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Performance of Back-to-Back Mechanically Stabilized Earth Walls Supporting the Rail Embankments

Study Memory To Performance of Back-to-Back Mechanically Stabilized Earth Walls Supporting the Rail Embankments This thesis is focused on the utilization of geosynthetic reinforcement in cascade walls and aims to analyze the factors contributing to a conservative study. The primary objective is to enhance the understanding of geogrid-reinforced soil walls by numerically evaluating tensile loads in geogrids, lateral earth pressures, and coping lateral displacements. To achieve a comprehensive understanding, various geometric and mechanical properties under rail conditioning were investigated and integrated into numerical modeling using Plaxis 2D software .

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‫الشعبية‬ ‫الديمقراطية‬ ‫الجزائرية‬ ‫الجمهورية‬
People's Democratic Republic of Algeria
‫العلمي‬ ‫والبحث‬ ‫العالي‬ ‫التعليم‬ ‫وزارة‬
Ministry of Higher Education and Scientific Research
Mohamed Khider University - Biskra ‫بــــسكرة‬ ‫خـيـضر‬ ‫محمد‬ ‫جـــامعة‬
Faculty of Science and Technology ‫التكــــنولوجــيا‬ ‫و‬ ‫الـعـلـــوم‬ ‫كــلية‬
Department: Civil and Hydraulic Engineering : ‫قـسـم‬
‫الــري‬ ‫و‬ ‫المـدنيـة‬ ‫الهنـدسـة‬
Ref: ………………………………… ‫المـرجع‬ : ............................
MASTER THESIS
Field: PUBLIC WORKS
Specialty: Roads and Works of Art
Theme
Performance of Back-to-Back Mechanically Stabilized
Earth Walls Supporting the Rail Embankments
Presented by: Supervisor:
MESAI AOUN Ahmed
ZEGHDI Ahmed Larouci
Dr. DRAM Abdelkader
Academic Year: 2022-2023.
ACKNOWLEDGEMENTS
First and foremost, I would like to express my gratitude
and praise to Almighty Allah for granting me the strength and
time to successfully complete this research. I am truly
thankful for the blessings and guidance I have received
throughout this journey.
I would also like to extend my sincere appreciation to Dr.
Abdelkader DRAM from the University of Biskra, who served as
my supervisor and thesis director. His scientific supervision,
guidance, and support were invaluable. Dr. DRAM's profound
knowledge and expertise played a crucial role in directing me
during my master's thesis and this research. I am grateful for
his availability, experience, and thoroughness, which
contributed to the success of this thesis. It has been an honor
to work under his guidance.
Furthermore, I would like to express my deepest gratitude
to my father, mother, brother, and sisters for their unwavering
support, encouragement, and love. Their constant presence and
belief in me have been instrumental in my accomplishments.
Without their support, none of this would have been possible.
Abstract
This thesis is focused on the utilization of geosynthetic reinforcement in cascade
walls and aims to analyze the factors contributing to a conservative study. The
primary objective is to enhance the understanding of geogrid-reinforced soil walls
by numerically evaluating tensile loads in geogrids, lateral earth pressures, and
coping lateral displacements. To achieve a comprehensive understanding, various
geometric and mechanical properties under rail conditioning were investigated and
integrated into numerical modeling using Plaxis 2D software.
Keywords: Retaining walls, Geosynthetics, Reinforced soil, Numerical Modelling.
Rail
‫ملخص‬
‫تحليل‬ ‫إلى‬ ‫وتهدف‬ ‫المتتالية‬ ‫الجدران‬ ‫في‬ ‫الجيولوجي‬ ‫التمثيل‬ ‫تقوية‬ ‫استخدام‬ ‫على‬ ‫األطروحة‬ ‫هذه‬ ‫تركز‬
‫دراسة‬ ‫في‬ ‫تساهم‬ ‫التي‬ ‫العوامل‬
‫المعززة‬ ‫التربة‬ ‫جدران‬ ‫فهم‬ ‫تعزيز‬ ‫هو‬ ‫الرئيسي‬ ‫الهدف‬ .‫محافظة‬ geogrid
‫الجيوجريدات‬ ‫في‬ ‫الشد‬ ‫ألحمال‬ ‫العددي‬ ‫التقييم‬ ‫خالل‬ ‫من‬
.‫الجانبي‬ ‫والتشرد‬ ،‫الجانبي‬ ‫األرضي‬ ‫والضغط‬ ،
‫العددية‬ ‫النمذجة‬ ‫في‬ ‫ودمجها‬ ‫المختلفة‬ ‫والميكانيكية‬ ‫الهندسية‬ ‫الخصائص‬ ‫فحص‬ ‫تم‬ ،‫شامل‬ ‫فهم‬ ‫لتحقيق‬
.Plaxis 2D ‫برنامج‬ ‫باستخدام‬
.‫االستناد‬ ‫جدران‬ ،‫مدعمة‬ ‫تربة‬ ،‫جوستتيك‬ ،‫الرقمية‬ ‫النمذجة‬ :‫مفتاحية‬ ‫كلمات‬
CONTENTS
LIST OF ABBREVIATIONS
LIST OF FIGURES
LIST OF TABLES
General introduction………………………………………………………..……………………...1
Thesis organization……………………………………………………..………………………….2
First Part: Literature Review
Chapter 1
Generalities about Reinforced Soil Retaining Walls
1.1. Introduction …………………………………………………………………….…… 4
1.2. Types of reinforced embankment structures... ……………………………………... 4
1.2.1. Mechanically Stabilized Earth Walls ………………………………………...…… 5
1.2.2. Sheet pile walls ……………………………………………………………….……6
1.2.3. Geocell Walls ………………………………………………………………………6
1.2.4. Soil Nailing ………………………………………………………………………. 7
1.2.5. Anchored Walls …………………………………………………………………... 7
1.2.6. Hybrid Walls ……………………………………………………………………... 8
1.2.7. Gabion Walls ……………………………………………………………………... 8
1.3 Elements of retaining structures in reinforced soil ………………………………... 9
1.3.1. Panels ………………………………………………………………………………9
1.3.2. Reinforcements ……………………………………………………………...…...14
1.3.2.1. Metalic …………………………………………………………………...……. 14
1.3.2.1. Geosynthetic …………………………………………………………………... 15
1.4. Implementation of Reinforced Earth …………………………………………….... 17
1.4.1. Excavation ………………………………………………………………………. 17
1.4.2. Mounting the facing panels …………………………………………………....... 18
1.4.3. Installation of the reinforcement …………………………………………………19
1.4.4. Backfilling and compacting …………………………………………………...…19
1.5. Application of soil reinforced structures …………………………………………..20
1.5.1. Retaining walls …………………………………………………………………..20
1.5.2. Slope stabilization ……………………………………………………………….21
1.5.3. Bridge abutments ………………………………………………………...……...22
1.5.4. Embankment reinforcement ………………………………………………..…....22
1.5.5. Underground structures ………………………………………………………….21
1.6. Advantages and Limitations ……………………………………………………....22
1.7. Summary ………………………………………………………………………….22
Chapter 2
Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls
2.1. Introduction…………………………………………………………………………………..23
2.2. Analysis of single-reinforced retaining walls………………………………………………...23
2.2.1 Experimental Studies………………………………………………………………………………..23
2.2.1.1 Shaking Table Tests……………………………………………………………………………….23
2.2.1.2 Dynamic Centrifuge Tests………………………………………………………………...27
2.2.2 Numerical Studies……………………………………………………………………………………29

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Performance of Back-to-Back Mechanically Stabilized Earth Walls Supporting the Rail Embankments

  • 1. ‫الشعبية‬ ‫الديمقراطية‬ ‫الجزائرية‬ ‫الجمهورية‬ People's Democratic Republic of Algeria ‫العلمي‬ ‫والبحث‬ ‫العالي‬ ‫التعليم‬ ‫وزارة‬ Ministry of Higher Education and Scientific Research Mohamed Khider University - Biskra ‫بــــسكرة‬ ‫خـيـضر‬ ‫محمد‬ ‫جـــامعة‬ Faculty of Science and Technology ‫التكــــنولوجــيا‬ ‫و‬ ‫الـعـلـــوم‬ ‫كــلية‬ Department: Civil and Hydraulic Engineering : ‫قـسـم‬ ‫الــري‬ ‫و‬ ‫المـدنيـة‬ ‫الهنـدسـة‬ Ref: ………………………………… ‫المـرجع‬ : ............................ MASTER THESIS Field: PUBLIC WORKS Specialty: Roads and Works of Art Theme Performance of Back-to-Back Mechanically Stabilized Earth Walls Supporting the Rail Embankments Presented by: Supervisor: MESAI AOUN Ahmed ZEGHDI Ahmed Larouci Dr. DRAM Abdelkader Academic Year: 2022-2023.
  • 2. ACKNOWLEDGEMENTS First and foremost, I would like to express my gratitude and praise to Almighty Allah for granting me the strength and time to successfully complete this research. I am truly thankful for the blessings and guidance I have received throughout this journey. I would also like to extend my sincere appreciation to Dr. Abdelkader DRAM from the University of Biskra, who served as my supervisor and thesis director. His scientific supervision, guidance, and support were invaluable. Dr. DRAM's profound knowledge and expertise played a crucial role in directing me during my master's thesis and this research. I am grateful for his availability, experience, and thoroughness, which contributed to the success of this thesis. It has been an honor to work under his guidance. Furthermore, I would like to express my deepest gratitude to my father, mother, brother, and sisters for their unwavering support, encouragement, and love. Their constant presence and belief in me have been instrumental in my accomplishments. Without their support, none of this would have been possible.
