Study of Rock Damage Constitutive Model Considering Temperature Effect Based on Weibull Distribution

The deformation and damage process of rocks is accompanied by crack extension and penetration. The rock strength criterion, as a macroscopic characterization of the rock strength microelement, is the basis for establishing the damage constitutive modeling of rock. Aiming at the problem of the Hoek–Brown (H–B) strength criterion having a large strength prediction value under high confining pressure, the H–B strength criterion is corrected by considering the influence of the initial cracks on the development of the rock strength, and its applicability is verified. Based on the damage theory, assuming that the rock strength microelement obeys the Weibull distribution and considering the influence of residual strength, the damage correction coefficient is introduced, and a thermal damage statistical constitutive model that can reflect the whole process of the development of initial cracks inside the rock is established. The degree of penetration up to the damage is established, and the method of determining the parameters of the model is given. The theoretical curves of the established model are compared and analyzed with the curves of a conventional triaxial compression test of rock samples, and the study shows that the statistical constitutive model of the thermal damage of rock, established based on the modified H–B strength criterion, can better simulate the stress–strain relationship of rock under a conventional triaxial test. It also verifies the reasonableness and applicability of the model, which is expected to provide a basis for the exploitation of deep resources and the safety assessment of underground engineering.