Analysis of arbitrarily shaped, planar cracks in a three-dimensional transversely isotropic thermoporoelastic medium

The displacement discontinuity boundary integral equation method is extended to analyze planar cracks of arbitrary shape embedded in a three-dimensional, transversely isotropic, thermoporoelastic medium. Based on the general solutions and Hankel transform technique, the fundamental solutions for unit-point, extended displacement discontinuities (including the displacement discontinuities, pore pressure discontinuity, and the temperature discontinuity) are derived. The extended displacement discontinuity boundary integral equations are established for an arbitrarily shaped, planar crack in the isotropic plane of the thermoporoelastic medium in terms of the extended displacement discontinuities. Using the boundary integral equations method, the singularities of near-crack front fields are analyzed, and the stress, fluid flux and heat flux intensity factors are derived in terms of the extended displacement discontinuities. To validate the analytical solution, the EDD boundary element method is proposed. The numerical simulation of a penny-shaped crack under combined uniform mechanical-pore pressure-thermal loadings is compared with the analytical solution to validate the correctness of the proposed method. As an application, two coplanar elliptical cracks are numerically simulated. The influences of the applied, combined mechanical-pore-pressure-thermal loadings, the crack distance, the ellipticity ratio as well as the size of cracks are all studied.