Three-dimensional fracture modelling of heterogeneous and anisotropic rock material under true triaxial compression

Underground excavation inevitably disturbs natural in-situ stress equilibrium of rocks, leading to localized deformation, fracture initiation, and potential large-scale failure. Understanding the failure mechanisms of rock under complex stress states is of great importance for ensuring the safety and stability of underground structures. To this end, a mesoscale numerical approach combining Weibull random fields with a hybrid phase-field model is adopted to investigate the failure mechanisms of heterogeneous rock materials under true triaxial compression. The isotropic model is further extended to anisotropic formulation by incorporating an anisotropic crack surface density function to account for directional fracture behaviour. First, the isotropic model is calibrated against experimental data by simulating triaxial compression of intact cuboid sandstone specimens, with the effects of confining stress and mesoscale heterogeneity systematically analysed. Next, the influence of pre-existing notches on 3D crack propagation is studied using the calibrated model. Finally, the anisotropic model is used to simulate the failure of intact and notched laminated rocks. It is found that rock fracture behaviour is governed by the combined effects of confining stress, mesoscale heterogeneity, and notch geometry. The incorporation of anisotropic fracture toughness enables directional control of crack propagation along bedding planes, successfully capturing joint-induced compression–shear failure. The developed approach provides a robust tool for simulating 3D failure in heterogeneous and anisotropic rocks under complex loading conditions.