## 4 Engineering Application
### Parameter Identification Results  
The back analysis of displacement and stress can be used to further solve not only the problem of the low accuracy, but also the problem of the low authenticity caused by the increase in back-analysis parameters. At the same time, real changes in the surrounding rocks of the station can be fully considered in the joint analysis of displacement and stress, so that it is more real and effective. According to the actual monitoring, the settlement displacement of each point of the surrounding rocks was DW-1 = 12.53 mm, DW-2 = 10.75 mm, DW-3 = 10.71 mm, TY-1 = 176.97 kPa, TY-2 = 125.8 kPa, and TY-3 = 120.55 kPa. Taking the measured displacement and stress values as the control values while applying MATLAB to conduct a joint back analysis on displacement and stress, the initial parameters setting of differential evolution are shown in Table 6.  
It was found that when the cross factor was CR = 0.7 and F = 0.8, the optimal mechanical combination parameter of moderately weathered quartzite obtained through inversion was \(E\) = 1.3 GPa, \(\mu\) = 0.33, and \(\varphi\) = 35\({}^{\circ}\), and the inversion results of surrounding rock parameters are shown in Table 7. The results obtained from the inversion were substituted into the finite-element software for a forward calculation, the results obtained from which were compared with the monitoring values at the monitoring section of Shikui Road Station and the single displacement back analysis. The results are shown in Table 8.  
The back analysis of displacement and stress can be used to further solve not only the problem of the low accuracy, but also the problem of the low authenticity caused by the increase in back-analysis parameters. At the same time, the joint analysis of displacement and stress real changes in the surrounding rocks of the station can be fully considered, so that it is more real and effective. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Initial Parameter Type** & \begin{tabular}{c} **Number of** \\ **Optimization** \\ **Variables** \\ \end{tabular} & \begin{tabular}{c} **Number of** \\ **Population** \\ \end{tabular} & **Cross Factor CR** & **Variation Factor F** & \
\begin{tabular}{c} **Maximum** \\ **Evolution** \\ **Algebra** \\ \end{tabular} &
\begin{tabular}{c} **Population Size** \\ **NP** \\ \end{tabular} \\ \hline numerical value & 5 & 100 & 0.7 & 0.8 & 200 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Initial parameters of differential evolution. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Measuring Point** & \begin{tabular}{c} **Actual Monitoring** \\ **Value** \\ \end{tabular} & \
\begin{tabular}{c} **Displacement Back Analysis** \\ **Stress** \\ \end{tabular} &
\begin{tabular}{c} **Joint Back Analysis of Displacement and** \\ **Stress** \\ \end{tabular} \\ \cline{2-5}  & & **Calculated Value** & **Relative Error/\%** & **Calculated Value** & **Relative Error/\%** \\ \hline DW-1/mm & 12.53 & 11.86 & 5.35 & 12.58 & 0.40 \\ DW-2/mm & 10.75 & 10.18 & 5.30 & 10.84 & 0.84 \\ DW-3/mm & 10.71 & 10.15 & 5.23 & 10.81 & 0.93 \\ TY-1/kPa & 176.97 & — & — & 180.20 & 1.83 \\ TY-2/kPa & 125.8 & — & — & 130.35 & 3.62 \\ TY-3/kPa & 120.55 & — & — & 124.79 & 3.52 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Inversion results of surrounding rock parameters. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Factor** & **E/GPa** & \(\mu\) & \(\varphi\)\({}^{c}\) \\ \hline Parameter value & 1.3 & 0.33 & 35 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of inversion calculation results and actual measurement results. According to the data in Table 4, only when the settlement value of the displacement at the arch cover of the station was used as the control value for the back analysis of surrounding rock parameters could the maximum relative error be 5.35%, while when the displacement and stress value at the arch cover of the station was combined for the back analysis, the maximum error was only 3.62%.