Abstract: Under the influence of external factors, micro-cracks and pores develop within rock materials. Continuous damage mechanics define these internal micro-defects and investigates the physical and mechanical behavior of rock under damaged states. Within the theoretical framework of continuous damage mechanics, and based on the Mohr-Coulomb criterion, a statistical damage model is established by coupling power-law and exponential damage formulations, and its applicability and accuracy are verified. The main work includes two aspects: first, the classical coupling form and the exponential coupling form are compared, and their respective abilities to characterize stress-strain curve features are analyzed. Second, a suitable random variable for the micro-element strength distribution is derived based on the Mohr-Coulomb criterion so that the probability function satisfies the domain requirements of the random variable. On this basis, a constitutive equation is constructed and subsequently validated. The results provide a solid theoretical foundation for further engineering applications of statistical damage-based research.

Key words: Thermal Coupling, Mohr-Coulomb Criterion, Power-Law Distribution, Damage Coupling