A statistical thermal damage constitutive model for rock considering characteristics of the void compaction stage based on normal distribution

Given the major impact of thermal treatment on the deformation and failure characteristics of rocks in deep rock engineering, it is crucial to understand the relevant behaviors of rocks with the temperature effect being taken into account. For this purpose, the deformation of rocks after exposure to high temperature is divided into void and skeleton portions based on the deformation analysis of rock mechanics. Then, a constitutive statistical model for rocks is established by assuming that the probability density function of the stress level of rock mesoscopic elements is consistent with normal random distribution, and the thermal damage variable is introduced. The theoretical results of the thermal damage deformation model based on characteristics of the void compaction stage are well in line with experimental data from conventional compression tests of Nanan granite after high temperature. Optical microscopy shows that the obvious void compaction stage is related to the propagation and development of original and initiated microcracks. Compared to the classic damage model, the improved model better captures the void compaction stage of the strain–stress curves of granite after high temperature. The extreme value method was used to determine the normal statistical distribution parameters based on conventional rock mechanical tests. This theoretical model is therefore convenient in engineering applications involving high-temperature effects.