# A Study on the Effects of Hob Temperature on the Rock-Breaking Characteristics of Sandstone Strata
## 3 Calibration of Thermodynamic Parameters
A final determination of the thermodynamic parameters is shown in \[q_{i}=-k_{ij}\frac{\partial T}{\partial x_{i}} \tag{2}\]0 From indoor experiments, it was observed that during heating, some rock debris falls off the surface of the rock sample and partial micro-cracks appear. According to numerical simulations, it can be observed that as the temperature propagates inward, the contact bonds between PFC particles first fracture at the locations where the external contact forces are weaker. Moreover, with increasing temperature, the contact forces between particles fail, leading to the detachment of fractured particles. This phenomenon is consistent with the shedding of rock debris observed in indoor experiments. The changes in contact bonds are clearly evident in the numerical simulation results. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Temperature** & **Laboratory Test Value** & **Numerical Simulation Value** & **Error (\%)** \\ \hline
25 & 58.72 & 59.70 & 0.017 \\
300 & 57.30 & 57.52 & 0.004 \\
600 & 53.56 & 53.79 & 0.004 \\
900 & 46.09 & 48.79 & 0.059 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Calibration results of compressive strength. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Temperature** & **Laboratory Test Value** & **Numerical Simulation Value** & **Error (\%)** \\ \hline
25 & 52.14 & 51.13 & 1.98 \\
300 & 52.69 & 52.26 & 0.82 \\
600 & 51.34 & 53.06 & 3.34 \\
900 & 49.84 & 53.83 & 8.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Calibration results of internal friction angles. Figure 9: _Cont._  
As shown in Figure 10, by comparing the contact force and contact number distribution plots at different temperatures, we found that at a temperature of 300 \({}^{\circ}\)C, the cracks produced by the specimen under the temperature alone break the contact bonds of the particles in the weaker parts of the contact and the number of contacts decreases for the first time. Because it is heated around, the temperature of the outermost particles rises the fastest and is the first to reach the fracture strength. As the temperature increases, the maximum contact force of the particles keeps increasing from 30.12 N to 70.69 N. The temperature of the particles in the outer ring of the specimen gradually transfers inward, and the particles inside the specimen also reach the fracture temperature. Then, the contact fracture is destroyed and the number of contacts decreases rapidly. This is consistent with the phenomenon of tiny rupture of the outer layer after heating in indoor experiments. \begin{table}
\begin{tabular}{c c c c} \hline
**Micro-Parameter** & **Thermal Resistance** & **Coefficient of Linear Expansion** & **Specific Heat** \\ \hline value & \(1.367\times 10^{6}\) & \(5.6\times 10^{-6}\) & \(1015\) \\ \hline \end{tabular}
\end{table} 
Table 5: Initial determination of microscopic thermodynamic parameters. Figure 9: Comparison of numerical simulation and laboratory experiments at different sandstone temperatures. (**a**) Stress–strain diagram at 25 \({}^{\circ}\)C. (**b**) Stress–strain diagram at 300 \({}^{\circ}\)C. (**c**) Stress–strain diagram at 600 \({}^{\circ}\)C. (**d**) Stress–strain diagram at 900 \({}^{\circ}\)C. (**e**) Relationship of \(\sigma_{1}\) and \(\sigma_{3}\) at 25 \({}^{\circ}\)C. (**f**) Relationship of \(\sigma_{1}\) and \(\sigma_{3}\) at 300 \({}^{\circ}\)C. (**g**) Stress–strain diagram at 600 \({}^{\circ}\)C. (**h**) Relationship of \(\sigma_{1}\) and \(\sigma_{3}\) at 900 \({}^{\circ}\)C.  
Figure 10: _Cont._