# Analysis of Lateral Displacement of Pile Foundation Caused by Large-Diameter Shield Tunneling
## 3 Numerical Simulation Verification Results  
To ensure the validity of the theoretical calculations, the numerical simulation is utilized in conjunction with the ongoing project to compare their results. As depicted in Figure 4, the project consists of a single C40 concrete cast-in-place pile with a diameter of 0.9 m in the axial direction of the shield tunnel. The shield tunnels towards the single pile, with the constant additional thrust \(p\) and friction \(f\) of the shield shell throughout the process. The calculation assumes a horizontally uniform soil distribution, without accounting for the influence of the groundwater level. For ease of verification, both the theoretical calculations and the numerical simulation simplify the soil into a homogeneous layer. According to the geological survey report on the project, the soil parameters are detailed in Table 1.  
The numerical model of the influence of the shield construction on the displacement of the front pile is established using PLAXIS three-dimensional finite element software ([[https://www.bentley.com/software/plaxis-3d/](https://www.bentley.com/software/plaxis-3d/)]([https://www.bentley.com/software/plaxis-3d/](https://www.bentley.com/software/plaxis-3d/))). The constitutive model of the soil adopts the simple, fast, and easy-to-converge Mohr-Coulomb elastic-plastic model, which is often used in engineering design. The shield shell is simulated using the plate element. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Soil Layer**} & **Unit Weight** & **Elastic Modulus** & **Poisson Ratio** & **Cohesion Force** & **Internal Frictional Angle** \\  & \(\gamma\)**/kN**-\(\mathbf{m^{-3}}\) & \(E_{s}\)**/MPa** & \(\
u\) & \(C\)**/kPa** & \(\psi\)/\({}^{\circ}\) \\ \hline silty clay & 19 & 3.8 & 0.35 & 17 & 10.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of soil and rock. Figure 4: Schematic diagram of the engineering case (unit: m). In order to avoid the influence of the boundary conditions of the model, the size of the model should be at least three times larger than the size of the main structure. The model is 200 m long, 100 m wide, and 120 m high. The upper surface of the model is free, the horizontal constraint is applied to the side, and the bottom surface is completely fixed. The rationality verification of this numerical model based on the actual field data is referred to [18]. The grid sensitivity is checked at the time of the model's building to ensure that the numerical model is consistent with the actual engineering situation. In this model, the soil element uses a 10-node tetrahedral element, the plate element uses a 6-node triangular element, and the 12-node interface element is used to simulate the interaction between the structure and the soil. The global density of the model is set to medium, and a total of 235,051 units are generated. The specific material parameters are shown in Table 2. The numerical model is shown in Figure 5.  
MATLAB software is used to assist in the theoretical calculation. First, the displacement of the soil during the shielding process is obtained using the Mindlin solution. Then, the lateral displacement of the pile foundation under the soil displacement is solved by combining it with the horizontal displacement equation of the pile foundation under the Kerr foundation model. The calculation ignores the upper boundary conditions, and the buried depth of the shield is determined from the height of the pile top. The calculation parameters of the theoretical model are presented in Table 3.  
In Figure 6, we can see the lateral displacement of the pile obtained from both the numerical simulation and the theoretical calculation. The two methods show similar trends in the displacement of the pile foundation. However, there are some differences in their results. For the upper half of the pile, the numerical calculation produces slightly larger displacement results than the theoretical calculation does.