## 2 Methods
### Establishment of Numerical Model  
Based on the design scheme and geological conditions, a three-dimensional finite element method model (hereafter referred to as the FEM model) was developed using Midas GTS NX software to simulate the study area in this project. The dimensions of the FEM model were 320 m by 170 m in length and width, respectively, with a height of 100 m. A hexahedral mesh was implemented for meshing the model. Normal constraints were applied to all boundary surfaces except for the upper boundary surface of the model. Figure 4 depicts the resulting FEM model. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Soil Layer** & **Height/m** & \begin{tabular}{c} **Specific** \\ **Weight/(kN\(\cdot\)m\({}^{-3}\))** \\ \end{tabular} & **Poisson Ratio** & \
\begin{tabular}{c} **Elastic** \\ **Modulus/MPa** \\ \end{tabular} & **Cohesion/kPa** &
\begin{tabular}{c} **Friction** \\ **Angel/(\({}^{\circ}\))** \\ \end{tabular} \\ \hline Filled & 1.4 & 18.1 & 0.34 & 8.39 & 0 & 10 \\ Silty clay & 5.6 & 18.6 & 0.28 & 23.47 & 18.9 & 22.9 \\ Cobble 1 & 10.4 & 18.6 & 0.28 & 24.94 & 0 & 34.5 \\ Cobble 2 & 6 & 19.9 & 0.28 & 27.25 & 0 & 34.3 \\ Cobble 3 & 13.8 & 19.9 & 0.25 & 40 & 4.5 & 32 \\ Sandy silt & 2.8 & 19.9 & 0.27 & 55 & 0 & 34 \\ Cobble 4 & 5.8 & 19.2 & 0.28 & 55 & 0 & 34 \\ Cobble 5 & 10.6 & 19.9 & 0.25 & 70 & 0 & 35 \\ Cobble 6 & 6.6 & 19.7 & 0.28 & 90 & 0 & 36 \\ Silty clay & 16 & 19.3 & 0.28 & 66.67 & 52.7 & 17.7 \\ Sand & 19.5 & 19.9 & 0.25 & 100 & 0 & 36 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical parameters of soil layers. Figure 4: The finite element model: (**a**) overall schematic diagram of the model; (**b**) I-I’ section diagram of the model; (**c**) II-II’ section diagram of the model. The Mohr-Coulomb model was utilized as the soil constitutive model, while an elastic constitutive model was employed for the reinforced concrete structure. It is worth mentioning that when the Mohr-Coulomb criterion and the linear elastic model are combined within the same numerical model, there is a certain degree of error introduced due to the implicit assumption that the soil exhibits elastic deformation characteristics before failure [28, 29]. However, in this model, considering that the parameters of the Mohr-Coulomb criterion could be directly obtained from the geological survey report of a professional surveying agency without the need for further estimation of other parameters required by alternative constitutive models (which were not provided in the geological survey report), the Mohr-Coulomb criterion were chosen to avoid errors resulting from the selection of parameters. Furthermore, regarding the aforementioned error caused by the implicit assumption, as the total deformation in this case is not significant, the error remains within an acceptable range. To simplify the model, the reinforcement within the concrete was not accounted for, and the elastic modulus of the reinforced concrete structure was substituted with an equivalent value. Moreover, to consider the impact of segment joints on the overall strength, the concrete strength of the shield segment was reduced to 85% of its original strength. The soil layer parameters are presented in Table 1, while the parameters of other components are displayed in Table 2.  
During the actual working conditions, the excavation of the left line tunnel was carried out initially. Subsequently, the right line tunnel was excavated after the shield machine had completely passed through the bottom of the foundation pit. Prior to the tunnel construction, a 2 m thick layer of lightweight concrete was backfilled to the top of the underground structure to prevent it from floating due to the impact of the tunnel construction. To control the surface subsidence while the shield machine was crossing the foundation pit, both synchronous grouting and backwall grouting were employed. In the numerical model employed in this research, the equivalent layer method was utilized to simulate the soil disturbance and loss caused by the shield machine.