## 3 Comparison Study on Experimental and Numerical Results
### Comparison Study  
The model was loaded at a constant strain rate of 1/s. During the loading process, the average temperature change \(\Delta T_{ave}\) was recorded as Equation (13):  
\[\Delta T_{ave}=\frac{1}{i}\sum_{1}^{i}T_{i} \tag{13}\]  
where \(i\) is the number of particles and \(T_{i}\) is the temperature of the \(i\)-th particle. The change in average temperature change \(\Delta T_{ave}\) exhibited in Figure 5 is associated with increasing axial strain and stress, respectively. According to Figure 5a, for both the laboratory and numerical experiments, \(\Delta T_{ave}\) increases gradually with the increasing strain to a maximum value of about 0.28 \({}^{\circ}\)C and then goes down quickly. It should be noted that there is a small gap between the two curves because the compaction-induced strain at the initial loading stage cannot be shown in the particle flow model with densely packed balls [55]. Figure 5b shows that the general trend of \(\Delta T_{ave}\) in the numerical model has quite a good agreement with that in the laboratory experiment. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Thermal Expansion Coefficient** & **Specific Heat Capacity** & **Thermal Conductivity** \\
**(K)** & **(J (kg-K))** & **(W/(m-K))** \\ \hline \hline \(1.35\times 10^{-5}\) & 800 & 2.68 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Thermal parameters of the granite thermodynamic model [based on [54]]. Figure 5: Changes in average temperature \(\Delta T_{ave}\) are associated with increasing axial strain (**a**) and axial stress (**b**) in the laboratory experiment and the numerical experiment. However, there are also several differences between the laboratory and numerical experiment results, as follows:  
1. The temperature rise covers most of the area in the numerical model (Figure 6d), while it is much more significant in the middle part than the two ends of the rock specimen (Figure 2d). This difference is due to the adiabatic environment applied in the numerical model. There is no heat exchange between the specimen and the sidewalls connected to the two ends in the numerical model, but the heat will flow to the steel loading platen in the laboratory experiment, so the temperature in the rock specimen is quite lower than that at both ends. This is also the reason why the temperature variation range in the numerical model (\(-\)0.1 \({}^{\circ}\)C-0.5 \({}^{\circ}\)C) is slightly larger than that in the rock specimen (\(-\)0.1 \({}^{\circ}\)C-0.3 \({}^{\circ}\)C). 2. The temperature variation is more heterogeneous in the numerical model (Figure 6d) than that in the rock specimen (Figure 2d) in the laboratory experiment. At the initial stage of loading, the temperature is low and evenly distributed for both the numerical model and rock specimen. As the loading continues, the temperature increases and decreases are more clearly observed in different areas of the numerical model. This can be better understood when compared with the distribution evolution of force chains (Figure 7) and crack propagation (Figure 8). The larger contact force means higher concentration, which will lead to a localized temperature rise. Crack propagation can induce some stress drop and, as a result, some localized temperature reduction. This result is more obvious in the 2D numerical model than in the rock specimen because the stress concentration may occur inside the specimen and crack propagation may not go through it [52]. Another possible reason is that the heat exchange between the rock and the steel loading platen or the air environment is helpful for a more homogeneously distributed temperature. In the post-peak stage, macrofractures can be observed in both the rock specimen (Figure 2e) and numerical model (Figure 6e), and the temperature distributions are both heterogeneous, showing the temperature variation influenced by the fractures.