Modeling Rock Fracturing Processes Using the Phase Field Numerical Manifold Method

The phase field method (PFM) has been proposed and incorporated into the finite element method (FEM) for complex crack evolution problems. However, explicit cracks cannot be obtained in the phase field FEM (PFFEM). In the field of rock engineering, explicit cracks are indispensable for hydraulic fracturing problem in which crack opening displacement should be known, and compression-shear crack problems in which contact region should be determined. In this paper, the recently proposed phase field numerical manifold method (PFNMM) is developed to model rock fracturing processes. In PFNMM, PFM is regarded as a fracturing criterion, which deals with crack initiation, propagation, bifurcation and coalescence in a unified form; then crack paths are reconstructed and reproduced from smearing cracks; finally, the physical patches and manifold elements are cut with the reconstructed paths to obtain explicit cracks. The numerical results for several typical examples indicate that rock fracturing processes, including crack initiation without any preset cracks, crack propagation and crack merging, can be explicitly predicted. Besides, the results are in good agreement with the literature. Compared with PFFEM, explicit cracks and jump displacement fields across rock crack faces can be easily obtained by PFNMM.