  • 3. Abstract This thesis is focused on the utilization of geosynthetic reinforcement in cascade walls and aims to analyze the factors contributing to a conservative study. The primary objective is to enhance the understanding of geogrid-reinforced soil walls by numerically evaluating tensile loads in geogrids, lateral earth pressures, and coping lateral displacements. To achieve a comprehensive understanding, various geometric and mechanical properties under rail conditioning were investigated and integrated into numerical modeling using Plaxis 2D software. Keywords: Retaining walls, Geosynthetics, Reinforced soil, Numerical Modelling. Rail
  • 4. ‫ملخص‬ ‫تحليل‬ ‫إلى‬ ‫وتهدف‬ ‫المتتالية‬ ‫الجدران‬ ‫في‬ ‫الجيولوجي‬ ‫التمثيل‬ ‫تقوية‬ ‫استخدام‬ ‫على‬ ‫األطروحة‬ ‫هذه‬ ‫تركز‬ ‫دراسة‬ ‫في‬ ‫تساهم‬ ‫التي‬ ‫العوامل‬ ‫المعززة‬ ‫التربة‬ ‫جدران‬ ‫فهم‬ ‫تعزيز‬ ‫هو‬ ‫الرئيسي‬ ‫الهدف‬ .‫محافظة‬ geogrid ‫الجيوجريدات‬ ‫في‬ ‫الشد‬ ‫ألحمال‬ ‫العددي‬ ‫التقييم‬ ‫خالل‬ ‫من‬ .‫الجانبي‬ ‫والتشرد‬ ،‫الجانبي‬ ‫األرضي‬ ‫والضغط‬ ، ‫العددية‬ ‫النمذجة‬ ‫في‬ ‫ودمجها‬ ‫المختلفة‬ ‫والميكانيكية‬ ‫الهندسية‬ ‫الخصائص‬ ‫فحص‬ ‫تم‬ ،‫شامل‬ ‫فهم‬ ‫لتحقيق‬ .Plaxis 2D ‫برنامج‬ ‫باستخدام‬ .‫االستناد‬ ‫جدران‬ ،‫مدعمة‬ ‫تربة‬ ،‫جوستتيك‬ ،‫الرقمية‬ ‫النمذجة‬ :‫مفتاحية‬ ‫كلمات‬
  • 5. CONTENTS LIST OF ABBREVIATIONS LIST OF FIGURES LIST OF TABLES General introduction………………………………………………………..……………………...1 Thesis organization……………………………………………………..………………………….2 First Part: Literature Review Chapter 1 Generalities about Reinforced Soil Retaining Walls 1.1. Introduction …………………………………………………………………….…… 4 1.2. Types of reinforced embankment structures... ……………………………………... 4 1.2.1. Mechanically Stabilized Earth Walls ………………………………………...…… 5 1.2.2. Sheet pile walls ……………………………………………………………….……6 1.2.3. Geocell Walls ………………………………………………………………………6 1.2.4. Soil Nailing ………………………………………………………………………. 7 1.2.5. Anchored Walls …………………………………………………………………... 7 1.2.6. Hybrid Walls ……………………………………………………………………... 8 1.2.7. Gabion Walls ……………………………………………………………………... 8 1.3 Elements of retaining structures in reinforced soil ………………………………... 9 1.3.1. Panels ………………………………………………………………………………9 1.3.2. Reinforcements ……………………………………………………………...…...14
  • 6. 1.3.2.1. Metalic …………………………………………………………………...……. 14 1.3.2.1. Geosynthetic …………………………………………………………………... 15 1.4. Implementation of Reinforced Earth …………………………………………….... 17 1.4.1. Excavation ………………………………………………………………………. 17 1.4.2. Mounting the facing panels …………………………………………………....... 18 1.4.3. Installation of the reinforcement …………………………………………………19 1.4.4. Backfilling and compacting …………………………………………………...…19 1.5. Application of soil reinforced structures …………………………………………..20 1.5.1. Retaining walls …………………………………………………………………..20 1.5.2. Slope stabilization ……………………………………………………………….21 1.5.3. Bridge abutments ………………………………………………………...……...22 1.5.4. Embankment reinforcement ………………………………………………..…....22 1.5.5. Underground structures ………………………………………………………….21 1.6. Advantages and Limitations ……………………………………………………....22 1.7. Summary ………………………………………………………………………….22 Chapter 2 Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls 2.1. Introduction…………………………………………………………………………………..23 2.2. Analysis of single-reinforced retaining walls………………………………………………...23 2.2.1 Experimental Studies………………………………………………………………………………..23 2.2.1.1 Shaking Table Tests……………………………………………………………………………….23 2.2.1.2 Dynamic Centrifuge Tests………………………………………………………………...27 2.2.2 Numerical Studies……………………………………………………………………………………29
  • 7. 2.3 Design and Analysis of Geosynthetic-Reinforced SoilRetaining Walls ……………………..34 2.3.1 Federal Highway Administration (FHWA) Methodology……………………………………….34 2.3.2FHWA External Stability Evaluation……………………………………………………………....35 2.3.3FHWA Internal Stability Evaluation…………………………………………………………….…38 2.4 Back-to-Back Retaining wall…………………………………………………………………41 2.5 Conclusions……………………………………………………………….………………......51 Second Part: Numerical Modeling Chapter 3 Analysis of Back-to-Back Reinforced Retaining Walls with Panel Facing Under Railway Condition 3.1 Introduction…………………………………………………………………………………...52 3.2 Finite Element Modeling …………………………………………………………………….52 3.2.1 Soil Proprieties……………………………………………………………………………………….52 3.2.2 Reinforcement……………………………………………………………………………....54 3.2.3 Facing: Precast Panels……………………………………………………………………………..55 3.2.4 Interface properties………………………………………………………………………………….55 3.4 Results and Discussions………………………………………………………………………56 3.4.1 Displacements of the wall…………………………………………………..……………………….56 3.4.2 Earth pressures behind wall…………………………………………………..…………………….57 3.4.3 Distribution of tensile force in reinforcements…………………………………………………..57 3.4.4. Tensile Forces in Geogrids length ……………………………………………………………….58
  • 8. 3.4.5 Vertical deformation ………………………………………………………………………………..59 3.4.6 Load vs settlement response of back-to-back MSE wall model ……………………………….60 3.4.7 Mechanisms of Potential Failure …………………………………………………………………61 3.5 Conclusions…………………………………………………………………………………..62 LIST OF ABBREVIATIONS a acceleration g acceleration due to gravity fmax maximum frequency of the seismic input motion f frequency of the seismic input motion fn natural frequency of soil mass λmin wavelength of shear wave α, β Rayleigh damping parameters K stiffness matrix of the system M mass matrix of the system Fh horizontal inertial force Fv vertical inertial force H height of the retaining wall h application point locations of the dynamic thrust Δx lateral displacement of the stem z height of the stem t thickness of tire shreds cushion γ unit weight of the soil
  • 9. E Young's modulus φ friction angle of backfill ψ dilatancy angle δ’ interface friction angle c cohesion ν Poisson's ratio vs shear wave velocity Rinter interface strength-reduction factor EA elastic stiffness EI flexural rigidity θ rotation of the stem N * normalized shear force M* normalized bending moment σ *E normalized seismic earth pressure σh effective vertical pressure σv effective lateral confining pressure Pstem seismic earth pressure thrust at the stem Pheel seismic earth pressure thrust at the vertical section the heel L reinforcement length D distance between two opposing walls Tmax maximum tensile force in each reinforcement SH horizontal spacing between reinforcement SV vertical spacing between reinforcement KA earth pressure coefficient
  • 10. PA static active earth pressure KAE total (static and dynamic) earth pressure coefficient ΔKAE incremental dynamic earth pressure coefficient PAE total thrust (static and dynamic) ΔPAE incremental dynamic earth thrust M-O Mononobe-Okabe S-W Seed and Whitman 2D two-dimensional LVDT linear variable displacement transformers STD scraps tire-derived TDA Tire Derived Aggregate STC sand–tire chips EPS expanded polystyrene BBMSE Bak-to-back mechanically stabilized earth FHWA Federal Highway Administration LIST OF FIGURES Chapter 1 Generalities about Reinforced Soil Retaining Walls Figure 1.1 Reinforced Soil Retaining Wall .…….………………………………………….5 Figure 1.2 Examples of cruciform facing panels ..…………………………………………5 Figure 1.3 Example Sheet pile walls …………….…………................................................6 Figure 1.4 Example Geocell Walls …………………………………………………………6 Figure 1.5 Example Soil Nailing …………………………………………………………...7 Figure 1.6 Example Anchored Walls ……………………………………………………….7 Figure 1.7 Example Hybrid Walls …………………………………………………………..8
  • 11. Figure 1.8 Example Gabion Walls ……………………..........................................................8 Figure 1.9 Back face of Cruciform panel with embedded tie strips……………………...…..9 Figure 1.10 Type of Precast concrete facing panels ……………… ………………………...10 Figure 1.11 Type of modular block facings ………………………………………………… 11 Figure 1.12 Examples of segmental retaining wall units……………………………... …….12 Figure 1.13 Type of Partial height retaining walls …………………………. ……………….12 Figure 1.14 Type of Cast-in-place full-height facing ………………………………………...13 Figure 1.15 Type of Gabion facing …………………………………………………….…….14 Figure 1.16 Type of Metallic reinforcements ………………….…. …………………………15 Figure 1.17 Type of geosynthetics Geotextiles ………………………………………… ……15 Figure 1.18 Type of geosynthetics Geogrids ……………………………………….…………16 Figure 1.19 Type of geosynthetics Geocells ……………………………………….…………16 Figure 1.20 Type of geosynthetics Geomembranes…………………………………………...17 Figure 1.21 Step of excavate the soil …………………………………………………………18 Figure 1.22 Step of install the face of panel ………………………………………………….18 Figure 1.23 Step of Installation of the reinforcement .…………….………………………….19 Figure 1.24 Step of Backfilling and compacting ……………………………………………...20 Figure 1.25 Model Retaining walls …………………………………………………………...21 Figure 1.26 Model of Slope stabilization ………………………………………….………….21 Figure 1.27 Model of Bridge abutments ……………………………………………………...22 Chapter 2 Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Figure 2.1 Predicted factors of safety for a model cantilever-type retaining wall during shaking table tests…………………………………………………………………………………………24 Figure 2.2 Predicted factors of safety for a model reinforced soil; Type 1 retaining wall during shaking table testes……………………………………………………………………………….24
  • 12. Figure 2.3 Cross-section arrangement and instrumentation layout of reduced-scale reinforced soil model walls (EL-Emam and Bathurst 2005) ………………………………………………….....25 Figure 2.4 Cross-section instrumentation and layout of Wall 1 in full-scale shaking table tests (Ling et al. 2005a) …………………………………………………………………………….…26 Figure 2.5 A schematic diagram of a typical rigid-faced wall configuration and instrumentation (Krishna and Latha 2007) ………………………………………………………………...……...27 Figure 2.6 Setup of centrifuge model walls……………………………………………………...28 Figure 2.7 Input accelerations: (a) Test 1; (b) Tests 2 and 3…………………………………....29 Figure 2.8 Example full-scale reinforced soil retaining wall…………………………………....30 Figure 2.9 Finite-element discretization of large-scale connection test………............................31 Figure 2.10 Effects of earthquake motions on seismic wall performance (a) facing lateral displacement; (b) maximum reinforcement force (c) lateral earth pressure behind facing; (d) crest surface settlement and (e) acceleration amplification…………………………………..…………32 Figure 2.11 Numerical model dimensions adopted in the parametric study ……………….……..34 Figure 2.4. Seismic external stability of a GRS wall with level backfill in FHWA method……....37 Figure 2.13 Seismic external stability of a GRS wall with sloping backfill in FHWA method….37 Figure 2.14 Seismic internal stability of a GRS wall in FHWA method………………...……......41 Figure 2.15 Back-to-back MSE walls…………………………………………….………………43 Figure 2.16 Influence of angle of shearing resistance of backfill on critical failure surface in back- to back walls in (a) W/H=1.4 and (b) W/H= 2…………………………………………………….45 Figure 2.17 Variations in normalized total earth pressures at facing and end of reinforcement zone of connected and unconnected walls showing (a) total and (b) incremental value………………...48 Figure 2.18 Shear strain contours at failure with the c- reduction at end of construction (EoC) for walls with different interaction distances (Di)between the back of the reinforced soil zones for opposite walls .Note: results range from 01%................................................................................49
