# Mechanical Response Law and Parameter Influence Analysis of Karst Tunnel Dynamic Excavation
## 6 Orthogonal
### Data Analogy of Karst Collapse Induced Factors
#### 6.3.2 Range Analysis of Bottom Plate Safety Thickness  
Range analysis is conducted on the orthogonal test data of the lower karst cave, and the results are shown in Table 9.  
It can be seen from Table 9 that the three factors' influence on the safety thickness of the bottom plate is in descending order: \(D\) > \(H\) > \(L\). The changing trend of safety distance under the influence of various factors is shown in Figure 18. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sources of** **Variability**} & **Sum of** **Squares of** **Deviations** & **Degree of Freedom** & **Mean Square** & **F-Test** & **Statistical Significance** \\ \hline \(L\) & 9.82 & 3 & 3.276 & 327.6 & Significant \\ \(D\) & 0.078 & 3 & 0.026 & 2.6 & Not significant \\ \(H\) & 60.80 & 3 & 20.226 & 2022.6 & Significant \\ \(e\) & 0.031 & 3 & 0.01 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Influence analysis table of each factor. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Span of the Cave, \(L\)** & **Height of the Cave, \(D\)** &
\begin{tabular}{c} **Buried Depth of the Tunnel, \(H\)** \\ \end{tabular} \\ \hline \(K_{1}\) & 27.5 & 21.75 & 25 \\ \(K_{2}\) & 28.75 & 26 & 28 \\ \(K_{3}\) & 27.5 & 31.75 & 30.5 \\ \(K_{4}\) & 29.25 & 33.5 & 29.5 \\ \(k_{1}\) & 6.875 & 5.4375 & 6.25 \\ \(k_{2}\) & 7.1875 & 6.5 & 7 \\ \(k_{3}\) & 6.875 & 7.9375 & 7.625 \\ \(k_{4}\) & 7.3125 & 8.375 & 7.375 \\ \(R\) & 1.75 & 11.75 & 5.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Range analysis of lower cave safety distance. As can be seen from Figure 18:  
* There is a weak correlation between the safety thickness of the bottom plate and the cave span of the lower karst cave. * The safety thickness of the bottom plate of the lower karst cave is positively correlated with the cave height, and it can be seen from the range analysis table that the cave height is an important factor affecting the safety thickness of the bottom plate. * The safety thickness of the bottom plate of the lower 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 has an important influence on the safety thickness of the bottom plate. Furthermore, with the increase of the tunnel burial depth, the safety distance tends to change gradually. After that, the data were further analyzed. The impact analysis of the F test is shown in Table 10: Influence analysis table of each factor. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \begin{tabular}{c} **Sources of** \\ **Variability** \\ \end{tabular} & \begin{tabular}{c} **Sum of** \\ **Squares of** \\ **Deviations** \\ \end{tabular} & \begin{tabular}{c} **Degree of** \\ **Freedom** \\ \end{tabular} & \begin{tabular}{c} **Mean** \\ **Square** \\ \end{tabular} & \
\begin{tabular}{c} **F-Test** \\ **Square** \\ \end{tabular} &
\begin{tabular}{c} **Statistical** \\ **Significance** \\ \end{tabular} \\ \hline \(L\) & 0.596 & 3 & 0.199 & 1.064 & Not significant \\ \(D\) & 21.784 & 3 & 7.261 & 38.829 & Significant \\ \(H\) & 4.315 & 3 & 1.438 & 7.690 & Significant \\ \(e\) & 0.561 & 3 & 0.187 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Influence analysis table of each factor. Figure 18: Trend of safety distance of lower caves under the influence of various factors: (**a**) Span of the cave; (**b**) Height of the cave; (**c**) Buried depth of the tunnel. According to the F distribution table, F\({}_{0.05}\)(3,4) = 6.59, F\({}_{0.01}\)(3,4) = 16.69; F\({}_{L}\)! F\({}_{0.05}\) (3,4) = 6.59, showing that the span of the karst cave has the least influence on the test results. F\({}_{D}\)! F\({}_{0.01}\)(3,4) = 16.69, showing that the karst cave height has the greatest influence on the test results. F\({}_{0.05}\)(3,4) = 6.59! F\({}_{H}\)! F\({}_{0.01}\)(3,4) = 16.69, showing that the tunnel burial depth has a great influence on the test results.