## 3 Sensitivity Analysis of Influencing Factors
### Optimal Combination of Results  
Applying the orthogonal experimental design method, the original data of the target variables of vertical displacement, first principal stress, and principal stress difference with 11 influencing factors operating together were statistically analysed. And according to the degree of sensitivity, the 11 influencing factors were ranked in ascending order by applying the range analysis method, and the optimal levels were selected on the basis of the factor level-target variable trend diagrams 7, 8, 9. In the procedure of tunnel construction in karst areas, the smaller the value of the target variable is, the more favourable it is to the stability of the tunnel surrounding rock and the rock and soil masses around the karst cave. Consequently, the optimised combination of influencing factors is shown in Table 7, considering the vertical displacement, the first principal stress, and the principal stress difference as response variables, respectively. As illustrated in Figure 11a, in terms of vertical displacement as the output variable, the quantity of vertical displacement derived from Case B2 was 42.99% smaller than that derived from Case B1, the quantity of vertical displacement derived from Case B3 was 1.49 times larger than that derived from Case B1, and the quantity of vertical displacement derived from Case B4 was 44.24% larger than that derived from Case B1. As depicted in Figure 11b, considering the first principal stress as the output variable, the value of the \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline
**Case** & **A1** & **A2** & **A3** & **A4** & **A5** & **A6** & **A7** & **A8** & **A9** & **A10** & **A11** & \(\begin{array}{c}d\\ \text{/mm}\end{array}\) & \(\begin{array}{c}\textbf{S1}\\ \text{/MPa}\end{array}\) & \(\begin{array}{c}\textbf{S1}\\ \text{/MPa}\end{array}\) \\ \hline B1 & 53 & 0.3 & 27 & 1000 & 45 & 6.7 & 3 & 3 & down & 20.1 & 1 & 140.20 & 0.572 & 0.197 \\ B2 & 53 & 0.35 & 28 & 1000 & 45 & 3.35 & 1 & 1 & down & 13.4 & 1.5 & 79.93 & 0.607 & 0.069 \\ B3 & 53 & 0.35 & 25 & 1000 & 45 & 3.35 & 5 & 3 & down & 100 & 1 & 349.72 & 0.472 & 0.475 \\ B4 & 40 & 0.35 & 27 & 800 & 54 & 3.35 & 1 & 1 & up & 13.4 & 1 & 78.17 & 0.529 & 0.144 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Optimal combination table of influencing factors. first principal stress derived from Case B2 was 7.02% larger than that derived from Case B1, the value of the first principal stress derived from Case B3 was 17.54% smaller than that derived from Case B1, and the value of the first principal stress derived from Case B4 was 7.02% smaller than that derived from Case B1. As demonstrated in Figure 11c, considering the principal stress difference as the output variable, the principal stress difference output from Case B2 was 65% smaller than that output from Case B1, the principal stress difference output from Case B3 was 1.4 times larger than that output from Case B1, and the principal stress difference output from Case B4 was 30% smaller than that output from Case B1. To summarise, the vertical displacement, the first principal stress, and the principal stress difference output from Case B4 were all smaller than those outputs from Case B1, considering the principal stress difference as the target variable. Therefore, it emerges that the parameter combination consisting of the 11 influencing factors is more balanced with the principal stress difference as the target variable. The combination of the two methods of a random forest model and the range analysis method could be determined: taking vertical displacement as the target variable, the two influencing factors that have the greatest impact on the construction safety of karst tunnels are A6 (tunnel diameter) and A10 (tunnel buried depth), and one of the factors that has the least impact is A4 (cohesion).