## 4 Model Validation and Parameter Analysis at Room Temperature  
### Model Validation  
A selection of the data of granite at normal temperatures in the literature [29] is made in order to verify the statistical thermal damage constitutive model established in this paper. The mechanical parameters of granite at normal temperatures are shown in Table 2.  
The samples were taken from the granite of a mine in Weifang, Shandong Province, and were processed into standard cylindrical samples with a diameter of 50 mm and a length of 100 mm according to the standards of the International Society for Rock Mechanics (ISRM), with an error of \(\pm 0.5\) mm. The average density of the samples at room temperature was 2.612 g/cm\({}^{3}\), and the uniaxial compressive strength was 116.852 Mpa. Among them, feldspars were mainly sodium feldspars, and mica was mainly acicular mica. During testing, the samples were heated to 25 \({}^{\circ}\)C, 200 \({}^{\circ}\)C, 400 \({}^{\circ}\)C, 600 \({}^{\circ}\)C, and 800 \({}^{\circ}\)C. In order to ensure uniformity of the heat inside the rock samples, each piece of rock sample was kept at a constant temperature for 2 h after heating, and then the furnace was opened and naturally cooled to room temperature, with 5 pieces of sample at each temperature point, making a total of 25 pieces of rock samples. Then, the MTS815.02 electro-hydraulic servo material testing system from the State Key Laboratory of Deep Geotechnics and Underground Engineering of China University of Mining and Technology was used to conduct conventional triaxial compression tests on the heated rock samples, with the peripheral pressure set to five levels: 0, 10, 20, 30 and 40 Mpa. During the test, a predetermined peripheral pressure was first applied to the rock samples to keep the samples \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Confining Pressure** & **Peak Strength** & **Peak Strain** & **Residual Strength** & **Residual Strain** & **\& **\& \\
**/MPa** & **/MPa** & **/10\({}^{-3}\)** & **/MPa** & **/10\({}^{-3}\)** & **8** & **\& \\ \hline
0 & 116.852 & 4.147 & 7.082 & 7.037 & 0.940 & 0.865 \\
10 & 208.038 & 6.805 & 17.210 & 8.200 & 0.958 & 0.910 \\
20 & 301.143 & 7.557 & 108.000 & 10.096 & 0.801 & 0.877 \\
30 & 370.961 & 9.458 & 107.714 & 14.111 & 0.842 & 0.867 \\
40 & 364.571 & 11.394 & 144.000 & 18.546 & 0.704 & 0.646 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mechanical parameters of granite under different confining pressures. in hydrostatic pressure, and then the samples were loaded axially at a displacement rate of 0.003 mm/s until the samples were damaged. The peak strength of the samples was reached, and then the MTS815.02 electro-hydraulic servo material testing system continued to apply pressure to the samples and recorded the post-peak stress and deformation of the samples so as to obtain the full stress-strain curves of the samples under triaxial compression. After reaching the peak strength, the MTS815.02 hydraulic servo material testing system continued to apply pressure to the sample and recorded the post-peak stress and deformation of the sample so as to obtain the full stress-strain curves of the samples under triaxial compression. The parameter values under different confining pressures in Table 1 were substituted into the model established in this paper, and the obtained model curve is shown in Figure 3.  
Under low confining pressures (0-10 MPa), the model that was established based on the revised strength criterion can better characterize the pre-peak stress-strain relationship  
Figure 3: Theoretical and experimental curves under different confining pressures. of rock in the pre-peak stage compared to the model established based on the original strength criterion, and the constitutive model established based on the modified H-B strength criterion can better characterize the stress drop and residual strength in the post-peak stage due to the consideration of the damage repair value.