Study on Probabilistic Damage Constitutive Relation of Rocks Based on Maximum-Entropy Theory

The Weibull-distribution–based probabilistic damage model is widely used to represent the mesoscopic strength distribution of rock. However, it is unable to adequately describe the entire rock failure process. In this paper, based on the maximum entropy theory, a new probabilistic damage model is proposed to characterize the entire rock failure process. The reasonableness of this new model was verified against experimental data. The physical meaning of entropy, which is used to describe rock failure, was analyzed using the statistical method. It is demonstrated that when entropy is used to build the probabilistic damage model, an increase in the entropy corresponds to an increase in the rock damage, and the maximum entropy corresponds to the maximum probability of damage occurring. Thus, it is reasonable to use the maximum entropy to establish a probabilistic damage model. Finally, the effects of the constraint conditions on this maximum-entropy-based model are discussed.