Anisotropic fracture phase-field model to characterize multi-mode fracture behavior of laminated rocks under various loading conditions

Abstract

Accurately capturing the anisotropic fracture behavior of laminated rocks, such as initiation, propagation, branching, and coalescence, is challenging. This study introduces an anisotropic fracture phase-field model to capture the complex fracture patterns of laminated rocks. A structural tensor is constructed to characterize the rock’s anisotropy and is embedded into a crack density function to quantify the anisotropic fracture energy. Energy decomposition based on strain tensor and a shear failure energy criterion are utilized to derive equations describing tensile–shear and compressive–shear actions, which account for different fracture mechanisms. The equations and the anisotropic fracture energy function are integrated into a fracture variational framework to develop a mixed phase-field model that simulates the multi-mode fracture behavior of laminated rocks. The performance of the proposed model is evaluated by comparing it with experimental data and existing models, demonstrating its effectiveness in simulating crack propagation under tensile, tensile–shear, compressive–shear, and mixed-mode fractures. The influences of the anisotropic properties, stress paths, and critical energy release rate ratio on crack propagation in laminated rocks are comprehensively examined.