the disposal of waste, which is very difficult to find because there is not enough land and people do not want a lump of waste near to their houses. It is a truth that we should be looking for more space on dumping of wastes and should focus on reuse and recycling; however it cannot be denied that need for more land is a reality. Relating to this problem, an innovative idea of providing more space in the landfill by increasing the slope of the landfill has been proposed in this research.
Geogrids have been used as reinforcement within the landfill to increase the stability of the landfill.
Since Florida is near the tropics and westerly winds blow off the African coasts, it is vulnerable to climatic effects like sea level rise, hurricanes, and tornadoes. Hence, the effect of hurricanes on the slope stability of the landfills through the use of finite element analysis has been observed in this research.
1 1.2 Motivation and Significance
According to USEPA data, from 1960 to 2013, total MSW generation in the U.S. increased by 188 percent. During this time, the U.S. population increased by 75 percent and the size of the U.S. economy as measured by real GDP grew by 407 percent. MSW generation per capita increased by 70 percent from 1960 to 1990 (from 2.7 to 4.6 pounds per person per day), but has leveled off since then. MSW generation per dollar GDP has decreased steadily over the last five decades, with a 43 percent decrease from 1960 to
2013. In 2013, 25 percent of MSW was recycled, 9 percent was composted, 13 percent was combusted with energy recovery, and 53 percent was landfilled or disposed of using other methods.
Generation of Municipal Solid Waste in United States from 1960 to 2013 300,000
250,000
200,000
150,000
100,000
50,000
0
Municipal Solid Waste Generation Tons Recycled, Waste Generation and Municipal Solid
1992 1960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 Time, Years
Figure 1.1 MSW Generation in United States (1960-2013), Data Source: USEPA
U.S. has 3,091 active landfills and over 10,000 old municipal landfills, according to the Environmental Protection Agency. According to the 1997 U.S. Census, there are
2 39,044 general purpose local governments in the United States - 3,043 county governments and 36,001 sub-county general purpose governments (towns & townships).
One suspects that there are many more old and abandoned commercial, private, and municipal dumps than the 10,000 estimated by the EPA.
Figure 1.2 MSW Management in United States, 2013 (Source: USEPA)
Landfills require a lot of space, and current landfill facilities are filling very fast. A simple rule of thumb indicates that every 10,000 people require approximately 3 acre-ft of space each year, i.e., three feet (1 meter) of compacted trash spread over one acre each year. For a large city of a million people, the space is a considerable chunk of real estate.
So, there is an urge to come up with some innovative solution to increase the storage capacity of landfills.
1.3 Impact of Climate Change on Waste Management
With the increase in the effect of global warming, there has been increase in the adverse climatic effects especially in coastal areas. One of them is the sunshine state,
Florida, which has very low elevation and high water table. According to the study of
World Resources Institute, sea levels along Florida’s coastal could rise an additional 9 inches to 2 feet by 2060. There are 8, 23, and 73 hazardous waste sites less than one, two 3 and, three ft. above current sea level (WRI, 2014). Looking at these numbers, we can see the challenge of designing the landfill system so that there will less effect of sea level rise.
Similarly, Florida has witnessed an increase in extreme weather events due to the climate change. The state has broken 34 heat records, 27 rainfall records, and also experienced some cases of extreme drought in multiple counties. According to the study done by Congressional Research Service, widespread tropical storms and hurricanes have resulted in 24 major disaster declarations from 2000 to 2013. And, in near future it has been predicted that hurricanes could be even stronger with higher winds and heavier rainfall, potentially resulting in more Category 4 and 5 storms.
Florida is already hot, but it is getting even hotter. According to the recent study done by National Climate Assessment temperatures in the US Southeast have risen by an average of 2º F, with higher temperatures striking the months of summer.
All these effects due to climate change cannot be ignored. Hence, keeping these things in mind, a noble design of landfill has been proposed in this research with the use of geogrids.
1.4 Technical Background
The research focuses on the comprehensive literature search for the materials, design of landfill and use of geogrids in landfills. Some types of landfills with kind of waste they are composed, design of landfill, slope stability, geogrids along with finite element modeling has been described here.
4 1.4.1 Definition of Landfill
Landfill is a place to dispose refuse and other waste material by burying it and covering it over with soil, especially as a method of filling in or extending usable land.
They are very complicated structures, which functions under many systems so that our waste is stored safely with minimal impact of the environment. Landfills cannot be built in environmentally-sensitive areas, and they are placed using in-site environmental monitoring systems. These monitoring systems check for any sing of groundwater contamination and for landfill gas, as well as provide additional safeguards.
1.4.2 Types of Landfills
According to USEPA, landfills are regulated under Resource Conservation and
Recovery Act (RCRA) Subtitle D (solid waste) and Subtitle C (hazardous waste) or under the Toxic Substances Control Act (TSCA).
Subtitle D emphasizes on state and local governments as the primary planning, regulating, and implementing entities for the management of nonhazardous solid waste, like household garbage and nonhazardous industrial solid waste. Subtitle D landfills are categorized as follows:
1.4.2.1 Municipal Solid Waste Landfills (MSWLFs)
A municipal solid waste landfill (MSWLF) is a discrete area of land or excavation that receives household waste. A MSWLF may also receive other types of nonhazardous wastes, such as commercial solid waste, nonhazardous sludge, conditionally exempt small quantity generator waste, and industrial nonhazardous solid waste. In 2009, there were approximately 1,908 MSWLFs in the continental United States all managed by the states where they are located.
5 1.4.2.2 Industrial Waste Landfill
An industrial waste landfill is any landfill other than a municipal solid waste landfill, a Resource Conservation and Recovery Act (RCRA) Subtitle C hazardous waste landfill, or a Toxic Substances Control Act hazardous waste landfill. It is used to dispose of industrial solid waste, such as RCRA Subtitle D wastes, commercial solid wastes, or conditionally exempt small-quantity generator wastes.
1.4.2.3 Construction and Demolition (C&D) Landfills
C&D landfills are those type which receives construction and demolition debris, which typically consists of roadwork material, excavated material, demolition waste, construction/renovation waste, and site clearance waste. C&D landfills do not receive any hazardous or industrial solid waste, unless those landfills meet certain standards and are permitted to receive such wastes. Materials like concrete, wood (from buildings), asphalt
(from roads and roofing shingles), gypsum (the main component of drywall), metals, bricks, glass, plastics, salvaged building component (doors, windows, and plumbing fixtures), trees, stumps, earth and rock from clearing sites comes under C&D materials.
But, it should be remembered that reducing and recycling of C&D materials conserves landfill space, reduces the environmental impact of producing new materials, creates jobs, and can reduce overall building project expenses through avoided purchase/disposal costs.
1.4.2.4 Cleanfills
Cleanfills are a landfill that only accept material that when buried have no adverse effect on people or the environment. Cleanfill material includes virgin natural materials
6 such as clay, soil and rock, and other inert materials such as concrete or brick that are free
of:
combustible, putrescible, degradable or leachable components
hazardous substances
products or materials derived from hazardous waste treatment, hazardous waste
stabilization or hazardous waste disposal practices
materials that may present a risk to human or animal health such as medical and
veterinary waste, asbestos or radioactive substances
liquid waste
1.4.3 Design of Landfill
Landfill design is an interactive process incorporating the conceptual design
proposals, the findings of the environmental assessment and environmental monitoring
results, risk assessment, and the conclusions reached in investigations. The fundamental
objective behind waste management is that of sustainability. According to the design
manual of USEPA, 2000 following things should be kept in mind while designing the
landfills:
Nature and quantities of waste
Water control
Protection of soil and water
Leachate management
Gas control
Environmental nuisances
Stability
7 Visual appearance and landscape
Operational and restoration requirements
Monitoring requirements
Estimated cost of the facility
Afteruse
Construction
Risk Assessment
The design of landfill starts with performing site investigation of the landfill.
Surface and subsurface conditions of soils and waste materials must be evaluated for proper design, operation and maintenance, and future utilization of a disposal facility.
Investigation starts with desk study, preliminary investigation and final investigation.
Drilling methods like Hollow-Stem Continuous Flight Auger, Rotary Drilling, Reverse
Rotary, Air Rotary etc. are used to obtain the samples, which can be broadly grouped as
“disturbed” or “undisturbed” samples (Oweis & Khera, 1998). Also, for the insitu measurement of the soil properties, tests like Standard Penetration Test, Cone Penetration
Test, Pressuremeter Test and Field Load Tests can be done. Along with this groundwater level measurements and field permeability tests are carried out to measure the hydraulic conductivity of in situ materials. Series of tests like sieve analysis, consolidation tests, shear strength tests, moisture content tests, compression tests, and Atterburg limit tests are done in the lab to obtain the properties of the existing soil conditions such as unit weight, density, compression index, liquid and plastic limits, porosity, moisture content, coefficient of consolidation, settlement, along with some other properties. All these
8 properties will assist engineers to obtain the existing condition of soil and properly design the foundations against any slope failures.
After carrying out the site investigation of the landfill, other important factor is the volume of the waste generated and capacity of landfill required. Since the area is limited, the capacity is determined by the compaction factor, slope and height of the landfill. Landfill slope failure can involve failure in the waste reaching upto the foundation. In this research, the slope stability are analyzed by looking into the shear strengths and different geotechnical properties of the slope.
1.4.4 Slope Stability Analysis
Slope failure is a phenomenon that a slope collapses abruptly due to weakened self-retainability of the earth. Because of sudden collapse of slope, many people fail to escape from it if it occurs near a residential area, thus resulting in a higher rate of fatalities. Stability is determined by the balance of shear stress and shear strength.
Figure 1.3 Type of slip surfaces in the slopes
Triggering factors of a slope failure can be climatic events can then make a slope actively unstable, leading to mass movements. Mass movements can be caused by increase in shear stress, such as loading, lateral pressure, and transient forces.
9 Blight (2008) in his paper, reported six large-scale failures of municipal solid waste dumps and landfills between 1977 and 2005. Volumes of waste mobilized in these failures were varied from 10-12000 m3, which killed nearly 300 people.
To prevent from the failure, stability of the slope can be evaluated by various methods like Modified Bishop’s method of slices, Spencer’s method, Janbu’s simplified method etc. Table 1.1 shows different values of factor of safety for different methods and soil properties (Das and Sobhan, 2007). In this research, Modified Bishop’s method has been adopted.
Table 1.1 Factor of Safety by various methods (Das and Sobhan, 2007)
10 According to Modified Bishop’s Method, it is assumed that tangential interslice forces are equal and opposite but horizontal forces are not equal. One of the circular failure surface is assumed at the beginning of analysis. The portion of the soil or MSW is discretized into number of small elements called slices. If there are more slices, then the solution is assumed to be more refined.
Figure 1.4 Bishop's Modified Method showing slip surface & weight slices
The component of the weight acting in the direction of the bottom of the slice is the shear stress in this method and the shear strength is obtained from Mohr-Coulomb
Theory. The factor of safety is given by the following equation:
1.1 c m W/ b cos um tan
FS W/ b sin
In the above equation ψ is given by:
sin. tan 1.2 cos FS
Analysis has to be done several times to come up with the critical slip surface.
Critical slip surface is the failure surface which gives minimum factor of safety. These days many software available to obtain the critical slip surface. We have used GEO-
11 SLOPE in our analysis. Within the GEO-SLOPE, SLOPE/W is used to analyze slope stability. SLOPE/W can effectively analyze both simple and complex problems for a variety of slip surface shapes, pore-water pressure conditions, soil properties, analysis methods and loading conditions.
1.4.5 Mohr-Coulomb Failure Theory
When the soil sample has failed, the shear stress on the failure plane defines the shear strength of the soil. Thus, it is necessary to identify the failure plane. For the present, it can be assumed that a failure plane exists and it is possible to apply principal stresses and measure them in the laboratory by conducting a triaxial test. Then, the Mohr circle of stress at failure for the sample can be drawn using the known values of the principal stresses.
The Mohr-Coulomb failure criterion for soils and MSW, states that the shear strength of soils and MSW is defined by the cohesion (c) of soil and MSW, and the angle of friction (φ) of the soil and MSW. The shear strength (S) is given by (Holtz and
Kovacs, 1981):
S c tan 1.3
If data from several tests, carried out on different samples upto failure is available, a series of Mohr circles can be plotted. It is convenient to show only the upper half of the Mohr circle. A line tangential to the Mohr circles can be drawn, and is called the Mohr-Coulomb failure envelope (Figure 1.5).
12
Figure 1.5 Stress vs Strain showing Mohr-Coulomb failure Envelope
If the stress condition for any other soil sample is represented by a Mohr circle that lies below the failure envelope, every plane within the sample experiences a shear stress which is smaller than the shear strength of the sample. Thus, the point of tangency of the envelope to the Mohr circle at failure gives a clue to the determination of the inclination of the failure plane. The orientation of the failure plane can be finally determined by the pole method (Figure 1.6).
Figure 1.6 Stress-Strain Diagram showing Pole Method
13 The Mohr-Coulomb failure criterion can be written as the equation for the line that represents the failure envelope. The general equation is
Sff c tan 1.4
The factor of safety FS is given by following general equation:
Shear stress S f 1.5 FS Shear Strength f
1.4.6 Finite Element Method
Finite Element Method is a numerical technique for finding approximate solutions by dividing a large problem into smaller and simpler parts called finite elements, which is then assembled into a larger system of equations that models the entire problem. FEM is widely accepted in almost all engineering disciplines. The method is often used as an alternative to the experimental test method set out in many standards. This method is suitable for structural/mechanical engineering design, product development, manufacturing processes, improving the efficiency of existing designs, failure analysis investigations, etc. FEA solution of engineering problems, such as finding deflections and stresses in a structure, requires three steps:
Pre-process or modeling the structure
Analysis
Post processing
Many software are available for finite element analysis of slopes. In this research,
ANSYS (Analysis of Systems) has been used as a finite element software. ANSYS is a general purpose software, used to simulate interactions of all disciplines of physics, structural, vibration, fluid dynamics, heat transfer and electromagnetic for engineers. It
14 has widely been used in geotechnical engineering. It can be employed to solve the problems which involves foundation analysis, deep foundations, slope stability, seepage problems etc.
1.4.7 Geosynthetics in Landfill Applications
ASTM (2006) D 4439 defines a geosynthetic as a plan product manufactured from a polymeric material used with soil, rock, earth, or other geotechnical-related material as an integral part of a civil engineering project, structure, or system. Number of geosynthetics are available like geotextiles, geogrids, geomembranes, geonets, geomeshes, geowebs, and geocomposites. This is not the new term in the area of civil engineering. It has been used previously in ground improvement, pavements, railways, erosion control, and landfills (liners). In this research, geogrids has been used as different layers as reinforcement to increase the stability of the landfill.
A geogrid is geosynthetic material used to reinforce soils and similar materials, and are commonly used to reinforce retaining walls, as well as subbases or subsoils below roads or structures. Compared to soil, geogrids are strong in tension which allows them to transfer forces to a larger area of soil than would otherwise be the case.
Figure 1.7 Different Types of Geogrids (Uniaxial, Biaxial, and Triaxial)
15 There has been a tremendous increase in the use of geosynthetics as reinforcement for earth structures within the last two decades. There are a lot of standards already developed by Florida Department of Transportation (FDOT). Also, various charts were developed by R.A. Jewell for reinforcing slopes with geogrids. Soil-reinforcement interaction parameters for the design of reinforced soil systems are usually evaluated by measuring pullout resistance. The primary pullout interaction mechanism of sheet reinforcement is classical soil-reinforcement interface friction which will be called the two-dimensional (2-D) interaction mechanism.
The frictional force developed between the geogrids and the soil or MSW is a function of the normal effective stress acting on the geogrids, the interface angle of friction between the soil or MSW and geogrid, and the cohesion of the soil or MSW.
1.4.8 Biodegradation of the waste
Degradation of the Municipal Solid Waste can be defined as the conversion of organic matter to biogas, which process is characterized by physical, chemical, and biological decomposition of waste mass (Reddy et al, 2015). Approximately 53 percent of the waste was landfilled or disposed of using other methods in 2013 according to
USEPA. Reddy et al (2015), in his study, showed that the engineering properties of field
MSW are affected by degradation of the waste and these changes should be properly accounted in the analysis of the landfills. Changes in unit weight and compressibility affect the volume of MSW in the landfill and the extent of differential settlements (Reddy et al, 2015).
