Modeling the cracking process of rocks from continuity to discontinuity using a cellular automaton

Abstract

A rock discontinuous cellular automaton (RDCA) was developed for modeling rock fracturing processes from continuous to discontinuous deformation under mechanical loading. RDCA is an integration of the following basic concepts: (1) representation of heterogeneity and strong discontinuity of rock material; (2) moving crack tracking with level set method; (3) the cellular automaton updating rule; (4) rock yield criteria and crack growth laws, etc. This model uses a local, “bottom–up” cellular automaton rule set and state input from neighboring cells to update the state of each cell in a stepped manner, avoiding the need to develop and solve large scale linear equations and the complexity therein. RDCA has the ability to simulate the non-linear and discontinuous deformation behaviors such as plastic yielding, crack initiation, propagation and coalescence etc., in the fracturing process of rocks. The theoretical background and numerical implementation of RDCA are introduced, and the associated numerical code is compiled in the C++ environment. Problems involving a central single crack, edge single crack propagation and three-point bending tests were numerically studied, and the results were compared with the analytical and experimental results to demonstrate the robustness of the method.