Cellular Automata to Simulate Rock Failure

Rock fracture process that shows strong nonlinearity and complexity is simulated by cellular automata method. Cellular automata are considered as an efficient method to simulate complex system and study mechanisms of physical phenomena due to their locality and parallelization. In this paper rock samples can be discretized into cell elements that are connected with beam elements. Force and displacement are taken as the basic state variables. Based on equilibrium equations, constitutive equations and deformation equations local rules are attained, which overcomes the shortcoming of arbitrary decision of local rules. Maximum tensile strain criterion and Mohr-Coulomb criterion are introduced to judge the beginning of tensile failure and shearing failure respectively. And based on damage mechanics deformation and strength properties of damaged cell elements are estimated. This model can simulate heterogeneity of rock and crack propagation and coalescence. Finally based on this model fracture process and crack propagation and coalescence are simulated. The simulated results are in good accordance with typical experimental results and it proved that cellular automata method is a promising method to study rock fracture.