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The aim of this book is to provide a new angle on the analysis of slope stability with the Boundary Element Method. The main advantages of BEM are the reduction of the dimensionality of the problem to be solved and accurate selective calculation of internal stresses. This makes it possible, as shown in the book, to develop the algorithms of slip surface analysis of slope more accurate, more rigorous and more easy to be used than in the conventional limit equilibrium methods. The full elastoplastic analysis of slope is also investigated. Besides, the interested reader can find a detailed study of Melan's fundamental solution such as its displacements, its corresponding Galerkin tensor and the treatment of body forces in the half-plan. The basic theory of BEM is outlined in the book so that undergraduate and graduate students of civil engineering, mining engineering and engineering geology can read it without difficulty.
List of contents
1 Introduction.- 1.1 Statement of the problem.- 1.2 Limit equilibrium methods.- 1.3 Finite element method.- 1.4 Boundary element method.- 2 Basic Theory and Techniques of Boundary Element Method.- 2.1 Governing equations.- 2.2 Integral equations.- 2.3 Fundamental solutions.- 2.4 Implementation of the boundary element method.- 3 Galerkin Tensor and Transformation of Body Force Integral.- 3.1 Transformation of body force integral.- 3.2 Galerkin tensor.- 3.3 Gravitational force integral for the half plane.- 3.4 Examples.- 4 Direct Boundary Element Approaches for Slope Stability Analysis.- 4.1 Formulations of the plastic ratio method.- 4.2 Calculations of the excess stresses.- 4.3 Implementation.- 4.4 Plastic ratio.- 4.5 Examples.- 4.6 Slope analysis using the joint elements.- 4.7 Elastoplastic analysis of slope stability.- 5 Indirect Boundary Element Algorithm for Slope Stability Analysis.- 5.1 Introduction.- 5.2 Constant quadrupole element.- 5.3 Indirect boundary element algorithm.- 5.4 About redistributions of excess stresses.- 5.5 Slope stability analysis.- 6 General Conclusions.- References.- Appendix A Displacements of Melan's Solution Deduced from the Corresponding Airy's Functions.- Appendix B Developments of Galerkin Tensor Corresponding to Melan's Solution.