  • 13. Chapter 3 Analysis of Back-to-Back Reinforced Retaining Walls with Panel Facia Figure 3.1 Finite element models of back-to-back MSE walls………………………………….53 Figure 3.2 Horizontal Displacements UX for the wall ………………………….………..….56 Figure 3.3 Earth pressure at the facing ………………………………………………………....57 Figure 3.4 Maximum tension in reinforcement. …………….………………………………….58 Figure 3.5 Maximum tensile forces along the reinforcements ..………………………………..59 Figure 3.6 Vertical deformation between the walls …………………………………………….60 Figure 3.7 The load settlement responses observed from the model tests LR=0.2H and W =2H ………………………………………………………………………………………………………………...61 Figure.3.8 The distribution of plastic points and of shear strain increment contours in both overlapped and speared …………………………………………………………………………62 LIST OF TABLES Table 3. 1 Material properties used in numerical simulations…………………………………..54 Table 3. 2 Reinforcement properties…………………………………………………………….55 Table 3. 3 Material properties of concrete panel facing elements and sleeper ………………....55
  • 14. GENERAL INTRODUCTION Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 1 GENERAL INTRODUCTION In recent decades, reinforced soil retaining walls have become widely used throughout the world, including in Algeria. The economic aspect, architectural advantages over conventional retaining walls, and stable behavior have made these structures very popular. The interposition of reinforcing elements, notably geotextile layers, in a soil structure is one way to give the constituent soils a certain tensile strength. As a result, reinforcement solutions using geotextiles can make it possible to use poor quality fill materials and be economically advantageous. A specific application of geosynthetics that concerns the subject of this research thesis is reinforced embankment walls using geosynthetic elements to improve the resistance of the fill material to support heavy loads, especially for bridge-road structures. The reinforced soil abutment is often the terminal part of an access embankment, which can be limited by double-faced reinforced soil walls. This type of reinforcement is now more suitable than the old type of steel reinforcement. The behavior of load-bearing abutments and double-faced reinforced soil walls using geosynthetics is very complex, involving important factors such as the geometric data of the structure, soil properties, reinforcing materials, and their interaction. The complexity of this phenomenon limits the use of analytical calculations. Two essential methods of sizing a reinforced soil abutment can be found in the literature. The calculation method following the French standard NF P94-270, 2009: geotechnical calculations - supporting structures - reinforced soil fills and anchored soil masses and the other method following the American standard AASHTO, 2007 (The American Association of State Highway and Transportation Officials) and the FHWA guide, 2009 (Federal Highway Administration). These two methods are diverse and varied and do not all rely on the same assumptions. In the case of double-faced reinforced soil walls, the available design rules for this wall system are limited. This point is not addressed at all in the most recent French standard NF P94-270, 2007.
  • 15. GENERAL INTRODUCTION Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 2 However, the American FHWA guide, 2009 proposes a sizing method. This situation is the subject of a parametric study in chapter 3. The results obtained from numerical simulations indeed contribute well to the reinforcement of analytical calculation methods. ORGANIZATION OF THE THESIS The thesis titled “Performance of Back-to-Back MSE Walls Supporting the Rail Embankments” consists of three Chapters. The thesis outline is presented below: Chapter 1 introduces the basics of soil reinforcement and reinforced earth structures, including a historical overview of soil improvement techniques, types of retaining structures, geosynthetic reinforcements, facing options, and implementation methods. Chapter 2 focuses on reviewing the relevant literature for the current research work. The literature review encompasses the study of single reinforced retaining walls and back-to-back reinforced retaining walls. Additionally, the chapter includes a discussion on the American FHWA 2009 guide, which provides design guidelines for reinforced soil structures. Chapter 3 presents the findings of the reinforcement study conducted on back-to-back walls under railway conditions. A numerical model was created to analyze the tensile forces exerted on the geogrid layers and the maximum displacements of the back-to-back mechanically stabilized earth (BBMSE) walls. The obtained results were then compared with the conventional Rankine method.
  • 16. Chapter 1: Generalities about Reinforced Soil Retaining Walls. Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 3 FIRST PART LITERATURE REVIEW
  • 17. Chapter 1: Generalities about Reinforced Soil Retaining Walls. Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 4 Chapter 1 Generalities about Reinforced Soil Retaining Walls 1.1 Introduction Reinforced soil retaining structures have gained significant attention in recent years as an alternative to traditional retaining walls due to their cost-effectiveness, versatility, and durability. These structures are constructed by combining the inherent strength of soil with the reinforcement provided by various materials such as geotextiles, geogrids, and geocells. The reinforcement effectively increases the strength and stability of the soil, allowing it to resist lateral earth pressures and maintain its shape under load. The use of reinforced soil structures dates back to the early 1960s, when French engineer Henri Vidal developed the first reinforced soil retaining wall. Since then, the technology has evolved and expanded to include various types of reinforcement materials, such as geotextiles, geogrids, steel strips, and synthetic fibers, and a wide range of applications, from small garden walls to large highway embankments. Despite the numerous advantages of reinforced soil retaining structures, their design and construction require careful consideration of various factors such as soil properties, load requirements, reinforcement materials, and construction techniques. The success of these structures depends heavily on the proper selection and integration of these factors. 1.2. Types of reinforced embankment structures Reinforced embankment structures are used to provide additional support and stability to embankments or slopes, often in areas where there is a risk of erosion or landslides. There are several types of reinforced embankment structures, including:
  • 18. Chapter 1: Generalities about Reinforced Soil Retaining Walls. Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 5 Figure 1.1 Reinforced Soil Retaining Wall. 1.2.1 Mechanically Stabilized Earth Walls: Mechanically stabilized earth (MSE) walls are a type of reinforced embankment structure that use a combination of soil, reinforcement, and backfill to provide stability against lateral forces. They are commonly used in infrastructure projects such as highways, bridges, and retaining walls. Figure 1.2 Example of cruciform facing panels
  • 19. Chapter 1: Generalities about Reinforced Soil Retaining Walls. Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 6 1.2.2 Sheet pile walls: Sheet pile walls are a type of reinforced embankment structure that use interlocking steel or concrete sheets to provide lateral support to soil or other materials. They are commonly used in waterfront construction, underground parking garages, and other projects that require excavation in soft soil conditions. Figure 1.3 Example Sheet pile walls 1.2.3 Geocell Walls: Geocell walls use three-dimensional honeycomb-like geocells filled with soil or other granular materials to provide reinforcement against earth pressures. Figure 1.4 Example Geocell Walls
  • 20. Chapter 1: Generalities about Reinforced Soil Retaining Walls. Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 7 1.2.4 Soil Nailing: Soil nailing involves the insertion of steel reinforcement elements (nails) into a soil slope or wall and grouting them in place. The soil around the nails provides lateral support and stability against earth pressures Figure 1.5 Example Soil Nailing 1.2.5 Anchored Walls: Anchored walls use tensioned steel cables or rods anchored into a stable soil layer behind the retaining wall to provide reinforcement and stability against earth pressures. Figure 1.6 Example Anchored Walls
  • 21. Chapter 1: Generalities about Reinforced Soil Retaining Walls. Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 8 1.2.6 Hybrid Walls: Hybrid walls combine multiple reinforcement techniques to provide increased stability and load-bearing capacity against earth pressures. Figure1.7 Example Hybrid Walls 1.2.7 Gabion Walls: Gabion walls use wire mesh baskets filled with rocks or other large, durable materials to provide reinforcement and stability against earth pressures. Figure 1.8 Example Gabion Walls
  • 22. Chapter 1: Generalities about Reinforced Soil Retaining Walls. Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 9 1.3. Elements of reinforced soil retaining structures: 1.3.1. Panels: Panels are one of the key components of retaining structures in reinforced soil, as they form the visible face of the wall and are designed to resist the lateral soil pressure. The panels can be made of a variety of materials, including precast concrete, steel, or other materials, and are often designed with a textured surface to improve the aesthetic appearance of the wall. Panels are also designed with specific dimensions and configurations based on the project requirements, such as the height and slope of the wall, the soil conditions, and the expected loads. The panels may also be reinforced with additional elements, such as steel reinforcement bars or fiber reinforcement, to provide additional strength and stability to the structure. The usual dimensions for reinforced soil panels used in retaining walls depend on the specific application and design requirements. However, some typical dimensions for reinforced soil panels are: Thickness: 50-150 mm Length: 1-3 meters Width: 0.5-1-meter Weight: 30-150 kg/m2 Figure 1.9 Back face of Cruciform panel with embedded tie strips A. Precast concrete facing panels: Precast concrete facing panels are a common type of panel used in retaining structures in reinforced soil. These panels are typically made of high-strength concrete and are designed to resist the lateral soil pressure, provide an attractive finish, and protect the underlying reinforcement material from environmental and weathering effects.
