THE EDGE FUNCTION-METHOD AND SINGULAR PROBLEMS IN ROCK MECHANICS

The edge function method is considered as an alternative to convention al numerical schemes for the solution of singular plane problems in is otropic and anisotropic rock masses. Particular interest is focused on the interaction of singularities, such as discontinuous loads and cra ck problems, with a gravity body force term. The essence of the edge f unction approach is the approximation of the solution by a linear comb ination of solutions of the field equations. The unknowns in the linea r combination are obtained from a system of equations which follows fr om the approximation of the boundary conditions by a boundary Galerkin energy method. No mesh generation is required over the domain or boun dary of the problem. In this paper, discontinuous loads are modeled us ing special solutions which satisfy polynomial boundary data in the ne ighborhood of a vertex. Crack behavior is modeled using special soluti ons which satisfy prescribed tractions on the crack faces. Accurate re sults are obtained for step loads and crack problems using approx. 100 degrees of freedom. The gravity term does not adversely affect the co nvergence and the high level of accuracy achieved in earlier edge func tion fracture work is maintained.