A three-dimensional boundary element method for piecewise homogeneous viscoelastic media and its application in mining engineering

Abstract

A 3-D boundary element method of viscoelasticity is presented for analyzing the time-dependent deformation and stress state around underground mine workings. It assumes that the rocks are stratified with bedding planes and reinforced by fully or partially grouted rock bolts. The Kelvin-Voight and Burgers models are used to represent the viscoelastic behavior of rock strata. Boundary integral equations for these types of separately homogeneous media are developed based on the correspondence principle of viscoelasticity. The time-dependent functions involved in the equations are obtained through the use of the Laplace transformation technique. Thus, the method can compute the stress state of a rock structure without the need to discretize variables which alter with time. An example is presented to show the application of this method to mining engineering.