## 2 Methodology
### Finite Element Analysis  
To further explore the deformation laws of steel-pipe piles after the foundation pit excavation, finite element software Midas GTS-NX was used to conduct a numerical analysis and simulation of the foundation pit excavation process.  
Figure 11: Monitoring point layout.  
Figure 12: Excavation of the foundation pit.  
Figure 10: Elevation drawing of the monitoring points of the horizontal displacement of the pile top.  
The soil is an isotropic medium in this calculation model and presented a stratified distribution in the horizontal direction. The influence of underground water was disregarded in the numerical analysis and calculation process. The hardening soil model can take into account the non-linear characteristics of the stress and strain of soil, and can reflect the complex stress path of soil during the excavation of a foundation pit [29,30]. Therefore, the modified Mohr-Coulomb constitutive model was used during the calculation process.  
The dimension of the foundation pit excavation in the model was 40 m \(\times\) 40 m (length \(\times\) width), and the excavation depth was 6.5 m. A total of six times the excavation depth of the foundation pit was set in the horizontal direction of the soil outside the foundation pit, whereas 3.6 times the depth was set below the undersurface of the foundation pit. The calculation model dimension was 80 m \(\times\) 80 m \(\times\) 30 m (length \(\times\) width \(\times\) height). The numerical model is shown in Figure 13. The soil was simulated using solid elements, according to the geological survey report from the Beijing Institute of Geological Survey and Design. Table 1 displays the material mechanical parameters of the soil. The steel-pipe piles and cap beam were simulated using the beam elements. Table 2 lists the material mechanical parameters of the supporting structure according to the support structure design documents.  
During the numerical simulation of the foundation pit excavation under the supporting of the large-diameter steel-pipe piles, three steps were performed.  
First, the soil grids of the model were activated. Then, the boundary constraint and soil load were applied to grids. Finally, the displacement was reset to 0.  
Second, the piles and cap beams were constructed. Then, the displacement was also reset to 0.  
Third, the foundation pit was excavated 3 times with excavation depths of 2, 2, and 2.5 m.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Name** & **Thickness (m)** & **Poisson Ratio** & \begin{tabular}{c} **Unit Weight** \\ **(kN/m3)** \\ \end{tabular} & **Cohesion (kPa)** & \
\begin{tabular}{c} **Internal Friction** \\ **Angle (\({}^{\circ}\))** \\ \end{tabular} &
\begin{tabular}{c} **Compression** \\ **Modulus (MPa)** \\ \end{tabular} \\ \hline Miscellaneous fill & 0.8 & 0.35 & 16.5 & 0 & 8 & 5 \\ Clayey silt & 5.7 & 0.25 & 19.7 & 9 & 16 & 11 \\ Sandy silt & 4.5 & 0.26 & 19.9 & 14 & 18 & 14 \\ Fine sand & 1.8 & 0.27 & 19.5 & 0 & 30 & 30 \\ Silty clay & 17.2 & 0.26 & 20 & 20 & 22 & 26 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Material mechanical parameters of the soil.  
Figure 13: Components of numerical model gridding. (**a**) Overall model gridding (**b**) Steel-pipe pile beam model.