16 1.4.9 Wind load
Florida has always been prone to hurricanes. Since it is near the tropics and westerly winds blow off the African coasts along the equator, Florida is vulnerable.
Based on the wind speeds and potential to cause damages, hurricanes are classified into five categories.
i. Category 1: Winds 74-95 miles per hour
ii. Category 2: Winds 96-110 miles per hour iii. Category 3: Winds 111-130 miles per hour iv. Category 4: Winds 131-155 miles per hour
v. Category 5: Winds greater than 155 miles per hour
Experts in National Hurricane Center, which is located in Miami, are particularly busy during the Atlantic hurricane season from June 1 through November 30. Specially strengthened and electronically equipped aircraft are sent into the eye of a hurricane to help in the analysis of a hurricane’s strength.
Similarly risk category of buildings and other structures also have been categorized for flood, wind, snow, earthquake, and ice loads which is shown in the following Table 1.2.
17 Table 1.2 Risk Category of Buildings and Other Structures (ASCE 7-10)
In this research, wind load has been applied as uniformly distributed load. The pattern is shown in Figure 1.8.
Figure 1.8 Application of wind load on slopes
1.5 Scope and Limitations
In this research, layers of the landfill has been divided to four layers, and material properties are calculated as per the layers. Slope/w software is used to analyze the slope
18 of varying angles (1:1, 1:2 and 1:3) with and without the geogrids. Also, the same analysis is done after the landfill will go biodegradation. Groundwater level is considered to be below the foundation of the landfill. So, no water level is taken in the analysis. In the finite element analysis, geogrid forces were applied as the horizontal frictional forces.
For the wind loading, the forces are applied as uniformly distributed load perpendicular to the surface.
1.6 Objectives
1. To conduct comprehensive literature search on geosynthetic reinforced landfills,
and the effects of biodegradation and extreme wind loading on the stability of
landfills.
2. To determine the effect of biodegradation and extreme wind loading on landfill
stability having slope angles of 1:1, 1:2, and 1:3, with and without the use of
geogrids.
3. To obtain local and global factors of safety for different steepened slopes using
Bishop’s Methods (SLOPE/W Program) and Finite Element Modeling
(ANSYS®).
4. To explore the existence of a new critical slip surface by identifying cluster of
nodal failure points based on Mohr-Coulomb Failure Criteria.
5. To utilize some of the techniques developed in this study on the stability analysis
of a case history involving a geogrid reinforced landfill in Austria.
19 1.7 Thesis Organization
Chapter 1 discusses about the brief introduction of the related topics that has been addressed in the research. Also, the scope and limitations of the research along with the objectives of the thesis has been described in this chapter.
Chapter 2 describes the literature search done for the research. It provides the previous works done by the researchers in the related field. Some of them are directly applied in the research.
Chapter 3 focuses on the material properties, which are obtained for different layers.
Since the research does not involve any experiments for the properties, this section is very important part of the research.
Chapter 4 concentrates on the research methodology of the thesis, describing the analysis of slope stability of landfill using the software GEO-SLOPE and finite element method. It describes the applied conditions and how the analysis was done using this software for unreinforced and reinforced landfill.
Chapter 5 shows all the results from the analysis done by GEO-SLOPE software and
Finite element modeling. This is the most important section of the analysis, where the results are analyzed and discussed critically.
Chapter 6 describes the case study done for one of the landfill in Austria using some of the techniques developed in the research.
Chapter 7 points out the conclusion about the landfills, with geogrids, bio- degradation and wind loading. Also, some recommendations for the future has been listed in this chapter.
20 Chapter 8 of the thesis is the appendices. The data used in the research, various screenshots of the analysis, all the results from SLOPE/W and ANSYS.
The last part of the thesis contains all the references for the books, papers, and websites used in the research.
21 Chapter 2: Literature Review
2.1 Slope Instability
Seed, R. B., Mitchell, J. K., & Seed, H. B. (1990) performed some analyses to determine the cause for the failure of landfill slope at Kettleman City, California. With their analyses, engineering estimates of the factor of safety of the landfill/liner system at the time of the failure was found to be the order of 0.85 to 1.25.
There was the largest slope failure in United States municipal solid waste (MSW) landfill, based on the volume of waste involved. Eid, H. T., Stark, T. D., Evans, W. D., &
Sherry, P. E. (2000) conducted analyses and related studies to determine the cause of the failure which could be important for the operation, expansion, and stability of existing landfill slopes. Large-scale laboratory and field test results and back analysis of failed waste slopes suggested that the shear strength of MSW can be represented by an effective stress friction angle of 35 and cohesion ranging from 0 to 50 kPa (Eid et al, 2000).
Wright et al. (1973), using finite element analysis, demonstrated that the local factor of safety for slopes can vary significantly along the failure surface. This shows that there is not a constant FS within a slope, unlike what is assumed in simplified overall stability checks. Wright et al. (1973) also found that the failure surface within a slope can be determined by locating the points of maximum strain. Huang and Yamasaki (1993) determined critical slip surfaces within slopes by connecting local factors of safety, and they found that the local factor of safety method yielded an FS nearly the same as the FS given by the Modified Bishop’s method of slices (1955).
22 Koerner & Soong (2000) in their paper, researching for the stability assessment of ten large landfill failures, focused on the determination of the representative shear strength values. The reasons for failure of these ten landfills along with factor of safety and wedge factor are shown in Table 2.1. According to this paper, any computer code used in the analysis is more dependent on shear strength than any other parameter.
Table 2.1 Case histories showing factor of safety for 2D & 3D models (Koerner & Soong, 2000)
2.2 Geotechnics of Landfill
Landva & Clark (1990) reported the unit weights measured in situ varied from 6.8 to 16.2 kN/m3. Also, it has been stated that friction angle for the landfill varies between
24° and 41°, and cohesion parameter between zero and 23 kPa which is also shown in
Figure 2.1 and 2.2. In the same paper, it is reported that the shear strength of the waste fill is highly variable, depending on the type of material involved.
23
Figure 2.1 Cohesion and Friction angle values, Landva & Clark (1990)
Figure 2.2 Cohesion and Friction angle values, Landva & Clark (1990)
Tieman et al. (1990) concluded that the used of geogrids for subgrade reinforcement, synthetics for flexibility, and the combination of textured HDPE liner material maximized the economic benefit and permissible landfill capacity.
24 Singh & Murphy (1990) plotted the strength estimates (cohesion and friction angle) for the refuse samples based on the laboratory test data and back-calculations of field tests and operational records, calculated by various authors, which is shown in Figure 2.3.
Figure 2.3 Cohesion vs Friction angle, Singh & Murphy (1990)
Jones et al (1997) performed the stability analysis of the waste for the height of 30m with the friction angle of 20º and zero cohesion and following results were reported as shown in Table 2.2.
Table 2.2 Factor of Safety for different slope angles, Jones et al (1997)
Biodegradable waste constituents, including food waste, yard waste, and different types of paper, are consumed by microorganisms and eventually converted to biogas which consists primarily of methane (CH4) and carbon dioxide (CO2). Thus, the composition and density of MSW changes during degradation (Fei & Zekkos, 2008).
25 Wall & Zeiss (1995) concluded that in the short term there is no significant increase in the settlement rate due to biodegradation; however, extrapolation suggests that in the long term the settlement rate will likely increase as the effects of decomposition become more significant. Kolsch and Ziehmann (2004) performed the stability analysis on Ihlenberg landfill using waste properties estimated from lab results in Germany, and found that the toe of the slope was the most vulnerable slip body, where the solid waste properties were already decomposed or old refuse.
Bareither et al (2012) evaluated the effects of waste composition and decomposition on the shear strength of municipal solid waste and concluded that friction angle increases with decreasing volatile solids or increasing decomposition. Also, it was found that there is no relation between ‘c’ and waste composition or the degree of waste decomposition (Bareither et al, 2012).
2.3 Interaction between Soil and Geogrid
Tatiannikov, D. A., & Kleveko, V. I. (2015) investigated for the interaction of geogrid and geotextile with the ground (sand) using shear test and pull-out test. They concluded from the coefficients of efficiency obtained from their studies that the reinforcing elements reduce the strength characteristics of the soil on contact between soil and reinforcing materials.
Wilson-Fahmy & Koerner (1993) performed the finite element modeling of the soil-geogrid interaction with application to the behavior of geogrids in a pullout loading condition. Solutions of which leads to the following results:
Nodal displacements;
Tension and strain distribution along geogrid;
26 Shear-stress distribution along longitudinal ribs;
Shear and bearing stresses on transverse ribs;
Total frictional resistance provided by all longitudinal ribs; and
Total frictional and bearing resistances provided by all transverse ribs.
The results indicated that the contribution of the transverse ribs to pullout resistance is greatly affected by their flexibility, especially at low pullout loads (Wilson-Fahmy &
Koerner, 1993).
It is possible to develop enough resistance to pullout through the friction between reinforcement and soil acting over a sufficient development length, so that the full tensile strength of the reinforcement can be mobilized to help stabilize the slope (Duncan, 1996).
Wei et al. (2002) looked over the performance of geosynthetics reinforced steep slope in residual soil and concluded that the interaction coefficients obtained from laboratory are conservative than those obtained from field.
The reinforced composite mass is better in mechanical characteristics due to the effect of reinforcement (Zhong-Chun & Feng, 2002). Figure 2.4 shows the Mohr’s circle of stress for reinforced and unreinforced soil.
27
Figure 2.4 Mohr's circle of Stress for reinforced and unreinforced soil, Zhong-Chun & Feng, 2002
Unreinforced Soil, .tan 2.1
Reinforced Soil, r r .tan C r 2.2
Clogh & Duncan, 1971, provided the relationship between the shear stress and the relative displacement at the interface which is expressed by using the hyperbolic formulation as follows:
/ ab 2.3
Where ‘a’ and ‘b’ are constants.
Wu et al (2002) concluded that the incipient point moves away from the toe when the length of the reinforcement is increased along with the increase of number of layers of reinforcement layers. Slopes with sufficient inclusion lengths will increase the factor of safety (Wu et al, 2002), which is also shown in Figure 2.5.
28
Figure 2.5 Inclusion length vs safety factor, Wu et al (2002)
Wulandari & Tjandra (2006, August) analyzed the factor of safety for various tensile strength of geogrid ranging from 20 kN/m to 240kN/m and the results obtained has been shown in Figure 2.6. Factor of safety was increased linearly with the increase of reinforcement strength (Wulandari & Tjandra, 2006). Wulandari & Tjandra (2006,
August) also stated that “According to the USACE, the minimum allowable factor of safety of 1.5 was satisfied by tensile strength of at least 100 kN/m for factor of safety as
1.63.”
29
Figure 2.6 Factor of Safety vs Tensile Strength of Geogrid, Wulandari & Tjandra (2006)
2.4 Finite Element Analysis of Landfills
The finite element method was introduced to the geotechnical engineering profession by Clough and Woodward (1967), in a paper written for the first Berkeley conference on the stability and performance of slopes and embankments. Chowdhury (1978), in his book,
Slope Analysis, focused on analyzing the stability of slopes using the stresses by finite element method. Chowdhury, mentioned that triangular elements is widely used since they works good with irregular boundaries (1978).
Realistic analyses of deformations of slopes and embankments were not possible until about 25 years ago, but which are possible now because of the finite element method.
(Duncan, 1996). Duncan (1996) in his paper stated that the stiffness of the soil depends on the stresses in the soil and the forces that are applied to simulate excavation of the soil are calculated using the before excavation stresses on the boundary of the excavation. These forces can be calculated only by knowing the initial stresses, which can be vertical stresses.
30 Duncan (1996) indicated that the linear elastic finite element analyses result in reasonable values of stress and patterns of displacement. Also, if only stresses are needed, and if there are not zones of strongly differing stiffness, like a stiff shell and a soft core in a zoned dam, linear elastic analyses is as good as nonlinear analyses (Duncan, 1996).
Hossain & Haque (2009) performed the stability analyses of municipal solid waste landfills with decomposition. They used finite element program PLAXIS for numerical modeling and limit equilibrium program STABL for stability analyses. 15 node triangular elements were used in the modeling and the foundation was considered stiff, making the bottom boundary fixed which is shown in Figure 2.7.
Figure 2.7 Triangular Elements with 15 nodes used in slope stability, Hossain & Haque (2009)
The phases for the decomposition and parameters used in the analysis is shown in
Table 2.3 and 2.4. Solid waste layers will advance to next phases of decomposition, and finally all the solid waste layers would be at the final stage of the decomposition (Hossain
& Haque, 2009).
31 Table 2.3 Phases of decomposition at different stages, Hossain & Haque (2009)
Table 2.4 Material properties at different phases of decomposition, Hossain & Haque (2009)
The factor of safety decreased as the solid waste degraded with time for all three slopes, which is shown in Figure 2.8. Also, when the slope of the landfill decrease the factor of safety decreases. GSTABL predicted a factor of safety of more than 1 in all the cases, whereas PLAXIS predicted a factor of safety of less than 1 at the advance stages of decomposition for a slope of 2:1 (Hossain & Haque, 2009). Also, Hossain & Haque (2009) stated that the critical failure surface predicted by both programs were very similar.
32
Figure 2.8 Factor of Safety for different phases of decomposition and different slopes, Hossain & Haque (2009)
Templeton (2007) conducted preliminary investigation on the effect of geogrid on
MSW landfill FS. The result indicated the beneficial effect of geogrid inclusion during the construction process of the landfill. In addition, Templeton (2007) provided a conceptual framework for the design and construction of geogrid reinforced landfill. It was concluded that the landfill slopes could be steepened up to 1:1 using geogrids reinforcement, resulting in higher in higher storage capacity and consequential environmental and economic benefits.
2.5 Wind on slopes
Whenever the building or slope is hit by the wind, it has the effects on the leeward sides. In the leeward side, there is a suction which is a negative pressure. This is also shown in Figure 2.9.
33
Figure 2.9 Wind Phenomenon on buildings showing pressure and suction
Ikhwan & Ruck (2004) performed experimental investigations on flow and pressure characteristics around pyramidal buildings. Figure 2.10 shows the size of the recirculation zone increases with the increasing base angle or height, Ikhwan & Ruck
(2004).
Figure 2.10 Flow and Pressure Characteristics of Wind on Pyramidal Structures, Ikhwan & Ruck (2004)
34 Mendis et al (2011) designed the tall buildings considering the effects of wind loading. Figure. 2.11 shows the stream line flow of the wind over a tall building model
(Mendis et al, 2011). It shows that there is the formation of vortex in the leeward side of the building, which is the area of negative pressure (suction).
Figure 2.11 Stream line of a flow over a building model - Vertical view & Pressure Distribution, Mendis et al (2011)
One of the most important factor in the wind loading is the drag coefficient, which has been described in earlier chapter. Ikhwan & Ruck, reported that the greater base angle will have greater drag coefficient (2004) which has been shown in Figure 2.12 and 2.13. In this figure, it can be seen that minimum cd occurs at wind direction (α’) 0º and 90º, and the maximum occurs at α’=15º and 75º. There is an increase in drag coefficient with the increase in base angle and at wind direction 0º the drag coefficients are minimum (Ikhwan & Ruck, 2004).
Hafeez et al (2011) analyzed the stability of the conical tanks and looked into the effects of wind loads. Hafeez et al (2011) used the wind force as uniformly distributed load, and the drag coefficient value of 0.5 for conical shape.
35
Figure 2.12 Drag Coefficient vs Wind Direction for different slope angles of pyramid, Ikhwan & Ruck (2004)
Figure 2.13 Drag coefficient vs Base angle at different angles of wind directions, Ikhwan & Ruck (2004)
Bathurst (1995), in his paper, concluded that the uplift of wind on geomembranes depends on the inclination of the side slope on which the geomembrane is exposed.
36 Chapter 3: Material Properties
3.1 Landfill Geometry
In this investigation, a landfill with a height of 122 m and a width of 1067 m, having the slopes of 1:3, 1:2 and 1:1 (slope angles 18.43º, 26.56º, and 45º), has been analyzed. The landfill has been divided into four layers, having 30.5 m height of each layer. Typical section of the layout has been shown in Figure 3.1.
