# Experimental Study on Damage Constitutive Model of Rock under Thermo-Confining Pressure Coupling
## 5 Conclusions  
This study utilizes triaxial compression tests to investigate the effects of temperature and confining pressure on the deformation and mechanical properties of four typical rock types: granite, red sandstone, gray sandstone, and shale. The primary conclusions are as follows:  
1. Temperature influences the elastic modulus of rocks differently. Granite and shale show an increase in elastic modulus with temperature. Red sandstone's elastic modulus increases initially, then decreases after a threshold, while gray sandstone exhibits the opposite trend. These differences are attributed to variations in internal structure, mineral composition, and the behavior of microcracks. Confining pressure significantly impacts elastic modulus and strain, with more pronounced changes under low confining pressure.
2. The combined effects of temperature and confining pressure enhance the peak strength and strain of granite, gray sandstone, and shale at 120 \({}^{\circ}\)C and 25 MPa, compared to 20 \({}^{\circ}\)C and 0 MPa, indicating increased density, load-bearing capacity, and ductility. Conversely, red sandstone shows reduced strength at higher temperatures, likely due to thermal expansion and internal crack propagation. The coupling also affects rock failure characteristics, with smoother fracture surfaces under triaxial conditions compared to uniaxial conditions.
3. A fitting model for the tangent elastic modulus (\(E_{t}\)) under temperature and confining pressure was developed. A polynomial model captures temperature-induced changes, particularly the decline in \(E_{t}\), while a composite exponential model fits the confining pressure effects. The combined model accurately predicts \(E_{t}\) under dual influences, with a high goodness-of-fit (R\({}^{2}\) close to 1), offering a reliable reference for evaluating rock deformation.
4. A constitutive model accounting for temperature and confining pressure coupling was formulated based on the Drucker-Prager criterion and Weibull statistical damage theory. Empirical formulas were derived for different rocks under varying conditions, and the model was validated against experimental results, showing strong consistency.  
Conceptualization, Z.Z.; methodology, Z.Z., Y.Z. and C.H.; software, C.H.; validation, T.P., Y.J. and X.L.; formal analysis, Z.Z.; investigation, Z.Z.; resources, Y.Z. and X.L.; data curation, Z.Z.; writing--original draft preparation, Z.Z.; writing--review and editing, Z.Z., Y.Z., C.H. and T.P.; visualization, Z.Z.; supervision, T.P. and Y.J.; project administration, Y.Z. and C.H.; funding acquisition, Y.Z. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data presented in this study are available upon request from the corresponding author. The data are not publicly available due to privacy.  
The authors would like to thank [PERSON] for his great help in this article, and his support has made it possible to present the article in a better way. The authors sincerely thank all the anonymous reviewers for their comments that improved the quality of the paper.  
The authors declare no conflicts of interest.