Boundary Element Method in Geomechanics

1 Introduction.- 2 Material Behaviour and Numerical Techniques.- 2.1 Introduction.- 2.2 Linear Elastic Material Problems.- 2.3 Nonlinear Elastic Material Problems.- 2.4 Inelastic Material Problems.- 2.5 Time-Dependent Problems.- 3 Boundary Integral Equations.- 3.1 Introduction.- 3.2 Governing Equations and Fundamental Solutions.- 3.3 Integral Equations.- 3.4 Body Force Problem.- 3.5 Prestress Force Problem.- 3.6 Temperature Shrinkage and Swelling.- 4 Boundary Integral Equations for Complete Plane Strain Problems.- 4.1 Introduction.- 4.2 Governing Equations and Fundamental Solutions.- 4.3 Integral Equations for Interior Points.- 4.4 Boundary Integral Equation.- 5 Boundary Element Method.- 5.1 Introduction.- 5.2 Discretization of the Integral Equations.- 5.3 Subregions.- 5.4 Traction Discontinuities.- 5.5 Thin Subregions.- 5.6 Solution Technique.- 5.7 Practical Application of Boundary Element on Linear Problems.- 6 Notension Boundary Elements.- 6.1 Introduction.- 6.2 Rock Material Behaviour.- 6.3 Method of Solution.- 6.4 Application of No-Tension in Rock Mechanics.- 7 Discontinuity Problems.- 7.1 Introduction.- 7.2 Plane of Weakness.- 7.3 Analysis of Discontinuity Problems.- 7.4 Numerical Applications.- 8 Boundary Element Technique for Plasticity Problems.- 8.1 Introduction.- 8.2 Elastoplastic Problems in One Dimension.- 8.3 Theory of Plasticity for Continuum Problems.- 8.4 Numerical Approach for the Plastic Solution.- 8.5 Practical Applications in Geomechanics.- 9 Elasto/Viscoplastic Boundary Element Approach.- 9.1 Introduction.- 9.2 Time-Dependent Behaviour in One Dimension.- 9.3 Elasto/Viscoplastic Constitutive Relations for Continuum Problems.- 9.4 Outline of the Solution Technique.- 9.5 Time Interval Selection and Convergence.- 9.6 Elasto/Viscoplastic Applications.- 10 Applications of the Nonlinear Boundary Element Formulation.- 10.1 Introduction.- 10.2 Strip Footing Problem.- 10.3 Slope Stability Analysis.- 10.4 Tunnelling Stress Analysis.- 11 Conclusions.- References.- Appendices.