  • 23. Chapter 1: Generalities about Reinforced Soil Retaining Walls. Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 10 Figure 1.10 Type of Precast concrete facing panels The manufacturing process for precast concrete facing panels involves casting the panels in a controlled environment, typically off-site, to ensure consistent quality and durability. The panels are cast in molds that are designed to the specific dimensions and configuration required for the project and may include various surface treatments and finishes to improve the aesthetics of the wall. B. Segmental concrete walls (SRWs) (modular block facings): Segmental Retaining Walls (SRWs) are a type of retaining wall made from modular concrete blocks. They are designed to provide structural support to retain soil, while also offering a visually appealing finish to the wall face. The blocks are interlocking, meaning that they can be stacked and secured without the need for mortar. The modular block facings are typically attached to the SRWs using mechanical connectors or adhesive materials. The facing units are designed to interlock with the modular blocks, providing a seamless and secure connection. The facings can also be designed to provide additional structural support to the retaining wall, further enhancing its performance. One of the main advantages of SRWs with modular block facings is their ease of installation. The interlocking nature of the modular blocks and facings allows for quick and efficient
  • 24. Chapter 1: Generalities about Reinforced Soil Retaining Walls. Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 11 installation, reducing labor and construction costs. Additionally, the modular design allows for flexibility in design, as walls can be easily modified or expanded as needed. Figure 1.11 Examples modular block facings C. Wrap-around facing: A wrap-around facing is a type of facing or cladding that is used on retaining structures to provide a decorative or protective outer layer. It is typically made of precast concrete, masonry, or other durable materials and is installed around the exposed face of the retaining wall or panel. When designing a wrap-around facing for a retaining structure, several factors should be taken into consideration, including the type of material used, the size and shape of the facing units, and the method of installation. The facing should be designed to withstand the forces exerted by the soil and any external loads, and it should be securely attached to the retaining structure. Overall, a wrap-around facing can be an effective way to enhance the appearance and durability of a retaining structure, but it should be carefully designed and installed to ensure that it meets the necessary performance requirements. D. Precast full-height concrete facing: this type of facing consists of precast concrete panels that are installed vertically on the face of the retaining structure. The panels can be designed in a variety of sizes and shapes and can be customized to match the aesthetic requirements of the project. The precast concrete panels are typically installed using a mechanical anchoring system, which provides a secure and durable connection to the retaining structure. The panels are designed to
  • 25. Chapter 1: Generalities about Reinforced Soil Retaining Walls. Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 12 resist the forces exerted by the soil and any external loads and are reinforced as needed to ensure their structural integrity. One of the main advantages of precast full-height concrete facing is its durability. The high- strength concrete panels are designed to withstand the harsh environmental conditions and heavy loads that are often associated with retaining structures. They are also resistant to fire, water, and other types of damage, making them a long-lasting and low-maintenance solution. Figure 1.13 Type of Partial height retaining walls E. Cast-in-place full-height facing: Cast-in-place full-height facing is another type of facing that can be used on retaining structures. As the name suggests, this type of facing is cast directly onto the face of the retaining structure using concrete. The process of casting the facing involves pouring concrete into a formwork that has been placed on the face of the retaining structure. The formwork is designed to match the size and shape of the desired facing and can be customized to meet the specific design requirements of the project. Once the concrete is poured into the formwork, it is left to cure and harden. Once the facing is fully cured, the formwork is removed, revealing the finished facing on the retaining structure. Cast-in-place full-height facing offers several advantages over other types of facing. One of the main advantages is its customization. The formwork can be designed to match the specific design requirements of the project, allowing for a wide range of sizes, shapes, and textures.
  • 26. Chapter 1: Generalities about Reinforced Soil Retaining Walls. Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 13 Figure1.14 Type of Cast-in-place full-height facing G. Gabion facing: Gabion facing is a type of facing that involves using wire mesh baskets filled with rocks or other materials to cover the face of a retaining structure. The wire mesh baskets, also known as gabions, are designed to be strong and durable, and they can be customized to match the aesthetic requirements of the project. The gabion baskets are installed on the face of the retaining structure using a variety of methods, such as anchoring them to the structure using steel rods or cables. The baskets are stacked on top of each other to create a solid facing that provides both structural support and visual appeal. One of the main advantages of gabion facing is its versatility. The use of locally sourced materials and the customizable design of the gabion baskets allow for a wide range of options in terms of size, shape, and color. Additionally, the baskets can be easily modified or expanded as needed, making them a flexible solution for retaining structures.
  • 27. Chapter 1: Generalities about Reinforced Soil Retaining Walls. Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 14 Figure 1.15 Type of Gabion Facing Overall, the choice of panel material and design is an important consideration in the design of retaining structures in reinforced soil, as it can impact the overall performance and durability of the structure. 1.3.2. Reinforcements Linear elements such as bars, strips, plates, meshes, grids, sheets, etc. are primarily utilized as reinforcements in retaining structures, with minimal to no bending capability. These reinforcements rely on their shear and pullout strength to interact with the soil and offer sufficient friction, and ribbed or gridded shapes provide additional passive strength. The composition of these elements can vary depending on the intended use. 1.3.2.1. Metalic: Metallic reinforcements exhibit significantly less deformation than the soil when they fail, owing to their high modulus of rigidity. This implies that the maximum tensile strength of the reinforcements is activated by a small deformation, typically around 2% to 3%.
  • 28. Chapter 1: Generalities about Reinforced Soil Retaining Walls. Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 15 Figure 1.16 Type of Metallic reinforcements 1.3.2.1. Geosynthetic: Geosynthetics are a type of reinforcement commonly used in reinforced soil structures. They are synthetic materials made from polymers that are specifically designed for use in civil engineering applications. Geosynthetics are commonly used in retaining walls, embankments, and slopes, and can provide several benefits over traditional reinforcement materials. Some common types of geosynthetics used in reinforced soil structures include: Geotextiles: These are permeable fabrics that are used to separate, filter, reinforce, protect, or drain soil. They can be made from a variety of materials, including polypropylene, polyester, or nylon. Figure 1.17 Type of geosynthetics Geotextiles
  • 29. Chapter 1: Generalities about Reinforced Soil Retaining Walls. Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 16 Geogrids: These are high-strength polymer or metal meshes that are used to reinforce soil and improve its bearing capacity. They are typically used to reinforce steep slopes, retaining walls, and bridge abutments. Figure 1.18 Type of geosynthetics Geogrids Geocells: These are three-dimensional honeycomb structures made of geotextiles or plastic that provide lateral support to soil and prevent soil movement. They are commonly used for slope stabilization, erosion control, and retaining wall construction. Figure 1.19 Type of geosynthetics Geocells
  • 30. Chapter 1: Generalities about Reinforced Soil Retaining Walls. Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 17 Geomembranes: These are impermeable sheets of polymer that are used to line and protect the soil from water, chemicals, or gases. They are commonly used in landfills, reservoirs, and ponds. Figure 1.20 type of geosynthetics Geomembranes Both types of reinforcements are typically placed in the soil at regular intervals and are connected to the facing material to create a cohesive structure. The reinforcements are then covered with a layer of soil, which is compacted to provide additional stability. The size, spacing, and orientation of the reinforcements are determined based on the soil properties, the height of the retaining structure, and the expected loads. The reinforcements work together with the other elements of the retaining structure, such as the facing material, drainage system, and anchors, to create a stable and durable structure. 1.4. Implementation of Reinforced Earth Reinforced Earth is a popular technique used in civil engineering for constructing retaining walls, abutments, bridge supports, and other structures that require support against soil or water pressure. The following are the four main steps involved in implementing the Reinforced Earth technique: 1.4.1 Excavation: The first step in constructing a Reinforced Earth structure is to where the structure will be built. The excavation depth should be enough to accommodate the reinforcement and facing panels. The
  • 31. Chapter 1: Generalities about Reinforced Soil Retaining Walls. Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 18 excavation should be performed according to the design specifications and should take into account any potential risks or obstacles Figure 1.21 Step of excavate the soil 1.4.2 Mounting the facing panels: Once the excavation is complete, the facing panels are mounted on the exposed soil face. The facing panels can be made of concrete, steel, timber, or geosynthetics and are designed to provide stability to the soil mass. The facing panels are connected to the reinforcement elements to create a cohesive structure Figure 1.22 Step of install the face of panel.
  • 32. Chapter 1: Generalities about Reinforced Soil Retaining Walls. Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 19 1.4.3 Installation of the reinforcement: After the facing panels are mounted, the reinforcement elements are installed. The reinforcement elements are typically made of steel or geosynthetics and are placed in the soil at regular intervals according to the design specifications. The reinforcements are anchored to the facing panels and provide tensile strength to the soil mass Figure1.23 Step of Installation of the reinforcement 1.4.4 Backfilling and compacting: Once the reinforcement elements are installed, the backfilling process can begin. The backfill material is placed in layers between the reinforcement elements, and each layer is compacted using heavy equipment to ensure that the soil is dense and stable. The backfilling process continues until the structure is completed to the design specifications.
  • 33. Chapter 1: Generalities about Reinforced Soil Retaining Walls. Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 20 Figure 1.24 Step of Backfilling and compacting Overall, the implementation of Reinforced Earth requires careful planning, precise execution, and adherence to safety protocols. When done correctly, it can result in a durable and long-lasting structure that can withstand significant loads and pressures. 1.5 Application of reinforced soil structures: Soil reinforced structures are a type of geotechnical engineering solution that involve reinforcing soil to improve its strength, stability, and load-bearing capacity. These structures are commonly used in a variety of applications, including: 1.5.1 Retaining walls: Soil reinforced structures can be used to create retaining walls that hold back soil, rocks, or other materials on a slope or embankment. These walls are commonly used in transportation infrastructure, such as highways and railways, as well as in building and construction projects.
  • 34. Chapter 1: Generalities about Reinforced Soil Retaining Walls. Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 21 Figure 1.25 Model Retaining walls 1.5.2 Slope stabilization: Soil reinforced structures can also be used to stabilize slopes and prevent landslides or soil erosion. This application is particularly important in areas with steep topography, where slope failure can pose a significant risk to infrastructure and human safety. Figure1.26 Model Slope stabilization
  • 35. Chapter 1: Generalities about Reinforced Soil Retaining Walls. Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 22 1.5.3 Bridge abutments: Soil reinforced structures can be used to support bridge abutments and approach embankments, which are typically subjected to heavy loads and lateral pressures from the surrounding soil. Figure1.27 Model of Bridge abutments 1.5.4 Embankment reinforcement: Soil reinforced structures can be used to reinforce embankments and improve their load-bearing capacity. This application is commonly used in road and railway construction, as well as in the construction of dams and other large-scale infrastructure projects. 1.5.5 Underground structures: Soil reinforced structures can be used to support underground structures, such as tunnels, mines, and storage facilities. These structures are typically subjected to significant vertical and lateral loads, and require a high degree of stability and structural integrity. Overall, soil reinforced structures offer a versatile and cost-effective solution for a wide range of geotechnical engineering challenges, and are an essential component of many infrastructure and construction projects.
  • 36. Chapter 1: Generalities about Reinforced Soil Retaining Walls. Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 23 1.6 Advantages and Limitations: Advantages: Reinforced soil structures are typically less expensive to construct than traditional concrete or masonry structures. The use of lightweight and flexible materials in soil reinforcement allows for faster and easier construction and reduces the need for heavy equipment. Reinforced soil structures are resistant to corrosion and can withstand harsh environmental conditions, making them suitable for use in coastal or marine environments. The use of reinforced soil structures can also provide environmental benefits, such as reducing the need for excavation and reducing the amount of waste generated during construction. Limitations: The effectiveness of reinforced soil structures depends on the quality of the soil and the accuracy of the design and construction process. The use of lightweight and flexible materials in soil reinforcement may make the structure vulnerable to damage from weather events, such as earthquakes or high winds. The lifespan of reinforced soil structures may be shorter than that of traditional concrete or masonry structures, and maintenance may be required to ensure their durability. 1.7 Conclusion: Soil reinforced structures are widely used in civil engineering for a variety of applications, including retaining walls, bridge abutments, embankments, waterfront structures, and mining applications. The use of lightweight and flexible materials in soil reinforcement allows for faster and easier construction, reduces costs, and provides environmental benefits. However, the effectiveness of reinforced soil structures depends on the quality of the soil and the accuracy of the design and construction process. The lifespan of reinforced soil structures may be shorter than traditional structures, and maintenance may be required to ensure their durability.
