Limit Analysis and Soil Plasticity

1st Edition - January 1, 1975
Editor: Wai-Fah Chen
Language: English
eBook ISBN:
9 7 8 - 0 - 4 4 4 - 6 0 1 0 6 - 3

Developments in Geotechnical Engineering, Volume 7: Limit Analysis and Soil Plasticity covers the theory and applications of limit analysis as applied to soil mechanics. Organized… Read more

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Developments in Geotechnical Engineering, Volume 7: Limit Analysis and Soil Plasticity covers the theory and applications of limit analysis as applied to soil mechanics. Organized into 12 chapters, the book presents an introduction to the modern development of theory of soil plasticity and includes rock-like material. The first four chapters of the book describe the technique of limit analysis, beginning with the historical review of the subject and the assumptions on which it is based, and then covering various aspects of available techniques of limit analysis. The subsequent chapters deal with the applications of limit analysis to what may be termed “classical soil mechanics problems” that include bearing capacity of footings, lateral earth pressure problems, and stability of slopes. In many cases, comparisons of limit analysis solution and conventional limit equilibrium and slip-like solutions are also presented. Other chapters deal with the advances in bearing-capacity problem of concrete blocks or rock and present theoretical and experimental results of various concrete bearing problems. The concluding chapter examines elastic-plastic soil and elastic-plastic-fracture models for concrete materials. This book is an ideal resource text to geotechnical engineers and soil mechanics researchers.

