## 3 Engineering Application
### Parameters Identification Results  
During the GP-DE feedback analysis process, the population size NP was 100, the variation factor F was 0.7, the cross factor CR was 0.9, the maximum evolutionary algebra was 200 and SE was selected as the kernel function. After tunnel excavation, the measured values of AZ, DZ, BC, AB, P and F were 8 mm, 3.17 mm, 3.02 mm, 6.31 mm, 0.122 MPa and 3.77 m3/m \(\times\) d, respectively. The optimal parameters obtained by back analysis were E1 = 2.83 GPa, \(\upmu\)1 = 0.33, E2 = 1.24 GPa, \(\upmu\)2 = 0.36, K1 = 0.285 m/d and K2 = 0.658 m/d.  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & **Elastic** & & **Cohesion** & **Internal Friction** & **Permeability** \\  & **Modulus/GPa** & **Poisson’s Ratio** & **/kPa** & **Angle/\({}^{c}\)** & **Coefficient/(m/d)** \\ \hline \hline \multicolumn{1}{c}{Slightly weathered genesis} & 4.19 & 0.26 & 27 & 38 & 0.025 \\ \multicolumn{1}{c}{Moderately weathered genesis} & — & — & 21 & 42 & — \\ \multicolumn{1}{c}{Strongly weathered genesis} & — & — & 15 & 46 & — \\ \multicolumn{1}{c}{Subgrade soil} & 0.15 & 0.35 & 23 & 19 & 0.843 \\ \multicolumn{1}{c}{Primary support} & 25 & 0.18 & 20,000 & 34 & \(6.3\times 10^{-4}\) \\ \multicolumn{1}{c}{Bolt} & 200 & — & — & — & 25 & — \\ \multicolumn{1}{c}{Middle wall} & 25 & 0.18 & 20,000 & 34 & — \\ \hline \end{tabular}
\end{table}
Table 1: The parameters of calculation.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline  & **E1** & **E2** & **K1** & **K2** & **AZ** & **AB** & **BC** & **DZ** & **P (10\({}^  
According to Table 4, compared with the numerical simulation results, the maximum relative error of the back analysis is 9.40%, which meets the requirements of engineering construction. This back analysis method can be used for surrounding rock parameter prediction.  
Figure 4 shows the fitness values in the iterative process. It can be seen from the figure that with the increase in evolutionary algebra, the distribution of solution vector in space tends to converge. The iterative process of parameter acquisition is shown in Figure 5. In the initial stage of iteration, the fluctuation range of parameters is extensive. When the number of iterations reaches 45, the obtained parameters no longer fluctuate and the optimal solution is generated.  
\begin{table}
\begin{tabular}{c} **K2** \\ **(\%)** \\ \end{tabular} \\ \hline
1 & 3.85 & 0.29 & 1.81 & 0.33 & 0.36 & 0.82 & 0.00 & \(-9.40\) & 8.74 & 6.81 & 4.49 & 7.24 \\
2 & 6.96 & 0.35 & 2.39 & 0.22 & 0.26 & 0.78 & \(-6.69\) & 3.79 & 3.39 & \(-8.19\) & 9.15 & 0.00 \\
3 & 3.37 & 0.47 & 2.49 & 0.37 & 0.20 & 0.73 & 6.43 & \(-1.72\) & 4.54 & 7.50 & 0.00 & \(-6.16\) \\
4 & 6.19 & 0.23 & 3.26 & 0.27 & 0.45 & 0.58 & \(-5.80\) & \(-8.41\) & 5.56 & \(-8.45\) & \(-7.01\) & 2.02 \\
5 & 3.07 & 0.34 & 3.49 & 0.41 & 0.33 & 0.52 & 0.00 & \(-7.98\) & \(-7.14\) & 9.22 & \(-1.60\) & \(-4.81\) \\
6 & 6.43 & 0.39 & 3.74 & 0.28 & 0.25 & 0.38 & 4.55 & 6.33 & \(-8.85\) & 7.14 & \(-4.57\) & 5.26 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Parameters of surrounding rock of uniform testing scheme analysis results.  
Figure 4: Fitness values with different evolutions. (**a**) 1 st evolution. (**b**) 15 th evolution. (**c**) 30 th evolution. (**d**) 45 th evolution.