Modification of the boundary element method for computation of three-dimensional fields of strain–stress state of cavities with cracks

Abstract

In order to solve the three-dimensional problem of crack initiation in a cavity and propagation in an elastic medium under the effect of pumping a viscous liquid inside the cavity, a modification of the boundary element method is used for determining the strain–stress state in vicinity of the cavity with the crack connected to it, loaded with the pumped-in viscous liquid. The foundation of the method is equations of elastic equilibrium written in the form of boundary integral equations. The conventional boundary element method cannot be used for this problem because the boundary integral equation for displacements degenerates at the crack. In the known dual boundary element method, with the purpose of eliminating this drawback of the conventional method, an additional boundary integral relation at the discontinuous part of the boundary is constructed. Therewith, discontinuing elements are introduced, which allow to approximate integral relations and regularize and calculate singular integrals. The goal of this study is to modify the dual boundary element method for three-dimensional model of crack propagating from cavity under the effect of pumped-in viscous liquid in an elastic unbounded medium. One of the problems is a fully three-dimensional modeling of the hydraulic crack process starting from well, for the solution of which the developed profit-proved modification of the dual method was successfully employed. The research results are presented thereof.