# Study on Shielding Effect of the Pile Group in a Soft-Soil Foundation
## 2 Materials and Methodology
### Numerical Modeling  
A three-dimensional numerical model of a foundation containing a pile group was established to study the hydrostatic pile-soft soil interaction, using the FLAC\({}^{\text{3D}}\) Version 7.0 software. In the modeling, both piles and the soft soil foundation were constructed using solid elements. Specifically, the construction of pile zones and adjacent soil zones was conducted based on the geometric parameters of the piles; the pile tip was set to be semi-spherical and the pile shaft was cylindrical. The piles had a diameter of 0.25 m and a length of 15 m, establishing a 2.5 m spaced matrix of pile group. To facilitate the analysis, the soft soil layer was presumed to be homogeneous. Thus, a symmetric three-dimensional numerical model was developed, centered on a 3 \(\times\) 3 pile group (Figure 2). Considering the special properties of the soft soil foundation, the boundaries were assumed to be impervious. The top boundary of the grid was set to the stress-free ground surface, and normal displacement constraints were applied around and at the bottom of the model. To eliminate the influence of boundary effects, the distances from the model edges to the pile group edges in the horizontal direction were greater than 1.5 times the pile length, and the bottom edge was greater than 0.6 times the pile length. Finally, a grid model of 52.5 m \(\times\) 52.5 m \(\times\) 24 m was established (Figure 2), comprising a total of 76,068 zones and 80,015 grid points.  
Thereafter, the model parameters (Table 1) were assigned to the soil. To compute the initial state of the numerical model, initial ground stresses were imposed. Subsequently, pile installation was simulated based on the cavity expansion theory. Soil compaction during piling was simulated by simultaneously expanding the pile body and the pile tip to reach the final pile diameter; for this simulation, the initial radius was set to one-third of the final radius. The pile was modeled using an elastic constitutive model, and the parameters in the model are consistent with the standard parameters of the precast pile used in this project, as shown in Table 2. The procedure of installing piles primarily involved expanding the  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Parameters** & **Density** & **Compression** & **Rebound** & **Critical** & **Reference** & **Initial** & **Over** \\  & (\(\rho\)/ kg\(\cdot\)m\({}^{-3}\)) & **Lorex (\(C_{s}\))** & **Rebound** & **Failure Ratio (\(e_{1}\))** & **Porosity** & **Consolidation** \\  & & & & **(M)** & **Ratio (\(e_{1}\))** & **Ratio (\(e_{0}\))** & **Ratio (\(R\))** \\ \hline Value & 1699 & 0.1192 & 0.0173 & 0.5183 & 0.5183 & 0.7709 & 2.0 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters used in the modified Cam–Clay model.  
Figure 2: Three-dimensional numerical model of a foundation containing a pile group.  
cylinder (pile body) and semi-sphere (pile tip), then activating the pile grids. To realize this, the reserved pile position grids were initially closed, and expansion displacement vectors were applied (Figure 3). After reaching the actual pile diameter, the adjusted node pile body grids were activated, and the displacement and stress fields of the completed pile-soil interaction were computed. As this study focuses on the lateral interaction between pile and soil, the interface element is not defined as a simplification. This numerical simulation method, which approximates the pile installation process to the expansion of a finite radius cavity, has been implemented in previous studies [31,32].