# Mechanical Response Law and Parameter Influence Analysis of Karst Tunnel Dynamic Excavation
## 6 Orthogonal
### Data Analogy of Karst Collapse Induced Factors
#### 6.3.1 Range Analysis of Top Plate Safety Thickness  
Range analysis is conducted on the orthogonal test data of the upper karst cave, and the results are shown in Table 7. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Test Number**} & \multicolumn{4}{c}{**Influence Parameters**} \\ \cline{2-5}  & **Span of the Cave, L (m)** & **Height of the Cave, D (m)** & **Buried Depth of the Tunnel, H (m)** & **Critical Safety Distance (m)** \\ \hline
1 & 2 & 0.5 & 14 & 5.00 \\
2 & 2 & 1.0 & 16 & 6.00 \\
3 & 2 & 1.5 & 18 & 8.25 \\
4 & 2 & 2.0 & 20 & 8.25 \\
5 & 3 & 0.5 & 16 & 5.25 \\
6 & 3 & 1.0 & 18 & 7.25 \\
7 & 3 & 1.5 & 20 & 8.75 \\
8 & 3 & 2.0 & 14 & 7.50 \\
9 & 4 & 0.5 & 18 & 5.75 \\
10 & 4 & 1.0 & 20 & 6.75 \\
11 & 4 & 1.5 & 14 & 6.50 \\
12 & 4 & 2.0 & 16 & 8.50 \\
13 & 5 & 0.5 & 20 & 5.75 \\
14 & 5 & 1.0 & 14 & 6.00 \\
15 & 5 & 1.5 & 16 & 8.25 \\
16 & 5 & 2.0 & 18 & 9.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The orthogonal test of the lower cave. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Test Number**} & \multicolumn{4}{c}{**Influence Parameters**} \\ \cline{2-5}  & **Span of the Cave, L (m)** & **Height of the Cave, D (m)** & **Buried Depth of the Tunnel, H (m)** & **Critical Safety Distance (m)** \\ \hline
1 & 0.5 & 0.5 & 14 & 3.00 \\
2 & 0.5 & 1.0 & 16 & 4.50 \\
3 & 0.5 & 1.5 & 18 & 6.00 \\
4 & 0.5 & 2.0 & 20 & 8.25 \\
5 & 1.0 & 0.5 & 16 & 5.25 \\
6 & 1.0 & 1.0 & 18 & 7.00 \\
7 & 1.0 & 1.5 & 20 & 9.00 \\
8 & 1. In Table 7, \(K_{1}\) represents that when the span of the cave is 0.5 m, the sum of all safety distances between the cave and the tunnel under the action of other influencing factors; \(k_{1}=K_{1}/4\). \(R\) is range, indicating the effect of the three defined influencing factors on the safety distance; the larger the range is, the more critical the factor plays in this simulation. Therefore, in the above range analysis table, it is not difficult to find that the three factors' influences on the safe top plate thickness from large to small are: \(H>L>D\). The changing trend of tunnel safety thickness under the influence of various factors is shown in Figure 17. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Span of the Cave, \(L\)** & **Height of the Cave, \(D\)** & **Buried Depth of the Tunnel, \(H\)** \\ \hline \(K_{1}\) & 21.75 & 26 & 16.25 \\ \(K_{2}\) & 25 & 26.5 & 22.25 \\ \(K_{3}\) & 27.5 & 25.75 & 28.75 \\ \(K_{4}\) & 30.25 & 26.25 & 37.25 \\ \(k_{1}\) & 5.4375 & 6.5 & 4.0625 \\ \(k_{2}\) & 6.25 & 6.625 & 5.5625 \\ \(k_{3}\) & 6.875 & 6.4375 & 7.1875 \\ \(k_{4}\) & 7.5625 & 6.5625 & 9.3125 \\ \(R\) & 8.5 & 0.75 & 21 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Range analysis of upper cave safety distance. Figure 17: Trend of safety distance of upper caves under the influence of various factors: (**a**) Span of the cave; (**b**) Height of the cave; (**c**) Buried depth of the tunnel. As can be seen from Figure 17:
* The safety thickness of the top plate of the upper karst cave is positively correlated with the cave span, and it can be seen from the range analysis table that the cave span is an important factor affecting the safety thickness of the top plate. * There is a weak correlation between the safety thickness of the top plate and the height of the karst cave. * The safety thickness of the top plate of the upper karst cave is positively correlated with the tunnel burial depth, and it can be seen from the range analysis table that the tunnel burial depth is the most important factor affecting the safety thickness of the top plate. After the above intuitive analysis, the next step is to estimate the magnitude of the error by conducting an analysis of variance and find the factors that can be disregarded.