Thermal damage constitutive model for rock considering damage threshold and residual strength

With the gradual depletion of mineral resources in the shallow part of the earth, resource exploitation continues to move deeper into the earth, it becomes a hot topic to simulate the whole process of rock strain softening, deformation and failure in deep environment, especially under high temperature and high pressure. On the basis of Lemaitre’s strain-equivalent principle, combined with statistics and damage theory, a statistical constitutive model of rock thermal damage under triaxial compression condition is established. At the same time, taking into account the existing damage model is difficult to reflect residual strength after rock failure, the residual strength is considered in this paper by introducing correction factor of damage variable, the model rationality is also verified by experiments. Analysis of results indicates that the damage evolution curve reflects the whole process of rock micro-cracks enclosure, initiation, expansion, penetration, and the formation of macro-cracks under coupled effect of temperature and confining pressure. Rock thermal damage shows logistic growth function with the increase of temperature. Under the same strain condition, rock total damage decreases with the rise of confining pressure. By studying the electron microscope images (SEM) of rock fracture, it is inferred that 35.40 MPa is the critical confining pressure of brittle to plastic transition for this granite. The model parameter F reflects the average strength of rock, and M reflects the morphological characteristics of rock stress–strain curves. The physical meanings of model parameters are clear and the model is suitable for complex stress states, which provides valuable references for the study of rock deformation and stability in deep engineering.