  • 37. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 23 Chapter 2 Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls 2.1 Introduction This chapter offers a comprehensive and evaluative analysis of the effectiveness of reinforced soil, drawing upon existing studies in the field. The chapter is structured into two main sections: (a) a review of research studies on single-reinforced retaining walls, and (b) a review of studies on back-to-back reinforced retaining walls. 2.2 Analysis of single-reinforced retaining walls 2.2.1 Experimental Studies 2.2.1.1 Shaking Table Tests Richardson and Lee (1975) conducted the first known study on the behavior of reinforced soil walls under dynamic loads, using shake table tests on a small-scale model of a 380 mm high wall reinforced with aluminum strips. However, the study suggested that more research was needed to fully understand how reinforced walls behave under seismic loading conditions. Sakaguchi (1996) conducted shake table tests on reduced scale models of 1.5 m high reinforced soil walls with wrapped faces and lightweight modular block forms to investigate the effects of geosynthetic length, soil density, and strength on horizontal wall displacements under seismic loading. The study found that increasing the number of reinforcement layers significantly reduced maximum wall displacement. Koseki et al. (1998) also used shake table tests on models of reinforced soil walls with rigid facing and conventional retaining walls of 0.5 m height. They found that increasing the length of the upper and fourth reinforcement layers decreased the critical acceleration related to lateral displacement, with a 20% increase when the length of the upper layer was increased by a factor of four and the fourth layer by a factor of 2.25. Matsuo et al. (1998) conducted shake table tests on six scaled-down models of soil walls reinforced with geogrids to investigate the behavior and reinforcement mechanism in GRS. The models had different heights of 1m and 1.4m, with discrete and continuous panel facings and varying ratios of reinforcement length to wall height (L/H ratios of 0.4 and 0.7). Five models were subjected
  • 38. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 24 to sinusoidal motion, while one model was tested under the Kobe earthquake. The study concluded that increasing the reinforcement length ratio from 0.4 to 0.7 was an effective method for reducing wall deformation. Figure 2.1 Predicted factors of safety for a model cantilever-type retaining wall during shaking table tests (Koseki et al.1998). Figure 2.2 Predicted factors of safety for a model reinforced soil; Type 1 retaining wall during shaking table testes (Koseki et al.1998).
  • 39. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 25 Other model studies have also confirmed that reducing the reinforcement length-to-height (L/H) ratio can increase wall displacement. El-Emam and Bathurst (2007) found that reducing the L/H ratio from 1 to 0.6 (a 40% decrease) increased the maximum lateral displacement by approximately 30% at a base acceleration of 0.32 g (see Figure 2.3). This finding is consistent with Sakaguchi et al. (1992), who also reported a 40% decrease in lateral displacement with an increase in reinforcement layers. Figure 2.3 The cross-sectional configuration and instrumentation arrangement of reduced- scale reinforced soil model walls are presented in EL-Emam and Bathurst's (2005) study. Ling et al. (2005) performed a full-scale shake table test on three modular block-faced GRS walls to investigate their seismic behavior. The walls were 2.8 m high and had a 0.2 m thick foundation soil. Walls 1 and 2 had reinforcement spacing of 40 cm, while Wall 3 had a spacing of 60 cm. All walls were subjected to vertical acceleration, while Wall 3 was also subjected to horizontal acceleration of 0.4g followed by 0.8g. The study concluded that using longer reinforcement at the top layer and smaller vertical reinforcement spacing improved the seismic performance of GRS walls. The greatest lateral displacement was observed at the top of the wall. Krishna (2008) and Krishna and Latha (2007) conducted shake table tests on a 0.6 m-high model GRS walls reinforced with geotextile to investigate the effect of backfill soil density on the seismic response of three different wall designs at acceleration levels of 0.1 g and 0.2 g.
  • 40. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 26 The study found that retaining walls with facing panels experienced less acceleration compared to reinforced soil walls with rigid facing. Figure 2.4 Cross-section instrumentation and layout of Wall 1 in full-scale shaking table tests (Ling et al. 2005a). Nova-Roessig and Sitar (2006) have reported similar findings in their centrifuge model studies, where retaining walls with facing panels experienced less acceleration compared to reinforced soil walls with a rigid facing. The influence of the relative density of the backfill on the seismic response of GRS walls was found to be more pronounced at low relative densities and higher base excitations. Krishna and Latha (2009) conducted an experimental study to investigate the effects of reinforcement on the seismic performance of GRS walls with a full-height rigid facing. The study revealed a reduction in lateral displacements facing the wall when compared to the measured displacements of unreinforced walls.
  • 41. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 27 Figure 2.5 A schematic diagram of a typical rigid-faced wall configuration and instrumentation (Krishna and Latha 2007). 2.2.1.2 Dynamic Centrifuge Tests Sakaguchi et al. (1996) conducted centrifugal tests to investigate the effects of soil density, geosynthetic length, and strength on the magnitude of horizontal wall displacements of geosynthetic reinforced retaining walls under earthquake loading. They found that the maximum tensile force in the geotextile had a slight influence on the seismic responses of the walls, as the tensile forces developed during seismic effects were well below the particular tensile limits. Takemura and Takahashi (2003) used centrifuge tests to investigate the influences of reinforcement length, vertical reinforcement spacing, and backfill dry density on the dynamic response of GRS walls. The prototype wall was 7.5 m high and was subjected to sinusoidal excitation. The low-density backfill wall specimen underwent greater horizontal translation and greater tensile strains in the reinforcement. Siddharthan et al. (2004) conducted studies of centrifuge models on soil retaining walls reinforced with bar-mat subjected to seismic ground motions. The results of the tests showed that the maximum lateral displacement of the facing occurred at mid-height of the reinforced walls. However, walls with longer reinforcements underwent less deformation.
  • 42. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 28 Liu et al. (2010) studied the different performance levels of retaining walls of reinforced geosynthetic soil with modular block facing under different earthquakes. They conducted dynamic centrifuge tests on three GRS walls and highlighted the importance of the overall acceleration and duration of the earthquake. The acceleration within GRS walls amplified greatly under simple excitation, indicating that designing tall GRS walls against a modest seismic load may require considering a change in acceleration with height (refer Figure 2.6 and 2.7). Liu et al. (2010) proposed that the design of GRS high walls may need to account for the change in acceleration with height. Figure 2.6 Setup of centrifuge model walls (Liu et al. 2010). Figure 2.7 Input accelerations: (a) Test 1; (b) Tests 2 and 3 (Liu et al. 2010).
  • 43. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 29 2.2.2 Numerical Studies Several studies have used finite element modeling to investigate the seismic response of reinforced soil retaining walls. Segrestio and Bastick (1988) validated a dynamic finite element model using measured results from a shaking table test on a steel strip-reinforced soil wall. Yogendrakumar et al. (1991) used a similar approach to study the seismic response of steel strip-reinforced soil walls. Bachus et al. (1993) and Yogendrakumar and Bathurst (1992) also conducted dynamic finite element modeling of reinforced soil walls subjected to blast loading. Cai and Bathurst (1995) investigated the dynamic response of a geosynthetic reinforced soil retaining wall with modular blocks using the finite element method. They found that an accurate estimation of interface shear properties is crucial for the seismic design of retaining walls. They also noted that the maximum tensile forces in the reinforcement layers increased with the amplitude of the maximum acceleration of the base. Bathurst and Hatami (1998) studied the influence of boundary conditions and base acceleration records on the seismic response of a GRS wall using FLAC. They showed that the wall incremental loads increased with increasing reinforcement stiffness over a wide range of values that included relatively flexible geosynthetic reinforcement materials as well as metallic reinforcement. Hatami and Bathurst (2000b) simulated the dynamic response of GRS walls with modular block facing subjected to different ground motions. They found that low-frequency ground motions with high intensity could result in significant structural responses of short-period GRS walls. Deformations and reinforcement forces for GRS walls subjected to a single frequency harmonic motion were larger than the responses of walls subjected to actual earthquake ground motions with comparable predominant frequencies.
  • 44. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 30 Figure 2.8 Example full-scale reinforced soil retaining wall (Hatami and Bathurst 2000). In their study, Hatami and Bathurst (2000a) examined the impact of various design parameters on the fundamental frequencies of reinforced-soil retaining wall models, including wall height, backfill width, reinforcement length and stiffness, backfill friction angle, and toe restraint condition. Surprisingly, they found that the fundamental frequency was not significantly influenced by reinforcement stiffness, reinforcement length, or the conditions of restraint of the toes. The resistance of the granular backfill, characterized by its friction angle, also did not show any observable effect on the fundamental frequency of the models. Helwany et al. (2001) used a shaking table test on a small-scale GRS segmental wall to verify a finite element model generated using the program DYNA3D. The model simulated the nonlinear hysteretic behavior of the backfill soil under cyclic loading using the Ramberg- Osgood model with parameters determined from laboratory tests. The geotextile was modeled as a linearly elastic material. Helwany and McCallen (2001) investigated the effect of facing block connection on the static and dynamic behavior of GRS walls using the validated model. They found that the wall using facing blocks with pin connections had smaller lateral facing displacement than the wall without pin connections at the end of construction, but experienced larger seismic-induced displacements. The authors suggested that smaller seismic-induced lateral displacements in the wall without pin connections were due to smaller lateral earth
  • 45. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 31 pressures behind the facing, as the blocks without pin connections permit more relative sliding between blocks. Figure 2.9 Finite-element discretization of large-scale connection test Helwany and (McCallen 2001). Ling et al In 2004, . used a modified version of Diana-Swandyne II to validate a finite element model for both static and dynamic analyses. They used a generalized plasticity model to characterize the backfill soil and a bounding surface model to simulate the cyclic behavior of the uniaxial geogrid. The dynamic finite element model was validated using measured results from dynamic centrifuge tests. The study showed good agreement between predicted and measured results for acceleration, wall facing displacements, crest settlement, and maximum tensile forces in the geogrid. Ling et al. In 2005, conducted parametric studies using the validated finite element model to investigate the effects of soil and reinforcement properties, reinforcement length and spacing, and block interaction properties on the performance of GRS walls at the end of construction and under earthquake loading. They found that lateral facing displacements and crest settlement were mainly influenced by soil cyclic behavior, reinforcement layout, and earthquake motions. They also found that the reinforcement vertical spacing had a more significant effect on wall deformation, reinforcement forces, and lateral earth pressure than reinforcement length.
