## 4 Engineering Application
### Orthogonal Design  
Orthogonal design is a multi-factor and multi-level test method, through which representative points can be selected for test design, thus reducing the difficulties caused by a large number of tests and the facilitation of efficient tests [34]. In the back analysis, the stability and displacement settlement of the station mostly depend on the surrounding rock parameters, and the influence of different surrounding rock parameters on the failure and deformation of rock mass is different; at the same time, if there are many inversion parameters, the authenticity of parameters obtained from the back analysis will also be affected. Therefore, the parameters of surrounding rocks that have a great impact on the station were obtained through a sensitivity analysis for back analysis. An orthogonal design scheme was adopted, the parameter values were divided into five grades according to the determined parameter range, and then the values of different grades of each parameter were reasonably combined according to the orthogonal scheme; that is, 25 combinations were formed according to the L25 (5\({}^{\circ}\)) orthogonal table (as is shown in Table 4). According to the field investigation and survey data, 25 combinations of five test parameters at five levels were designed. The parameter and value range: tensile strength f = 0.07\(\sim\)0.19 MPa, Poisson's ratio \(\mu\) = 0.3\(\sim\)0.35, cohesion \(c\) = 0.2\(\sim\)0.7 MPa, internal friction angle \(\varphi\) = 27\({}^{\circ}\)-39\({}^{\circ}\), and elastic modulus \(E\) = 1.3\(\sim\)6 GPa. The parameters of each scheme were substituted into a three-dimensional finite element model for forward calculation, and the three points (as is shown in Figure 7), where the sensors were located at the station  
Figure 8: Field monitoring data curve of displacement measuring point. Figure 7: Field monitoring data curve of earth pressure box. arch cover, were, respectively, selected to obtain the corresponding displacement and stress, whose results are shown in Table 4.  
In the back analysis, the mechanical parameters had a great relationship with the stability of the surrounding rocks. The failure and deformation of rock mass were different with different rock mass parameters. Moreover, the authenticity of the parameters obtained from back analysis decrease with the increase in the number of inversion parameters [35]. Therefore, sensitivity analysis was used in this paper to obtain the factors that have a greater impact on the stability of the station for an inverse analysis, and a range analysis was carried out on the settlement displacement value of the arch crown and arch waist. See Table 5 for the range value of DW-1, DW-2, and DW-3 as well as the order of their impact on the displacement. In Tables 4 and 5, DW-2 is the settlement displacement value at the left arch waist of the arch cover; DW-3 is that at its right arch waist; DW-1 is that at its arch crown; TY-1, TY-2, and TY-3 are the total stress at these three points of the arch cover of the station; and the range, order as well as average range of DW-1, DW-2, and DW-3 are the range value of the settlement displacement at the corresponding measuring points of at the arch cover, the primary and secondary relationship of the influence of various parameters, as well as the average range value. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Factor**} & \multirow{2}{*}{\(\mathbf{E/}\)} & \multirow{2}{*}{\(\mathbf{\mu}\)} & \multirow{2}{*}{\(\mathbf{c/}\)} & \multirow{2}{*}{\(\mathbf{\varphi^{l}}\)} & \multirow{2}{*}{\(\mathbf{t/}\)} & \multirow{2}{*}{\(\mathbf{DW-1/}\)} & \multirow{2}{*}{\(\mathbf{DW-2/}\)} & \multirow{2}{*}{\(\mathbf{DW-3/}\)} & \  
As can be seen from Table 3, the order of sensitive factors affecting the three points at the arch cover is elastic modulus \(E\), Poisson's ratio \(\mu\), internal friction angle \(\varphi\), tensile strength \(t\), and cohesion force \(c\).