Slope Analysis Using Boundary Elements

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.- 2.3.1 Kelvin's solution(2D).- 2.3.2 Melan's solution.- 2.4 Implementation of the boundary element method.- 2.4.1 Boundary integral equations.- 2.4.2 Numerical implementation.- 2.4.3 Subregions.- 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.- 3.4.1 Shallow tunnel.- 3.4.2 Vertical slope.- 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.- 4.5.1 Slope in homogeneous cohesive soil.- 4.5.2 Vertical slope in soil with friction.- 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.- Example 5-1.- Example 5-2.- Example 5-3.- 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.