Two-dimensional linear variation displacement discontinuity method for three-layered elastic media

Abstract

A new displacement discontinuity method is developed for the analysis of multi-layered elastic media. This approach is based on a novel superposition scheme and the analytical solution to the problem of a displacement discontinuity element within bonded half-planes. A three-layered elastic region is obtained by superposing two sets of bonded half-planes and subtracting one infinite plane. The advantages of this approach are: (1) it is not necessary to introduce elements at the interface, (2) the method is applicable for three dimensional modelling and (3) it can be extended to an N (N > 3) layer system easily. The accuracy of the model is illustrated by comparing the numerical results with the analytical solutions for a hole in an infinite strip in tension and with the numerical solution for a pressurized crack within a three-layered system. In order to show the efficacy of the developed model, the simulation results of a typical South African mining problem and general tunnel excavation problems are also presented.