A phase field model with modified volumetric-deviatoric decomposition for the mixed-mode fracture of rock

Recent attempts of phase field models to simulate rock fracture problems have been regarded as fruitful, owing to their powerful crack characterization capability. However, existing phase field models still exhibit limitations in simulating quasi-coplanar shear cracks and related coalescence patterns that often occur in rock failure. In this study, we propose a novel phase field model to simulate the mixed-mode fracture, in which a modified volumetric-deviatoric decomposition that combines the advantages of the volumetric-deviatoric decomposition and the spectral decomposition is conducted to distinguish between tensile, tensile-shear, and compressive-shear fractures; to reduce unrealistic damage in the area outside the crack trajectory, a threshold parameter is introduced into the degradation function to control whether the related energy participates in damage evolution; and the hybrid formulation is employed to efficiently and robustly solve the displacement and phase fields alternately. The feasibility of the proposed phase field model is first validated by a benchmark example. Next, the application of this model to the simulations of different rock specimens under uniaxial compression reveals a better agreement with experimental observations than previous simulation results, demonstrating an advancement over existing phase field models.