Phase-field modeling of crack growth and interaction in rock

A better understanding of crack growth and interaction in rock is of great significance to investigate the mechanical properties of rock at a macroscopic scale. In the present paper, we present and implement a crack growth model into the phase field method (PFM) to investigate crack nucleation, growth, and interaction in rock. The PFM-based crack growth model is validated against constant strain rate tests on sandstone samples containing a single pre-existing inclined crack in which digital image correlation was used to monitor crack growth and deformation. The numerical failure patterns and stress–strain curves are in good agreement with the laboratory experimental results. The experimental and numerical results both demonstrate that the initiation position of the wing cracks changes from the middle to the tips of the pre-existing crack as the pre-existing crack inclination angle is increased. The numerical simulation results also show that the rock bridge ligament angle (β) exerts an important influence on crack interaction and the peak stress of sandstone containing two pre-existing cracks. Furthermore, three different types of crack coalescence (non-coalescence mode, inner-inner tips coalescence mode, and inner-outer tip coalescence mode) were observed at different rock bridge ligament angles. The extended PFM-based crack growth model presented in this paper helps to understand the complex fracture process of rock in an engineering geological environment.