## 3 Establishment of Numerical Analysis Models  
### Geometric Models and Boundary Conditions  
The tunnel foundation pit construction adopted the open-cut method. Figure 4a shows the overall appearance of the numerical analysis model of the tunnel and steel sheet pile coffedam. In this model, X represented the horizontal direction, with the east as the positive direction of the X-axis, Y represented the direction of the tunnel extension, with the north as the positive direction of the Y-axis, Z represented the depth direction of the foundation pit, with the upward direction as the positive direction of the Z-axis, and the lake's bottom was located on the left side of the foundation pit. To eliminate the influence of boundary effects, the left range of the foundation pit was taken as five times the construction depth of the tunnel foundation pit, the right and bottom ranges were taken as four times the construction depth of the tunnel foundation pit, and the length direction of the tunnel was taken as 30 m. The material parameters of the sheet pile coffedam and enclosure structure are shown in Table 1.  
The depth of the foundation pit was 13.8 m, and the width was 40 m. In the foundation pit's supporting structure, the top layer was concrete support with a size of 0.8 m \(\times\) 0.8 m, and the lower three layers were steel supports with a diameter of 0.69 m and a thickness of 0.0016 m. The diameter of the drill-pouring pile was 0.85 m, and the length was 30 m. The underground continuous wall was composed of C35 concrete, and the thickness of the underground continuous wall was 0.8 m. The coffedam was 18 m away from the foundation pit, which is the minimum distance from the foundation pit of the Yinshan Lake  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type of Material** & **Density (g/cm\({}^{3}\))** & \
\begin{tabular}{c} **Elastic Modulus** \\ **(MPa)** \\ \end{tabular} &
\begin{tabular}{c} **Poisson’s Ratio** \\ **(-)** \\ \end{tabular} \\ \hline Larsen VI Sheet Pile & 8.01 & 206,000 & 0.31 \\ Round Steel Tie Rod & 7.95 & 200,000 & 0.20 \\ Underground Diaphragm Wall & 2.45 & 31,500 & 0.20 \\ Concrete support & 2.38 & 30,000 & 0.20 \\ Steel support & 7.85 & 200,000 & 0.20 \\ Column pile & 2.50 & 30,000 & 0.20 \\ Backfilled soil & 1.85 & 20 & 0.20 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Material parameters of retaining structure and sheet pile coffedam.  
Figure 3: Locations of measurement points for coffedam deformation and tie rod axial forces.  
Figure 2: Cross-section of cofferdam.  
Tunnel Project. The cofferdam structure adopted Larsen IV steel sheet piles, and the length of steel sheet piles on the adjacent lakeside was 23 m; the length of steel sheet piles on the pit side was 17 m, and the width of the cofferdam was 8 m. In the steel sheet pile cofferdam structure, there were 15 round steel tie rods with a diameter of 0.048 m and spacing of 2 m. The steel cofferdam and tunnel construction supporting structure are shown in Figure 4b.  
The mesh model was modeled and meshed by the finite element software Abaqus and then converted into a mesh file in the Flac3d format, which was called the calculation file. The model was then divided into 94,437 nodes and 87,060 hexahedral meshes.  
The boundary conditions in the numerical analysis model included the surface around the model, restricted normal displacement, and the bottom, which restricted the displacement in X, Y, and Z directions. The groundwater level was considered according to the design water level and was set at 1.5 m below ground level.  
The water pressure above the lake bottom was applied in loading form. The lake's bottom surface adopts a fixed head boundary. When the groundwater was lowered below the construction surface in time during the foundation pit construction, it could be assumed that there waso water in the foundation pit during construction and that the seepage of groundwater in the soil followed [PERSON]'s law.