## 3 Numerical Simulation Modeling
### Material Parameters
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Item** & **Code Name** & **Thickness** & **Unit Weight** & \(f_{c}\) & **Modulus of Elasticity** & **Poisson’s Ratio** \\  & & **(m)** & **(kN/m3)** & **(kg/cm2)** & **(kN/m2)** & **Poisson’s Ratio** \\ \hline Diaphragm wall & DW & 0.8 & 24 & 280 & \(1.76\times 10^{7}\) & 0.17 \\ Cross wall & CW & 0.8 & 24 & 280 & \(1.76\times 10^{7}\) & 0.17 \\ Foundation & FS & 0.6 & 24 & 210 & \(1.52\times 10^{7}\) & 0.17 \\ Steel sheet pile & SP & 0.08 & 78.5 & - & \(1.68\times 10^{8}\) & 0.28 \\ Box culvert & BC & 1.0 & 24 & 210 & \(1.52\times 10^{7}\). & 0.17 \\ Pipe roof & PR & 0.72 & 26 & 210 & \(2.3\times 10^{7}\) & 0.23 \\ \hline \hline \end{tabular} Notes: \(f_{c}^{\prime}\) = 28-day compressive strength of concrete.  
\end{table} 
Table 4: Material parameters of the structures. Figure 11: Schematic diagram of the underpass cross-sectional area with different aspect ratios. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type of H-Shape Steel** & **Cross-Sectional Area** & **Modulus of Elasticity** & **Reduction Coefficient** & **Effective Stiffness** \\  & **(m2)** & **(kN/m2)** & **(kN)** \\ \hline H 350 \(\times\) 350 \(\times\) 12 \(\times\) 19 & 0.0172 & \(2.1\times 10^{8}\) & 0.75 & \(2.71\times 10^{6}\) \\ H 400 \(\times\) 400 \(\times\) 13 \(\times\) 21 & 0.0219 & \(2.1\times 10^{8}\) & 0.75 & \(3.45\times 10^{6}\) \\ H 414 \(\times\) 400 \(\times\) 18 \(\times\) 28 & 0.0295 & \(2.1\times 10^{8}\) & 0.75 & \(4.65\times 10^{6}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Parameters of the support materials for the diaphragm wall. The excavation of the underground underpass adopted three rounds of excavation, and each round was two meters long. During the excavation process, temporary supports were used to resist the surrounding earth pressure. In the numerical simulation, \"line load\" was used to simulate the temporary supports of the underpass, as shown in Figure 12. The parameter values of the temporary supports are shown in Table 8.  
This site was surrounded by Sun Yat-Sen Memorial Hall, Taipei Dome, existing underground box culverts, and roads, as shown in Figure 13. In order to ensure the safety of the project construction, the impact of the above-mentioned adjacent structure load and road load on the excavation process was analyzed. According to the field survey, the length and width of the surrounding structures, the length and width of the road, and the relative distance between the diaphragm wall of the excavation base and the adjacent buildings were measured. The coordinates of the floor plan of the structures around the construction \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Type of H-Shape Steel** & \begin{tabular}{c} **Modulus of Elasticity** \\ **(kN/m2)** \\ \end{tabular} & \begin{tabular}{c} **Unit Weight** \\ **(KN/m2)** \\ \end{tabular} & \begin{tabular}{c} **Cross-Sectional Area** \\ **(m2)** \\ \end{tabular} & \
\begin{tabular}{c} **I2** \\ **(m4)** \\ \end{tabular} &
\begin{tabular}{c} **I3** \\ **(m4)** \\ \end{tabular} \\ \hline H 350 \(\times\) 350 \(\times\) 12 \(\times\) 19 & \(2.1\times 10^{8}\) & 78.5 & 0.0172 & \(9.87\times 10^{-5}\) & \(9.87\times 10^{-5}\) \\ H 400 \(\times\) 400 \(\times\) 13 \(\times\) 21 & \(2.1\times 10^{8}\) & 78.5 & 0.0219 & \(1.63\times 10^{-4}\) & \(1.63\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Parameters of the support materials for the steel sheet pile. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Construction Stage** & \
\begin{tabular}{c} **Preload of Diaphragm Wall End** \\ **(kN)** \\ \end{tabular} &
\begin{tabular}{c} **Preload of Steel Sheet Pile End** \\ **(kN)** \\ \end{tabular} \\ \hline The first stage & 60 & 50 \\ The second stage & 140 & 130 \\ The third stage & 220 & 180 \\ The fourth stage & 320 & 350 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Axial preload of the supports. Figure 12: Schematic diagram of simulating the forces on the underpass temporary supports by “line load”.