Figure 3.1 Layout of the landfill for 1:1 slope
It is very important to have proper geotechnical properties of the materials for analyzing the landfill with the use of Finite Element Method. However, it is difficult to obtain the exact properties for landfill materials. So, rigorous literature search was done to obtain reasonable values for the relevant geotechnical properties, as summarized in this
Chapter.
37 3.2 Unit Weight
The selection of a representative MSW unit weight profile has been an important factor in engineering analyses. Zekkos et al (2006) proposed the following equation for the calculation of unit weight:
z 3.1 i z
Where, γ = Calculated Unit Weight at Depth (m) of ‘z’ (kN/m3)
3 γi = Near-Surface in-place Unit Weight (kN/m )
z = Depth (m) at which MSW unit weight (γ) is to be estimated
α (m4/kN) and β (m3/kN) = Modeling Parameters
Table 3.1 provides the unit weight parameters at various compaction effort and soil amount.
Table 3.1 Unit Weight Parameters, Zekkos et al (2006)
Since, we are analyzing municipal solid waste, in this analysis, compaction effort and soil amount has been considered as low which will make it more conservative. Values are chosen from above Table 3.1 accordingly. Using Equation 3.1 and Table 3.1, unit weights have been calculated as 11.04 kN/m3, 12.53 kN/m3, 13.21 kN/m3 and 13.59 kN/m3 for the height ranges of 0-30.5 m, 30.5-61 m, 61-91.5 m and 91.5-122 m, respectively.
38 3.3 Shear Strength and Friction Angle
The shear strength for municipal solid waste is defined by two parameters which are cohesion, c, and angle of friction, ϕ. The Mohr-Coulomb theory states that the shear strength, S, of the soil, or MSW in this case, is given as (Das and Sobhan, 2014):
S c''' tan 3.2
Where σ’ is the effective normal stress acting on the MSW.
Jones et al (1997) provided a comprehensive summary of materials data on the shear strength parameters of MSW materials as shown in Table 3.2.
Table 3.2 Cohesion and Friction angles, Jones et al (1997)
39 Based on the study done by Reddy et al (2011), drained cohesion of synthetic MSW varied from 1-40 kPa and the drained friction angle ranged from 35°-28°. Qian et al. (2002), reported that the cohesions for the MSW ranges from 0 to 50 kN/m2, while the angle of friction remains constant at 35°. Based on the available data, the following values were selected for the present study: c’ = 11.5 kN/m2 and ϕ’ = 32°.
3.4 Initial Void Ratio and Poisson’s Ratio
Zekkos (2005), reported that the Poisson’s ratio of MSW ranges from 0 to over 0.4.
He also concluded that the more fibrous content present in the MSW, the lesser the value of the Poisson’s ratio. For the current study, Poisson’s ratio of 0.3 has been selected.
Reddy et al (2011) reported the moisture content of the MSW Landfill to be 44% for the fresh MSW. According to their study, maximum dry density of 420 kg/m3 was reached at 70% optimum moisture content. Also, Hettiarachchi (2005) reported a maximum dry density of 525 kg/m3 at 62% optimum moisture content for a MSW sample generated in the laboratory.
The average specific gravity of MSW was reported as 1.6 by Reddy et al (2009). In a recent study, Reddy et al (2011) investigated the properties of fresh and degraded synthetic MSW and reported specific gravity of fresh synthetic MSW to be 1.06.
The initial void ratio for each layer was calculated using Equation 3.3, and assuming specific gravity of MSW to be 2.0 and dry unit weight from Table above.
G 3.3 sw d 1 eo
Based on the Figure 3.1, Equation 3.3, and assuming the optimum moisture content of 70%, maximum dry unit weights of various layers have been calculated, as shown in
Table 3.3.
40 Table 3.3 Material Properties at different heights Height Unit weight, γ Dry Unit weight, γd Maximum Dry Initial void
3 3 3 (m) (kN/m ) (kN/m ) Density (kg/m ) ratio, e0 0-30.5 11.04 6.49 662.22 2.02 30.5 -61 12.53 7.37 751.59 1.66 61-91.5 13.21 7.77 792.38 1.52 91.5- 122 13.59 7.99 815.17 1.45
3.5 Compressibility Parameters
Mohammed & Stephen (1995) performed laboratory experiments for the geotechnical properties of the MSW and found that mean specific gravity of the waste’s entire grain size distribution was 2.0, and for the fines fraction ( 2.4. Also, in their test, maximum dry unit weight was found to be 9.3 kN/m3 at an optimum molding moisture content of 31%. Results from consolidation tests conducted in their study yielded values of Cc that ranged from 0.4 to 0.9, Cα values that ranged from 0.03 to 0.009, and initial void ratio, e0, ranging between 1.0 to 3.0, as shown in Figure 3.2 & Figure 3.3. Figure 3.2 Initial Void Ratio vs Compression Index, Mohammed & Stephen (1995) 41 Figure 3.3 Initial Void Ratio vs Secondary Compression Index, Mohammed & Stephen (1995) Summary for Cce and Cα Parameters from Literature Review has been shown in Table 3.4. Table 3.4 Cce and Cα Parameters Reference Primary Ccε Secondary Cα a Sowers (1973) (for e0=3) 0.1-0.41 0.02-0.07 Zoino (1974) a 0.15-0.33 0.013-0.03 Converse (1975) a 0.25-0.3 0.07 Rao et al. (1977) a 0.16-0.235 0.012-0.046 Oweis and Khera (1986) a 0.08-0.217 Landva et al. (1984) a 0.2-0.5 0.0005-0.029 Bjarngard and Edgers (1990) a 0.004-0.04 Wall and Zeiss (1995) a 0.21-0.25 0.033-0.056 Gabr and Valero (1995) a 0.2-0.23 0.015-0.023 Boutwell and Fiore (1995) 0.09-0.19 0.006-0.012 Stulgis et al. (1995) a 0.16 0.02 Green and Jamenjad (1997) a 0.01-0.08 Landva et al. (2000) a 0.17-0.24 0.01-0.08 Zaminskie et al. (1994) a 0.01-0.04 0.01-0.016 42 El-Fadel and Al-Rashed 0.1-0.32 with leachate (1998) a recirculation 0.18-0.26 with leachate Earth Tech (2001) a recirculation Park et al. (2002) a 0.014-0.063 for 'fresh waste' 0.087-0.34 for waste undergoing active decomposition aData originally presented by Sharma, H. D., & De, A. (2007). A value of 0.25 was taken for this project for the modified compression index, Ccε of MSW. Value of compression index, Cc, can then be calculated from Equation 3.4 (Das and Sobhan, 2014). C 3.4 C c c 1 e0 Where, Cce = Compression Ratio 3.6 Elastic Modulus According to Lambe (1969), constrained modulus, D, of the soil can be determined from compression index, Cc, the initial void ratio, e0, and the average vertical effective ' stress, v as follows: ' 3.5 2.3 1 e0 v D Cc Knowing the constrained modulus, D, and the Poisson’s ratio, υ, the modulus of elasticity, E, can be determined by Equation 3.6 (Poulos, 1974). D1 1 2 3.6 E 1 43 Assuming 0.3, the modulus of elasticity for various layers have been calculated using Equations 3.4, 3.5, and 3.6. These values are presented in Table 3.5, and are consistent with the values reported by Mohammed & Stephen (1995). Figure 3.4 shows the relevant properties of all four layers in the landfill model. Table 3.5 Elastic Modulus of soil at different depths ' 2 2 2 Height (m) e0 Cc v (kN/m ) D (m /kN) E (kN/m ) 0-30.5 2.02 0.76 168.36 1548.91 1150.62 30.5-61 1.66 0.67 573.25 5273.88 3917.74 61-91.5 1.52 0.63 1007.26 9266.82 6883.92 91.5-122 1.45 0.61 1450.73 13346.74 9914.72 Figure 3.4 Different layers of soil and its properties 3.7 Geotechnical Properties after Biodegradation Reddy et al (2015) studied the effects of biodegradation (also called decomposition) on geotechnical properties of municipal solid waste and concluded that angle of friction decreases from 30° to 12° from initial stage to the degraded stage. 44 Although there was not any particular trend for cohesion values, it showed decreasing trend from 65 to 29 kPa, as shown in Figure 3.5. Reddy et al (2015) stated that the compression ratio, Cc values ranged from 0.24 to 0.32 with different degrees of decomposition, showing an increasing trend (Figure 3.6). Equation 3.7 was used to calculate the degree of decomposition. Figure 3.5 Relation between Cohesion, Friction Angle and Degree of Decomposition, Reddy et al (2015) 45 Figure 3.6 Compression Ratio vs Degree of Decomposition 3.7 X fi 1 DOD 1 100 X fo 1 X fi Where, X fo is initial organic fraction and is organic fraction after partial decomposition. Fei and Zekkos (2008) conducted waste degradation testing on municipal solid waste from a landfill in Michigan, USA in a laboratory landfill simulator for 1460 days (≈ 4 years). They performed simple shear testing on compacted reconstituted fresh and degraded waste specimens, and an “undisturbed” degraded specimen. They concluded the shear strength of the fresh waste to be 14% higher than the shear strength of the degraded waste. Also, there was a decrease in effective friction angle from fresh waste to degraded waste which is from 22º to 20º. Similarly, they found the unit weights to be increasing from 5.8 kN/m3 to 8.5 kN/m3 at moisture content below field capacity which is shown in Figure 3.7. 46 Figure 3.7 Unit weight vs Time (Fei and Zekkos, 2008) Based on Fei and Zekkos (2008), following post biodegradation properties were used in this study for the finite element modeling (Table 3.6). But, the properties after biodegradation maybe different for Florida because compared to Michigan, Florida has higher temperature and the biodegradation maybe higher. Table 3.6 Unit weight and Dry Unit Weight of the layers after Biodegradation Height Unit weight, γ Density Dry Unit weight, γd Maximum Dry (m) (kN/m3) (kg/m3) (kN/m3) Density (kg/m3) 0-30.5 16.23 1654.88 9.55 973.46 30.5-61 18.42 1878.23 10.83 1104.84 61-91.5 19.42 1980.16 11.42 1164.80 91.5-122 19.98 2037.12 11.75 1198.30 The compressibility and elastic properties after biodegradation are calculated using Equations 3.4, 3.5, and 3.6 which are shown in Table 3.7 and Figure 3.8. 47 Table 3.7 Elastic Modulus of the different layers of Landfill after Biodegradation ' 2 2 2 Height (m) e0 Cc v (kN/m ) D (m /kN) E (kN/m ) 0-30.5 1.06 0.51 247.49 2276.90 1691.41 30.5-61 0.81 0.45 842.67 7752.60 5759.07 61-91.5 0.72 0.43 1480.68 13622.22 10119.36 91.5-122 0.67 0.42 2132.58 19619.71 14574.64 Figure 3.8 Different layers of landfill with soil properties after degradation 48 Chapter 4: Research Methodology 4.1 Approach The current research is comprised of a comprehensive literature search to obtain the geotechnical properties of the material, which were described in Chapter 3. The study effort included analyses of landfills with or without geogrids, with or without biodegradation, consideration of extreme conditions due to hurricane force winds, and slope angle of 1:1, 1:2, and 1:3. The size of the model was based on the area of the western landfill site. Techniques applied in this study were applied to a case history which involves a geogrid reinforced composite landfill constructed in one of the hilly region of Austria (Alexiew et al, 2015). Two major approaches were used: (1) Limit Equilibrium Method using SLOPE/W, GeoStudio 2012, August 2015 Release; and (2) Finite Element Method using ANSYS® Academic Research, Release 17, 2016. Figure 4.1 shows the flowchart for the research methodology adopted in this investigation. SLOPE/W is the slope stability CAD software product, which can compute factor of safety of earth and rock slopes. It uses limit equilibrium method and can model heterogeneous soil types, complex stratigraphic, and slip surface geometry, and variable pore-water pressure conditions. This program was used in this research for the case with or without geogrids and with or without biodegradation. In SLOPE/W, critical slip surface and global factor of safety were provided by the software. However, in ANSYS®, coordinates and stresses at each nodes are collected, and the concept of local factor of safety by Huang and Yamasaki (1993) was used to find the FS at each nodes. 49 Slope Stability Material Properties (With and Without Bio- degradation) Without With Geogrids Geogrids Vertical Spacing and Length of Geogrids Finite Finite Geo- Geo- Element Element Slope Slope Modeling Modeling Extreme Extreme Wind Wind Loading Loading Geogrid Reinforced forces as Layer by Reinforcement Stresses at Slip surface Frictional Rule of and Pullout every nodes and Global FS force Mixtures resistance Stresses at every Slip surface nodes and Global FS Slip surface from SLOPE/W Slip surface from SLOPE/W Slip Slip Local and Local Surface Local Surface Global FS and and FS and and FS from Global from Global from geogrids as FS from Centroid FS Centroid frictional Rule of Method Method force Mixtures Figure 4.1 Flowchart showing the procedures followed in the research 50 4.1.1 Local Factor of Safety The FS at each point within a slope is called the Local Factor of Safety (FSL) and is defined as the ratio of the Coulomb stress at the current state of stress to the Coulomb stress of the potential failure state under the Mohr-Coulomb criterion. Figure 4.2 Mohr's Failure Criterion (Huang and Yamasaki, 1993) Huang and Yamasaki (1993) stated that any slope movement must be a compound effect of the stresses induced in the soil, and the resisting strength within the soil itself. The local factor of safety, FSL, on the plane at point P can be defined as (Figure 4.2): 51 s 4.1 FS L Where, s = shear strength available; and τ = shear stress acting on the plane For the orientation and the value of FSmin, following equations were used (Huang and Yamasaki, 1993): r sin 4.2 r cos 4.3 Where, r 12 and 12 2 2 AB cos 4.4 FS L r sin Where, Actan and Br tan B And, cos A 4.1.2 Global Factor of Safety Global Factor of Safety, also called Total Factor of Safety, is defined as the ratio of the available shear strength along the slip surface to the driving shear stress along the whole slip surface, and given by the Equation 4.5 (Cheng and Lau, 2014). n 4.5 Ncitan i i i1 Fs n Si i1 Where, Fs = Global Factor of Safety i = Slice No. 52 i = Effective Friction Angle It is also defined as the average value of the local factors of safety as shown in Equation 4.6 (Kourdey et al, 2001). FS_ global f ( FS12 _ local , FS _ local ,..... FSn _ local ) 4.6 Where, n = number of elements on the considered surface of failure 4.2 Analysis without Geogrids Analysis of the landfill was done without the use of geogrids considering the effect of biodegradation and hurricane force wind loads. The material properties for different layers has been shown in Chapter 3 (Table 3.5, 3.6, and 3.7). As explained earlier, SLOPE/W and ANSYS® was used in this research, and the detailed methodology is described below. 