## 4 Numerical Study
### Analysis of Vertical Deformation of Subway Tunnel  
Figure 8 is a cloud map of the vertical deformation of the subway tunnel caused by the excavation of section A of the foundation pit under some working conditions. According to the simulation results of finite element software, as the excavation depth increases, the maximum vertical deformation of the subway tunnel increases continuously. When excavating to the design elevation at the bottom of the foundation pit, the vertical deformation of the subway tunnel reaches 1.32 mm. With the removal of the reinforced concrete inner support of the foundation pit, the vertical deformation of the subway tunnel is further increased. When all the inner supports are removed, the vertical deformation has reached 2.45 mm. Figure 9 is a cloud map of the vertical deformation of the subway tunnel caused by the excavation of section B of the foundation pit under some working conditions. The vertical deformation of the subway tunnel caused by the excavation of the foundation pit section B and the removal of the inner support is similar to the construction of section A, which leads to an increase in the vertical deformation of the subway tunnel. The vertical deformation of the subway tunnel corresponds to the excavation of the foundation pit section B to the design elevation and the removal of the first layer inner support is 1.61 and 2.61 mm, respectively. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Name** & \begin{tabular}{c} **Y** \\ **(kN/m3)** \\ \end{tabular} & \begin{tabular}{c} **E** \\ **(MPa)** \\ \end{tabular} & \begin{tabular}{c} **v** \\ **(kPa)** \\ \end{tabular} & \
\begin{tabular}{c} **c** \\ **(c)** \\ \end{tabular} &
\begin{tabular}{c} **\(\varphi\) \\ **(c)** \\ \end{tabular} \\ \hline Fill & 19.4 & 2.00 & 0.35 & 10.0 & 15.0 \\ \hline Silty clay & 19.7 & 3.00 & 0.25 & 77.9 & 19.2 \\ \hline Silty clay mixed pebbles & 19.8 & 3.00 & 0.25 & 40.0 & 18.0 \\ \hline Fully weathered argillaceous sandstone & 19.7 & 3.90 & 0.25 & 57.8 & 18.8 \\ \hline Strongly weathered argillaceous sandstone & 23.4 & 4.50 & 0.25 & 60.0 & 19.0 \\ \hline Moderately weathered argillaceous sandstone & 23.8 & 5.00 & 0.20 & 110.0 & 25.0 \\ \hline Fill & 19.4 & 2.00 & 0.35 & 10.0 & 15.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Soil physical and mechanical parameters of finite element model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Name** & \begin{tabular}{c} **\(\gamma\)** \\ **(kN/m3)** \\ \end{tabular} & \begin{tabular}{c} **E** \\ **(MPa)** \\ \end{tabular} & \begin{tabular}{c} **v** \\ **(m)** \\ \end{tabular} & \
\begin{tabular}{c} **h (m)** \\ \end{tabular} &
\begin{tabular}{c} **b (m)** \\ \end{tabular} \\ \hline Rotary cast-in-place piles & 25.0 & 30.0 & 0.20 & \(1.1\) \\ \hline First layer concrete support & 25.0 & 30.0 & 0.20 & 0.70 & 0.60 \\ \hline Second layer concrete support & 25.0 & 30.0 & 0.20 & 0.80 & 0.70 \\ \hline Third layer concrete support & 25.0 & 30.0 & 0.20 & 0.85 & 0.75 \\ \hline Fourth layer concrete support & 25.0 & 30.0 & 0.20 & 0.85 & 0.8 \\ \hline Concrete lining & 25.0 & 30.0 & 0.20 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Physical and mechanical parameters of concrete members in finite element model. Figure 8: Vertical deformation caused by construction of section A. (**a**) Excavate to \(-2.20\) m elevation. (**b**) Excavate to the design elevation of the bottom of the foundation pit. (**c**) The inner supports on the fourth layer are removed. (**d**) All inner supports are removed. Figure 9: Vertical deformation caused by construction of section B. (**a**) Excavate to \(-2.20\) m elevation. (**b**) Excavate to the design elevation of the bottom of the foundation pit. (**c**) The inner supports on the fourth layer are removed. (**d**) All inner supports are removed.