## 3 Numerical Simulation Modeling
### Material Parameters
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Layers**} & \multicolumn{2}{c}{**Depth (m)**} & \multicolumn{2}{c}{\(\gamma_{\text{\tiny{unsat}}}\)} & \(\gamma_{\text{\tiny{sat}}}\) & \(E_{\text{\tiny{50}}}^{ref}\) & \(E_{\text{\tiny{odd}}}^{ref}\) & \(E_{\text{\tiny{arf}}}^{ref}\) & \(\sigma^{\prime}\) & \(\psi\) & \multirow{2}{*}{\(m\)} \\  & **Top** & **Bottom** & **(kN/m3)** & **(kN/m2)** & **(kN/m2)** & **(kN/m2)** & **(kN/m2)** & **(kN/m2)** & **(kN/m2)** & **(°)** & **(°)** \\ \hline SF & 0 & \(-1.0\) & 18.6 & 19.1 & 22,000 & 22,000 & 66,000 & 0.5 & 30 & 0 & 0.5 \\ CL1 & \(-1.0\) & \(-3.0\) & 18.0 & 18.3 & 22,300 & 18,000 & 66,900 & 1 & 29 & 0 & 1.0 \\ CL2 & \(-3.0\) & \(-35.0\) & 18.3 & 18.8 & 29,000 & 23,000 & 87,000 & 1 & 28 & 0 & 1.0 \\ RL & \(-35.0\) & \(-50.0\) & 21.5 & 21.8 & 90,000 & 90,000 & 27,000 & 80 & 34 & 4 & 0.5 \\ AFI & 0 & \(-15.0\) & 22 & 22.5 & 70,000 & 70,000 & 21,000 & 1 & 34 & 4 & 0.5 \\ \hline \hline \end{tabular}  
Notes: \(\gamma_{\text{\tiny{unsat}}}=\) unsaturated unit weight; \(\gamma_{\text{\tiny{sat}}}=\) saturated unit weight; \(c_{\text{\tiny{ref}}}^{\prime}=\) effective cohesion; \(\varphi^{\prime}=\) effective friction angle; AFI = after geological improvement.  
\end{table} 
Table 3: Material parameters of the Hardening Soil model. area occupied by concrete in a single composite; \(A_{total}\) = cross-sectional area of a single composite material; \(\gamma_{s}\) = unit weight of steel pipe; \(\gamma_{c}\) = unit weight of concrete; \(v_{s}\) = the volume occupied by the steel pipe in a single composite material; \(v_{c}\) = the volume occupied by concrete in a single composite; \(v_{total}\) = the volume of a single composite material. Diaphragm walls, cross walls, and foundations are all reinforced concrete structures, and their concrete materials were simulated in elastic mode. According to the information of the actual project in this case, the thickness of the diaphragm wall was 0.8 m and its depth was 21.5 m; the thickness of the steel sheet pile was 0.08 m, the penetration depth of the north side was 13 m, and the penetration depth of the other side was 18 m; the thickness of the cross wall was 0.8 m, and its depth was 12.15 to 21.5 m below the surface; the thickness of the foundation was 0.6 m and its depth was 12.15 m below the surface. The foundation of the launching shaft with a thickness of 0.6 m was to facilitate the construction of the pipe roof and provided a certain degree of stiffness. The material parameters of the above structures are shown in Table 4. On the other hand, under the same underpass cross-sectional area, four different aspect ratios (0.30, 0.36, 0.40, and 0.45) were designed in this study, as shown in Figure 11.  
This case was divided into two deep excavation areas, namely the diaphragm wall excavation area and the steel sheet pile excavation area. Both areas adopted five-stage excavation and four-stage support. The support system used H-shape steel sections as temporary support, most of which were used in the early stage of the project. When the structure reached a certain strength, the support system was dismantled. In this study, the node-to-node anchor was used to simulate the axial support and the beam element was used to simulate the base's fence. The support system consisted of three different types of H-shape steel, which were H 350 \(\times\) 350 \(\times\) 12 \(\times\) 19, H 400 \(\times\) 400 \(\times\) 13 \(\times\) 21, and H 414 \(\times\) 400 \(\times\) 18 \(\times\) 28. The relevant parameters of the support materials for the diaphragm wall and the steel sheet pile are shown in Tables 5 and 6, respectively. In addition, the axial forces of the supports at individual stages are shown in Table 7.