Foreword

Preface

Chapter 1. Introduction

1.1. Introduction

1.2. Slip-Line Method and Limit Equilibrium Method

1.3. Limit Analysis Method

1.4. A Brief Historical Account of Soil Plasticity

Chapter 2. The Assumptions and Theorems Used in Limit Analysis

2.1 Introduction

2.2. Perfectly Plastic Assumption and Coulomb Yield Criterion

2.3. The Kinematic Assumption on Soil Deformations and the Concept of Flow Rule

2.4. The Assumption of Small Change in Geometry and the Equation of Virtual Work

2.5. Theorems of Limit Analysis

2.6. Limit Theorems for Materials with Non-Associated Flow Rules

Chapter 3. Limit Analysis by the Upper-Bound Method

3.1. Introduction

3.2. Rigid Block Sliding Separated by Narrow Transition Layer

3.3. Intermixing of Homogeneous Deforming Regions and Rigid Block Sliding

3.4. Intermixing of Inhomogeneous Deforming Regions and Rigid Block Sliding

3.5. Evaluation of the Minimum Solution for an Assumed Mechanism

3.6. The Dissipation Functions

Chapter 4. Limit Analysis by the Lower-Bound Method

4.1. Introduction

4.2. Mohr's Diagram and Basic Relations

4.3. Discontinuities in the Stresses

4.4. Jump Conditions at a Discontinuity Surface of Tresca Material

4.5. Jump Conditions at a Discontinuity Surface of Coulomb Material

4.6. Discontinuous Fields of Stress Viewed as Pin-Connected Trusses — Tresca Material

4.7. Discontinuous Fields of Stress Viewed as Pin-Connected Trusses — Coulomb Materials

4.8. Graphical Construction of Discontinuous Stress Fields

4.9. Combined Method for Solving the Problems Involving Overlapping of Discontinuous Stress Fields

Chapter 5. Progressive Failure of Footings

5.1. Introduction

5.2. Plane Strain Notched Tensile Specimen (Von Mises Material)

5.3. Plain Strain Punch Indentation of Rectangular Blocks (Von Mises Material)

5.4. Uniform Strip Load on a Shallow Stratum of Undrained Clay (Von Mises Material)

5.5. Rigid Strip Footing on an Elastic Stratum

5.6. Rigid Strip Footing on an Overconsolidated Stratum of Insensitive Clay (Extended Von Mises Material)

5.7. Rigid Strip Footing on a Stratum of Undrained Clay (Von Mises Material)

5.8. Rigid Circular Punch on an Elastic—Plastic Strain Hardening Layer (Isotropic Hardening Von Mises Material)

5.9. A Brief Historical Sketch

5.10. Summary and Conclusions

Chapter 6. Bearing Capacity of Strip Footings

6.1. Introduction

6.2. Limit Analysis, Slip-Line and Limit Equilibrium Methods

6.3. Soil Governing Parameters

6.4. Bearing Capacity of a Strip Footing on a General c-φ—γ Soil

6.5. Bearing Capacity of a Strip Footing on Cohesionless Soils (Nγ Factor)

6.6. Bearing Capacity of a Strip Footing on a c-φ Weightless Soil (Nc and Nq Factors)

6.7. Bearing Capacity Determination by Slip-Line Method

6.8. Bearing Capacity of Footings on Nonhomogeneous Anisotropic Soils

6.9. Summary and Conclusions

Chapter 7. Bearing Capacity of Square, Rectangular and Circular Footings

7.1. Introduction

7.2. Square, Rectangular and Circular Footings on a Semi-Infinite Medium — Lower Bounds

7.3. Square and Rectangular Footings on a Semi-Infinite Medium — Upper Bounds

7.4. Square and Circular Footings on a Finite Block — Lower Bounds

7.5. Square and Circular Footings on a Finite Block — Upper Bounds

7.6. Square and Circular Footings on a Semi-Infinite Layer - Lower Bounds

7.7. Square and Circular Footings on a Semi-Infinite Layer - Upper Bounds

7.8. Bearing Capacity of Circular Footings by Slip-Line Method

Chapter 8 Active and Passive Earth Pressures

8.1. Introduction

8.2. Coulomb's Solution of Vertical Retaining Wall Problems

8.3. Coulomb's Solution of General Retaining Wall Problems (Fig. 8.7a)

8.4. Two-Triangle Mechanism (Fig. 8.8)

8.5. Logsandwich Mechanism (Figs. 8.9 and 8.10)

8.6 Arc-Sandwich Mechanism (Fig. 8.12)

8.7. Discussion of Results

8.8. Comparison with Known Solutions

8.9. Earth Pressure Tables

8.10. Summary and Conclusions

Chapter 9. Stability of Slopes

9.1. Introduction

9.2. Logspiral Mechanism Passing Through the Toe

9.3. Logspiral Mechanism Passing Below the Toe

9.4. Stability of Slopes in Anisotropic, Non-Homogeneous Soils

9.5. Shape of Critical Slip Surface and Its Associated Normal Stress Distribution

9.6. Summary and Conclusions

Chapter 10. Bearing Capacity of Concrete Blocks Or Rock

10.1. Introduction

10.2. A Simplified Material Model

10.3. A Modified Coulomb Stress Criterion with Zero Tension Cut-off (Fig. 10.8a)

10.4. A Modified Coulomb Criterion with a Small But Not Zero Tension Cut-off (Fig. 10.8b)

10.5. Bearing Capacity under a Strip Loading — Upper Bound

10.6 Bearing Capacity under a Strip Loading — Lower Bound

10.7. Three-Dimensional Square and Circular Punches—Upper Bound

10.8. Three-Dimensional Square and Circular Punches — Lower Bounds

10.9. Friction Effects on the Bearing Capacity of Blocks

10.10. Concrete Blocks with a Concentric Cable Duct (Fig. 10.4a)

10.11. Concrete Blocks with an Eccentric Cable Duct — Small Eccentricity (Fig. 10.4b)

10.12. Concrete Blocks with an Eccentric Cable Duct — Large Eccentricity (Fig. 10.4b)

10.13. Experimental Study of the Strain Field

10.14. Comparison of Test Results with Calculated Strengths

10.15. Approximate Solution

10.16. Summary and Conclusions

Chapter 11. Double-Punch Test for Tensile Strength of Concrete, Rock and Soils

11.1. Introduction

11.2. Elastic Stress Distribution in Splitting Tests

11.3. Limit Analysis of Splitting Tensile Tests

11.4. Plastic Stress Distribution in Splitting Tests by Slip-Line Method

11.5. Plastic Stress Distribution in Splitting Tests by Finite Element Method

11.6. Plastic Stress Distribution in Double-Punch Test and Limit Analysis Solution

11.7. Experimental Results of Double-Punch Test for Concrete Materials

11.8. Experimental Results of Double-Punch Test for Rocks

11.9. Experimental Results of Double-Punch Test for Soils

Chapter 12. Soil Plasticity - Theory and Application

12.1. Introduction

12.2. Extended Von Mises Perfectly Plastic Model for Soil

12.3. An Elastic—Plastic Strain Hardening Model for Soil

12.4. An Elastic—Plastic Strain Hardening-Fracture Model for Concrete

12.5. Finite Element Formulation

12.6. Integration of the Displacement Rate Equilibrium Equations

12.7. Example 1 — Rigid Strip Footing on a Soil Stratum

12.8. Example 2 — Plane Strain Punch-Indentation of Concrete Blocks

12.9. Summary and Conclusions

References

Author Index

Subject Index