# Safety Analysis of Secondary Lining of Yulinzi Tunnel Based on Field Monitoring
## 5 Numerical Simulation Analysis of Long-Term Stress on Secondary Lining  
The long-term stress and deformation of the secondary lining of the Yulinzi Tunnel were simulated using FLAC3D finite difference software. The simulation considered the structural response under the condition of a 25% water content in the yellow soil. The dimensions of the geological model were set to 170 m \(\times\) 130 m, with a tunnel depth of 50 m. The longitudinal length of the tunnel was much greater than its transverse dimension. The model was solved using a plane strain problem, with a longitudinal dimension of 1 m. The bottom and surrounding boundaries of the model were constrained, and the self-weight stress field was applied based on the tunnel depth. The construction design parameters are shown in Table 5, and the numerical model is shown in Figure 18. During the simulation, the creep effect of the surrounding rock during the construction phase was not considered, and the analysis focused only on the stress within 100 years after the secondary lining was constructed.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Position** & **Measure Point** & \begin{tabular}{c} **Safety Factor Final** \\ **Calculated Value** \\ \end{tabular} & \begin{tabular}{c} **Safety Factor Final** \\ **Predicted Value** \\ \end{tabular} & \begin{tabular}{c} **Fitting Function** \\ \end{tabular} & \begin{tabular}{c} **R2** \\ \end{tabular} \\ \hline Vault & 1 & 2.48857 & 2.83421 & \begin{tabular}{c} \(K=2.83421+330.74635e^{\frac{-1}{13081}}+\) \\ 18.10648e^{\frac{-1}{13081}}+\) \\ \end{tabular} & 0.99761 \\ \hline Arch shoulder & 4 & 5.51259 & 5.46581 & \begin{tabular}{c} \(K=5.46581+59.10097e^{\frac{-1}{1307243e^{\frac{-1}{1307243e^{\frac{-1}{1307243e^{ \frac{-1}{1307243e^{\frac{-1}{307243e^{\frac{-1}{307243e^{\frac{-1}{ 07243e^{\frac{-1}{0}{243}{4}{4}{4}{4}{4}{4}}{4}{4}}{4}}{4}}{4}}{4}}}}}}}\) \\ \end{tabular} & 0.99881 \\ \hline Arch waist & 11 & 7.68418 & 8.13949 & \begin{tabular}{c} \(K=8.13949+10723.92089e^{\frac{-1}{1307243e^{\frac{-1}{1307243e^{\frac{-1}{1307243e ^{\frac{-1}{1307243e^{\frac{-1}{307243e^{\frac{-1}{307243e^{\frac{-1}{ 307243e^{\frac{-1}{307243e^{\frac{-1{0}{4}{4}{4}}{4}}{4}{4}}{4}{4}}{4}{4}}{4}}{4}}{4}}}}}}\) \\ \end{tabular} & 0.99710 \\ \hline Arch Foot & 5 & 2.60743 & 2.81752 & \
\begin{tabular}{c} \(K=2.81752+116.28137e^{\frac{-1}{1288137}}+\) \\ 16.92097e^{\frac{-1}{1307243e^{\frac{-1}{1307243e^{\frac{-1}{1307243e^{\frac{- 1}{1307243e^{\frac{-1}{307243e^{\frac{-1{307243e^{\frac{-1{ 0}{4}{4}{4}}{4}}{4}{4}}{4}{4}}{4}}{4}}{4}}}}}}}\) \\ \end{tabular} & 0.99850 \\ \hline Arch foot & 7 & 2.37227 & 2.36814 &
\begin{tabular}{c} \(K=2.36814+33.3213e^{\frac{-1}{1307243e^{\frac{-1}{1307243e^{\frac{-1}{1307243e ^{\frac{-1}{1307243e^{\frac{-1}{307243e^{\frac{-1{307243e^{\frac{-1{ 0}{4}{4}}{4}}{4}}{4}}{4}{4}}{4}}{4}}}}}}}+\) \\ \end{tabular} & 0.9951 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Safety factor regression analysis results.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Density (kg/m\({}^{3}\))** & **Elastic Modulus (MPa)** & **Poisson’s Ratio** & **Thickness (m)** \\ \hline Primary support & 2360 & 2.95 \(\times\) 10\({}^{10}\) & 0.2 & 0.2 \\ Secondary lining & 2400 & 3.25 \(\times\) 10\({}^{10}\) & 0.2 & 0.7 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Primary support and secondary lining parameters.