A new mixed-mode phase-field model for crack propagation of brittle rock

Study on crack propagation process of brittle rock is of most significance for cracking-arrest design and cracking-network optimization in rock engineering. Phase-field model (PFM) has advantages of simplicity and high convergence over the common numerical methods (e.g. finite element method, discrete element method, and particle manifold method) in dealing with three-dimensional and multi-crack problems. However, current PFMs are mainly used to simulate mode-I (tensile) crack propagation but difficult to effectively simulate mode-II (shear) crack propagation. In this paper, a new mixed-mode PFM is established to simulate both mode-I and mode-II crack propagation of brittle rock by distinguishing the volumetric elastic strain energy and deviatoric elastic strain energy in the total elastic strain energy and considering the effect of compressive stress on mode-II crack propagation. Numerical solution method of the new mixed-mode PFM is proposed based on the staggered solution method with self-programmed subroutines UMAT and HETVAL of ABAQUS software. Three examples calculated using different PFMs as well as test results are presented for comparison. The results show that compared with the conventional PFM (which only simulates the tensile wing crack but not mode-II crack propagation) and the modified mixed-mode PFM (which has difficulty in simulating the shear anti-wing crack), the new mixed-mode PFM can successfully simulate the whole trajectories of mixed-mode crack propagation (including the tensile wing crack, shear secondary crack, and shear anti-wing crack) and mode-II crack propagation, which are close to the test results. It can be further extended to simulate multi-crack propagation of anisotropic rock under multi-field coupling loads.