A closed-form solution for the 3D steady-state thermoporoelastic field in an infinite transversely isotropic rock weakened by an elliptical crack. (May 2020)

• Record Type: Journal Article
• Authors: Li, Peidong; Fan, Haidong; Wang, Meng; Zhou, Kun; Wang, Qingyuan
• Is Part Of: International journal of rock mechanics and mining sciences. Volume 129(2020)
• Publication Date: 2020-05
• Subjects: Elliptic crack -- Thermoporoelastic rock -- Transverse isotropy -- Analytical solution -- Potential theory method; Rock mechanics -- Periodicals; Soil mechanics -- Periodicals; Mining engineering -- Periodicals; Roches, Mécanique des -- Périodiques; Sols, Mécanique des -- Périodiques; Technique minière -- Périodiques; 624.151305
• DOI: 10.1016/j.ijrmms.2020.104292
• Languages: English
• ISSNs: 1365-1609

Abstract

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.