3D simulation of complex fractures with a simple mesh

Rock masses are 3D in nature. The contained complex fracture networks pose great difficulty to its computer-aided design (CAD) modeling and bring meshing burdens to classic finite element analysis (FEA). Considering the efficiency of digital images capturing complex geometries, as an extension of the previous 2D work, the 3D implementation of the image-based simulation is carried out in this work. Continuous-discontinuous deformations of complex rock masses are simulated in 3D with a simple structured mesh based on the numerical manifold method (NMM). Characteristics of the developed voxel crack model and its differences with discrete and smeared crack models are summarized. Based on this voxel crack model, the generating algorithm of 3D physical patches to construct the continuous-discontinuous trial function is introduced in detail. In the developed method, the three spatial resolutions, respectively of the image model, integration voxels, and mathematical elements, are independent. These resolutions can be chosen freely by trading off the accuracy need and the computational expenses. Numerical examples investigate the accuracy and convergence of this method. Its 3D simulation capability of complex rock masses is demonstrated by calculating the continuous-discontinuous deformation of El Capitan rock located in the Yosemite National Park with assumed complex fracture networks.