A closed-form solution for the 3D steady-state thermoporoelastic field in an infinite transversely isotropic rock weakened by an elliptical crack

Abstract

This paper develops a closed-form analytical solution for the problem of an infinite transversely isotropic thermoporoelastic rock weakened by an elliptic crack lying in the transverse plane. The crack is symmetrically subjected to three pairs of uniform generalized loads, i.e., mechanical pressure, pore pressure and temperature increment, on the upper and lower crack surfaces. Based on the general solution, the three-dimensional (3D) steady-state thermoporoelastic field in the rock are explicitly derived in terms of elemental functions and elliptic integrals by the generalized potential theory method. The crack surface displacements, crack stiffness, normal stress in the cracked plane, and stress intensity factor at the crack tip are obtained as well. In the numerical calculation, the obtained analytical solution is first degenerated into the one for a circular crack for the purpose of verification, and then used to demonstrate the thermoporoelastic field around an elliptic crack and its geometric effect on the stress intensity factor at its tips. The present solution can serve as a convenient benchmark to various numerical codes for simulations of rock fracture.