Numerical Simulation of Spatial Crack Growth and the Local Failure Process of Rock Using the SMDSM Empowered by Structured 3-D Hierarchical Meshes

To accurately capture crack trajectory and failure morphology with continuum mesoscopic model-based methods in three-dimensional space, conventional global uniform refinement schemes may incur significant computational cost. This paper first presents a three-dimensional structured mesh refinement strategy to achieve the hierarchical discretization for the focused region. To deal with the mismatching problem caused by different-sized meshes, a coupling interface technique based on the discontinuous Galerkin framework is proposed. The validity and advantages of the present strategy are first verified by a benchmark example for elastic analysis. By strongly collaborating with the statistical meso-damage smear method, we further simulate the spatial crack growth (including a through-thickness crack, an embedded crack, and a surface crack) and the local failure process of a D-shaped tunnel. Great agreements between the simulation results and the available experiment or numerical reference results demonstrate that the present method can effectively simulate the rock fracturing process as well as save considerable computational time and memory storage.