3D probabilistic cellular automation modeling of transition to fracture in rocks under loading

Abstract

Abstract The three-dimensional model of the probabilistic cellular automaton, which has previously been constructed on the basis of the kinetic theory of strength, is studied in this paper. It describes the process of rock damage accumulation and formation of a damage cluster structure. Comparing the kinetic curves of damage accumulation and correlation functions of the model experiments, it is found that, depending on the sprouting probability of the damage cluster perimeter, which simulates the rate of material fracture under the action of local overstresses near the existing damage clusters, two qualitatively different modes of damage accumulation are observed in the 3D model. For the sprouting probabilities of the cluster perimeter higher than 0.2, the process of transition to irreversible fracture is significantly accelerated and becomes strongly correlated. Along with this, the best agreement of correlation functions in the model and in the physical experiments is observed for the sprouting perimeter probability values smaller than 0.2.