## 3 Numerical Simulation
The degree of dispersion is low, so there is no local deterioration. Therefore, the smaller the average value and standard deviation in the group, the more favorable the situation is for tunnel excavation. The whole test group is range standardized according to Formula (5), and the average value and standard deviation of the test group are normalized to the interval of [0-1]. According to Formula (6), \(d_{ECULID}^{ik}\), which is the distance between \(\left(x_{ik}^{*},\sigma_{ik}^{*}\right)\) and origin, can be calculated as follows:  
\[\overline{x}_{ik}=\frac{1}{n}\sum_{j=1}^{m}\left|x_{ijk}\right| \tag{3}\] \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Type of** & **Elasticity** & **Poisson’s** & **Density** & **Cohesion** & **Internal Friction** & **Porosity** & **Permeability** \\
**Surrounding** & **Modulus** & **Ratio** & _p/_kg m\({}^{-3}\) & _c/_kPa** & **Angle** & **Porosity** & **Coefficient** \\
**Rock** & _E_/**MPa** & \(m\) & _p/kg m\({}^{-3}\) & _c/_kPa** & **angle** & **Porosity** & **Coefficient** \\ \hline Limestone & 10,000 & 0.22 & 2650 & 2000 & 65 & 0.05 & 1 \(\times\) e\({}^{-11}\) \\ Backfilling & 500 & 0.25 & 2200 & 30 & 40 & 0.30 & 1 \(\times\) e\({}^{-1}\) \\ Crushed stone & & & & & & & \\ Backfilling & 1000 & 0.25 & 2400 & 500 & 45 & 0.20 & 1 \(\times\) e\({}^{-6}\) \\ Crushed slag & & & & & & & \\ Original crushed stone & & & & & & & \\ Original crushed clay & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The parameters of the surrounding rock. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Factor Name** & **Elastic** & **Density** & **Cohesion** & **Internal Friction** & **Porosity** & **Reduction Coefficient** \\  & **E/MPa** & _p/kg m\({}^{-3}\) & _c/kPa_ & **Angle** _q/\({}^{\circ}\)_ & _u/\%_ & \(k\) \\ \hline Level 1 & 600 & 2160 & 300 & 35 & 0.16 & 5\% \\ Level 2 & 800 & 2280 & 400 & 40 & 0.18 & 10\% \\ Level 3 & 1000 & 2400 & 500 & 45 & 0.20 & 15\% \\ Level 4 & 1200 & 2520 & 600 & 50 & 0.22 & 20\% \\ Level 5 & 1400 & 2640 & 700 & 55 & 0.24 & 25\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Levels of sensitivity factors. \[\sigma_{ik}=\sqrt{\frac{1}{n}\sum_{j=1}^{m}\left(\left|x_{ijk}\right|-\overline{x}_{ ik}\right)^{2}} \tag{4}\]  
\[\left\{ \begin{array}{l}x_{ik}^{*}=\frac{\overline{x}_{ik}-\overline{x}_{\min} }{\overline{x}_{\max}-x_{\min}}\\ \sigma_{ik}^{*}=\frac{\sigma_{ik}-\overline{x}_{\min}}{\overline{x}_{\max}- \overline{\sigma}_{\min}}\end{array} \right. \tag{5}\]  
\[d_{ECULID}^{ik}=\sqrt{\frac{\left(x_{ik}^{*}\right)^{2}+\left(\sigma_{ik}^{*} \right)^{2}}{2}} \tag{6}\]  
where \(i\) is the experimental group, \(1\leq i\leq 25\); \(j\) is the serial number of the tunnel section, \(1\leq j\leq 9\); \(k\) is the sequence number of six surrounding rock stability evaluation indexes: tunnel crown settlement, backfill body displacement under the bottom plate, convergence around the tunnel and internal force and bending moment of initial lining, \(1\leq k\leq 6\); \(\overline{x}_{ijk}\) represents the value of \(k\) evaluation index of \(j\) tunnel section in \(i\) test group; \(\overline{x}_{\max}\), \(\sigma_{\max}\), \(\overline{x}_{\min}\) and \(\sigma_{\min}\) is the average value of the \(k\) evaluation index and the maximum and minimum value of standard deviations in 25 experimental groups, respectively; and \(x_{ik}^{*}\) and \(\sigma_{ik}^{*}\) are the range standard value of the average value and the standard deviation of \(k\) evaluation index in group test \(i\), respectively. The smaller the \(d_{ECULID}\) of the experimental group, the higher the degree of optimization. Using this method can not only avoid redundant calculations when predecessors analyze multiple tunnel sections or multiple factors but also avoid the one-sidedness of single section and single factor analysis. Table 4 illustrates the results of \(d_{ECULID}\) evaluation indexes corresponding to the different parameters of each test group.