## 3 Numerical Simulation
The test group of factors \(E_{2}\rho_{4}c_{5}\rho_{1}n_{2}k_{3}\) represents the elastic modulus, density, cohesion, internal friction angle, porosity and water reduction coefficient for the backfill body, and their values are 800 MPa, 2520 kg/m\({}^{3}\), 700 kPa, 35\({}^{\circ}\), 0.18 and 15%, respectively. Based on the negative index characteristics of each evaluation index, the influence of six backfill parameters on different evaluation indexes within the given factor level range is obtained, and the optimal group for different evaluation indexes is obtained, as shown in Table 5. When the crown settlement is taken as the index, the elastic modulus of backfill soil has the greatest influence, followed by the reduction coefficient of water on backfill, cohesion, porosity and density. The internal friction angle has the least influence. When the elastic modulus, density, cohesion, internal friction angle, porosity and water reduction coefficient are 1400 MPa, 2160 kg/m\({}^{3}\), 300 kPa, 45\({}^{\circ}\), 0.16 and 5% respectively, the optimization of the tunnel crown settlement is the best. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Serial** & **Factor Level** & **Backfill Floor** & **Crown** & **Left** & **Right** & **Initial** & **Initial** \\
**Number** & **Combination** & **Displacement** & **Settlement** & **Convergence** & **Convergence** & **Lining Shaft** & **Bending** \\ \hline
1 & \(E_{1}\rho_{1}c_{1}\varphi_{1}n_{1}k_{1}\) & 0.700 & 0.367 & 0.526 & 0.222 & 0.134 & 0.321 \\
2 & \(E_{1}\rho_{2}c_{2}\varphi_{2}n_{2}k_{2}\) & 0.674 & 0.491 & 0.652 & 0.559 & 0.451 & 0.413 \\
3 & \(E_{1}\rho_{3}c_{3}\varphi_{3}n_{3}k_{3}\) & 0.642 & 0.724 & 0.791 & 0.855 & 0.736 & 0.535 \\
4 & \(E_{1}\rho_{4}c_{4}\varphi_{4}n_{4}k_{4}\) & 0.641 & 0.902 & 0.646 & 0.846 & 0.934 & 0.730 \\
5 & \(E_{1}\rho_{5}c_{5}\varphi_{5}n_{5}n_{5}k_{5}\) & 0.701 & 1 & 0.809 & 1 & 1 & 1 \\
6 & \(E_{2}\rho_{1}c_{5}\varphi_{3}n_{4}k_{5}\) & 0.275 & 0.543 & 0.782 & 0.650 & 0.319 & 0.744 \\
7 & \(E_{2}\rho_{2}c_{3}\varphi_{4}n_{5}k_{1}\) & 0.224 & 0.454 & 0.365 & 0.418 & 0.649 & 0.342 \\
8 & \(E_{2}\rho_{3}c_{4}\varphi_{5}n_{1}k_{2}\) & 0.284 & 0.448 & 0.404 & 0.464 & 0.848 & 0.424 \\
9 & \(E_{2}\rho_{4}c_{5}\varphi_{1}n_{2}k_{3}\) & 0.414 & 0.491 & 0.628 & 0.609 & 0.769 & 0.478 \\
10 & \(E_{2}\rho_{5}c_{1}\varphi_{2}n_{3}k_{4}\) & 1 & 0.521 & 0.698 & 0.265 & 0.081 & 0.596 \\
11 & \(E_{3}\rho_{1}c_{3}\varphi_{5}n_{5}n_{5}k_{5}\) & 0.054 & 0.426 & 0.381 & 0.510 & 0.679 & 0.291 \\
12 & \(E_{2}\rho_{2}c_{4}\varphi_{1}n_{3}k_{5}\) & 0.094 & 0.926 & 0.544 & 0.609 & 0.367 & 0.388 \\
13 & \(E_{3}\rho_{3}c_{3}\varphi_{5}n_{2}n_{4}k_{1}\) & 0.121 & 0.254 & 0.326 & 0.366 & 0.661 & 0.207 \\
14 & \(E_{3}\rho_{4}c_{1}\varphi_{3}n_{5}k_{2}\) & 0.576 & 0.102 & 0.415 & 0.036 & 0.075 & 0.298 \\
15 & \(E_{3}\rho_{5}c_{2}\varphi_{4}n_{1}k_{3}\) & 0.433 & 0.252 & 0.645 & 0.465 & 0.437 & 0.550 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Standard orthogonal experimental results (indicated by \(d_{ECULID}\)). In order to comprehensively consider the influence of various mechanical parameters of backfill soil on tunnel construction under the influence of groundwater and optimize the scheme design for the backfill soil, the weighted relative deviation distance minimum method [26] was adopted to form a comprehensive evaluation scheme for backfill reinforcement with the whole tunnel as the evaluation scheme, which is based on the principle of fuzzy mathematics and multi-objective comprehensive decision making. The schemes are compared and selected and combined with orthogonal experimental analysis. According to the principle of fuzzy mathematics, the six evaluation indexes are assigned according to importance degrees. Therefore, the importance degrees of backfill bottom displacement, crown settlement, left-side convergence, right-side convergence, initial lining axial force and initial lining bending moment were determined as 20%, 20%, 15%, 15%, 15% and 15% respectively.