Integral equations of the crack problem of poroelasticity: Discretization by Gaussian approximating functions

Abstract

The paper is devoted to the problem of poroelasticity for a homogeneous isotropic medium with a crack. The medium is subjected to external loading and fluid pressure arbitrary distributed on the crack surface. The solution is presented as a combination of the potentials of simple and double layers of poroelasticity. Boundary conditions on the crack surface provide integral equations for the densities of these potentials. 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. An example of a penny-shape crack subjected to a constant pressure is considered.