## 6 Conclusion and Discussion  
Considering the problem of the high prediction value of the H-B strength criterion for rock strength, the parameter value method of the H-B strength criterion is introduced to consider the crack-related element in the rock failure process, and a new damage correction coefficient is introduced to characterize the residual strength of rock in order to accurately predict the residual strength of rock. A constitutive model of rock statistical thermal damage considering initial crack and temperature correlation is established, and the following conclusions and discussion are drawn:  
1. Considering the effect of the presence of initial cracks in the rock on the strength of the rock, the H-B strength criterion is modified to solve the problem of the predicted strength value of H-B still being high under high confining pressures. The rationality of the revised strength criterion is verified by selecting rock sample data at normal temperatures and at high temperatures.
2. Based on the statistical damage theory, it is assumed that rock strength follows the Weibull distribution, combined with the revised H-B strength criterion and considering the damage correction related to residual strength. A statistical thermal damage constitutive model of rock under the condition of high temperatures and high confining pressures is established, and the physical significance of the model distribution parameters and their patterns of change, as well as the damage evolution of the rocks, are analyzed. By comparing the model in this paper with the model established by the H-B criterion, the model established in this paper is more consistent with the experimental data and has good applicability, which can provide a reference for the establishment of rock constitutive models under high temperatures and confining pressures.
3. The damage correction coefficient selected in this paper can better characterize the residual strength values of rocks and provide reference for the prediction of residual strength values of rocks, but there is still an error between the damage modification coefficients and the actual residual strength values, which needs to be further discussed and improved. In addition, this article only focuses on the investigation of the intrinsic model of the rock under high temperatures and high confining pressures, and the modeling of deep rock under high hydrostatic pressures and high perturbation conditions needs to be further considered in the future.  
Conceptualization, X.X.; methodology, X.X. and T.L.; validation, H.W. and T.L.; formal analysis, S.Y.; investigation, X.X. and T.L.; resources, S.Y. and H.W.; data curation, T.L. and H.W.; writing--original draft preparation, S.Y. and T.L.; writing--review and editing, X.X. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Open Research Fund of the Key Laboratory of Safety and High-efficiency Coal Mining, Ministry of Education (Anhui University of Science and Technology), No. JYBSYS2020208, and the Innovation Training Program for Jiangsu College Students, No. 202310304153Y. Postgraduate Research & Practice Innovation Program of School of Transportation and Civil Engineering, Nantong University (No. NTUJTXYZGIZ305).  
Not applicable.  
Data Availability Statement: Data are contained within the article.  
The authors declare no conflicts of interest.