Boundary Element Method in Geomechanics

Numerical techniques for solving many problems in continuum mechanics have experienced a tremendous growth in the last twenty years due to the development of large high speed computers. In particular, geomechanical stress analysis can now be modelled within a more realistic context. In spite of the fact that many applications in geomechanics are still being carried out applying linear theories, soil and rock materials have been demonstrated experimentally to be physically nonlinear. Soils do not recover their initial state after removal of temporary loads and rock does not deform in proportion to the loads applied. The search for a unified theory to model the real response of these materials is impossible due to the complexities involved in each case. Realistic solutions in geomechanical analysis must be provided by considering that material properties vary from point to point, in addition to other significant features such as non-homogeneous media, in situ stress condition, type of loading, time effects and discontinuities. A possible alternative to tackle such a problem is to inttoduce some simplified assumptions which at least can provide an approximate solution in each case. The validity or accuracy of the final solution obtained is always dependent upon the approach adopted. As a consequence, the choice of a reliable theory for each particular problem is another difficult decision which should be 2 taken by the analyst in geomechanical stress analysis.

Contenu
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.