Abstract

Stress-induced progressive deformations in fractured rocks with increasing effective pressure generally undergo nonlinear elastic (due to the closure of compliant pores), hyperelastic (due to residual stress), and inelastic (due to fracture 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. With attention to nonlinear elastic and hyperelastic deformations, we incorporate acoustoelasticity into the traditional Hudson/Cheng models to describe the coupling of fracture-induced and stress-induced anisotropies. The resulting acoustoelastic Hudson model (AHM) is valid for the crack density smaller than 0.1 whereas the Padé AHM could handle higher crack densities. We extend the Padé AHM to consider the stress-induced crack closure with nonlinear elastic deformations by incorporating the dual-porosity model. These models approach the coupled anisotropies with different accuracies and computational complexities. The plane-wave analyses and effective-moduli calculations of stressed fractured rocks with varying crack densities determine the accuracy of these models under the isotropic (confining) and anisotropic (uniaxial and pure shear) prestress conditions. The relevant Thomsen parameters are applied to experimental data to validate the applicability. Finite-difference simulations are implemented to identify the contribution of different anisotropies through the variety of wavefronts, depending on fracture orientation, crack density, prestress mode and magnitude, and loading direction. Particular attention is paid to the anisotropic prestress, where the coupled anisotropies are constructive or destructive interference, strongly related to the relativity between fracture strike and loading direction. The stress-induced crack closure will reduce the fracture anisotropy so that the stress-induced background anisotropy dominates the shape of wavefronts with increasing prestress.