# Mechanical Response Law and Parameter Influence Analysis of Karst Tunnel Dynamic Excavation
## 5 Numerical Results
### Dynamic Excavation Surrounding Rock Stress
It can be seen that the upper karst cave has no obvious influence on the maximum principal stress of the tunnel arch under the critical safety distance. The influence of the lower karst cave on the maximum principal stress of the tunnel arch under the critical safety distance is more obvious. As Table 3 shows, the minimum principal stress of the arch bottom is greater than the minimum principal stress of the vault. The minimum principal stress of the arch waist is about 2.7 times that of the minimum principal stress of the vault. The maximum principal stress of the arch waist is about 2.1 times that of the maximum principal stress of the arch bottom. Similarly, the data between the 15 m and 27 m sections were selected for analysis. As shown in Figure 15a, there is no significant difference in the minimum principal stress at the vault between the cavity-free and upper cavity cases. Compared with the no-cavity case, the minimum principal stress in the vault of the lower cavity increases by 2 kPa between 18 m and 21 m and decreases by 1 kPa at 24 m. When the distance between the cavity and the tunnel is the critical safety distance, the cavity above the tunnel has no obvious effect on the minimum principal stress in the arch, and the effect on the minimum principal stress in the arch of the cavity below the tunnel is obvious. As shown in Figure 15b, comparing the upper cavern with the no-cavern case, it can be seen that there is no significant difference in the minimum principal stress at the bottom of the arch. When there is a cavern in the lower part of the tunnel, the minimum principal stress at the arch bottom starts to increase at 18 m, it reaches a peak of 633 kPa at 21 m (cavern location), decreases to 628 kPa at 24 m, and then gradually increases. It can be seen that the influence of the lower cave on the minimum principal stress at the arch bottom is obvious. As shown in Figure 15c, the minimum principal stress at the arch waist still does not change significantly when there is a cavern in the upper part of the tunnel. When there is a cavern in the lower part of the tunnel, the minimum principal stress at the arch waist starts to increase at 15 m. At 18 m, the minimum principal stress at the arch waist increases by 3 kPa compared to the tunnel without cavities, and at 21 m the minimum principal stress at the arch waist increases by 4 kPa, with no significant difference at 24 m compared to the  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{\ \begin{tabular}{c} **Section** \\ **Position** \\ **(m)** \\ \end{tabular}  } & \multicolumn{2}{c}{**No Cave**} & \multicolumn{2}{c}{**Upper Cave**} & \multicolumn{2}{c}{**Lower Cave**} \\ \cline{2-10}  & **Arch** & **Arch** & **Arch** & **Arch** & **Arch** & **Arch** & **Arch** & **Arch** & **Arch** \\ \multirow{2}{*}{ \begin{tabular}{c} **Position** \\ **(m)** \\ \end{tabular}  } & **Crown** & **Bottom** & **Waist** & **Crown** & **Bottom** & **Waist** & **Crown** & **Bottom** & **Waist** \\  & **(kPa)** & **(kPa)** & **(kPa)** & **(kPa)** & **(kPa)** & **(kPa)** & **(kPa)** & **(kPa)** & **(kPa)** \\ \hline
9 & 504 & 643 & 1370 & 504 & 643 & 1370 & 504 & 644 & 1368 \\
12 & 500 & 638 & 1358 & 501 & 638 & 1357 & 501 & 637 & 1359 \\
15 & 497 & 635 & 1350 & 497 & 635 & 1349 & 497 & 634 & 1350 \\
18 & 494 & 633 & 1346 & 494 &arch waist of a tunnel without cavities. It can be seen that the down-lying cavern has a significant effect on the minimum principal stress in the arch waist of the tunnel. From the above results, the maximum principal stress and the minimum principal stress of the tunnel are not significantly affected by the upper cavity in the state of safety critical distance.