4.2.1 Slope Stability Analysis with SLOPE/W Program In the SLOPE/W program, the layers and properties of soil viz. cohesion (c), friction angle (ϕ), and unit weight (γ) of the soil need to be defined. The total height of the landfill analyzed was 122 m, with 4 layers, each layer having a thickness of 30.5 m. The actual plan size of the landfill is 2134 m x 2134 m. But, the length of landfill was taken only upto the center line for modeling (i.e. 1067 m), due to symmetry. All four layers were defined having different unit weights, but with the same value of cohesion and friction angle. For the case of unreinforced slope, two conditions were considered: with and without bio-degradation. The first case was without bio-degradation. To obtain the slip surfaces, slopes of 1:1, 1:2, and 1:3 were modeled using same layers and soil properties, making the difference only in the slope angle. Bishop’s modified method was chosen for 53 the analysis of the slopes. For the Bishop’s modified method, number of slices was taken as 20. Since we did not consider any involvement of the ground water level, peizometric line was not taken into account. Cohesion (c) value of 11.5 kN/m2 and friction angle of 32° was used in the analysis. The unit weights used, according to heights were shown in Chapter 3, Table 3.3. The model in SLOPE/W program along with the height and unit weights for the slope of 1:2 is shown in Figure 4.3. Figure 4.3 SLOPE/W Model for 1:2 slope with different layer properties without geogrids After the model is set-up as shown in Figure 4.3, the range of the slip surfaces for entry and exit has to be defined, which is 150 m (approx.) in the analysis, which can be any value. For this analysis, higher value than the length of the geogrids was chosen since the critical slip surface will be within the range of geogrids. SLOPE/W program automatically solves and gives the minimum factor of safety along with the critical slip surface. Also, forces and weights of each slice can be obtained and contour of FS can be plotted which is shown in the Results section of Chapter 5. For the analysis of the slopes with biodegradation, the soil properties were changed, all other dimensions remaining the same. Unit weights after the degradation are 54 shown in Chapter 3, Table 3.6. Cohesion (c) value of 9.81 kN/m2 and friction angle of 27.52° were used. 4.2.2 Slope Stability Analysis with Finite Element Method The conventional landfill stability analysis is generally carried out using analytical and numerical techniques. In contradistinction to the well-known analytical methods, i.e infinite slope analysis, Ordinary and Bishop’s modified method of slices, the finite element method enables slope stability analysis to be based on stress analysis, which identifies state of stress within a soil slope as well as the magnitude and direction of the principal stresses. This enables the identification of overstressed areas in a slope, using the Mohr-Coulomb failure criterion which is often exceeded even when the overall stability of a slope is considered adequate. By connecting the failure locations, the correct failure surface can be established, and by integrating the shear strength divided by the shear stress along that failure surface, a factor of safety can be obtained (Chowdhury, 1978). Furthermore, the finite element analysis enables engineers to locate zones of excessive strains, which might be ideal locations for field monitoring in a slope (Chowdhury, 1978). To perform the finite element analysis, very famous software ANSYS® (Analysis of Systems) has been used in this research. ANSYS® is a very strong finite element modeling software which can be used for a variety of sectors. It can solve very complex to very basic like linear elastic analysis. Following steps were used in the analysis. 4.2.2.1 Set up of the analysis Since simple linear elastic analysis were performed in this study, structural preference was chosen. However, we know that soil and MSW are always known to be non-linear. Hence, we used different equations as described in Chapter 3, to determine 55 the elastic modulus and Poisson’s ratio for the municipal solid waste, which has been defined earlier in Chapter 3. A 2-D analysis was performed in this research. Since the length of the landfill is quite large (1067m), plane strain condition was specified. This seemed to be the best scenario for the 2-D analysis because it does not allow for any strain in the z-direction, which simulates a section being taken. Plane stress would allow for strains to develop in the z-direction, which is not logical. 4.2.2.2 Element Type The element type chosen for this analysis was PLANE183, which is a higher order 2-D, 8-node or 6-node element shown in Figure 4.4. PLANE183 has quadratic displacement behavior and is well suited to modeling irregular meshes. This element is defined by 8 nodes or 6-nodes, having two degrees of freedom at each node: translations in the nodal x and y directions. The element may be used as a plane element (plane stress, plane strain and generalized plane strain) or as an axisymmetric element. This element has plasticity, hyperelasticity, creep, stress stiffening, large deflection, and large strain capabilities. It also has mixed formulation capability for simulating deformations of nearly incompressible elastoplastic materials and fully incompressible hyperelastic materials. Figure 4.4 PLANE 183 element with 8 nodes & 6 nodes 56 Both triangular and quadrilateral elements was used to perform geotechnical analysis, but the triangular elements are proved to be better suited for meshing irregular surfaces such as slope. So, in our case also, the analysis was done using triangular elements. 4.2.2.3 Defining Geometry The whole model was divided into four layers having different elastic properties and densities. The total height of the landfill was set to be 122m, with the idea of applying results for vertical expansions as well as construction of new landfills. The base dimensions for the model are approximately 1067m x 1067m. However, in ANSYS, model was drawn to the centerline of the landfill. Figure 4.5 shows geometry of the landfill. Separate areas were created since there were four different layers. But, the landfill acts as one solid body, so the areas had to be glued together using “Glue” command provided in ANSYS® program. 4.2.2.4 Input Properties Since a linear elastic analysis was performed in ANSYS, the properties of the soil, modulus of elasticity, density and Poisson’s ratio, had to be defined. Poisson’s ratio of the MSW was taken as 0.3 as described in earlier Chapter 3. A gravitational constant of 9.8 m/s2 was specified and all the loading in the model came from only body forces. Modulus of elasticity, unit weight and density, which were used in the model has been shown in Table 3.3 and 3.5 of Chapter 3. 57 Figure 4.5 ANSYS Model for Slope of 1:1 4.2.2.5 Element Size Specified element size was used in the ANSYS®. Mapped mesh was used to generate equal size and distribution. The size of the element was chosen according to the spacing of geogrids. For the 1:1 slope, element size of 3.05 m chosen, since the vertical spacing of geogrids is 3.05 m. Also, for the slope 1:2, element size of 3.81 m was used, since the vertical spacing is double of 3.81 m i.e. 7.63 m. For 1:3 slope, element size of 5.08 m was taken, since the vertical spacing of geogrids is 10.17 m. 4.2.2.6 Boundary Conditions and Loading From the investigation, it was found that the foundation condition is pretty strong. So, the bottom line of the model was considered fixed, which means all degrees of freedom were set to zero. Also, along the centerline of the landfill, the degree of freedom in the x-direction was set equal to zero. Since all the loading comes from body force, gravitational constant of 9.8 kN/m2 was defined. 58 4.2.2.7 Wind loading It was not possible to apply the wind load in the SLOPE/W program so, the effect of wind loading was analyzed only in the finite element method. This is also one of the benefit of using FEM. Risk category of buildings and other structures have been categorized for flood, wind, snow, earthquake, and ice loads, which is shown in Chapter 1. For this research, risk category IV was chosen. Wind load is calculated by the following equation (ASCE 7-10): F A P cd 4.7 Where, A = Area (Projected) P = Wind Pressure cd = Drag Coefficient F = Force PV0.00256 2 4.8 Where, V = Speed of the wind in miles per hour (mph) The speed of the wind for Risk Category III and IV Buildings and other structures was chosen as 200 mph, which is shown in Figure 4.6. Wind direction of 45º was applied and the value of 0.55 was considered for drag coefficient (Ikhwan and Ruck, 2004). Using Equations 4.8 and 4.9, wind loads was calculated for all three slopes. The calculated wind loads are shown in Table 4.1. Also, the wind loading of the model for the case “without geogrids” is shown in Figure 4.7. Pressure was applied on the wind ward side and suction on the leeward side. 59 Table 4.1 Calculation of Wind Forces for different slopes Wind Height Area(m2) Area(ft2) Wind force Slope Width (m) force (m) per m per ft (Newton) (pounds) 1:1 122 122 172.534 566.057 31880.308 141809.987 1:2 122 244 272.800 895.014 50407.193 224221.277 1:3 122 366 385.798 1265.741 71286.536 317096.771 Figure 4.6 Ultimate Design Speed for Risk Category III and IV Buildings and Other Structures (ASCE 7-10) 60 Figure 4.7 Slope of 1:1 without geogrids and wind load 4.2.2.8 Output from ANSYS From ANSYS, stresses and strains in each direction can be obtained as output. Concept of Huang and Yamasaki (1993) as explained earlier, was used to obtain the Local FS at each points using all these stresses. Basically, following two methods were used to obtain Global FS from Local FS. Method 1: Slip Surface from SLOPE/W The co-ordinates of the slip surface was obtained from SLOPE/W. These co- ordinates were utilized in ANSYS to obtain Local Factor of Safety at these points. These local Factor of Safety were then averaged to calculate Global Factor of Safety, as shown in Equation 4.6. Method 2: Centroid Method Similarly, as explained earlier, Local Factor of Safety can be obtained at each nodes of the model in FEM. A range of 0.1 e.g. 0.1-0.2, 0.2-0.3, etc. was considered for all these Local FS and centroid for each range was obtained. But, only the FS lower than 1.0 was used to find the range considering FS lower than one constitutes a failure condition. In addition to this, for the calculation of the centroids of different 61 ranges, only the area covered by the geogrids was taken into account. By joining these nodes of centroids, a new slip surface was defined. One of the example for this method is shown in Figure 4.8 for 1:1 slope without geogrids and without biodegradation. 140 120 100 80 60 Height(m) 40 20 0 0 20 40 60 80 100 120 140 160 180 200 Horizontal Distance (m) 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 0.8-0.9 0.9-1.0 1.0-1.1 1.1-1.2 1.2-1.3 1.3-1.4 1.4-1.5 1.5-2.0 >2 Centroids Figure 4.8 Example showing the centroids and the slip surface obtained from centroids 4.3 Analysis with Geogrids The first task in the analysis using geogrids, it is necessary to obtain the vertical spacing and length of the geogrids. 4.3.1 Vertical Spacing and Length of Geogrids To obtain the vertical spacing and length of geogrids, Jewell design chart has been used which is shown in Figure 4.9 (Jewell, 1991). The chart is chosen for the case of zero pore water pressure since no water pressure is considered in this analysis. Three different 62 graphs are shown in the chart. The first one is to obtain the value of Kreq , which is design earth pressure coefficient giving the minimum required reinforcement force. For this research, using angle of friction of 32 ̊ for MSW and for 1:1 (45º) slope, from chart is obtained as 0.02 from Figure 4.9. The spacing of the geogrids, Sv, is given as follows (Koerner, 2005): Treq 4.9 Sv Kzreq .. max Where, Treq = ultimate tensile strength or rupture strength of the geogrids = unit of the soil or MSW zmax = maximum depth at which the geogrids can be placed As described earlier in literature review, the minimum allowable factor of safety of 1.5 was satisfied by tensile strength of at least 100 kN/m. Accordingly, the ultimate tensile strength of the geogrid in this study was used 114 kN/m. The maximum depth for the geogrids is 122 m and unit weight of MSW used is 13.86 kN/m3. Treq 114 Sv 3.43 m Kzreq .. max 0.02 13.59 122 But, for ease of analysis, the spacing was conservatively taken as 3.05 m, having ten layers of geogrids for first and second layers of landfill. For third and fourth layers, the spacing of geogrids was 6.1 m, which is also satisfied by Equation 4.10. To obtain the minimum length of the geogrid, Jewell’s chart, as shown in Figure 4.9, provides two criteria which are overall stability and direct sliding. For MSW angle of LH/ LH/ friction of 32º and slope angle of 45 ̊ (1:1), r ovrl = 0.4 (approx.) and r dr = 0.4 as well. From both of these conditions, the minimum length of geogrids is obtained as 63 48.8 m, but for ease of modeling and defining the mesh, 61 m was used in the analysis. Also, half of the total height (122 m) of the landfill is 61 m, which makes it easier to model. This will also be a conservative approach. Figure 4.9 Jewell's Chart (1991) K 0 LHLH//0 For the slopes 1:2 and 1:3, req and rrovrl dr (Jewell, 1991). So, the spacing and the length of the geogrids were chosen such that the geogrid 64 will be well extended beyond the critical slip surface. For 1:2 slope, a constant spacing of 7.63 m and length of 122 m was used, and for 1:3 slope, vertical spacing of 10.17 m and length of 183 m were used. The geogrid layouts are shown in Figure 4.10, 4.11 & 4.12 for the slope of 1:1, 1:2, & 1:3, respectively. Figure 4.10 Geogrid Layers for Landfill Slope of 1:1 Figure 4.11 Geogrid Layers for Landfill Slope of 1:2 65 Figure 4.12 Geogrid Layers for Landfill Slope of 1:3 4.3.2 Slope Stability Analysis using SLOPE/W Program For reinforced slopes, the soil properties are exactly same as in unreinforced slope case for both with and without the effect of bio-degradation. Bishop’s modified method was chosen with total of 20 slices. Properties of the geogrids such as ultimate tensile strength, pull-out resistance and angle of reinforcement have to be provided. Calculations for the pull-out resistance is provided in Appendix A. All the geogrids are horizontal having the tensile strength of 114 kN/m. Identical properties of geogrids has been used for all three slopes. However, there will be difference in the pullout resistance since it depends on the vertical stress of the soil. The model with reinforcement for the slope of 1:2 in SLOPE/W is shown in Figure 4.13. Determination of vertical spacing and lengths of geogrids followed the same procedure as outlined earlier in Section 4.3.1. 66 Figure 4.13 SLOPE/W Model for 1:2 slope with different layer properties with geogrids 4.3.3 Slope Stability Analysis using Finite Element Modeling Two methods were used in this research to incorporate geogrids in the FE model. 