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.

Aiming at the acid-etched freeze-thaw rock for geotechnical engineering in cold regions, chemical damage variables, freeze-thaw damage variables, and force damage variables were introduced to define the degree of degradation of rock materials, the law of damage evolution, the total damage variable of acid-corroded rock under the coupling action of freeze-thaw and confining pressure was deduced. The continuous damage mechanics theory was adopted to derive the damage evolution equation and constitutive model of acid-eroded rock under the coupling action of freeze-thaw and confining pressure. The theoretical derivation method was used to obtain the required model parameter expressions. Finally, the model’s rationality and accuracy were verified by the triaxial compression test data of frozen-thawed rocks. Comparing the test curve’s peak point with the peak point of the model theoretical curve, the results show that the two are in suitable agreement. The damage constitutive model can better reflect the stress-strain peak characteristics of rock during triaxial compression, verifying the rationality and reliability of the model and the method for determining the model parameters. The model extends the damage model of rock under the coupling action of freeze-thaw and confining pressure in the chemical environment and further reveals the damage mechanism and failure law of acid-corroded rock under the coupling action of freeze-thaw and confining pressure.