## 1 Introduction  
With the depletion of surface and shallow resources, mines have entered a state of deep resource mining. However, the high-temperature and high-confining-pressure environment in deep rock mining also brings challenges to the safe construction of underground engineering. For example, the carbonate rock thermal reservoir in the Xiong'an New Area is rich in geothermal resources, and its buried depth is 1000-2000 m underground. The ambient temperature can reach more than 60 \({}^{\circ}\)C, and the surrounding geological structure is complicated, making construction and exploitation difficult [1]. For effective exploitation of geothermal resources, EGS (enhanced geothermal systems)-type geothermal power plants are rapidly developing, as shown in Figure 1a [2]. The maximum buried depth of the surrounding rock of the Danba Hydropower Station is 1220 m, the maximum ground stress is more than 30 MPa, which is close to the strength of the surrounding rock in the project, and its soft rock deformation problem is prominent [3]. As shown in Figure 1b [4], the deformation of the Muzhailing Tunnel even reaches 2.3 m. The problems of high temperatures and high confining pressures in these deep rocks put forward higher requirements for the safety and reliability of practical engineering, so it is of great significance to study the strength and deformation of rocks under high temperatures and high confining pressures. As a macroscopic characterization of the rock strength microelement, the rock strength criterion is the basis for the establishment of the rock constitutive model. A The rock constitutive model is a mathematical model describing the mechanical properties and mechanical behavior of rocks, which is crucial to the understanding of the deformation, the stress response as well as the behavior of the rock structure under different loading conditions. For this reason, scholars have carried out a lot of research on the strength criterion and the constitutive model of rocks. [PERSON] et al. [5] corrected the strength criterion error under different confining pressures of rocks and effectively solved the problem of a large strength prediction under high confining pressure by considering the error between the predicted strength and actual strength of the Hoek-Brown (H-B) criterion as a quadratic term with respect to the confining pressure, and they gave a formula for calculating the critical confining pressure. [PERSON] et al. [6] proposed the generalized Drucker-Prager (D-P) strength criterion from the perspective of the releasable strain energy of rocks, which solved the problem of the D-P strength criterion having large stress in the tensile-shear zone and which did not have the stress angle effect. [PERSON] et al. [7] modified the Mohr-Coulomb (M-C) strength criterion by introducing the principle of elastic strain energy, reflecting the effect of the medium principal stresses in the deformation process of rocks. [PERSON] et al. [8] combined the theory of the criterion of the maximum energy release rate of the rock rupture process with the theory of the maximum energy release rate of the rock rupture process, which gave results related to the thermal damage and initial cracking of the rocks under high-temperature conditions from a microscopic point of view. The parameter value of the H-B strength criterion related to the thermal damage and initial cracking in rocks under high-temperature conditions was given, and the reasonableness of the parameter value was proved with a large amount of data. [PERSON] et al. [9] established a statistical damage constitutive model reflecting the compaction stage and residual strength of rock by considering the compaction stage before the peak of the stress-strain curve and the existence of residual strength. [PERSON] et al. [10] used a  
Figure 1: Examples of underground engineering.