APPLICATION OF THE EDGE FUNCTION-METHOD TO ROCK MECHANICS PROBLEMS

The edge function method is considered as an alternative to convention al numerical schemes for the solution of plane problems in rock mechan ics. The essence of the approach is the approximation of the solution by a linear combination of solutions of the held equations. The unknow ns in the linear combination are obtained from a system of equations w hich follows from the approximation of the boundary conditions by a bo undary Galerkin energy method. No mesh generation is required over the domain or boundary of the problem. Previous edge function work in ani sotropic elasticity is enhanced by the incorporation of a special solu tion for the effect of gravity. Examples are presented to illustrate t he applicability of the method in determining stresses in various rock mechanics problems. A high level of accuracy is achieved with a relat ively small number of degrees of freedom. Convergence is rapid because of the inclusion of special analytic solutions to model stress concen trations. The inclusion of the gravity force does, however, lead to a small increase in the number of degrees of freedom needed to achieve a cceptable results. The optimum use of the edge function method, at pre sent, may be as a special element within more general finite element o r discrete element codes.