Rocks are natural materials with a heterogeneous microstructure, and the heterogeneity of the microstructure plays a crucial role in the evolution of microcracks during the compression process. A numerical model of a rock with a heterogeneous structure under compression is developed by digital image processing techniques and the discrete element method. On the grain scale, the damage mechanism and microcrack characteristics of a heterogeneous Biotite granite under compression fracture are investigated. First, the process of constructing a digital image-based heterogeneous grain model is described. The microscopic characteristics of geometric heterogeneity, elastic heterogeneity, and contact heterogeneity are all considered in the numerical model. Then, the model is calibrated according to the macroscopic properties of biotite granite obtained in the laboratory, and the numerically simulated microcrack cracking processes and damage modes are obtained with a high degree of agreement compared to the experiments. Numerical simulations have shown the following: (1) Microcracking occurs first at the weak side of the grain boundaries, and the appearance of intragranular shear cracks indicates that the rock has reached its peak strength. (2) The stress concentration caused by the heterogeneity of the microstructure is an essential factor that causes rock cracks and induces rupture. Intragranular cracks occur successively in quartz, feldspar (plagioclase), and biotite, with far more intragranular cracks in quartz and feldspar (plagioclase) than in biotite. (3) Microcracking in quartz occurs as clusters, fork and fracture features, and in feldspar (plagioclase) it tends to cause penetration microcracking, which usually surrounds or terminates at the biotite. (4) As the confining pressure increases, the tensile break between the grains is suppressed and the number of shear cracks increases. At the macro level, the rock failure mode of the numerical model changes from split damage to shear destruction, which is consistent with the law shown in laboratory experiments.

Based on Lemaitre’s strain equivalence hypothesis theory, it is assumed that the strength of acid-etching rock microelements under the coupling effect of temperature and confining pressure follows the Weibull distribution. Under the hypothesis that micro-element damage meets the D-P criterion and based on continuum damage mechanics and statistical theory, chemical damage variables, thermal damage variables and mechanical damage variables were introduced in the construction of damage evolution equations and constitutive models for acid-etching rocks considering the coupled effects of temperature and confining pressure. The required model parameters were obtained by theoretical derivation, and the model was verified based on the triaxial compression test data of granite. Comparing the experimental stress-strain curve with the theoretical stress-strain curve, the results show that they were in good agreement. By selecting reasonable model parameters, the damage statistical constitutive model can accurately reflect the stress-strain curve characteristics of rock in the process of triaxial compression. The comparison between the experimental and theoretical results also verifies the reasonableness and reliability of the model. This model provides a new rock damage statistical constitutive equation for the study of rock mechanics and its application in engineering, and has certain reference significance for rock underground engineering.

For thermal and loaded rock in engineering structures for some projects, triple-shear Drucker–Prager yield criteria, compaction coefficient K, damage variable correction factor δ, and thermal damage variable D_T are introduced in a new thermomechanical (TM) constitutive model for the entire process. The compaction stage of rock in uniaxial compression test and the strain softening of rock caused by thermal attack are considered in this article. The damage evolution of rocks is described by a damage variable and a constitutive equation, which are in agreement with the actual thermal experimental breakage. The uniaxial compressive strength of granite subjected to a TM coupling effect can be predicted properly by this new unified constitutive model. The new TM unified constitutive model considering the compaction stage and post-failure stage is in good agreement with the test curves throughout the entire process. The coupling effect of heat and load in the total damage of rock has obvious nonlinear properties, but the coupling effect significantly weakens the specimens. By using the new TM unified constitutive model, the whole process of changes in rock damage with strain after high temperature can be calculated. Meanwhile, the model well represents the stress–strain curve at the post-failure stage. It is expected that this model can provide references for studying the mechanical response of the rock damage propagation characteristics in the future.