4.3.3.1 Method 1: Frictional force The geogrid frictional force is calculated according to Mohr-Coulomb theory by using the following equation: 4.10 Agrid ' Ff L. .2( c v() avg tan ) Atotal Where, Ff = Frictional force in geogrids Agrid = Ratio of the area of the geogrids in the x-z plane Atotal = Total area over which the geogrid is placed 2 / 3 21.33o In this research, (/)AAgrid total has been used as 0.1336, which comes from a rib thickness of 0.006 ft. and an opening size of 0.092 ft. x 0.092 ft. The geogrid frictional force was calculated by using Equation 4.11. The areas were evenly distributed with the element size as specified earlier in Section 4.2.2.5 for each slope. The average height between nodes was used to calculate the frictional 67 resistance offered by the geogrids between the spans. This force was divided in half and each node received half of the force, which is similar to the equivalent nodal force for a distributed load in finite elements (Figures 4.14, 4.15 and 4.16). Figure 4.14 Calculation of Nodal Forces Figure 4.15 Nodes created to apply the geogrid forces for the slope of 1:1 68 Figure 4.16 Geogrid forces applied in ANSYS for the slope of 1:1 4.3.3.2 Method 2: Rule of Mixtures Rule of mixtures is a weighted mean used to predict various properties of a composite material made up of continuous and unidirectional fibers (Wikipedia). Modulus of elasticity for the new composite layer, Ec, can be obtained using Equation 4.12 as follows: 4.11 Ec fE f 1 f E m Where, V f f = Volume Fraction of fibers VVfm E f = Elastic Modulus of the Fibers Em = Elastic Modulus of the Matrix 69 V f = Volume of Fiber Vm = Volume of Matrix (Soil or MSW) The assumption is that it is continuous HDPE strand used as reinforcement. The thickness of the composite layer was taken as 1 m. Figure 4.17 Schematic Layout of the Geogrids as Composite Layers Since there were four different layers with different value of Young’s modulus, four different values for composite layers were computed. Young’s modulus of geogrids was taken as 1.04 x 1012 N/m2, which is the elastic modulus for the HDPE (High Density Poly Ethylene). Young’s modulus for composite layers calculated by Equation 4.12 are shown in Table 4.2. Table 4.2 Elastic Modulus of the composite layer E for E for E for , , V Layer f f fiber, soil, composite, 3 3 2 2 2 No. m /m m /m VVfm 1 f N/m N/m N/m 1 0.061 60.939 0.001 0.999 1.04E+12 9914720 9.82E+09 2 0.061 60.939 0.001 0.999 1.04E+12 6883900 6.84E+09 3 0.061 60.939 0.001 0.999 1.04E+12 3917740 3.9E+09 4 0.061 60.939 0.001 0.999 1.04E+12 1150620 1.15E+09 70 To incorporate the geogrids in ANSYS, the coordinates for each corner of each layer was needed. After modeling the layers, the respective properties viz. Density, Elastic Modulus, and Poisson’s Ratio, were provided in the ANSYS®. The element size was chosen as 1, to have finer mesh. Same slip surface from SLOPE/W for the reinforced case was used for this method. The table for all the coordinates of geogrids layout is shown in Appendix A. Figure 4.18 Geogrid layers according to Rule of Mixtures 4.3.3.3 Wind loading The wind load applied in the case with reinforcement is the same load as presented earlier in Table 4.1. Similar to the case without geogrids, the pressure was applied on the windward side and suction was applied on the leeward side, as shown in Figure 4.17. 71 Figure 4.19 Slope of 1:1 with geogrids and wind load 4.3.3.4 Output from ANSYS Similar to the case without geogrids, stresses and strains were collected at every nodes and Local FS was calculated. As presented in Section 4.2.2.8, two methods were used to calculate the Global Factor of Safety: (1) Slip Surface from SLOPE/W; and (2) Centroid Method. 72 Chapter 5: Data Analysis, Results, and Discussions 5.1 Data Analysis Two different software were used for the analysis of the slope stability of the landfill viz. SLOPE/W and ANSYS®, which uses limit equilibrium and finite element method respectively. SLOPE/W gives the factor of safety and the slip surfaces directly. However, it was quite challenging to analyze the data obtained from finite element method. There were thousands of nodes in each analysis. From them, the nodes lying on the slip surface had to be chosen which was tedious. Basically, principal stresses were used for the calculation of the factor of safety in finite element modeling, using the principle of Mohr’s Failure Criteria, which has been described in Chapter 3. Since it is 2D plane strain analysis, in most of the times one of the principal stress is zero or almost equal to zero. The two minimum values of principal stresses are chosen for the calculation. Factor of safety for each node was calculated. All the calculation sheets are provided in the Appendices. 5.2 Analysis without geogrids The factor of safety obtained from SLOPE/W were close to the factor of safety obtained from finite element modeling. This section has been divided into two cases: (1) With or Without Biodegradation; and (2) With Wind loads. 5.2.1 With and Without Biodegradation The results obtained from SLOPE/W, ANSYS® and Centroid Method has been shown in Table 5.1. Also, Figures 5.1 and 5.2 show the result from the SLOPE/W for the 73 slope of 1:1, along with the critical slip surface and the minimum factor of safety without and with biodegradation respectively. Similarly, Figures 5.3 and 5.4 show the result from the SLOPE/W for the slope of 1:2, along with the critical slip surface and the minimum factor of safety without and with biodegradation respectively. Table 5.1 Factor of safety obtained from FEM and SLOPE/W without geogrids Without Geogrids Different Without Bio-degradation With Bio-degradation slopes SLOPE ANSYS ANSYS (CM) SLOPE ANSYS ANSYS (CM) 1:1 0.826 0.848 0.656 0.65 0.744 0.603 1:2 1.482 1.71 0.755 1.202 1.274 0.707 1:3 2.184 1.177 0.93 1.791 1.12 0.904 CM: Centroid Method Figure 5.1 SLOPE/W result for Unreinforced Slope 1:1 without Biodegradation Figure 5.2 SLOPE/W result for Unreinforced Slope 1:1 with Biodegradation 74 Figure 5.3 SLOPE/W result for Unreinforced Slope 1:2 without Biodegradation Figure 5.4 SLOPE/W result for Unreinforced Slope 1:2 with Biodegradation Table 5.1 shows that the results from SLOPE/W are close to the results from Finite Element Modeling (ANSYS) for both cases, without and with bio-degradation. However, the factor of safety obtained from ANSYS are higher in values for slope of 1:1 and 1:2 and lower for 1:3. It shows that with the increase of slope angle, there is decrease in FS. Also, it can be seen that FS decreases after the effect of biodegradation. Using the Centroid Method, a new slip surface is located as follows: Nodal points representing FS ranges in 0.1 increment (i.e. 0.6-0.7, 0.7-0.8, etc.) are identified and grouped together. The centroid of each nodal group in space, whose FS<1, is located. A best-fit trend line drawn through the centroids is termed as the critical slip surface. The average FS of the centroids is termed as the minimum FS of the slope. 75 140 120 100 80 60 Height(m) 40 20 0 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 Horizontal Distance (m) Slip surface 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 0.8-0.9 0.9-1.0 1.0-1.1 1.1-1.2 1.2-1.3 1.3-1.4 1.4-1.5 1.5-2.0 >2 Centroids Slip Surface from CM (a) 140 120 100 80 60 Height(m) 40 20 0 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 Horizontal Distance (m) Slip surface 0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 0.8-0.9 0.9-1.0 1-1.1 1.1-1.2 1.2-1.3 1.3-1.4 1.4-1.5 1.5-2.0 >2 Centroids Slip Surface from CM (b) Figure 5.5 Local FS and Critical Slip Surface for Unreinforced Slope 1:1 using the Centroid Method without geogrids (a) Without Biodegradation (b) With Biodegradation 76 140 120 100 80 60 Height(m) 40 20 0 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 Horizontal Distance (m) Slip surface 0.5-0.6 0.6-0.7 0.7-0.8 0.8-0.9 0.9-1 1.0-1.1 1.1-1.2 1.2-1.3 1.3-1.4 1.4-1.5 1.5-2.0 >2.0 Centroids Slip Surface from CM (a) 140 120 100 80 60 Height(m) 40 20 0 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 Horizontal Distance (m) Slip surface 0.4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 0.8-0.9 0.9-1.0 1.0-1.1 1.1-1.2 1.2-1.3 1.3-1.4 1.4-1.5 1.5-2.0 >2 Centroids Slip Surface from CM (b) Figure 5.6 Local FS and Critical Slip Surface for Unreinforced Slope 1:2 using the Centroid Method without geogrids (a) Without Biodegradation (b) With Biodegradation 77 After the landfill undergoes biodegradation, it can be seen from Table 5.1 that there is a decrease in FS. Similar to the case without bio-degradation, as the slope angle increases, there is a decrease in FS for the case with bio-degradation as well. Also, using the Centroid Method, a slip surface can be plotted as shown in Figures 5.4 and 5.5 for slope 1:1 and Figures 5.6 and 5.7 for slope 1:2. Comparing Figures 5.4 and 5.4 for slope 1:1, there is a decrease in every nodal FS due to degradation. This case is similar for slope 1:2 as well. Data from Table 5.1 are combined in Figures 5.7 and 5.8 for the case without and with biodegradation respectively. The following general observations are made: 1. FS is decreased due to the effect of biodegradation. 2. FS decreases as the slope angle increases. 3. Centroid Method produces the lowest FS since only the FS lower than 1 were used for this method. 78 2.5 2 1.5 1 1:3 1:2 FactorSafety of 0.5 1:1 SlopeAngles 0 SLOPE/W ANSYS ANSYS (Centroid Method) Figure 5.7 FS for the slopes without geogrids & without Biodegradation 2.5 2 1.5 1 1:3 Factor Safety 0.5 1:2 1:1 SlopeAngles 0 SLOPE/W ANSYS ANSYS (Centroid Method) Figure 5.8 FS for the slopes without geogrids & with Biodegradation 5.2.2 Effect of Extreme Wind loading For the sustainable and resilient landfill design, wind load was applied in the ANSYS® model which was described in Chapter 4. FS was obtained for both side viz. windward and leeward side after applying the wind load, as shown in Figure 5.9 (a and b) for 1:1 slope. Data for all slopes are combined into Figure 5.10. It can be seen that FS at 79 leeward side is decreased significantly due to the effect of wind. However, it helped in the windward side which is due to the fact that the wind load is in the same direction as the frictional forces of the geogrids (when used). Also, the trend is same as in the other cases, higher the slope lower is the factor of safety, and the Centroid Method produces the lowest FS. Table 5.2 Factor of Safety from FEM for the effect of extreme wind loading for unreinforced case Without Geogrids Windward side Leeward side Different slopes ANSYS ANSYS ANSYS (Centroid ANSYS (Centroid Method) Method) 1:1 1.26 0.75 0.627 0.62 1:2 2.374 0.853 0.88 0.571 1:3 1.258 0.93 0.851 1.03 80 140 120 100 80 60 Height(m) 40 20 0 0 20 40 60 80 280 100 120 140 160 180 200 220 240 260 300 320 340 360 380 400 420 Horizontal Distance (m) 0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 0.8-0.9 0.9-1.0 1.0-1.1 1.1-1.2 1.2-1.3 1.3-1.4 1.4-1.5 1.5-2.0 >2 Series18 (a) 140 120 100 80 60 Height(m) 40 20 0 2000 1720 1740 1760 1780 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2020 2040 2060 2080 2100 2120 2140 Horizontal Distance (m) 0.6-0.7 0.7-0.8 0.8-0.9 0.9-1.0 1.0-1.1 1.1-1.2 1.2-1.3 1.3-1.4 1.4-1.5 1.5-2.0 >2 0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6 Centroid Method (b) Figure 5.9 Local FS and Critical Slip Surface for extreme wind loading for Unreinforced Slope 1:1 using the Centroid Method without geogrids (a) Windward side (b) Leeward side 81 Data from Table 5.2 are combined in Figure 5.10 for the case of extreme wind loading and without the use of geogrids in windward and leeward side of the landfill. Following observations were made: 1. FS in leeward side are significantly lower compared to the windward side. 2. FS decreases with the increase in slope angle. 2.5 2 1.5 1 1:3 FactorSafety of 0.5 1:2 1:1 0 ANSYS ANSYS ANSYS ANSYS SlopeAngles (Centroid (Centroid Method) Method) Windward side Leeward side Without Geogrids 1:1 1:2 1:3 Figure 5.10 FS for the slopes without geogrids & with wind loads on windward and leeward side 5.3 Results for the analysis with geogrids Geogrids were applied in various layers for all the slopes by using SLOPE/W and ANSYS as described in Chapter 3. Analysis has been done with or without biodegradation and with extreme wind loading. In the finite element analysis, the geogrid was incorporated by considering the presence of geogrids as frictional forces and as a 82 composite layer by using the Rule of Mixtures. In addition, the Centroid Method was used to determine a critical slip surface and the average FS. 5.3.1 With and Without Biodegradation The results are shown in Table 5.3. It can be seen that the results obtained from SLOPE/W and ANSYS® are in close agreement. FS obtained from centroid method is always less than 1, since only the FS lower than one were selected in this method. Figures 5.11 and 5.12 show the result from the SLOPE/W for the slope of 1:1, along with the critical slip surface and the minimum factor of safety without and with biodegradation, respectively. Comparing with the results from Table 5.3 with Table 5.3 presented earlier, it can be seen geogrid reinforcement increases FS for both cases, with and without biodegradation. Table 5.3 Factor of safety obtained from FEM and SLOPE/W with geogrids With Geogrids Without Bio-degradation With Bio-degradation Differen ANSYS ANSYS t slopes (Rule of ANSYS (Rule of ANSYS SLOPE ANSYS SLOPE ANSYS Mixtur (CM) Mixtur (CM) es) es) 1:1 1.014 1.117 0.525 0.604 0.742 0.919 0.491 0.656 1:2 1.522 1.07 0.93 0.607 1.229 0.835 0.92 0.604 1:3 2.199 2.15 1.1 1.03 1.802 1.84 1.12 0.906 83 Figure 5.11 SLOPE/W result for Geogrid Reinforced slope 1:1 without Biodegradation Figure 5.12 SLOPE/W result for Geogrid Reinforced slope 1:1 with Biodegradation Figure 5.13 SLOPE/W result for Geogrid Reinforced slope 1:2 without Biodegradation Figure 5.14 SLOPE/W result for Geogrid Reinforced slope 1:2 with Biodegradation 84 As in the case without geogrids, for the case with geogrids, using the centroid method, a slip surface was located by following same procedure as described in Section 5.2.1. After the landfill undergoes biodegradation, it can be seen from Table 5.2 that there is a decrease in FS. Also FS decreases when the slope angle increases. A slip surface constructed using the Centroid Method shown in Figure 5.15 (a and b). Comparing the two figures (Figures 5.15, a and b) of nodal FS, we can see that the FS decreases at every nodes. Trends are similar for slopes 1:2, which are presented in Figures 5.13, a and b. FS for each slopes from SLOPE/W and ANSYS, with and without biodegradation but with the use of geogrids has been shown in Figure 5.17 & 5.18. 