  • 46. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 32 Figure 2.10 Effects of earthquake motions on seismic wall performance (a) facing lateral displacement ; (b) maximum reinforcement force (c) lateral earth pressure behind facing ; (d) crest surface settlement and (e) acceleration amplification. Validated numerical models are useful for understanding the dynamic behavior of GRS walls, but previous validations have had limitations, such as reduced-scale testing, which may not accurately represent real-world conditions. Full-scale shaking table tests conducted by Ling et al. (2005a) on GRS walls with modular block facing provided valuable data for calibrating
  • 47. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 33 dynamic numerical models. Ling et al. (2010) improved previous constitutive models and validated a dynamic finite element model using experimental results. Other researchers, such as El-Emam et al. (2004) and Fakharian and Attar (2007), have validated their FLAC models using reduced-scale shaking table tests, but their validations are limited to GRS walls with a rigid full-height facing panel. Lee et al. (2010) used LS-DYNA to simulate full-scale shaking table tests, and Lee and Chang (2012) conducted a series of parametric studies to evaluate the effects of different design parameters on the seismic performance of GRS walls. Their results showed that decreasing the batter angle of the wall facing can make GRS walls less stable, and a small vertical reinforcement spacing of 0.2 m can be effective in decreasing wall deformations and reinforcement forces. Figure 2.11 Numerical model dimensions adopted in the parametric study (Lee et al. 2010). 2.3 Design and Analysis of Geosynthetic-Reinforced Soil Retaining Walls This section provides an overview of the current design and analysis practices for geosynthetic-reinforced soil (GRS) retaining walls under earthquake loads. In North America, the Federal Highway Administration (FHWA) manual, developed by Elias et al. (2001), is a widely accepted design guideline for GRS retaining walls, which includes seismic design considerations. The National Concrete Masonry Association (NCMA) manual, developed by Bathurst (1998), also provides a seismic design method for GRS walls. Design of reinforced
  • 48. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 34 soil slopes can be found in the US Army Corps of Engineers Waterways Experiment Station publication by Leshchinsky (1997). Additionally, design methodologies from other countries have been summarized by Zomberg and Leshchinsky (2003) and Koseki et al. (2006). The design criteria and analysis methods outlined in the FHWA and NCMA manuals are presented, along with the assumptions involved in the design process 2.3.1 Federal Highway Administration (FHWA) Methodology Limit equilibrium (LE) method is adopted in the FHWA methodology, where one can only estimate the margins of safety against collapse and cannot estimate the deformation of the structure given the external loads. In the seismic design of GRS walls, the FHWA methodology requires both the external stability and the internal stability be evaluated in addition to the static design considerations. The design peak horizontal acceleration at a site can be obtained from Division I-A (AASHTO 2002) and Section 3.10 (AASHTO 2007) of the AASHTO Specifications. As specified by the FHWA methodology, the seismic design is needed whenever the peak acceleration coefficient (A) at the site being considered is greater than 0.05. The coefficient is expressed as a fraction of gravitational constant, g, and is dimensionless. The maximum limiting value of A in which the FHWA seismic design requirements are applicable is 0.29, and the FHWA methodology recommends that the seismic design of a GRS wall should be reviewed by a specialist when A at the project site exceeds 0.29 (Lee, Z. Z. (2011)). 2.3.1.1 FHWA External Stability Evaluation In the external stability evaluation for GRS walls, three potential modes of failure considered are: (1) base sliding, (2) eccentricity, (3) bearing capacity. Taking into account the flexibility/ductility exhibited by the GRS walls, the recommended minimum seismic factors of safety with respect to the failure modes are assumed as 75 percent of the static factors of safety, and the eccentricity should be within L/3 (L= length of the reinforcement) for both soil and rock foundations. Two forces in addition to the static forces in the external stability evaluation are the horizontal inertia force (PIR) and the seismic horizontal thrust increment (DPAE). DPAE is exerted on the reinforced soil by the retained soil. Both DPAE and PIR are shown in Figures 2.12 and 2.13 for level and sloping backfill conditions, respectively (Lee, Z. Z. (2011)). The seismic external stability is evaluated in the following steps: • Select the acceleration coefficient A from Section 3 of AASHTO Division 1-A.
  • 49. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 35 • Calculate the maximum acceleration (Am) developed within the GRS wall system. ( ) 1.45 * Am A A = − (2.10) • Calculate the horizontal inertia force PIR and the seismic horizontal thrust increment DPAE. The height H2 should be used in finding PIR and DAE for sloping backfill condition (see Figure 2.13). 2 tan .0.5 (1 0.5tan ) 1 0.5tan H H H H    = + = − − (2.1) The horizontal inertia force PIR is calculated as follows : IR ir is P P P = + (2.2) 2 0.5 ir m f P A H H  = (2.3) 2 2 0.125 ( ) tan is m f P A H   = (2.4) Note that Pir is the inertial force caused by acceleration of the reinforced backfill, and Pis is the inertial force cased by acceleration of the sloping soil surcharge above the reinforced backfill. The seismic horizontal thrust increment DPAE is calculated using the pseudo-static Mononobe-Okabe method with the horizontal acceleration coefficient kh equal to Am and vertical acceleration coefficient kv equal to zero (Lee, Z. Z. (2011)). The total seismic earth pressure coefficient KAE is calculated following the general Mononobe- Okabe expression: 2 2 cos ( ) / cos cos cos( ) sin( )sin( ) 1 cos( )cos( ) AE K                     + − − +   =   + − − +   − + +   (2.5) where, ϕ = peak soil friction angle, β = backfill surface slope angle from the horizontal,ξ = seismic inertial angle given by ξ = tan-1 (kh/1±kv), and kh and kv are the peak horizontal and vertical seismic coefficients, respectively.
  • 50. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 36 The seismic earth pressure coefficient associated with the seismic thrust increment (DPAE) is DKAE, and DKAE = KAE - KA . Note that the mobilized interface friction angle δ is assumed to be equal to β in the FHWA method. Note also that the wall batter angle 0) in the FHWA method is with the facing blocks inclined into the backfill, which is the opposite of the Coulomb method (Lee, Z. Z. (2011)).. Check factors of safety against failures of base sliding, eccentricity and bearing capacity with PIR and 50% of DPAE. The reduction of 50% on DPAE was reasoned with possible phase lag between the inertial force and the seismic thrust from the retained backfill (Lee, Z. Z. (2011)).. For level backfill condition (β = 00 ), H2 = H, Pis=0, and PIR = Pir Figure 2.12 Seismic external stability of a GRS wall with level backfill in FHWA method. Figure 2.13 Seismic external stability of a GRS wall with sloping backfill in FHWA method.
  • 51. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 37 As indicated by the FHWA manual, the use of full value of Am for kh in the pseudo-static Mononobe-Okabe method to find PAE can result in an excessively conservative design (Lee, Z. Z. (2011)). To achieve a more economical GRS wall, a reduced kh can be used if the following conditions are met: •The wall is unrestrained regarding its ability to slide, other than soil friction along its base and minimal soil passive resistance. •If the wall functions as an abutment, the top of the wall must also be unrestrained, e.g., the superstructure is supported by sliding bearings. With the conditions listed above and provided that the GRS wall can tolerate displacements up to 250·A (mm), kh may be reduced to 0.5·A (i.e., kh = OSA). FHWA methodology also provides an alternative method for estimating the horizontal acceleration coefficient kh in finding L1PAE . kh can be computed as: 0.25 1.66 h Am K Am d   =     (2.6) where d is the anticipated lateral wall displacement in mm. Noted that this equation should not be used for displacement of less than 25 mm or greater than 200 mm. FHWA manual suggests that typical anticipated lateral wall displacement in seismically active area ranges from 50 mm to 100 mm. It is to be noted that although a trapezoidal dynamic pressure distribution was proposed by the FHWA methodology (see Figures 2.12 and 2.13), and the actual dynamic pressure distribution was not specified. The equation for determining the seismic horizontal thrust increment DPAE has otherwise suggested a triangular dynamic pressure (hydrostatic) distribution. For the seismic thrust to be located at 0.6H and with a trapezoidal pressure distribution, the ratio of long length (at the top) to the short length (at the bottom) of the trapezoid needs to be 4 (Lee, Z. Z. (2011)). 2.3.1.2 FHWA Internal Stability Evaluation The internal stability of a GRS wall can be compromised in three ways: (1) pullout of reinforcement, (2) reinforcement rupture, and (3) connection pullout failure. To evaluate the internal stability, the maximum tensile force developed in each reinforcement layer, the critical slip surface, and the resistance provided by the reinforcements in the resistant zone must be
  • 52. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 38 determined. The critical slip surface is assumed to coincide with the locus of the maximum tensile force in each reinforcement layer, and is assumed to be linear in the case of extensible reinforcements, passing through the toe of the wall (see Figure 2.14). The location and slope of the linear critical slip surface are assumed to be unaffected by seismic loads. The critical static slip surface is inclined at an angle αA from the horizontal, based on Coulomb's active condition: 1 1 2 tan tan A C C     −   − − + = +     (2.7) As has mentioned earlier, in the FHWA methodology, the mobilized interface friction angle δ is assumed to be equal to the backfill slope angle p (i.e., δ = β). The static maximum tensile force in each reinforcement Trnax is a function of horizontal stress at each reinforcement level along the critical slip surface (σH) and reinforcement spacing (Sv), and Tmax is computed as: max . H V T S  = (2.8) Furthermore, the horizontal stress σH is a function of the overburden stress, uniform surcharge loads, and concentrated surcharge loads. Alternatively, the tributary area from horizontal stress distribution can be used to calculate Tmax for each of the reinforcements. Note that the reinforcement spacing should not exceed 800 mm as required by the FHWA methodology. In a seismic event, seismic loads would produce an inertial force PI acting horizontally in addition to the static forces (see Figure 2.14). The inertial force PI is calculated as: . I m A P A W = (2.9) where WA is the weight of the active zone (shaded area in Figure 2.14), and Am is the maximum acceleration. Each reinforcement layer would receive additional seismic tensile force induced by the inertial force PI. The additional seismic tensile force Tmd in each reinforcement layer is determined by proportionally distributing the PI based on the embedment length of reinforcements in the resistant zone and is computed as follows: 1 ei md I n ei i L T P L = =  (2.10)
  • 53. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 39 where n is number of reinforcement layers in the GRS wall. Knowing Tmax and Tmd, the total tensile force in each reinforcement layer Ttotal is calculated as: ult rs rt T S S = + (2.11) Ttotal is then used to evaluate the reinforcement pullout failure. Note that the factor of safety against reinforcement pullout failure FSpo under static condition should be greater than or equal to 1.5, and in seismic design, the factor of safety is said to be 75% of the static value. The total tensile force in each reinforcement layer Ttotal should not exceed the pullout resistance Pr at that layer as: (0.75) r c total po P R T FS = (2.12) where Re is the coverage ratio and is often assumed to be unity for geotextiles and geomembranes. Pr is a function of embedment length Le, overburden stress, and coefficient of friction (or the friction bearing-interaction factor). According to the FHWA methodology, the coefficient of friction between the soil and reinforcement in the seismic condition should be reduced to 80% of the static value. In evaluating the rupture failure during seismic loading, the reinforcement is to be designed to resist both the static and seismic forces, which requires the following: max . (0.75). . . . rs c CR D ID S R T RF RF RF FS  (static component) (2.13) max . (0.75). . . rt c D ID S R T RF RF FS  (seismic component) (2.14) where Rc = coverage ratio, RFCR= creep reduction factor, RFD = durability reduction factor, RFID = installation damage factor, FS = overall factor of safety, Srs = reinforcement strength to resist static load, and Srt = reinforcement strength to resist seismic load. Note that the creep reduction factor RFCRis not applicable to Tmd, since seismic load occurs in a short time. The values of various reduction factors have been suggested in the FHWA methodology. Moreover, with both Srs and Srt known, the required ultimate strength of the geosynthetic reinforcement Tult can be calculated as follows : ult rs rt T S S = + (2.15)
  • 54. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 40 A particular geosynthetic reinforcement can be selected based on the value of Tult. The connection pullout failure during seismic loading is evaluated using the following conditions: max . . rs c D S CR T RF FS  (2.16) max . 0.8 . rt ult D S CR T RF FS        (2.17) where CRcr = connection strength reduction factor resulting from long-term testing and CRuit = connection strength reduction factor resulting from quick connection tests. Both CRcr and CRult are to be determined using the laboratory testing technique described in Appendix A of the FHWA manual. Both CRcr and CRult are a function of normal stress, which is developed by the weight of the facing units. Calculation of normal stress should be limited by the hinge height in the case of a batter wall. Figure 2.14 Seismic internal stability of a GRS wall in FHWA method.
