## 3 Numerical Computation Model
### Verification of Numerical Calculation Models  
Based on the established site model and its determined HSS soil constitutive model, we conducted validity tests on the numerical model established. The verification plan for this project is to only excavate the circular deep foundation pit to the bottom elevation, which is consistent with the actual construction and progress on site, and to compare and verify based on the monitoring data of the deep level on site. The specific monitoring points for deep horizontal displacement are shown in Figure 5.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline
**Soil** & **Properties** & \(\gamma_{unsat}\) & \(\gamma_{sat}\) & \(\varphi^{\prime}\) & \(c^{\prime}\) & \(E_{oed}^{ref}\) & \(E_{50}^{ref}\) & \(E_{ur}^{ref}\) & \(K_{0}^{ac}\) & \(G_{0}^{ref}\) & \(\gamma_{0.7}\) \\ \hline
1 & Fill & 15.50 & 19.58 & 10 & 0 & 2.5 & 5.2 & 18.2 & 0.8264 & 36.4 & \(2\times 10^{-4}\) \\ \hline
2 & Silty Clay & 19.03 & 19.53 & 23.6 & 15.72 & 11.6 & 11.6 & 40.6 & 0.5997 & 81.2 & \(2\times 10^{-4}\) \\ \hline
3 & Fine Sand & 15.43 & 19.12 & 28 & 0 & 30 & 30 & 105 & 0.5305 & 210 & \(2\times 10^{-4}\) \\ \hline
4 & Fine Sand & 16.98 & 20.26 & 28 & 0 & 45 & 45 & 158 & 0.531 & 315 & \(3\times 10^{-4}\) \\ \hline
5 & Fine Sand & 16.98 & 20.26 & 28 & 0 & 50 & 50 & 175 & 0.531 & 350 & \(3\times 10^{-4}\) \\ \hline
6-1 & Silty Clay & 20.35 & 20.40 & 35 & 15.72 & 13.1 & 13.1 & 45.9 & 0.775 & 91.7 & \(3\times 10^{-4}\) \\ \hline
6 & Fine Sand & 20.21 & 20.21 & 28 & 0 & 65 & 65 & 325 & 0.531 & 650 & \(3\times 10^{-4}\) \\ \hline
7 & Silty Clay & 19.49 & 19.49 & 28 & 58.6 & 21.2 & 21.2 & 106 & 0.531 & 212 & \(3\times 10^{-4}\) \\ \hline
8 & Fine Sand & 20.4 & 20.4 & 28 & 0 & 80 & 80 & 400 & 0.531 & 480 & \(3\times 10^{-4}\) \\ \hline
9 & Fine Sand & 20.4 & 20.4 & 28 & 0 & 90 & 90 & 450 & 0.531 & 540 & \(3\times 10^{-4}\) \\ \hline
10 & Silty Clay & 19.72 & 19.72 & 14 & 51.1 & 20.6 & 20.6 & 103 & 0.758 & 124 & \(3\times 10^{-4}\) \\ \hline
11 & Fine Sand & 20.6 & 20.6 & 28 & 0 & 100 & 100 & 500 & 0.531 & 250 & \(3\times 10^{-4}\) \\ \hline
12-1 & Silty Clay & 19.52 & 19.52 & 14.4 & 55.2 & 22.6 & 22.6 & 113 & 0.751 & 250 & \(3\times 10^{-4}\) \\ \hline
12 & Fine Sand & 20.60 & 20.60 & 28 & 0 & 110 & 110 & 550 & 0.531 & 250 & \(3\times 10^{-4}\) \\ \hline
13 & Silty Clay & 19.94 & 19.94 & 19.7 & 76.7 & 25.6 & 25.6 & 128 & 0.663 & 250 & \(3\times 10^{-4}\) \\ \hline
14 & Silty Clay & 19.82 & 19.82 & 18.7 & 91.8 & 28.8 & 28.8 & 144 & 0.679 & 250 & \(3\times 10^{-4}\) \\ \hline
14-1 & Medium Sand & 20.60 & 20.60 & 20 & 0 & 200 & 200 & 600 & 0.658 & 250 & \(3\times 10^{-4}\) \\ \hline \end{tabular} Note: \(\gamma_{unsat}\), \(\gamma_{sat}\) are in units of KN/m\({}^{3}\); \(\varphi^{\prime}\) is in degrees (\(\lx@math@degree\)); \(c^{\prime}\) is in KPA; \(E_{oed}^{ref}\), \(E_{50}^{ref}\), \(E_{ur}^{ref}\) are in MPa; \(G_{0}^{ref}\), \(P^{ref}\) are in \(\text{KN/m}^{2}\); \(K_{0}^{ac}\), \(\gamma_{0.7}\), \(R_{f}\), \(\gamma_{var}\), m are dimensionless.  
\end{table}
Table 2: Parameters of HSS model for foundation pit site soils.  
The horizontal displacement of the selected node varies with the depth of the connecting wall during excavation up to \(-18.75\) m (stage 1), \(-27.75\) m (stage 2), and \(-42.5\) m (stage 9), as shown in Figure 6. The horizontal displacement of the diaphragm wall at each measurement point increases to a maximum value with the increase in the burial depth of the diaphragm wall, and then gradually decreases. From the comparison of on-site measurement and the simulation calculation of horizontal displacement, it can be seen that the simulation results of this study can better describe the variation law of on-site measurement results, and the magnitude level of the obtained displacement is not significantly different. Overall, the finite element method of the HSS model used in this article can better reflect the effect of soil excavation on structural deformation, and is suitable for the simulation and analysis of ultra-deep foundation pit excavation in the site.