# Mechanical Response Law and Parameter Influence Analysis of Karst Tunnel Dynamic Excavation
## 5 Numerical Results
### Dynamic Excavation Surrounding Rock Stress  
The maximum principal stress and minimum principal stress of the vault and arch bottom at 9 m, 12 m, 15 m, 18 m, 21 m ( karst cave position), 24 m, 27 m, 30 m and 33 m sections after excavation are extracted, respectively. The values of the maximum principal stress are shown in Table 2. It can be seen that the maximum principal stress of the vault is greater than the maximum principal stress of the arch bottom. The maximum principal stress of the arch waist is four times the maximum principal stress of the vault and five times the maximum principal stress of the arch bottom. To eliminate the influence of the edge effect of the model size, the data between the 15 m and 27 m sections were selected for analysis. It can be seen from Figure 14a that the maximum principal stress of the vault without the karst cave, and with upper and lower karst caves, gradually decreases with the increase of the tunnel section position. However, the maximum principal stress of the vault at each section is not much different. Under the condition of critical safety distance, the upper karst cave has no obvious influence on the  
Figure 13: Horizontal displacement curve of the monitoring point at the arch waist. maximum principal stress of the tunnel vault. The lower karst cave has no obvious effect on the maximum principal stress of the tunnel vault. It can be seen from Figure 14b that there was no significant difference in the maximum principal stress of the arch bottom under the condition of no karst cave and with the upper karst cave. It showed a gradually decreasing trend. The maximum principal stress of the arch bottom of the lower karst cave began to increase at the 18 m section, reached the peak value of 53.8 kPa at the 21 m section (k karst cave location), and then the stress gradually decreased. The maximum principal stress recovered to the same level as that without 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{3}{c}{**No Cave**} & \multicolumn{3}{c}{**Upper Cave**} & \multicolumn{3}{c}{**Lower Cave**} \\ \cline{2-10}  & **Arch Crown** & **Arch Bottom** & **Arch Waist** & **Arch Crown** & **Arch Bottom** & **Arch Waist** & **Arch Crown** & **Arch Bottom** & **Arch Waist** \\  & **(QFa)** & **(QFa)** & **(QFa)** & **(QFa)** & **(QFa)** & **(QFa)** & **(QFa)** & **(QFa)** & **(QFa)** & **(QFa)** \\ \hline
9 & 65.4 & 59.5 & 249 & 65.1 & 59.8 & 249 & 64.2 & 58.4 & 249 \\
12 & 64.6 & 55.0 & 247 & 64.9 & 54.7 & 246 & 65.2 & 53.5 & 247 \\
15 & 63.5 & 52.3 & 245 & 63.2 & 52.5 & 245 & 64.6 & 50.6 & 244 \\
18 & 62.4 & 51.3 & 245 & 62.7 & 52.1 & 244 & 63.7 & 51.0 & 244 \\
21 & 61.8 & 51.4 & 244 & 61.7 & 50.9 & 244 & 62.2 & 53.8 & 245 \\
24 & 59.8 & 49.6 & 244 & 60.3 & 50.1 & 244 & 60.2 & 52.9 & 243 \\
27 & 57.0 & 47.7 & 244 & 57.1 & 47.8 & 244 & 54.9 & 49.5 & 245 \\
30 & 51.6 & 42.9 & 244 & 51.7 & 41.8 & 245 & 49.1 & 41.2 & 246 \\
33 & 41.3 & 31.5 & 244 & 41.4 & 33.1 & 245 & 38.5 & 32.1 & 246 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Maximum principal stress at different cross-sectional locations in the tunnel. Figure 14: Maximum principal stress curve: (**a**) Arch crown; (**b**) Arch bottom; (**c**) Arch waist. cavern at the 27 m section. It can be seen that the upper karst cave had no obvious effect on the tunnel arch bottom under the critical safety distance; the lower karst cave had an obvious influence on the tunnel arch bottom under the critical safety distance. It can be seen from Figure 14c that the maximum principal stress without the karst cave and with the upper karst cave are basically maintained at about 244 kPa. The maximum principal stress of the arch waist of the lower karst cave began to increase at the 18 m section, reached the first peak of 245 kPa at the 21 m section (karsat cave location), then decreased to 243 kPa at the 24 m section, and then gradually increased.