85 140 120 100 80 60 Height(m) 40 20 0 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 Horizontal Distance (m) Series10 0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 0.8-0.9 0.9-1.0 1.0-1.1 1.1-1.2 1.2-1.3 1.3-1.4 1.4-1.5 1.5-2.0 >2 Series18 Slip Surface from CM (a) 140 120 100 80 60 Height(m) 40 20 0 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 Horizontal Distance (m) Slip Surface 0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 0.8-0.9 0.9-1.0 1.0-1.1 1.1-1.2 1.2-1.3 1.3-1.4 1.4-1.5 1.5-2.0 >2 Centroids Slip Surface from CM (b) Figure 5.15 Local FS and Critical Slip Surface for Reinforced Slope 1:1 using the Centroid Method without geogrids (a) Without Biodegradation (b) With Biodegradation 86 140 120 100 80 60 Height(m) 40 20 0 0 50 100 150 200 250 300 350 400 Horizontal Distance (m) Slip surface 0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 0.8-0.9 0.9-1.0 1.0-1.1 1.1-1.2 1.2-1.3 1.3-1.4 1.4-1.5 1.5-2.0 >2 Centroids Slip Surface from CM (a) 140 120 100 80 60 Height(m) 40 20 0 0 50 100 150 200 250 300 350 400 Horizontal Distance (m) Slip surface 0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 0.8-0.9 0.9-1.0 1.0-1.1 1.1-1.2 1.2-1.3 1.3-1.4 1.4-1.5 1.5-2.0 >2 Centroids Slip Surface form CM (b) Figure 5.16 Local FS and Critical Slip Surface for Reinforced Slope 1:2 using the Centroid Method without geogrids (a) Without Biodegradation (b) With Biodegradation 87 Data from Table 5.3 are combined in Figures 5.17 and 5.18 for the case without and with biodegradation respectively. The following general observations are made: 1. FS increases after the use of geogrids for all slope angles. 2. FS decreases with increment in slope angles and with the effect of biodegradation. 3. FS decreases as the slope angle increases. 4. FS obtained by incorporating geogrids using the method “Rule of Mixtures” also shows that FS decreases as the slope angle increases. 5. In this case as well, Centroid Method produces the lowest FS since only the FS lower than 1 were used for this method. 2.5 2 1.5 1:3 1 1:2 0.5 1:1 0 SLOPE/W ANSYS ANSYS (Rule of ANSYS Mixtures) (Centroid Method) 1:1 1:2 1:3 Figure 5.17 FS for the slopes with geogrids & without Biodegradation 88 2.5 2 1.5 1:3 1 1:2 0.5 1:1 0 SLOPE/W ANSYS ANSYS (Rule of ANSYS Mixtures) (Centroid Method) 1:1 1:2 1:3 Figure 5.18 FS for the slopes with geogrids & with Biodegradation 5.3.2 Effects of Extreme Wind loading As in the case without geogrids, FS was obtained in both side viz. windward and leeward side after applying the wind load, shown in Figures 5.19 (a and b). It can be seen that FS at leeward side has been decreased a lot due to the effect of wind, the reason for which is described in section 5.2.2. Also, the trend is same as in the other cases, higher the slope lower is the factor of safety. Table 5.4 Factor of Safety from FEM for the effect of extreme wind loading for reinforced case With Geogrids Windward side Leeward side Different ANSYS ANSYS slopes ANSYS ANSYS ANSYS (Rule of ANSYS (Rule of (CM) (CM) Mixtures) Mixtures) 1:1 1.87 0.892 0.467 0.893 0.377 0.57 1:2 1.8 1.161 0.636 1.367 0.773 0.642 1:3 1.234 1.115 0.977 1.23 0.707 0.641 89 140 120 100 80 60 Height(m) 40 20 0 0 50 100 150 200 Horizontal Distance (m) 0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 0.8-0.9 0.9-1.0 1.0-1.1 1.1-1.2 1.2-1.3 1.3-1.4 1.4-1.5 1.5-2.0 >2 Centroids Slip Surface fron SLOPE/W Slip Surface from Centroid Method (a) 140 120 100 80 60 Height (m) Height 40 20 0 1940 1990 2040 2090 2140 Horizontal Distance (m) 0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 0.8-0.9 0.9-1.0 1.0-1.1 1.1-1.2 1.2-1.3 1.3-1.4 1.4-1.5 1.5-2.0 >2 Centroids Slip surface from SLOPE/W Slip Surface from SLOPE/W (b) Figure 5.19 Local FS and Critical Slip Surface for extreme wind loading for Reinforced Slope 1:1 using the Centroid Method without geogrids (a) Windward side (b) Leeward side 90 Data from the wind loading analysis as shown in Table 5.4 were combined and shown in Figure 5.20. Following general observations were made after running the analysis: 1. After the use of geogrids, there is an increase in FS in both windward and leeward side for all slopes. 2. Centroid Method does not show the same result after application of geogrids. FS in leeward side are decreased in CM after geogrids are applied. 3. Rule of Mixture shows higher FS for the slope of 1:2 rather than for the slope of 1:3. 2 1.5 1 0.5 1:3 1:1 0 ANSYS ANSYS ANSYS ANSYS ANSYS ANSYS (Rule of (Centroid (Rule of (Centroid Mixtures) Method) Mixtures) Method) Windward side Leeward side With Geogrids 1:1 1:2 1:3 Figure 5.20 FS for the slopes with geogrids & with wind loads on windward and leeward side 5.4 Result Summary Summary of the result has been divided into three different sections as follows: 91 5.4.1 Effects of Geosynthetics With the use of SLOPW/W, FS increased by 22.76%, 2.7%, and 0.69% for the slope of 1:1, 1:2, and 1:3 respectively. With the ANSYS®, it increased by 31.72% and 82.67% for the slope of 1:1 and 1:3. However, it was found to be decreased for the slope of 1:2 (Figures 5.7, 5.8, 5.17 and 5.18). 2.5 2 1.5 1 FactorofSafety 0.5 0 SLOPE/W ANSYS SLOPE/W ANSYS Without Geogrids With Geogrids 1:1 1:2 1:3 Figure 5.21 FS of the Landfill Without and With Geogrids 5.4.2 Effects of Biodegradation From SLOPE/W, it was obtained that FS decreased by 27.08%, 23.29%, and 21.94% for slopes 1:1, 1:2, and 1:3 respectively, and from ANSYS it was 13.98%, 34.22%, and 5.09% respectively for the unreinforced case. For the reinforced case, FS decreased by 36.66%, 23.84%, and 22.03% from SLOPE/W, and from ANSYS, it decreased by 21.55%, 28.14%, and 22.03% for the slopes of 1:1, 1:2, and 1:3 (Figures 5.7, 5.8, 5.17 and 5.18). 92 2.5 2 1.5 1 FactorofSafety 0.5 0 SLOPE/W ANSYS ANSYS SLOPE/W ANSYS ANSYS (CM) (CM) With Biodegradation With Geogrids 1:1 1:2 1:3 Figure 5.22 FS of the Landfill Without and With Geogrids after biodegradation 5.4.3 Effects of Extreme Wind Loading Leeward side is more vulnerable than the windward side. FS on windward side was found to be increased by 32.7%, 27.97%, and 6.44% for the slopes for 1:1, 1:2, and 1:3 respectively and on leeward side, it was found to be decreased by 35.25%, 94.32%, and 38.31% respectively. Use of geogrids increased FS by 42%, 55% and 44.5 % on the leeward side of the slope. 93 2.5 2 1.5 1 FactorofSafety 0.5 0 ANSYS ANSYS (CM) ANSYS ANSYS (CM) Wihout Geogrids With Geogrids 1:1 1:2 1:3 Figure 5.23 FS of the Landfill Without and With Geogrids after extreme wind loading for the windward side 2.5 2 1.5 1 FactorofSafety 0.5 0 ANSYS ANSYS (CM) ANSYS ANSYS (CM) Wihout Geogrids With Geogrids 1:1 1:2 1:3 Figure 5.24 FS of the Landfill Without and With Geogrids after extreme wind loading for the leeward side 94 Chapter 6: Case Study 6.1 Background A case study for one of the landfill in Austria has been done in this research. Paper entitled “A landfill with innovative reinforcing solutions: history, experience, solution flexibility” by Alexiew et al presented in the conference “Geotechnical Engineering for Infrastructure and Development” held in Edinburgh International Conference Center, Ediburgh from 13th-17th September, 2015, was the major source for this case study. Figure 6.1 Model used for slope stability analyses (Alexiew et al., 2015) A landfill was constructed in the mountainous region of Austria, with the height of 75 m in early 90’s. For the old landfill, one third of the basal system was only slightly inclined (almost horizontal) and two thirds were inclined following the excavated slope of 1v:2h with berms as shown in Figure 6.1. However, in 1994, there were questions raised for the local and global stability of the landfill. Hence, to resolve these instabilities, high-strength low-strain geogrids from Aramid (AR) were installed in 1995-1996 on the 95 two lowest slope sections as “anti-sliding” reinforcement. Then, it was closed for further service. Stability analyses of the landfill was run, which resulted in insufficient stability for the actual stage in 1995 and probable future infill stages as well. But then, it was decided to reactivate the landfill in 2013 and to deposit construction debris and/or ashes on top of the old MSW, up to 75m. The layout of the landfill has been shown in Figure 6.1 and the material properties in Table 6.1. Table 6.1Material Properties used in the landfill model 6.2 Unreinforced Case For this case study, the analyses was done following the same procedures described in Chapter 4. The model was created only for the new portion of the landfill. Analyses was done by Limit Equilibrium and Finite Element method using SLOPE/W and ANSYS® respectively. 6.2.1 Slope Stability Analysis with SLOPE/W In SLOPE/W, the model was drawn with the same dimensions as shown in Figure 6.1 utilizing the layer properties from Table 6.1. The model from SLOPE/W is shown in Figure 6.2. The slope of the model is 1:2.25, with the height of 75 m. Bishop’s modified method was used for the analyses and any peizometric line was not considered. The range of the slip surfaces for entry and exit was defined to be the complete width and height of the model. 96 Figure 6.2 Unreinforced Model used in SLOPE/W program with different layers 6.2.2 Slope Stability Analysis with Finite Element Method To run the analysis with finite element method, same software ANSYS® was used and similar steps described in Chapter 4 were followed, which are described below: 6.2.2.1 Material Properties The properties of the material for FEM were calculated following the procedures and formulae as described in Chapter 3. The unit weight were already provided in the paper. However, Void Ratio and Elasticity Modulus were calculated using the same procedure and properties as described in Chapter 3 and 4, and are provided in Table 6.2 and 6.3. Table 6.2 Unit weight and Maximum Dry Density for Case Study Unit weight, γ Dry Unit weight, Maximum Dry 3 3 3 Height (m) (kN/m ) γd (kN/m ) Density(kg/m ) Demolition waste 16.00 9.41 959.73 Slag 18.50 10.88 1109.69 MSW 14.00 8.24 839.77 97 Table 6.3 Void Ratio, Constrained and Young's Modulus of Landfill Materials ' 2 2 2 Height (m) e0 Cc v (kN/m ) D (m /kN) E (kN/m ) Demolition waste 1.08 0.52 264.00 2428.80 1804.25 Slag 0.80 0.45 860.25 7914.30 5879.19 MSW 1.38 0.60 1015.00 9338.00 6936.80 6.2.2.2 Modeling with ANSYS® Same procedure as explained in section 4.2.2 was done for modeling with ANSYS®. A 2-D analysis using 6-node PLANE183 as element type, was performed. The dimensions of the model along with the length of the geogrids has been shown in Figure 6.1. Exact model was built in ANSYS® as well, having the same layer dimensions. Since landfill always acts as one solid body, the areas were glued together, using “Glue” command provided in ANSYS® program. Modulus of elasticity, density, and Poisson’s ratio were defined as input properties, which are shown in Table 6.2 and 6.3. Value for the Poisson’s ratio was taken as 0.3, same as used for earlier analysis. A gravitational constant of 9.8 m/s2 was specified and all the loading in the model came from only body forces. Since this is the case of unreinforced model, it was easy to choose the element size. So, smaller element size of 0.5 was chosen to have very finer mesh for all the layers. As per the boundary conditions, since the new landfill is resting in the old landfill which has been closed for past 15 years, all the boundaries are considered as fixed. ANSYS models with different layers and elements are shown in Figures 6.3 and 6.4. 98 Figure 6.3 ANSYS® Model for the case history with different layers Figure 6.4 ANSYS® Model showing the elements used for the case history 99 6.3 Reinforced Case The first step for the analysis of reinforced case is to calculate the vertical spacing and the length of the geogrids. However, in this case study, the process for the calculation of the spacing and length of the geogrids was not described. Same spacing and length of the geogrids used in the construction was adopted in the analysis. For the case of reinforced model also, analyses was done by Limit Equilibrium and Finite Element method using SLOPE/W and ANSYS® respectively. Figure 6.5 Reinforced Slope from Case History (Alexiew et al, 2015) 6.3.1 Slope Stability Analysis with SLOPE/W In SLOPE/W, same model from unreinforced case was used, with the same dimensions and layer properties. The model from SLOPE/W for the reinforced case is shown in Figure 6.6. High-strength geogrids from Polyvinylalcohol (PVA) and Polyester (PES/PET) with up to 1600 kN/m strength were used in the landfill. Hence, in the SLOPE/W program, 1600 kN/m was used for ultimate tensile strength of the reinforcement and pullout resistance was calculated accordingly. The data is provided in the Appendix. Bishop’s modified method was used without considering any peizometric 100 line. Same range of the slip surfaces for entry and exit was defined as in the case of unreinforced case. Figure 6.6 Reinforced Model used in SLOPE/W program with different layers 6.3.2 Slope Stability Analysis with Finite Element Method Soil properties for different layers of the MSW are shown in Table 6.2 and 6.3. Vertical spacing and length of the geogrids were used as provided in the paper. Frictional forces were used to model the geogrids as explained in section 4.3.3.1. The calculation for the forces is shown in Appendix. 