Statistical thermal damage constitutive model of rocks based on Weibull distribution

Abstract

On the basis of Lemaitre’s strain equivalence theory, the effects of high temperatures on the mechanical parameters of rock are taken into account, and a thermal damage variable DT is introduced. A statistical thermal damage constitutive model is developed by adopting the modified Mohr-Coulomb criterion with the hypothesis that the mesoscopic unit strength of rock subjected to thermal treatment obeys a Weibull random distribution. The values of the model parameters are determined by the extreme value method according to the concept of yielding. The rationality of the model is verified by comparing the calculated results with experimental results from uniaxial and conventional triaxial experiments of granite, marble, and sandstone specimens that were subjected to different high-temperature treatments. The results indicate that the model can simulate the whole process of stress-strain relations of different lithological rocks under different confined pressure and temperature conditions; the model can also reflect the characteristics of strain softening. The model does not contain any unconventional rock mechanics parameters and is lithology independent, which is highly convenient for engineering applications. This research can provide a theoretical basis for the development and protection of high-temperature rock projects.