## 5 Model Verification
### Example Verification  
To validate the rationality of the proposed elastic-plastic constitutive model for high-temperature-load coupled damage, numerical simulations were conducted to compare the results with the uniaxial experimental data of granite under different high-temperature conditions, as reported by [PERSON] et al. and [PERSON] et al. [37; 38]. Two sets of experimental data were used for the comparison. The experimental granite was obtained by collecting on-site rock samples from local granite outcrops in the Gonghe Basin, based on the rock characteristics of the dry hot rock target area. X-ray diffraction composition analysis determined that the mineral contents of quartz, sodium feldase and mica were 10.96%, 81.65% and 7.39%, respectively. Before high-temperature treatment, the density and longitudinal wave velocity of each sample were determined, and the samples with abnormal density and wave velocity were removed to ensure the reliability and comparability of the test results. The average density of the samples used was 2.492 g/cm\({}^{3}\), and the average longitudinal wave velocity was 4176 m/s [37]. For the granite rock samples in the referenced paper with a dense structure and no obvious cracks, before high-temperature treatment, the density and longitudinal wave velocity of each sample were measured, and samples with abnormal density and wave velocity were removed. The test results were proved to be reliable and comparable. Numerical simulation parameters were selected as follows: Poisson's ratio \(\mu=0.35\), and density \(\rho=2492\) kg/m\({}^{3}\) for the first set; [PERSON]'s ratio \(\mu=0.32\), and density \(\rho=2260\) kg/m\({}^{3}\) for the second set. Because of little influence of damage on the internal friction angle, the internal friction angle and the expansion angle were set as constants, with \(\varphi=48^{\circ}\), and \(\psi=40^{\circ}\), respectively [38]. Other parameters are organized in Tables 1 and 2. The selection of numerical simulation parameters included Poisson's ratio, density, internal friction angle, dilation angle, elastic modulus, cohesive strength, and thermal damage parameters \(\alpha\) and \(\beta\). Poisson's ratio, internal friction angle, elastic modulus, and cohesive strength were obtained through rock triaxial compression tests. Density was calculated based on the relationship between mass and volume. The dilation angle was determined by applying confining pressure and measuring the change in sample volume. Generally, all of these parameters could be obtained through laboratory rock testing. The thermal damage parameters \(\alpha\) and \(\beta\) were acquired by fitting experimental curves. \begin{table}
\begin{tabular}{c c c c c} \hline
**Temperature/\({}^{\circ}\)C** & **E/GPa** & **\(c\)/MPa** & \(\alpha\) & \(\beta\) \\ \hline
25 & 7.8 & 26 & 0.00339 & 0.17614 \\
200 & 8.0 & 28 & 0.00254 & 0.31779 \\
300 & 7.6 & 26 & 0.00247 & 0.40011 \\
400 & 7.2 & 23 & 0.00177 & 0.39307 \\
500 & 6.8 & 21 & 0.00238 & 0.15821 \\
600 & 5.8 & 17 & 0.00130 & 0.38122 \\ \hline \end{tabular}
\end{table} 
Table 1: The relevant parameters for the numerical simulation of the first set. The numerical simulation results were compared to the experimental data in the literature, as presented in Figures 7 and 8. Since this model did not account for the deformation characteristics during the compaction stage, a certain level of deviation from the stress-strain curve was observed in tests. Comparing the elastic stage before the two peaks, as depicted in Figure 9, the error of peak stress and peak strain was less than 6.5%, and the temperature-dependent variation trends of peak stress and peak strain also verified the weakening effect of high temperature on rock strength again. After transitioning to the post-peak plastic deformation stage, the accumulation of damage caused a significant decline in the specimen's strength, and the stress-strain curve obtained from numerical simulation after reaching its peak displayed a similar trend compared with the experimental results.