## 4 Model Validation and Parameter Analysis at Room Temperature
### Model Validation
With the increase in confining pressure, the brittleness of the rock decreases, and the rock changes from brittle failure to ductile failure. Under high confining pressures (20-40 Mpa), the two models began to distinguish before the peak, and the model based on the modified strength criterion was better than the original strength criterion, in agreement with the test curve. To further validate the selection of rock samples for model reliability, a reliability analysis of the model was performed by quoting the reliability indices from ref. [30]:  
\[\lambda=1-\frac{1}{m}\sum_{i=1}^{m}\left(\frac{\left|\sigma_{(i)}-\sigma_{i} \right|}{\sigma_{i}}\right) \tag{31}\]  
where \(\sigma_{(i)}\) is the predicted principal stress value of the rock, \(\sigma_{i}\) is the principal stress value of the rock test sample and n is the number of samples to verify reliability. The calculation results are shown in Table 2.  
From Table 2, it can be seen that the correlation coefficients between each model curve and the experimental curves at room temperature are above 0.85 except at the high confining pressure of 40 Mpa, which proves its good applicability. Compared with the model that was established based on the modified strength criterion and the D-P criterion [35], the fitting degree of the model established based on the revised H-B strength criterion is superior to the former under various confining pressure conditions, which further indicates the reasonableness of the model. The value of the rock residual strength is related to the value of the rock correction coefficient \(\delta\). In order to further predict rock residual strength, the correction coefficient was introduced, as shown in Equation (20). The calculation method [36] and Equation (20) with the existing correction coefficient were substituted into the model in this paper, and the residual strength value was obtained as shown in Figure 4. The correction coefficient in Equation (20) was obviously more reasonable. As shown in Figure 5a, the relationship between the rock damage value and strain value under different confining pressures is drawn. At the same time, based on Figure 5a, the damage evolution curve was differentiated to obtain the damage evolution rate curve of the rock, as shown in Figure 5b. Taking into consideration the fact that the initial thermal damage of rocks at room temperature (25 \({}^{\circ}\)C) is 0 and that the damage evolution curves of rocks under different confining pressures all show an \"S\" shape, the rock damage evolution curve can be divided into three stages. In the first stage, the initial cracks are gradually closed, the rock samples  
Figure 4: Relationship between residual strength and confining pressure of granite. are in a stage of compaction and linear elasticity, and the damage evolution curve remains horizontal. In the second stage, with the increase in stress, the initial crack is completely closed, new cracks begin to appear inside the rock, and the cracks gradually expand and penetrate. This results in macroscopic cracks, and the damage value gradually increases until the rock is completely broken. In the third stage, the damage value does not increase after the rock is completely broken, and the damage value reaches 1. The relationship between the maximum damage evolution rate of rocks and confining pressure is further studied, as shown in Figure 6. The maximum damage evolution rate of rocks decreases exponentially, and the fitting curve and correlation coefficient are as follows:  
\[y=2.451\ e^{(\frac{-x}{2.438})}-0.358,\ R^{2}=0.982 \tag{32}\]  
where \(x\) represents the confining pressure value of the rock and \(y\) represents the maximum damage evolution rate value of the rock. Figure 5: Damage evolution of granite under different confining pressures. Figure 3.0 Relationship between distribution parameters and confining pressures.