  • 55. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 41 2.4 Back-to-Back Retaining wall Back-to-back walls are commonly used in highway ramps to provide support on both sides of the ramp. When analyzing the external stability of such walls, a modified value of lateral pressure needs to be taken into consideration. There are two cases to be considered as shown in Figure 2.15: Case 1: The back-to-back walls are separated by a distance less than or equal to twice the height of the wall (2H). In this case, the lateral earth pressure on the walls should be modified as follows: Active earth pressure (Ka) should be used on the wall facing the active soil. Passive earth pressure (Kp) should be used on the wall facing the passive soil. The lateral earth pressure coefficient (K) should be taken as 1/2 for both walls. Case 2: The back-to-back walls are separated by a distance greater than twice the height of the wall (2H). In this case, the lateral earth pressure on both walls should be calculated using the same approach as for a single wall, with the following modification: The lateral earth pressure coefficient (K) should be taken as 3/4. For Case II geometries with overlaps (LR) greater than 0.3H2, the following guidelines should be used: • L1/H1 ≥ 0.6 where L1 and H1 is the length of the reinforcement and height, respectively, of the taller wall. • L2/H2 ≥ 0.6 where L2 and H2 is the length of the reinforcement and height, respectively of the shorter wall. • Wb/H1 ≥ 1.1 where Wb is the base width as shown in Figure 2.15 and H1 is the height of the taller wall. The above guidelines are valid for static load conditions or in areas where the seismic horizontal accelerations at the foundation level are less than 0.05g. Back-to-back walls in seismically active areas should be designed based on a more detailed analysis that includes effects of potential non-uniform distribution of seismic and inertial forces within the wall.
  • 56. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 42 Figure 2.15 Back-to-back MSE walls. Ling et al. (2003) used FLAG to simulate an overpass in Turkey and computed tensions in reinforcements and lateral displacements under seismic loading. However, their model was basic and may not fully simulate field conditions. Hardianto and Truong (2010) analyzed the impact of the aspect ratio of back-to-back walls on tensile forces during seismic loading using FLAC 6.00. However, their study was limited as it did not account for staged construction and compaction stresses. Han and Leshchisnskv (2010) investigated the behavior of back-to-back MSE retaining walls using two software programs, FLAC and ReSSA. The study focused on the impact of the W/H ratio and quality of backfill on the critical failure surface, reinforcement tensile strength, and lateral pressures at the end of the reinforced zone under seismic loading. The analysis was conducted at the limit state condition using FLAC, and the limit equilibrium analysis was performed for single walls, and results were compared with the back-to-back walls. The study considered walls of 6-m height, with W/H ratios of 1.4, 2.0, and 3.0 and backfill angle of shearing resistance (ϕ) of 25° and 34°. The critical failure surface was determined to pass through the toe of the walls by providing the weaker bond strength at the bottom blocks of the facing. The study found that in low W/H ratios, the critical failure surface of one wall interfered with the reinforced zone of the other wall. The interference of failure extended to greater depths as the angle of shearing resistance decreased. In W/H = 1.4, and ϕ =25°, the interaction between the failure surfaces extended up to about half the depth of the walls. The percentage reduction of lateral force at the end of the reinforcement zone with W/H ratio was more significant in
  • 57. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 43 ϕ=25° than ϕ=34°. The distribution of maximum tension in reinforcements with the depth of the wall was reported as linearly increasing up to a certain depth and then remaining constant until the bottom of the wall in unconnected walls. However, in connected walls, the maximum tension was constant throughout the depth of the wall. The maximum reinforcement tensions in walls with ϕ=25° were 67% and 100% higher than those of walls with ϕ=34° in connected and unconnected walls, respectively. However, the study did not consider the effect of staged construction and compaction stresses. Anubhav and Basudhar (2011) investigated the response of a footing supported by double- faced, wrap-around reinforced walls using numerical modeling in PLAXIS 2D. The study analyzed the impact of the number of reinforcing layers and overlap length on the load- deformation behavior, ultimate bearing capacity of the footing, and lateral deformations. The accuracy of the numerical model was verified by comparing it with experimental data obtained from small-scale tank tests. The model was able to accurately predict the experimental data with minimal error. However, it is important to note that the experimental and numerical models simulated a wall of only 0.5 meters in height, and the results may differ for full-scale walls. Katkar and Viswanadham (2011) investigated back-to-back walls using the finite element software PLAXIS 2D. The study aimed to analyze the impact of the distance between the ends of the reinforcements of the walls (D) and the angle of shearing resistance of the backfill on lateral displacements and maximum tensions in the reinforcements. A wall with a height of 6 meters was considered, and four cases with different D/H ratios ranging from 0 to 1.6 were examined. The study also analyzed the effect of reinforcement connection. The results showed that lateral displacements decreased significantly in the case of connected reinforcements, but the maximum tension in the reinforcement was higher than that of the unconnected case. However, the model did not consider staged construction, which is a limitation of the study.
  • 58. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 44 Figure 2.16 Influence of angle of shearing resistance of backfill on ceitical failure surface in back-to back walls in (a) W/H=1.4 and (b) W/H= 2. Katkar and Viswanadham (2012) investigated the behavior of single vertical walls and back- to-back geogrid-reinforced walls using the wrap-around technique through centrifuge model tests. The study focused on the effect of reinforcement connection in the middle of the wall on lateral deformations, strains in the reinforcements, and surface settlements. Three cases were
  • 59. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 45 considered: single reinforced wall, back-to-back walls with unconnected reinforcement, and back-to-back walls with reinforcement connected in the middle. Loading was varied from 10g to 60g. The results showed that connected walls had lower lateral deformations compared to unconnected walls. However, the peak strains in the reinforcements were higher in the connected walls at 45g. It is important to note that the study was limited to small-scale models and may not fully represent the behavior of full-scale walls. El-Sherbiny et al. (2013) utilized PLAXIS finite element software to simulate a back-to- back walls model and investigate the effect of wall distance on lateral pressures, lateral displacements, and maximum tensions in the reinforcement under working-stress conditions. The formation of the critical slip surface and overall factor of safety of the back-to-back walls were also analyzed under limit-state conditions. The study showed that decreasing the distance between walls from 0.5H to zero resulted in a 25% reduction in lateral earth pressures and a decrease in maximum tensile force in the reinforcement by 5%-10%. Additionally, the impact of reducing the length of the reinforcement to less than 0.7H was studied, which increased the horizontal deformation and maximum tensile forces. However, the study did not mention the interfaces used, nor did it consider compaction stresses. Benmebarek et al. (2016) utilized the Finite Element Program (PLAXIS) to model back-to- back walls with staged construction. The study focused on investigating critical failure surfaces, lateral pressures at the end of the reinforcement zone, lateral displacements, and maximum tension profiles along the height of the wall for different W/H ratios. The results showed that even when the W/H ratio exceeded 2, an interaction between the walls was present for an internal angle of shearing resistance of backfill of 35°, which goes against FHWA guidelines. The W/H ratio had a significant impact on the lateral pressures at the end of the reinforcement zone. Additionally, the effect of cohesion in the backfill material was analyzed, resulting in a small reduction in lateral pressures. Djabri and Benmebarek (2016) investigated the behavior of back-to-back walls using a limit state approach. They studied the effect of the W/H ratio on lateral earth pressures, maximum tension profiles, and critical failure surfaces. However, they did not consider the effect of reinforcement stiffness or surcharge loads in their model. Similarly, another study by Djabri
  • 60. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 46 and Benmebarek (2016) analyzed the effect of W/H ratio on lateral displacements and maximum tension lines, but did not consider reinforcement stiffness or surcharge loads. Benmebarek and Djabri (2017a) conducted a study using PLAXIS to analyze the impact of overlapping length on back-to-back walls. The research focused on the influence of overlapping length on the factor of safety, lateral displacements, maximum tension in the reinforcement, and potential failure surface for internal stability. The study revealed that as the overlapping length increased from 0.1 LR/H to 0.4 LR/H, the factor of safety increased by 50%. The increase in overlapping length also reduced lateral displacements by over 20%, while having minimal effect on the reinforcement tension. The research also examined the impact of wall height on these factors. However, the simulation of the interface between the facing panels as hinges may not have accurately modeled the interaction of the facing panels. Benmebarek and Djabri (2017b) conducted a study on back-to-back walls under simple cyclic harmonic loading, using MSG reinforcement. The effect of W/H ratios on lateral deformations and maximum tensile force in the reinforcement were studied. The results showed that decreasing the W/H ratio led to a significant reduction in amplitude displacement. The study also found that the stability of the back-to-back walls was influenced by the peak ground acceleration and frequency of loading. However, the study did not consider the effects of compaction stresses or surcharge loads, and did not analyze the impact of reinforcement stiffness. Dram (2021) used the finite element method to investigate the dynamic response of connected and unconnected back-to-back mechanically stabilized earth walls under earthquake loading. The study presented the total seismic earth thrusts at the end of the reinforced zone and at the facing of BBMSE walls, along with their points of application (as shown in Figure 2.17).
