Abstract: The decrease of rock stability is caused by the possible deterioration of rock mechanical properties under high temperature environment. Therefore, the study of the constitutive behavior of rocks under high temperature is of great significance. Based on the recent researches of statistical rock damage constitutive model, the statistical damage constitutive model of rock after high temperature is established by adopting M-C criterion with the thermal damage variable and Weibull distribution function and the parameter expression is determined. The model is compared with the theoretical curve to verify its rationality. Finally, the model is verified by the uniaxial compression test results of sandstone under different temperature conditions (e.g., 25 ℃, 80 ℃, 100 ℃, 150 ℃). The results show that the theoretical curve of statistical damage constitutive model of the high-temperature rock established in this paper has the same trend as the theoretical curve in the literature, proving that the established constitutive model is reasonable. The theoretical curve of the model is in good agreement with the curve obtained in the experiments, implying that it can represent the stress-strain characteristics of sandstone failure under the condition of uniaxial test. This model does not contain unconventional mechanical parameters, and the physical meaning is clear. The research results can provide theoretical support for related calculations and numerical simulations of rock mechanics after high-temperature treatment.

Key words: Weibull distribution, high temperature rock, Mohr-Coulomb criterion, thermal damage, constitutive model