## 3 Finite-Element Model  
### Two-Dimensional Model  
As the project is located in an area with abundant groundwater, a complete fluid-solid coupling method was employed in the simulation. Owing to the existence of a soft soil layer and composite foundation with a low permeability coefficient, the following assumptions were made based on relevant studies before establishing the model [21; 22]: (1) The foundation was considered to have a horizontal distribution, and an average thickness was used for the analysis. (2) The composite foundation was assumed to be isotropic, homogeneous materials. (3) Deformation was assumed to conform to the plane strain principle. (4) The effect of construction time was not taken into consideration. Based on the above assumptions, a two-dimensional finite-element model was established as illustrated in Figure 5. The unit thickness of soil was chosen based on measured data in the vertical direction. The average thicknesses of strata 1, 21, 22, 33, and 11 are 9.2-11 m, 5 m, 6.4 m, 12.8 m, and 37.5 m, respectively. Other details of the model are shown in Figure 5.  
The Mohr-Coulomb constitutive model was used for both natural and reinforced strata. A linear structural element was employed to simulate the retaining structure of the foundation pit. The same contact model was set on both sides of the foundation pit. The steel corrugated pipe structure was simulated using the shell element without considering the contact between the structure and surrounding soil. A linear-elastic constitutive model was adopted for all the structural elements. The displacements of shell structural elements and the bottom boundary of the numerical model were constrained, and the top surface of the numerical model is the free boundary. After the initial pore pressure was established, the left and right sides of the model (AD and BC) were set as permeable boundaries, while the bottom was set as an impermeable boundary. The groundwater level was set at 3.0 m below the top surface of the model, and the pore water pressure at the free surface was zero. For safety, unfavorable working conditions should be analyzed. Equivalent parameters obtained from the non-metro-reinforced area were selected to represent the value of the composite foundation. Firstly, the relationship between the deformation modulus and unconfined compressive strength value \(q_{u}\) was investigated, and \(E_{50}=175q_{u}\) was selected according to the empirical formula [23; 24; 25]. Secondly, the natural foundation's deformation modulus \(E_{0}\) was estimated using the approximate conversion formula \(E_{0}=E_{s}[(1-2v^{2})/(1-v)]\) when there is no field test data. Subsequently, the comprehensive deformation modulus was determined using the bidirectional weight coefficient method. The equivalent formula is expressed in Formulas (1) and (2), and the calculation results are listed in Table 3. Other parameters used in the simulation are listed in Tables 4 and 5. In the simulation, the steel corrugated pipe was equivalent to a straight-wall structure of the same size. The calculation results are listed in Table 6.  
\[E_{0c}=\sum_{i=1}^{n}\alpha_{i}E_{i}/\sum_{i=1}^{n}\alpha_{i} \tag{1}\]  
Figure 5: Schematic of plane model. \[E_{0m}=\sum_{j=1}^{k}h_{j}E_{j}/\sum_{j=1}^{k}h_{j} \tag{2}\]  
where \(E_{0c}\) is the comprehensive deformation modulus of the foundation-reinforced layer, \(E_{i}\) is the deformation modulus of the soil and foundation-reinforced materials, \(\alpha_{i}\) is the area weight coefficient or replacement rate of different materials, \(E_{0m}\) is the comprehensive deformation modulus of the multilayer foundation, \(E_{j}\) is the deformation modulus of the soil in each layer, and \(H_{j}\) is the soil thickness.