Abstract
The problems of quasi-static poroelasticity for a cavity and a crack in an isotropic homogeneous medium are considered. The cavity (crack) surface is subjected to pressure of fluid injected inside by external sources. Using simple and double layer potentials of poroelasticity the problems are reduced to 2D-integral equations on the cavity and crack surfaces. The case of spherical cavity is considered in detail. It is shown that the 2D-integral equations of the crack problem contain operators with various time-asymptotics at infinity. Neglecting operators rapidly vanishing with time results in an approximate formulation of the crack problem. For numerical solution, the integral equations are discretized using Gaussian approximating functions. For planar cracks, an efficient numerical method based on the fast Fourier transform technique is proposed. Numerical solution for a penny shaped crack is presented.
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