6.4 Data Analysis and Results The data was analyzed in the similar manner that has been discussed earlier in the Chapter 5. Using the concept of Local Factor of safety by Huang and Yamasaki (1990), principal stresses were analyzed for the calculation of FS. 6.4.1 Unreinforced Case From the analysis using SLOPE/W, Global FS for unreinforced case was 1.486 while from ANSYS, it was 1.283. Figure 6.7 shows the slip circle and FS obtained from SLOPE/W. Likewise, Figure 6.8 shows local FS according to the range and also, the location of the centroid for these ranges. By joining these ranges, a new slip surface was 101 defined. Using the Centroid Method for local FS obtained from ANSYS®, FS was found to be 0.555. Figure 6.7 Result from SLOPE/W showing critical slip surface and Global FS for unreinforced case 120 100 80 60 Height(m) 40 20 0 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 Horizontal Distance (m) 0.1-0.2 0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 0.8-0.9 0.9-1.0 1.0-1.1 1.1-1.2 1.2-1.3 1.3-1.4 1.4-1.5 1.5-2.0 >2 Slip Surface Centroids Expon. (Centroids) Figure 6.8 Result from ANSYS® showing location of centroids and Slip Surface from Centroid Method for Unreinforced case 102 6.4.2 Reinforced Case Similarly for the reinforced case, FS obtained was 1.76 from SLOPE/W and from ANSYS, it was 1.63. Figure 6.9 shows the critical slip circle and FS from SLOPE/W. Also, Figure 6.10 shows the local FS according to the range and centroids of these ranges. Slip Circle obtained from Centroid Method is also shown in Figure 6.10. Figure 6.9 Result from SLOPE/W showing critical slip surface and Global FS for Reinforced case 120 100 80 60 Height(m) 40 20 0 0 50 100 150 200 250 300 350 400 Horizontal Distance (m) 0.1-0.2 0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 0.8-0.9 0.9-1.0 1.0-1.1 1.1-1.2 1.2-1.3 1.3-1.4 1.4-1.5 1.5-2.0 >2 Slip Surface Series18 Poly. (Series18) Figure 6.10 Result from ANSYS® showing location of centroids and Slip Surface from Centroid Method for Reinforced case 103 6.5 Result Summary The summary of the result has been shown in Table 6.4. It can be seen that after the application of geogrids there is increment in the FS (Figure 6.11). Table 6.4 FS for the landfill with and without Geogrids Items Without Geogrids With Geogrids ANSYS 1.283 1.63 SLOPE/W 1.486 1.76 Centroid Method 0.555 0.507 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 ANSYS SLOPE/W Centroid Method Without Geogrids With Geogrids Figure 6.11 Comparison of results with and without Geogrids 104 Chapter 7: Conclusions and Recommendations 7.1 Conclusions As the generation of the MSW is increasing every year, there is a need to think about the management of landfill. This research work describes about one of the approach that can be used in the vertical expansion of the landfill. According to this research work, following conclusions can be made: 1. Use of geosynthetics is beneficial and provides stability to the slope. 2. It shows that after certain years of construction, there is possibility for the failure of the landfill. So, landfill should be designed considering the effect of biodegradation. 3. Geogrids can be effective in the worst case of wind loading. Also, it is very necessary to study these effects on landfill slopes and design accordingly. 7.2 Recommendations for Future Work After performing this analysis, following recommendations can be made. 1. There may be a better way to incorporate the geogrids in the FEM other than the methods that are used in this research. 2. A 3-D model can be built, by modeling the geogrids with their actual properties and dimensions, and examine the various slip surfaces and FS. 3. The effects due to rainfall which causes pore water pressure should be investigated in the regions like South Florida. 105 4. While analyzing the effects of wind load, it has been treated as uniformly distributed load, but this is not a real case scenario. There can be moments and torsion in different directions, which is possible to apply in FEM and do the analysis. 7.3 Final Remarks Effect of biodegradation and extreme wind loading on landfill was analyzed. It was found that biodegradation causes decrease in the FS of the landfill, which means after certain years of construction, there is possibility for the failure of the landfill. So, landfill should be designed considering the effect of biodegradation. Similarly, for extreme wind prone areas like South Florida, it was found that FS decreases significantly due to the effect of wind. Hence, it is very necessary to study these effects on landfill slopes. New method of analyzing the local factor of safety was introduced and new critical surface was defined by identifying cluster of nodal failure points based on Mohr-Coulomb Failure Criteria, but the result obtained from this method was not consistent. A case history of landfill was analyzed using SLOPE/W and ANSYS® by incorporating geogrids with frictional force and FS were found close to each other with these methods, although the actual FS was not provided in the case history. 106 Chapter 8: Appendices 8.1 Appendix A: Calculation of pullout resistance of reinforcement for SLOPE/W Geogrid No. Height σ'z Lf (Front pullout length) Pullout Resistance 1 3.05 413.32 1.22 339.11 2 6.1 412.15 2.42 671.53 3 9.15 410.98 3.59 991.18 4 12.2 409.81 4.70 1295.50 5 15.25 408.64 5.77 1585.65 6 18.3 407.47 6.81 1864.79 7 21.35 406.30 7.81 2131.42 8 24.4 405.13 8.75 2382.74 9 27.45 403.95 9.66 2621.63 10 30.5 402.78 10.52 2847.45 11 33.55 400.72 11.32 3048.44 12 36.6 398.66 12.09 3238.58 13 39.65 396.60 12.82 3417.53 14 42.7 394.54 13.47 3572.57 15 45.75 392.47 14.09 3717.27 16 48.8 390.41 14.67 3848.46 17 51.85 388.35 15.15 3953.40 18 54.9 386.29 15.62 4053.85 19 57.95 384.23 16.04 4141.25 20 61 382.17 16.39 4209.20 21 67.1 373.08 16.89 4234.22 22 73.2 363.99 17.16 4196.79 23 79.3 354.90 17.14 4088.86 24 85.4 345.81 16.85 3914.71 25 91.5 336.72 16.26 3679.25 26 97.6 269.38 15.30 2769.82 27 103.7 202.03 14.01 1901.60 28 109.8 134.69 12.33 1115.63 29 115.9 67.34 10.13 458.48 107 Geogrid No. X-outside Y-outside X-inside Y-inside 1067 0 1006 0 1 1063.95 3.05 1002.95 3.05 2 1060.9 6.1 999.9 6.1 3 1057.85 9.15 996.85 9.15 4 1054.8 12.2 993.8 12.2 5 1051.75 15.25 990.75 15.25 6 1048.7 18.3 987.7 18.3 7 1045.65 21.35 984.65 21.35 8 1042.6 24.4 981.6 24.4 9 1039.55 27.45 978.55 27.45 10 1036.5 30.5 975.5 30.5 11 1033.45 33.55 972.45 33.55 12 1030.4 36.6 969.4 36.6 13 1027.35 39.65 966.35 39.65 14 1024.3 42.7 963.3 42.7 15 1021.25 45.75 960.25 45.75 16 1018.2 48.8 957.2 48.8 17 1015.15 51.85 954.15 51.85 18 1012.1 54.9 951.1 54.9 19 1009.05 57.95 948.05 57.95 20 1006 61 945 61 21 999.9 67.1 938.9 67.1 22 993.8 73.2 932.8 73.2 23 987.7 79.3 926.7 79.3 24 981.6 85.4 920.6 85.4 25 975.5 91.5 914.5 91.5 26 969.4 97.6 908.4 97.6 27 963.3 103.7 902.3 103.7 28 957.2 109.8 896.2 109.8 29 951.1 115.9 890.1 115.9 945 122 884 122 108 Geogrid No. Height σ'z Lf (Front pullout length) Pullout Resistance 1 7.625 411.57 27.32 7556.00 2 15.25 408.64 40.21 11043.17 3 22.875 405.71 47.31 12899.28 4 30.5 402.78 51.10 13831.25 5 38.125 397.63 52.47 14019.70 6 45.75 392.47 52.21 13769.02 7 53.375 387.32 50.56 13160.86 8 61 382.17 47.88 12296.30 9 68.625 370.80 44.21 11017.22 10 76.25 359.44 39.76 9604.98 11 83.875 348.08 34.63 8101.26 12 91.5 336.72 28.92 6543.90 13 99.125 252.54 22.61 3837.38 14 106.75 168.36 15.82 1789.33 15 114.375 84.18 8.61 487.26 16 122 0.00 1.00 0.00 Geogrid No. X-outside Y-outside X-inside Y-inside 1067 0 1006 0 1 1051.75 7.625 990.75 7.625 2 1036.5 15.25 975.5 15.25 3 1021.25 22.875 960.25 22.875 4 1006 30.5 945 30.5 5 990.75 38.125 929.75 38.125 6 975.5 45.75 914.5 45.75 7 960.25 53.375 899.25 53.375 8 945 61 884 61 9 929.75 68.625 868.75 68.625 10 914.5 76.25 853.5 76.25 11 899.25 83.875 838.25 83.875 12 884 91.5 823 91.5 13 868.75 99.125 807.75 99.125 14 853.5 106.75 792.5 106.75 15 838.25 114.375 777.25 114.375 16 823 122 762 122 109 Geogrid No. Height σ'z Lf (Front pullout length) Pullout Resistance 1 10.17 410.59 27.32 7538.08 2 20.33 406.69 40.21 10990.42 3 30.50 402.78 47.31 12806.19 4 40.67 395.91 51.10 13595.24 5 50.83 389.04 52.47 13716.80 6 61.00 382.16 52.21 13407.35 7 71.17 367.02 50.56 12470.99 8 81.33 351.87 47.88 11321.49 9 91.50 336.72 44.21 10004.54 10 101.67 224.48 39.76 5998.53 11 111.83 112.24 34.63 2612.28 12 122.00 0.00 28.92 0.00 Geogrid No. X-outside Y-outside X-inside Y-inside 1067 0.00 884 0.00 1 1035 10.17 852 10.17 2 1003 20.33 820 20.33 3 971 30.50 788 30.50 4 939 40.67 756 40.67 5 907 50.83 724 50.83 6 875 61.00 692 61.00 7 843 71.17 660 71.17 8 811 81.33 628 81.33 9 779 91.50 596 91.50 10 747 101.67 564 101.67 11 715 111.83 532 111.83 12 683 122.00 500 122.00 110 Geogrid No. Height σ'z Lf (Front pullout length) Pullout Resistance 1 3.05 607.68 1.22 498.57 2 6.1 605.97 2.42 987.33 3 9.15 604.27 3.59 1457.33 4 12.2 602.56 4.70 1904.82 5 15.25 600.85 5.77 2331.50 6 18.3 599.14 6.81 2741.99 7 21.35 597.43 7.81 3134.12 8 24.4 595.73 8.75 3503.75 9 27.45 594.02 9.66 3855.12 10 30.5 592.31 10.52 4187.30 11 33.55 589.26 11.32 4482.72 12 36.6 586.21 12.09 4762.18 13 39.65 583.16 12.82 5025.16 14 42.7 580.11 13.47 5252.97 15 45.75 577.06 14.09 5465.55 16 48.8 574.01 14.67 5658.27 17 51.85 570.96 15.15 5812.37 18 54.9 567.91 15.62 5959.85 19 57.95 564.86 16.04 6088.14 20 61 561.81 16.39 6187.82 21 67.1 548.45 16.89 6224.63 22 73.2 535.09 17.16 6169.63 23 79.3 521.73 17.14 6011.01 24 85.4 508.37 16.85 5755.02 25 91.5 495.02 16.26 5408.89 26 97.6 396.01 15.30 4071.93 27 103.7 297.01 14.01 2795.56 28 109.8 198.01 12.33 1640.10 29 115.9 99.00 10.13 674.01 111 Geogrid No. X-outside Y-outside X-inside Y-inside 1067 0 1006 0 1 1063.95 3.05 1002.95 3.05 2 1060.9 6.1 999.9 6.1 3 1057.85 9.15 996.85 9.15 4 1054.8 12.2 993.8 12.2 5 1051.75 15.25 990.75 15.25 6 1048.7 18.3 987.7 18.3 7 1045.65 21.35 984.65 21.35 8 1042.6 24.4 981.6 24.4 9 1039.55 27.45 978.55 27.45 10 1036.5 30.5 975.5 30.5 11 1033.45 33.55 972.45 33.55 12 1030.4 36.6 969.4 36.6 13 1027.35 39.65 966.35 39.65 14 1024.3 42.7 963.3 42.7 15 1021.25 45.75 960.25 45.75 16 1018.2 48.8 957.2 48.8 17 1015.15 51.85 954.15 51.85 18 1012.1 54.9 951.1 54.9 19 1009.05 57.95 948.05 57.95 20 1006 61 945 61 21 999.9 67.1 938.9 67.1 22 993.8 73.2 932.8 73.2 23 987.7 79.3 926.7 79.3 24 981.6 85.4 920.6 85.4 25 975.5 91.5 914.5 91.5 26 969.4 97.6 908.4 97.6 27 963.3 103.7 902.3 103.7 28 957.2 109.8 896.2 109.8 29 951.1 115.9 890.1 115.9 945 122 884 122 112 Geogrid No. Height σ'z Lf (Front pullout length) Pullout Resistance 1 7.625 605.12 27.32 11109.46 2 15.25 600.85 40.21 16237.54 3 22.875 596.58 47.31 18967.82 4 30.5 592.31 51.10 20339.45 5 38.125 584.69 52.47 20615.00 6 45.75 577.06 52.21 20244.78 7 53.375 569.44 50.56 19349.03 8 61 561.81 47.88 18076.44 9 68.625 545.11 44.21 16196.20 10 76.25 528.41 39.76 14120.17 11 83.875 511.71 34.63 11909.65 12 91.5 495.02 28.92 9620.24 13 99.125 371.26 22.61 5641.36 14 106.75 247.51 15.82 2630.51 15 114.375 123.75 8.61 716.33 16 122 0.00 1.00 0.00 Geogrid No. X-outside Y-outside X-inside Y-inside 1067 0 1006 0 1 1051.75 7.625 990.75 7.625 2 1036.5 15.25 975.5 15.25 3 1021.25 22.875 960.25 22.875 4 1006 30.5 945 30.5 5 990.75 38.125 929.75 38.125 6 975.5 45.75 914.5 45.75 7 960.25 53.375 899.25 53.375 8 945 61 884 61 9 929.75 68.625 868.75 68.625 10 914.5 76.25 853.5 76.25 11 899.25 83.875 838.25 83.875 12 884 91.5 823 91.5 13 868.75 99.125 807.75 99.125 14 853.5 106.75 792.5 106.75 15 838.25 114.375 777.25 114.375 16 823 122 762 122 113 Geogrid No. Height σ'z Lf (Front pullout length) Pullout Resistance 1 10.17 603.70 27.32 11083.33 2 20.33 598.00 40.21 16160.61 3 30.50 592.31 47.31 18832.06 4 40.67 582.14 51.10 19990.34 5 50.83 571.98 52.47 20166.92 6 61.00 561.81 52.21 19709.77 7 71.17 539.54 50.56 18333.39 8 81.33 517.28 47.88 16643.67 9 91.50 495.01 44.21 14707.76 10 101.67 330.01 39.76 8818.49 11 111.83 165.00 34.63 3840.33 12 122.00 0.00 28.92 0.00 Geogrid No. X-outside Y-outside X-inside Y-inside 1067 0.00 884 0.00 1 1035 10.17 852 10.17 2 1003 20.33 820 20.33 3 971 30.50 788 30.50 4 939 40.67 756 40.67 5 907 50.83 724 50.83 6 875 61.00 692 61.00 7 843 71.17 660 71.17 8 811 81.33 628 81.33 9 779 91.50 596 91.50 10 747 101.67 564 101.67 11 715 111.83 532 111.83 12 683 122.00 500 122.00 114 8.2 Appendix B: Results from SLOPE/W Figure B. 1 FS and Critical Slip surface for unreinforced slope 1:2 without biodegradation Figure B. 2 FS and Critical Slip surface for unreinforced slope 1:2 with biodegradation Figure B. 3 FS and Critical Slip surface for reinforced slope 1:2 without biodegradation 115 Figure B. 4 FS and Critical Slip surface for reinforced slope 1:2 with biodegradation Figure B. 5 FS and Critical Slip surface for unreinforced slope 1:3 without biodegradation Figure B. 6 FS and Critical Slip surface for unreinforced slope 1:3 with biodegradation 116 Figure B. 7 FS and Critical Slip surface for reinforced slope 1:3 without biodegradation Figure B. 8 FS and Critical Slip surface for reinforced slope 1:3 with biodegradation 117 8.3 Appendix C: Sample Calculation of Geogrid forces For first layer of slope 1:1 Internal friction angle(rad) δ 0.372279 tanδ 0.390487 Cohesion 11.5 kN/m2 Geogrid width per m 0.1336 Geogrids nos 1 20 Height 3.05 m Length Average stress Geogrid force Force/2 Point Applied Force (kN) 0 to 3.05 20.72475 15.9673 7.983652 1 7.983652 3.05 to 6.1 62.17425 29.15783 14.57892 2 22.56257 118 6.1 to 9.15 103.6238 42.34836 21.17418 3 35.7531 9.15 to 12.2 145.0733 55.53889 27.76944 4 48.94363 12.2 to 15.25 186.5228 68.72942 34.36471 5 62.13415 15.25 to 18.3 227.9723 81.91995 40.95997 6 75.32468 18.3 to 21.35 269.4218 95.11047 47.55524 7 88.51521 21.35 to 24.4 310.8713 108.301 54.1505 8 101.7057 24.4 to 27.45 352.3208 121.4915 60.74577 9 114.8963 27.45 to 30.5 393.1908 134.4976 67.24882 10 127.9946 30.5 to 33.55 433.4813 147.3193 73.65967 11 140.9085 33.55 to 36.6 473.7718 160.141 80.07052 12 153.7302 36.6 to 39.65 514.0623 172.9627 86.48137 13 166.5519 39.65 to 42.7 554.3528 185.7844 92.89222 14 179.3736 42.7 to 45.75 594.6433 198.6061 99.30307 15 192.1953 45.75 to 48.8 634.9338 211.4278 105.7139 16 205.017 48.8 to 51.85 675.2243 224.2495 112.1248 17 217.8387 51.85 to 54.9 715.5148 237.0712 118.5356 18 230.6604 54.9 to 57.95 755.8053 249.8929 124.9465 19 243.4821 57.95 to 61 795.0588 262.3846 131.1923 20 256.1388 For second layer of slope 1:1 Internal friction angle(rad) δ 0.372279 tanδ 0.390487 Cohesion 11.5 kN/m2 Geogrid width per m 0.1336 Geogrids nos 1 20 Height 3.05 m 119 Length Average stress Geogrid force Force/2 Point Applied Force (kN) 0 to 3.05 20.72475 15.9673 7.983652 1 7.983652 3.05 to 6.1 62.17425 29.15783 14.57892 2 22.56257 6.1 to 9.15 103.6238 42.34836 21.17418 3 35.7531 9.15 to 12.2 145.0733 55.53889 27.76944 4 48.94363 12.2 to 15.25 186.5228 68.72942 34.36471 5 62.13415 15.25 to 18.3 227.9723 81.91995 40.95997 6 75.32468 18.3 to 21.35 269.4218 95.11047 47.55524 7 88.51521 21.35 to 24.4 310.8713 108.301 54.1505 8 101.7057 24.4 to 27.45 351.7413 121.3071 60.65356 9 114.8041 27.45 to 30.5 392.0318 134.1288 67.06441 10 127.718 30.5 to 33.55 432.3223 146.9505 73.47526 11 140.5397 33.55 to 36.6 472.6128 159.7722 79.88611 12 153.3614 36.6 to 39.65 512.9033 172.5939 86.29695 13 166.1831 39.65 to 42.7 553.1938 185.4156 92.7078 14 179.0048 42.7 to 45.75 593.4843 198.2373 99.11865 15 191.8265 45.75 to 48.8 633.7748 211.059 105.5295 16 204.6482 48.8 to 51.85 674.0653 223.8807 111.9404 17 217.4699 51.85 to 54.9 714.3558 236.7024 118.3512 18 230.2916 54.9 to 57.95 753.6093 249.1941 124.597 19 242.9482 57.95 to 61 791.8258 261.3558 130.6779 20 255.2749 120 8.4 Appendix D: Sample Calculation in ANSYS Internal friction tanδ 0.625 angle(rad) δ Cohesion 11.5 kN/m2 x y S1 S2 S3 SEQV r 휎̅ A B cosθ θ In degrees FS 0.00 0.00 137.86 0.22 -4.52 140.18 2.37 -2.15 12.85 1.48 0.12 1.46 83.38 5.39 1.53 1.53 160.23 0.22 -29.68 178.90 14.95 -14.73 20.71 9.34 0.45 1.10 63.18 1.24 4.58 1.53 213.01 0.00 -29.01 230.31 14.50 -14.50 20.56 9.06 0.44 1.11 63.85 1.27 9.15 6.10 196.81 0.00 -58.05 231.36 29.03 -29.03 29.64 18.14 0.61 0.91 52.26 0.81 13.7 29.70 -29.70 30.06 18.56 0.62 0.91 51.87 0.80 3 7.63 204.66 0.00 -59.39 239.94 16.7 51.21 -51.21 43.50 32.00 0.74 0.74 42.64 0.58 8 10.68 187.29 0.00 -102.41 256.65 121 21.3 75.94 -75.94 58.96 47.46 0.80 0.64 36.39 0.46 5 12.20 139.76 0.00 -151.87 252.65 35.0 75.18 -75.18 58.48 46.98 0.80 0.64 36.55 0.46 8 22.88 119.66 0.00 -150.35 234.34 39.6 80.50 -80.50 61.81 50.31 0.81 0.62 35.52 0.45 5 27.45 89.86 0.00 -160.99 220.76 44.2 105.15 -105.15 77.22 65.72 0.85 0.55 31.67 0.39 3 32.03 54.25 0.00 -210.30 242.65 48.8 108.23 -108.23 79.14 67.64 0.85 0.55 31.27 0.38 0 33.55 45.83 0.00 -216.46 243.14 51.8 112.69 -112.69 81.93 70.43 0.86 0.54 30.72 0.37 5 36.60 30.17 0.00 -225.39 242.01 56.4 115.61 -115.61 83.76 72.26 0.86 0.53 30.38 0.37 3 41.18 12.70 0.00 -231.22 238.02 61.0 126.14 -147.70 103.81 78.84 0.76 0.71 40.58 0.54 0 45.75 0.00 -21.55 -273.84 263.73 70.1 134.83 -139.23 98.52 84.27 0.86 0.54 31.21 0.38 5 51.85 1.87 -4.41 -274.06 272.85 65.5 100.61 -135.81 96.38 62.88 0.65 0.86 49.28 0.73 8 47.28 0.00 -35.20 -236.42 220.97 Internal friction tanδ 0.625 angle(rad) δ Cohesion 11.5 kN/m2 x y S1 S2 S3 SEQV r 휎̅ A B cosθ θ In degrees FS 73.2 108.95 -159.41 111.13 68.09 0.61 0.91 52.21 0.81 0 57.95 0.00 -50.46 -268.36 247.10 77.7 100.45 -166.36 115.47 62.78 0.54 1.00 57.06 0.96 8 59.48 0.00 -65.91 -266.81 240.72 82.3 85.79 -144.59 101.87 53.62 0.53 1.02 58.24 1.01 5 64.05 0.00 -58.80 -230.39 207.36 86.9 81.37 -142.35 100.47 50.86 0.51 1.04 59.59 1.06 3 71.68 0.00 -60.98 -223.73 200.35 91.5 77.55 -139.90 98.93 48.47 0.49 1.06 60.67 1.11 0 76.25 0.00 -62.35 -217.45 193.95 96.0 71.17 -138.32 97.95 44.48 0.45 1.10 62.99 1.23 8 80.83 0.00 -67.16 -209.49 185.33 122 100. 