## 4 Evolution Characteristics of Plastic Zone in Jointed Rock Mass
### Impact of joints on Rock Mass Temperature  
In order to reveal the influence of jointed rock mass on high ground temperature, an intact rock mass model was introduced to compare and describe the temperature distribution. The typical surface was selected for analysis. Figure 7(a),b show the cloud charts of the temperature field of the intact and jointed rock mass, respectively, and Figure 9 shows the temperature variation curve of the rock mass. From Figure 8, it can be seen that the varied temperature field of the intact rock mass is much larger than the jointed rock mass. From Figure 9, it can be seen that the temperature variation shows a nonlinear increasing trend along the thickness direction of rock mass, which gradually tends to stabilize. The simulated and on-site measured temperature values of the jointed rock mass and the intact rock mass, as well as the calculated values of Equation (6) at depths of 11.7 m, 22.8 m, 11.3 m, and 10.6 m, respectively, show a stable trend. The simulated and on-site measured values of the jointed rock mass are basically consistent with the calculated values of Equation (6), which to some extent confirms the accuracy of the numerical simulation and theoretical formula derivation. However, it was far less than the simulated temperature value of the intact rock mass. For instance, when the rock mass depth was 5.3 m from the tunnel axis, the simulated value, the on-site measured value, and the theoretical calculation value of the jointed rock mass were 58.6 \({}^{\circ}\)C, 57.0 \({}^{\circ}\)C, and 51.5 \({}^{\circ}\)C, respectively, which were far lower than the simulated value of 45.4 \({}^{\circ}\)C of the \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Uniaxial compressive strength (MPa) & 28.7 \\ Density (g/cm\({}^{-3}\)) & 2.7 \\ Cohesion (MPa) & 1.3 \\ Poisson’s ratio & 0.25 \\ Elastic modulus (GPa) & 18.0 \\ Internal friction angle (\({}^{\circ}\)) & 37 \\ Uniaxial tensile strength (MPa) & 5.1 \\ Thermal conductivity (w/(m\(\cdot\)k)) & 1.49 \\ Specific heat capacity (J/(kg\({}^{-1}\)/k)) & 985 \\ Thermal expansion coefficient (\(10^{-5}\)/kw/(m\(\cdot\)k)) & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical parameters of rock mass. Figure 8: Cloud chart of rock mass temperature field (unit: \({}^{\circ}\)C). in intact rock mass temperature. When the rock mass depth was 11.3 m from the tunnel axis, the simulated value, the on-site measured value, and the theoretical value of the jointed rock mass were 79.5 \({}^{\circ}\)C, 79.8 \({}^{\circ}\)C, and 80.0 \({}^{\circ}\)C, respectively, which were far lower than the simulated values of 64.8 \({}^{\circ}\)C of the intact rock mass temperature. In addition, the average temperature change rate of the jointed rock mass was 5.13 \({}^{\circ}\)C/m, while that of the intact rock mass was 2.76 \({}^{\circ}\)C/m, indicating that the temperature variation area in the jointed rock mass was significantly reduced and the constant temperature area was increased. To facilitate the establishment of the simulation models, the three joint groups in practical engineering were simplified as follows in the model: inclination dd = 0\({}^{\circ}\), spacing space = 2 m, and dip angles = 0\({}^{\circ}\), 45\({}^{\circ}\), and 90\({}^{\circ}\) corresponding to the horizontal joint group, inclined joint group, and vertical joint group, respectively. The temperature field distribution cloud charts of the typical surfaces of the three joint groups are shown in Figure 10.  
From Figure 10, it can be seen that joint groups with different dip angles generate different sizes of temperature variation areas. The radii of the temperature variation area of the horizontal joint group (dip angle of 0\({}^{\circ}\)), inclined joint group (dip angle of 45\({}^{\circ}\)), and vertical joint group (dip angle of 90\({}^{\circ}\)) were 22.8 m, 13.4 m, and 24.9 m, respectively.