The edge function method and singular problems in rock mechanics

Abstract

The edge function method is considered as an alternative to conventional numerical schemes for the solution of singular plane problems in isotropic and anisotropic rock masses. Particular interest is focused on the interaction of singularities, such as discontinuous loads and crack problems, with a gravity body force term. The essence of the edge function approach is the approximation of the solution by a linear combination of solutions of the field equations. The unknowns in the linear combination are obtained from a system of equations which follows from the approximation of the boundary conditions by a boundary Galerkin energy method. No mesh generation is required over the domain or boundary of the problem. In this paper, discontinuous loads are modeled using special solutions which satisfy polynomial boundary data in the neighborhood of a vertex. Crack behavior is modeled using special solutions which satisfy prescribed tractions on the crack faces. Accurate results are obtained for step loads and crack problems using approx. 100 degrees of freedom. The gravity term does not adversely affect the convergence and the high level of accuracy achieved in earlier edge function fracture work is maintained.