## 3 Numerical Simulation of Deep Foundation Pit  
### Model Establishment  
Given the complex surrounding environment of the foundation pit, it is essential to conduct a simplified analysis to facilitate subsequent finite element modeling and calculations. This analysis encompassed the following assumptions: (1) the soil conditions within the foundation pit were considered to be horizontally and homogeneously distributed; (2) vehicle loads on the road were converted into uniformly distributed loads acting on the cover plate equal to 20 kPa; (3) a linear elastic plate element model was utilized for the diaphragm wall; (4) a beam element model was employed for the concrete struts; (5) an embedded pile model was utilized for the lattice columns; (6) the numerical simulation process excluded the influence of the diaphragm wall construction and the disturbance of soil caused by construction machinery; (7) time-related effects were not taken into account.  
Figure 2: Standard cross-section of Zhong Yi Station.  
Contact between different materials is the default setting, taking into account gravity and earth pressure loads as well as vehicle loads.  
In this study, we used the PLAXIS 3D version 2021 program to conduct finite element modeling analysis on a subway foundation pit at the Zhongyilu Station in Wuhan City. According to [PERSON]'s principle and relevant specifications, the influence range of deep foundation pit excavation was approximately three times that of the excavation depth. The maximum excavation depth for this foundation pit was 28.2 m. Based on actual working conditions, the dimensions of the model were established as 35 m \(\times\) 160 m \(\times\) 80 m (x \(\times\) y \(\times\) z). The boundary conditions are set as follows: the horizontal displacements at the four sides of the model are constrained to simulate the lateral restraint of the soil in actual engineering; full constraints are applied at the bottom to prevent the model from undergoing unreasonable overall movement; the top is kept free to more realistically reflect the deformation of the soil at the top. In terms of the mesh refinement strategy, we focus on the key areas, with the element size controlled at around 0.1 m to ensure the calculation accuracy of these areas, thereby accurately capturing the detailed changes in stress and deformation. For other non-key areas, larger-sized meshes are used for transition, which not only ensures the simulation accuracy of the key areas but also effectively balances the calculation efficiency of the entire model, avoiding the problems of wasted computing resources and excessive calculation time caused by excessive meshing. In this configuration, the x-axis, y-axis, and z-axis represent the longitudinal, transverse, and vertical directions of the foundation pit, respectively. The numerical model of the foundation pit is illustrated in Figure 3. The support system of the foundation pit comprises a diaphragm wall and an internal support system. The diaphragm wall and steel pipe columns are retained as permanent structures, while the internal supports include reinforced concrete supports, steel supports, and bored piles. The diaphragm wall and the main structure of the foundation pit were modeled using solid elements, whereas the lattice columns and bored piles were simulated using the embedded pile model. The main structural parameters are shown in Table 2.  
Figure 3: Numerical model of foundation pit.