Stress-Dependent Wave Propagation in Fractured Rocks With Nonlinear Elastic and Hyperelastic Deformations

Abstract

Stress-induced progressive deformations in fractured rocks with increasing differential stress generally undergo nonlinear elastic (due to crack closure), hyperelastic (due to stress accumulation), and inelastic (due to crack growth) deformations prior to mechanical failure. Wave propagation in such rocks involves the complex interaction of fracture- and stress-induced changes in both velocity and anisotropy. By focusing on nonlinear elastic and hyperelastic deformations, we incorporate acoustoelasticity into the traditional Hudson and Padé–Hudson models of penny-shaped ellipsoidal cracks to describe the coupling of fracture- and stress-induced anisotropies. The resulting acoustoelastic Hudson model (AHM) and Padé AHM can be used to describe the stress-dependent anisotropy of fractured rocks with varying crack densities. We integrate the dual-porosity model into the Padé AHM to account for the stress-induced closure of cracks with nonlinear elastic deformations. The plane-wave analyses and effective-moduli calculations of fractured rocks with varying crack densities and loading stresses determine the accuracy of these models under the isotropic (hydrostatic) and anisotropic (uniaxial and pure-shear) prestresses. The resulting Thomsen parameters are applied to experimental data to validate their applicability. Finite-difference simulations are implemented to differentiate the contribution of fracture- and stress-induced anisotropies through wavefront changes, depending on fracture orientation, crack density, prestress mode, and loading direction. Particular attention is paid to the anisotropic prestress perpendicular to the fracture strike, where the stress-induced crack closure reduces the fracture anisotropy so that the stress-induced anisotropy dominates the shape of wavefronts.