  • 61. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 47 Brouthen (2022) conducted a finite element analysis using PLAXIS 2D software to investigate the effects of problem geometry, strip pre-tensioning, strip type, and surcharging on horizontal displacements, development of soil shear and plastic zones, lateral earth pressure, and reinforcement loads. The study found that the improved strength and stiffness of the polymeric-soil interface led to a reduction of approximately 30% in lateral earth pressure, as shown in Figure 2.18. Figure 2.17 Variations in normalized total earth pressures at facing and end of reinforcement zone of connected and unconnected walls showing (a) total ,and (b) incremental values.
  • 62. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 48 Figure 2.18 Shear strain contours at failure with the c- reduction at end of construction (EoC) for walls with different interaction distances(Di)between the back of the reinforced soil zones for opposite walls. Note: results range from 0-1%.
  • 63. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 49 Y Zheng (2023) studied the dynamic response of two back-to-back MSE walls with modular block facing and full-height rigid facing, respectively. Acceleration response, facing displacements, and reinforcement tensile strains under a series of sinusoidal motions with increasing amplitude is presented figure2.19 Figure2.19. Profiles of incremental maximum dynamic facing displacement of back-to-back MSE walls with different facing condation (a) left facing; (b) right facing . Vadavadagi, S. S., & Chawla, S. (2023) investigated the behavior of unconnected, connected and overlapped geogrid reinforced back-to-back mechanically stabilized earth walls supporting the railway tracks at bridge approaches. Scaled model tests were conducted to study the behavior of BBMSE walls. Overburden (OB) waste generated from coal mining was used as the sustainable backfill, as shown in Figure 2.20
  • 64. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 50 Figure 2.20. (a) BBMSE wall model test set up, (b) Mesh diagram of the model BBMSE wall. 2.5 Conclusions This chapter provides a comprehensive literature review on the response of retaining walls. Various analytical, numerical, and experimental methods have been utilized to investigate their behavior under load loading. The effects of compaction stress and surcharge on retaining walls have also been examined. However, limited research exists on back-to-back walls, specifically regarding reinforcement stiffness, wall facia types, and battered angle of the facia. Therefore, more extensive research is required to gain a deeper understanding of the complexities involved. Additionally, an overview of the available literature on the design procedures for Mechanically Stabilized Earth (MSE) walls is presented, which is of great importance for practitioners and researchers in this field.
  • 65. Chapter 2 : Analysis and Evaluation for Geosynthetic-Reinforced Soil Retaining walls Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 51
  • 66. Chapter 3: Analysis of Back-to-Back Reinforced Retaining Walls with Panel Facing Under Railway Condition Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 51 SECOND PART NUMERICAL MODELING
  • 67. Chapter 3: Analysis of Back-to-Back Reinforced Retaining Walls with Panel Facing Under Railway Condition Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 52 Chapter 3 Analysis of Back-to-Back Reinforced Retaining Walls with Panel Facing Under Railway Condition 3.1 Introduction This chapter presents the performance evaluation of speared, and overlapped geogrid reinforced back-to-back mechanically stabilized earth walls supporting the railway tracks at bridge approaches. A numerical model for four cases was developed to analyze study was also carried out on varying W= (1.4;2 and 3H), LR =0.2H. Train bogie load was used as a loading condition. Lateral earth pressures, vertical deformations of walls, geogrid strain, maximum tensile force developed in the geogrid for all the cases were investigated and discussed in detail. Geogrid arrangements were found to be critical in reducing the wall displacement. The overlapping length of the geogrid resulted in lesser deformation compared to the speared geogrid we will seeing this in the suit of the chapter. 3.2 Finite Element Modeling In the present study, a finite element-based program, PLAXIS 2D, was used to develop a plane- strain model to analysis of the BBMSE supporting the railway walls. A 6 m-high wall resting on a 2 m-thick soil foundation and 0.3m thick ballast above the builder was considered. Figure 3.1 represents a finite element model of back-to-back MSE walls. For this, a overlapped model is chosen with of LR/H = 0.2 and a three models speared ratio in W/H= (1.4; 2 and 3H) the length of the reinforcements for the two walls was considered as LR = 4.2 m (the typical rebar length recommended by FHWA design guidelines (FHWA 2009), i.e. LR=0.7H). 3.2.1 Soil Proprieties The foundation soil was modeled as Mohr-Coulomb material with very high deformation modulus (E=200 MPa) to simulate it as a rigid material. The model involves six input parameters, namely, deformation modulus (E), Poisson ratio (ν), cohesion (c), friction angle (φ), and dilatancy angle (ψ). Table 3.1 presents the values of the material properties considered in the study. The soil-
  • 68. Chapter 3: Analysis of Back-to-Back Reinforced Retaining Walls with Panel Facing Under Railway Condition Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 53 reinforcement interaction was modeled by relating the nonlinear elastic behavior of the soil to the linear elastic response of the reinforcement. For this purpose, the geogrids are selected from the elastoplastic elements with stiffness and tensile strength. The interaction between the geogrid and soil was simulated using interface element. Figure 3.1 Finite element models of back-to-back MSE walls.
  • 69. Chapter 3: Analysis of Back-to-Back Reinforced Retaining Walls with Panel Facing Under Railway Condition Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 54 Table 3. 1. Material properties used in numerical simulations (Benmebarek el al. 2016). Material Symbol Unit Reinforced backfill Foundation soil Ballast Unit weight γs KN/m3 18 22 21 Angle of shearing resistance ϕ degrees 35 30 35 Dilatancy angle ψ degrees 5 0 5 Young’s modulus E KPa 30×103 200×103 30×103 Cohesion c KPa 0 200 30 Poisson's ratio ν - 0.3 0.2 0.3 Table 3. 2. Reinforcement properties. Identification Model Ultimate tensile strength Allowable tensile strength, Ta Axial stiffness Uniaxial geogrid Elastoplastic 70 KN/m 25.6 KN/m 1,100 KN/m 3.2.2 Reinforcement Table 3.2 gives the properties of the reinforcement - uniaxial geogrid (UX-1400 type). Geogrids were placed at typical pacing of 0.75 m (AASTHO 2012). The well-known segmental precast concrete panels were considered in the current study to simulate the wall. Each wall contains 4 segmental concrete panels of 1.5 m in width and height and 0.14 m in thickness. 3.2.3 Facing: Precast Panels The concrete panel facia was modeled as a linear-elastic material. In the present model, the facing panel was hinged to a horizontal plate which is 0.5m embedded in the foundation soil. Hence the panel had the flexibility to move in horizontal direction. However, the panel cannot be moved in vertical direction. The boundary condition applied in the model, simulates the real situation of embedment with nominal footing at the bottom of the concrete panel. Hence, nominal
  • 70. Chapter 3: Analysis of Back-to-Back Reinforced Retaining Walls with Panel Facing Under Railway Condition Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 55 lateral displacements can be expected in the real time scenario for the seismic loading. In the finite element model, the properties of the facing panel were defined by its young’s modulus, E = 25 GPa and the unit weight γc= 23.5 KN/m3 . Table 3.3 gives the properties of the facia considered in the study. Table 3. 3. Material properties of concrete panel facing elements and sleeper. Identification Elastic stiffness (EA) Flexural rigidity (EI) Thickness (d) Weight of panel (Wc) Poisson ratio (νc) Concrete panel facing 3.5×106 KN/m 5,717 KN/m2 0.14 m 3.29KN/m 0.2 Sleeper 10.5×106 KN/m 7,875 KN/m2 0.30 m 7.5 KN/m 0.2 3.2.4 Interface properties The interaction between the facing panel elements and the backfill and between the backfill and reinforcement were modeled by using interface elements (refer to Figure 3.1). A partially rough interface was considered, such that the interface parameter, Rinter, was equal to tan δ’/ tan φ, where interface friction angle δ’ = 23.0° and backfill friction angle φ = 35°. For the present study, the interface strength was reduced by using the strength reduction factor = 0.60 < 1 in these analyses. 3.4 Results and Discussions 3.4.1 Displacements of the wall Figure 3.2 shows the differences in maximum displacement at the interface for different successive MSE walls (BBMSEWs) under the effect of rail load. Comparison of three separate variable distance D models for different W ratio (1.4; 2 and 3H) with the overlap model of length reinforcement distances (LR = 0.2H). The results indicate that the staggered walls on either side of the BBMSEWs significantly reduce the lateral displacements. On the other hand, the walls separated from each other cause the displacement to be almost the same for W/H = 3.0 and 2.0. The highest offset is at W/H = 1.4, however, increasing the aspect ratio from 1.4 to 3.0 increases the maximum horizontal offset. These results were justified because successive walls do not
  • 71. Chapter 3: Analysis of Back-to-Back Reinforced Retaining Walls with Panel Facing Under Railway Condition Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 56 interact with each other, therefore, the two successive walls must operate independently when the walls overlap LR = 0.2H Figure 3.2 Horizontal Displacements UX for the wall. 3.4.2 Earth pressures behind wall. Figure 3.3 depicts the lateral earth pressure behind the wall, the lateral earth pressure. Accordingly, the earth pressures from the numerical model were presented and compared with those the active Rankine. However, the lateral earth pressure decreases in the overlapping model LR=0.2H and increases in the separate models when compared with the overlapped model which means are the overlapped better than separate (W=1.4; 2 and 3H).
  • 72. Chapter 3: Analysis of Back-to-Back Reinforced Retaining Walls with Panel Facing Under Railway Condition Performance of Back-to-Back MSE Walls Supporting the Rail Embankments 57 Figure 3.3 Earth pressure at the facing 3.4.3 Distribution of tensile force in reinforcements Figure.3.4 shows the tensile forces along the geogrid layers in the overlapped model and speared models at the end of construction. The maximum tensile forces in the geogrid layers with the product of soil unit weight, the geogrid vertical and horizontal intervals (SV and SH), and the wall height (H). The results indicate that near the wall facing, the tensile forces in both the overlapped and speared reinforcements increased with depth due to the effect.