Plane-Strain Crack Problem in Transversely Isotropic Solids for Hydraulic Fracturing Applications

Abstract

This paper aims at understanding and predicting how pressurized cracks propagate in anisotropic brittle solids, a situation frequently encountered in hydraulic fracturing. Special attention is paid to transverse isotropy, often used to model shale. Although the theory of linear elastic fracture mechanics of anisotropic solids is well established at present, this paper shows that the application of Muskhelishvili’s formalism to Lekhnitskii’s anisotropic complex potentials provides a powerful tool to extend the validity of the classical tools of isotropic fluid-driven crack models to the anisotropic case, provided that the appropriate elastic constants are used. These elastic constants are identified and derived in closed form for transversely isotropic solids. The constants are shown to be directly related to quantities easily measured in a laboratory at macroscopic scale through indentation tests and acoustic measurements. Moreover, several crack-kinking criteria are compared. Contrary to the isotropic case, the crack-kinking criteria are not consistent among themselves, even in the case of a pure pressure loading. The orientation at which it is easier to propagate an already existing crack is sought. A critical crack length, below which this crack orientation is the one of minimal stiffness felt by the crack, is identified.