Limit Analysis in Soil Mechanics

1. INTRODUCTION. A short historical review of soil plasticity. Idealized stress-strain relations for soil. Limit analysis for collapse load. Finite-element analysis for progressive failure behavior of soil mass. 2. BASIC CONCEPTS OF LIMIT ANALYSIS. The perfectly plastic assumption and yield criterion. The kinematic assumption on soil deformations and flow rule. The stability postilate of Drucker. Restrictions imposed by Drucker's stability postulate - convexity and normality. The assumption of small change in geometry and the equation of virual work. Theorems of limit analysis. Limit theorems for materials with non-associated flow rules. The upper-bound method. The lower-bound method. 3. VALIDITY OF LIMIT ANALYSIS IN APPLICATION TO SOILS. Soil - a multiphase material. Mechanical behavior of soils. Soil failure surfaces. Validity of limit analysis in application to soils. Friction-dilation and related energy in cohesionless soils. Effect of friction on the applicability of limit analysis to soils. Some aspects of retaining wall problems and the associated phenomena at failure. 4. LATERAL EARTH PRESSURE PROBLEMS. Failure mechanism. Energy dissipation. Earth pressure analysis (passive). Earth pressure analysis (active). Comparisons and discussions. Some practical aspects. 5. RIGID RETAINING WALLS SUBJECTED TO EARTHQUAKE FORCES. General considerations. Seismic passive earth pressure analysis. Seismic active earth pressure analysis. Numerical results and discussions. Earth pressure tables for practical use. Appendix A: Seismic earth pressure tables for Ka and Kp. Appendix B: Earth pressure tables for NAc and NPc. 6. SOME PRACTICAL CONSIDERATIONS IN DESIGN OF RIGID RETAINING STRUCTURES. Theoretical considerations of the modified Dubrova method. Some numerical results and discussions of the modified Dubrova method. Evaluation of the modified Dubrova method. Effects of wall movement on lateral earth pressures. Earth pressure theories for design applications in seismic environments. Design recommendations. 7. BEARING CAPACITY OF STRIP FOOTING ON ANISOTROPIC AND NONHOMOGENEOUS SOILS. Analysis. Results and discussions. 8. EARTHQUAKE-INDUCED SLOPE FAILURE AND LANDSLIDES. Failure surface. Determination of the critical height for seismic stability. Special spiral-slope configurations. Calculated results and discussions. Concluding remarks. 9. SEISMIC STABILITY OF SLOPES IN NONHOMOGENEOUS, ANISOTROPIC SOILS AND GENERAL DISCUSSIONS. Log-spiral failure mechanism for a nonhomogeneous and anisotropic slope. Numerical results and discussions. Mechanics of earthquake-induced slope failure. 10. ASSESSMENT OF SEISMIC DISPLACEMENT OF SLOPES. Failure mechanisms and yield acceleration. Assessment of seismic displacement of slopes. Summary. Appendix 1: Plane failure surface. Appendix 2: Log-spiral failure surface. Appendix 3: Limit analysis during earthquake. 11. STABILITY ANALYSIS OF SLOPES WITH GENERALIZED FAILURE CRITERION. Variational approach in limit analysis and the combined method. Stability analysis of slopes. Layered analysis of embankments. Summary.