The phase field numerical manifold method for crack propagation in rock

Fracture is one of the most common failure modes of materials and components and greatly restricts engineering design. Understanding of the crack propagation and evolution of rock and other engineering materials is of great significance to engineering construction. For the current numerical methods there are more or less limitations when analyzing the evolution of cracks, such as the grid dependence of the crack path, the difficulty to deal with crack bifurcation and merging by the classic fracture criterion. In recent years, the phase field method (PFM) has been widely used in simulating crack growth. A phase field numerical manifold method (PFNMM) makes use of the advantages of the phase field method in simulating crack propagation and those of the numerical manifold method (NMM), and is proposed for crack growth in rock. The implementation details of the proposed numerical model are presented. Several benchmark examples, including notched semi-circular bend test and Brazilian disc test, are adopted to validate the proposed numerical approach. After that, the multi-crack propagation process with different rock bridge inclination angles under uniaxial compression is simulated, which is in good agreement with the results derived from laboratory and PFC. And the results indicate that the PFNMM has broad application prospects in simulating crack growth of rock.