## 4 Evolution Characteristics of Plastic Zone in Jointed Rock Mass
### Impact of Joint Spacing on Plastic Zone Range  
At the joint spacings of 0.5 m, 1.0 m, 1.5 m, 2.0 m, and 2.5 m, the effects of the horizontal joint group (dip angle of 0\({}^{\circ}\)), inclined joint group (dip angle of 45\({}^{\circ}\)), and vertical joint group  
Figure 10: Cloud chart of temperature distribution of three joint groups (unit: \({}^{\circ}\)C).  
Figure 9: High-temperature variation curve of rock mass.  
(dip angle of 90\({}^{\circ}\)) on the plastic zone range of the rock mass were analyzed. The model parameters are the same as those within Tables 1 and 2, and the initial stress was set to 5 Mpa. Table 3 lists the calculation results of plastic zone range at different joint spacings for the three joint groups. Figure 11 shows the morphological characteristics of the three joint groups at different joint spacings.  
From Table 3, in the horizontal joint group, the plastic zone radius first increases and then decreases with the increase in joint spacing, and then increases and decreases. In the inclined joint group, the plastic zone radius gradually decreases with the increase in joint spacing. In the vertical joint group, the plastic zone radius first increases and then decreases with the increase in joint spacing. Under different joint spacings, the ratios of the minimum radius to the maximum radius of the plastic zone of three joint groups ranged from 0.6 to 0.68, 0.70 to 0.76, and 0.76 to 0.94, respectively. At the same time, in the horizontal and inclined joint groups, the ratios of the minimum radius to the maximum radius of the plastic zone increased with the increase in joint spacing, while the ratio of the vertical joint group decreased with the increase in joint spacing. This indicates that with the increase in joint spacing, the influence of horizontal and inclined joint groups on the plastic zone morphology decreases, while the influence of the vertical joint group on the plastic zone morphology increases. As shown in Figure 11, in the vertical joint group, the plastic zone radius overall shows the most changes with the increase in joint spacing, and the plastic  
Figure 11: Relationship between joint spacing and plastic zone morphology.  
\begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Dip Angle/\({}^{\circ}\)**} & \multirow{2}{*}{**Joint Spacing/m**} & \multicolumn{4}{c}{**Radius of Plastic Zone/m**} \\ \cline{3-5}  & & **Maximum** & **Minimum** & **Ratio of Minimum Radius** \\  & & **Radius/m** & **Radius/m** & **to Maximum Radius** \\ \hline \multirow{5}{*}{0} & 0.5 & 4.80 & 2.86 & 0.60 \\  & 1.0 & 6.81 & 4.15 & 0.61 \\  & 1.5 & 4.26 & 2.64 & 0.62 \\  & 2.0 & 10.95 & 7.06 & 0.64 \\  & 2.5 & 8.25 & 5.62 & 0.68 \\  & 0.5 & 5.21 & 3.57 & 0.70 \\  & 1.0 & 4.76 & 3.43 & 0.72 \\
45 & 1.5 & 4.26 & 3.15 & 0.74 \\  & 2.0 & 3.82 & 2.87 & 0.75 \\  & 2.5 & 3.34 & 2.54 & 0.76 \\  & 0.5 & 4.29 & 4.05 & 0.94 \\  & 1.0 & 6.28 & 5.27 & 0.84 \\
90 & 1.5 & 8.55 & 6.67 & 0.78 \\  & 2.0 & 11.98 & 9.22 & 0.77 \\  & 2.5 & 9.23 & 6.97 & 0.76 \\ \hline \end{tabular}
\end{table}
Table 3: Calculation results of plastic zone range at different joint spacings for three joint groups.  
zone mainly develops in the vertical direction; followed by the horizontal joint group, with the plastic zone mainly developing in the horizontal direction; and the radius of the plastic zone in the inclined joint group changes the least, with the plastic zone mainly developing at an angle of 45\({}^{\circ}\) to the horizontal direction.