Abstract
Each porous rock will have unique mechanical behaviors due to its specific microstructural-lithologic combinations. There is no universal mathematical model for such porous rocks that present very different elastic properties. By focusing on nonlinear stress-velocity relations observed from the experimental measurement of individual porous rocks, we propose customized acoustoelastic models to account for stress-induced deformations with nonlinear strains that cannot be handled by traditional third-order elastic constants (3oeCs). Based on the nonlinear stress-strain curve from experimental data on artificial sandstones, we use nonlinear rock mechanics to identify several distinct phases developed during the stress-induced progressive deformations, i.e., nonlinear elastic (due to crack closure), hyperelastic (due to stress accumulation), nonlinear elastic (due to stable crack growth), and inelastic (due to unstable crack growth) deformations prior to mechanical failure. Different varieties of nonlinear Hooke’s law are applied within regions of the rock having significantly different stress strain behavior. The resulting nonlinear stress-strain constitutive relations are incorporated into the stiffness matrix of conventional acoustoelasticity to capture these stress-induced progressive deformations. Theoretical results from plane-wave analyses for stress-dependent velocity variations agree well with the laboratory measurements of artificial sandstones. Finite-difference simulations are implemented to solve the first-order velocity stress formulation of customized acoustoelastic equations for elastic wave propagation in porous rocks under hydrostatic and uniaxial prestresses. Comparisons with conventional acoustoelastic simulations provide a framework to estimate stress-induced inelastic strains from seismic responses in velocity and anisotropy.
Paper Information：
Yang, H., & Fu, L. Y. (2025). Customized acoustoelastic models for stress-dependent wave propagation in porous rocks with nonlinear strains. Geophysics, 91(2), 1-62. https://doi.org/10.1190/geo2025-0229.1
