Anisotropic acoustoelastic effective-medium model for stress-dependent elastic moduli of fractured rocks

Prestress significantly influences the mechanical properties of fractured rocks due to stress-induced anisotropy in the surrounding matrix and the stress-induced closure of cracks. Understanding the stress-dependent elastic moduli and anisotropic properties is crucial for various geoscience applications. The theory of acoustoelasticity only accounts for weak nonlinear elasticity with finite strains through the third-order elastic constants (3oECs) that are strictly valid for an isotropic homogeneous medium. Incorporating the David-Zimmerman (DZ) and Mori-Tanaka (MT) models into the theory of acoustoelasticity leads to an acoustoelastic DZ-MT model of fractured rocks. In this study, we extend the isotropic acoustoelastic DZ-MT model to address anisotropic conditions by examining two scenarios: one involving isotropic prestress applied to rocks with aligned cracks, and the other involving uniaxial prestress applied to rocks with isotropic cracks. The resulting anisotropic acoustoelastic DZ-MT model of fractured rocks is validated by experiment data measured from an artificial sample with aligned cracks and three isotropic sandstones (Massilon, Portland, and Berea). For the artificial sample, applying isotropic pressure will reduce the crack-induced anisotropy due to crack closure, leading in turn to increase the acoustoelastic effect on the background matrix as well as the effective elastic moduli of rocks. Aligned cracks primarily reduce the P-wave modulus for waves propagating perpendicular to the crack surfaces, making the P-wave modulus undergo significant changes because of its sensitivity to crack closure. For the natural sandstones with isotropic cracks subjected to uniaxial prestress, some existing cracks are closed, strongly depending on the relativity between crack orientation and loading direction. The P-wave modulus normal to the loading direction exhibits a slight increase, indicating the integrated effect of both acoustoelasticity and crack deformation. The complex microstructural changes in the case of uniaxial loading influence the application of acoustoelasticity and crack-closure model, potentially reducing the accuracy of the proposed DZ-MT model.