58.03 -138.91 98.32 36.27 0.37 1.19 68.35 1.57 65 85.40 0.00 -80.88 -196.95 171.55 105. 62.28 -102.43 75.52 38.92 0.52 1.03 58.98 1.04 23 89.98 0.00 -40.16 -164.71 148.76 109. 56.96 -95.02 70.89 35.60 0.50 1.04 59.85 1.08 80 97.60 0.00 -38.06 -151.98 136.98 114. 45.05 -77.41 59.88 28.16 0.47 1.08 61.95 1.17 38 102.18 0.00 -32.36 -122.46 110.05 115. 19.11 -47.96 41.47 11.95 0.29 1.28 73.26 2.08 90 106.75 0.00 -28.84 -67.07 58.27 122. 20.47 -31.42 31.14 12.79 0.41 1.15 65.74 1.39 00 115.90 0.00 -10.95 -51.90 48.54 126. 19.67 -32.85 32.03 12.29 0.38 1.18 67.43 1.50 58 120.48 -13.18 -52.51 0.00 51.50 1.06 8.5 Appendix E: Calculation for Rule of Mixtures Without Biodegradation Young's Modulus of Elasticity S.No. Vol of fiber Vol of soil Vol ratio of fiber Vol ratio of soil E for fiber E for soil E for composite 1 0.061 60.939 0.001 0.999 1.035E+12 9914720 9820736921 2 0.061 60.939 0.001 0.999 1.035E+12 9914720 9820736921 3 0.061 60.939 0.001 0.999 1.035E+12 9914720 9820736921 4 0.061 60.939 0.001 0.999 1.035E+12 9914720 9820736921 5 0.061 60.939 0.001 0.999 1.035E+12 9914720 9820736921 6 0.061 60.939 0.001 0.999 1.035E+12 9914720 9820736921 7 0.061 60.939 0.001 0.999 1.035E+12 9914720 9820736921 123 8 0.061 60.939 0.001 0.999 1.035E+12 9914720 9820736921 9 0.061 60.939 0.001 0.999 1.035E+12 9914720 9820736921 10 0.061 60.939 0.001 0.999 1.035E+12 9914720 9820736921 11 0.061 60.939 0.001 0.999 1.035E+12 6883900 6838462112 12 0.061 60.939 0.001 0.999 1.035E+12 6883900 6838462112 13 0.061 60.939 0.001 0.999 1.035E+12 6883900 6838462112 14 0.061 60.939 0.001 0.999 1.035E+12 6883900 6838462112 15 0.061 60.939 0.001 0.999 1.035E+12 6883900 6838462112 16 0.061 60.939 0.001 0.999 1.035E+12 6883900 6838462112 17 0.061 60.939 0.001 0.999 1.035E+12 6883900 6838462112 18 0.061 60.939 0.001 0.999 1.035E+12 6883900 6838462112 19 0.061 60.939 0.001 0.999 1.035E+12 6883900 6838462112 20 0.061 60.939 0.001 0.999 1.035E+12 6883900 6838462112 21 0.061 60.939 0.001 0.999 1.035E+12 3917740 3902980991 Young's Modulus of Elasticity S.No. Vol of fiber Vol of soil Vol ratio of fiber Vol ratio of soil E for fiber E for soil E for composite 22 0.061 60.939 0.001 0.999 1.035E+12 3917740 3902980991 23 0.061 60.939 0.001 0.999 1.035E+12 3917740 3902980991 24 0.061 60.939 0.001 0.999 1.035E+12 3917740 3902980991 25 0.061 60.939 0.001 0.999 1.035E+12 3917740 3902980991 26 0.061 60.939 0.001 0.999 1.035E+12 1150620 1149343541 27 0.061 60.939 0.001 0.999 1.035E+12 1150620 1149343541 28 0.061 60.939 0.001 0.999 1.035E+12 1150620 1149343541 29 0.061 60.939 0.001 0.999 1.035E+12 1150620 1149343541 After Biodegradation 124 S.No. Vol of fiber Vol of soil Vol ratio of fiber Vol ratio of soil E for fiber E for soil E for composite 1 0.061 60.939 0.001 0.999 1.035E+12 14574640 14372452705 2 0.061 60.939 0.001 0.999 1.035E+12 14574640 14372452705 3 0.061 60.939 0.001 0.999 1.035E+12 14574640 14372452705 4 0.061 60.939 0.001 0.999 1.035E+12 14574640 14372452705 5 0.061 60.939 0.001 0.999 1.035E+12 14574640 14372452705 6 0.061 60.939 0.001 0.999 1.035E+12 14574640 14372452705 7 0.061 60.939 0.001 0.999 1.035E+12 14574640 14372452705 8 0.061 60.939 0.001 0.999 1.035E+12 14574640 14372452705 9 0.061 60.939 0.001 0.999 1.035E+12 14574640 14372452705 10 0.061 60.939 0.001 0.999 1.035E+12 14574640 14372452705 11 0.061 60.939 0.001 0.999 1.035E+12 10119360 10021476409 12 0.061 60.939 0.001 0.999 1.035E+12 10119360 10021476409 S.No. Vol of fiber Vol of soil Vol ratio of fiber Vol ratio of soil E for fiber E for soil E for composite 13 0.061 60.939 0.001 0.999 1.035E+12 10119360 10021476409 14 0.061 60.939 0.001 0.999 1.035E+12 10119360 10021476409 15 0.061 60.939 0.001 0.999 1.035E+12 10119360 10021476409 16 0.061 60.939 0.001 0.999 1.035E+12 10119360 10021476409 17 0.061 60.939 0.001 0.999 1.035E+12 10119360 10021476409 18 0.061 60.939 0.001 0.999 1.035E+12 10119360 10021476409 19 0.061 60.939 0.001 0.999 1.035E+12 10119360 10021476409 20 0.061 60.939 0.001 0.999 1.035E+12 10119360 10021476409 21 0.061 60.939 0.001 0.999 1.035E+12 5759073 5727236681 22 0.061 60.939 0.001 0.999 1.035E+12 5759073 5727236681 23 0.061 60.939 0.001 0.999 1.035E+12 5759073 5727236681 1 24 0.061 60.939 0.001 0.999 1.035E+12 5759073 5727236681 25 25 0.061 60.939 0.001 0.999 1.035E+12 5759073 5727236681 26 0.061 60.939 0.001 0.999 1.035E+12 1691411 1688654138 27 0.061 60.939 0.001 0.999 1.035E+12 1691411 1688654138 28 0.061 60.939 0.001 0.999 1.035E+12 1691411 1688654138 29 0.061 60.939 0.001 0.999 1.035E+12 1691411 1688654138 Slope 1:3 without biodegradation and without geogrids 140 120 100 80 60 Height(m) 40 20 0 0 50 100 150 200 250 300 350 400 450 -20 Horizontal Distance (m) Slip surface 0.9-1.0 1.0-1.1 1.1-1.2 1.2-1.3 1.3-1.4 1.4-1.5 1.5-2.0 >2 Slope 1:3 without biodegradation and with geogrids 140 120 100 80 60 Height(m) 40 20 0 0 50 100 150 200 250 300 350 400 450 -20 Horizontal Distance (m) Slip surface 1.0-1.1 1.1-1.2 1.2-1.3 1.3-1.4 1.4-1.5 1.5-2.0 >2 126 Slope 1:3 with biodegradation and without geogrids 140 120 100 80 60 Height(m) 40 20 0 0 50 100 150 200 250 300 350 400 450 -20 Horizontal Distance (m) Slip surface 0.8-0.9 0.9-1.0 1.0-1.1 1.1-1.2 1.2-1.3 1.3-1.4 1.4-1.5 1.5-2.0 >2 Slope 1:3 with biodegradation and with geogrids 140 120 100 80 60 Height(m) 40 20 0 0 50 100 150 200 250 300 350 400 450 -20 Horizontal Distance (m) Slip surface 0.8-0.9 0.9-1.0 1.0-1.1 1.1-1.2 1.2-1.3 1.3-1.4 1.4-1.5 1.5-2.0 >2 127 Chapter 9: References Alexiew, D., Plankel, A., Widerin, M., & Jaramillo, J. (2015). A landfill with innovative reinforcing solutions: history, experience, solution flexibility. Bareither, C. A., Benson, C. H., & Edil, T. B. (2012). Effects of waste composition and decomposition on the shear strength of municipal solid waste. Journal of Geotechnical and Geoenvironmental Engineering, 138(10), 1161-1174. Bathurst, R. J. (1995). Uplift of geomembranes by wind. Blight, G. (2008). Slope failures in municipal solid waste dumps and landfills: a review. Waste Management & Research, 26(5), 448-463. Cheng, Y. M., & Lau, C. K. (2014). Slope stability analysis and stabilization: new methods and insight. CRC Press. Chowdhury, R. N. (1978). Slope analysis developments in geotechnical engineering 22. Duncan, J. M. (1996). State of the art: limit equilibrium and finite-element analysis of slopes. Journal of Geotechnical engineering, 122(7), 577-596. Eid, H. T., Stark, T. D., Evans, W. D., & Sherry, P. E. (2000). Municipal solid waste slope failure. I: Waste and foundation soil properties. Journal of Geotechnical and Geoenvironmental Engineering, 126(5), 397-407. Fei, X., & Zekkos, D. (2008). Large-size controlled degradation and simple shear testing of municipal solid waste from Michigan. Proceedings of the Institution of Civil Engineers, 161(3), 105-111. Hafeez, G., El Ansary, A. M., & El Damatty, A. A. (2011). Effect of wind loads on the stability of conical tanks. Canadian Journal of Civil Engineering,38(4), 444-454. Han, J. (2015). Principles and Practice of Ground Improvement. John Wiley & Sons. Hettiarachchi, C.H., 2005. Mechanics of Biocell Landfill Settlements, PhD Dissertation, Department of Civil & Environmental Engineering. New Jersey Institute of Technology, Newark NJ. Hossain, M. S., & Haque, M. A. (2009). Stability analyses of municipal solid waste landfills with decomposition. Geotechnical and Geological Engineering, 27(6), 659-666. Huang, S. L., & Yamasaki, K. (1993). Slope failure analysis using local minimum factor- of-safety approach. Journal of geotechnical engineering,119(12), 1974-1989. 128 Ikhwan, M., & Ruck, B. (2004). Wind Load Coefficients for Pyramidal Buildings. Fachtagung “Lasermethoden in der Strömungsmesstechnik”, German. Jewell, R. A. (1991). Application of revised design charts for steep reinforced slopes. Geotextiles and Geomembranes, 10(3), 203-233. Jones, D. R. V., Taylor, D., & Dixon, N. E. I. L. (1997). Shear strength of waste and its use in landfill stability analysis. In Proceedings Geoenvironmental Engineering Conference. Thomas Telford (pp. 343-350). Koerner, R. M. (2012). Designing with geosynthetics (Vol. 1). Xlibris Corporation. Koerner, R. M., & Soong, T. Y. (2000). Stability assessment of ten large landfill failures. GEOTECH SPEC PUBL, (103), 1-38. Kourdey, A., AIheib, M., Piguet, J. P., & Korini, T. (2001). Evaluation of slope stability by numerical methods. S. arkk. a, Eloranta, editors. Rock mechanics—a challenge for society. Swetz and Zeitlinger Lisse, ISBN,90(2651), 821. Lambe, T. W., & Whitman, R. V. (2008). Soil mechanics SI version. John Wiley & Sons. Mohammed, A. G., & Stephen, N. V. (1995). Geotechnical properties of municipal solid waste. Landva, A. O., & Clark, J. I. (1990). Geotechnics of waste fill. In Geotechnics of waste fills—Theory and practice. ASTM International. Mendis, P., Ngo, T., Haritos, N., Hira, A., Samali, B., & Cheung, J. (2007). Wind loading on tall buildings. EJSE Special Issue: Loading on Structures,3, 41-54. Park, H. I., Lee, S. R., & Do, N. Y. (2002). Evaluation of decomposition effect on long- term settlement prediction for fresh municipal solid waste landfills. Journal of Geotechnical and Geoenvironmental Engineering, 128(2), 107-118. Reddy, D. V., Navarrete, F., Rosay, C., Cira, A., Ashmawy, A. K., & Gunaratne, M. (2003). Long-Term Behavior Of Geosynthetic Reinforced Mechanically Stabilized Earth (MSE) Wall System-Numerical/Analytical Studies, Full Scale Field Testing, and Design Software Development (No. Final Report). Reddy, K. R., Hettiarachchi, H., Gangathulasi, J., & Bogner, J. E. (2011). Geotechnical properties of municipal solid waste at different phases of biodegradation. Waste Management, 31(11), 2275-2286. Reddy, K. R., Hettiarachchi, H., Giri, R. K., & Gangathulasi, J. (2015). Effects of Degradation on Geotechnical Properties of Municipal Solid Waste from Orchard Hills Landfill, USA. International Journal of Geosynthetics and Ground Engineering, 1(3), 1-14. Reddy, K. R., Hettiarachchi, H., Parakalla, N. S., Gangathulasi, J., & Bogner, J. E. (2009). Geotechnical properties of fresh municipal solid waste at Orchard Hills Landfill, USA. Waste Management, 29(2), 952-959. 129 Seed, R. B., Mitchell, J. K., & Seed, H. B. (1990). Kettleman hills waste landfill slope failure. II: stability analyses. Journal of Geotechnical Engineering, 116(4), 669- 690. Sharma, H. D., & De, A. (2007). Municipal solid waste landfill settlement: Postclosure perspectives. Journal of geotechnical and geoenvironmental engineering, 133(6), 619-629. Singh, S., & Murphy, B. J. (1990). Evaluation of the stability of sanitary landfills. In Geotechnics of Waste Fills—Theory and Practice. ASTM International. Sobhan, K., & Das, B M. (2011). Slope Stability. Geotechnical Engineering Handbook. Tatiannikov, D. A., & Kleveko, V. I. (2015). Investigation of the interaction of geosynthetics with ground on the example of shear test and pull-out test.Geosynthetics International, 22(3), 249-256. Templeton, R. H. (2007). Innovative Expansion of Landfill Capacity Using Geogrid Reinforcements. M.Sc. Thesis, Department of Civil Engineering, Florida Atlantic University, Boca Raton, FL. Tieman, G. E., Druback, G. W., Davis, K. A., & Weidner, C. H. (1990). Stability consideration of vertical landfill expansions. In Geotechnics of Waste Fills— Theory and Practice. ASTM International. U.S. EPA (U.S. Environmental Protection Agency). 2015a. Advancing sustainable materials management: Facts and figures report. Accessed May 2016. http://www.epa.gov/smm/advancing-sustainable-materials-management-facts- and-figures-report U.S. EPA (U.S. Environmental Protection Agency). 2000. Landfill Manuals. Accessed May 2016. https://www.epa.ie/pubs/advice/waste/waste/EPA_landfill_site_design_guide.pdf Wall, D. K., & Zeiss, C. (1995). Municipal landfill biodegradation and settlement. Journal of Environmental Engineering, 121(3), 214-224. Wei, J., Chua, K. C., Lim, S. K., Chew, S. H., Karunaratne, G. P., Tan, S. A., & Seah, Y. T. (2002). Performance of a geosynthetics reinforced steep slope in residual soil. Proceedings of the 7th ICG, Nice, France, Swets & Zeitlinger, Lisse, the Netherlands, 325-328. Wilson-Fahmy, R. F., & Koerner, R. M. (1993). Finite element modelling of soil-geogrid interaction with application to the behavior of geogrids in a pullout loading condition. Geotextiles and geomembranes, 12(5), 479-501. World Resources Institute. 2014. Sea-Level Rise and its impact on Miami-Dade County. Accessed May 2016. http://www.wri.org/sites/default/files/sealevelrise_miami_florida_factsheet_final. pdf 130 Wulandari, P. S., & Tjandra, D. (2006, August). Determination of optimum tensile strength of geogrid reinforced embankment. In International Civil Engineering Conference towards Sustainable Civil Engineering Practice (pp. 187-194). Zekkos, D., Bray, J. D., Kavazanjian Jr, E., Matasovic, N., Rathje, E. M., Riemer, M. F., & Stokoe, K. H. (2006). Unit weight of municipal solid waste.Journal of Geotechnical and Geoenvironmental Engineering, 132(10), 1250-1261. https://www.climaterealityproject.org/blog/how-climate-change-affecting-florida 131