Limit Analysis and Soil Plasticity
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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.
Table of Contents
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
Product details
- No. of pages: 638
- Language: English
- Copyright: © Elsevier 1975
- Published: January 1, 1975
- Imprint: Elsevier
- eBook ISBN: 9780444601063
About the Editor
Wai-Fah Chen
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