# Performance Analysis of Pile Group Installation in Saturated Clay
## 2 Numerical Modeling and Validation
### Model Validation  
During the installation of the pile, the compression and shearing of the pile induce significant soil deformation and generate notable EPP. Figure 2a,b show the distribution of radial displacement and EPP in the soil when a single pile penetrates to a depth of 10 m. The results indicate that radial displacement is concentrated near the pile and decreases rapidly with increasing radial distance. The EPP is mainly concentrated around the pile tip, while the pore pressure at the top and bottom of the pile is lower than the static pore pressure, resulting in the observation of negative pore pressure. A similar pore pressure distribution pattern was also reported by [PERSON] et al. [34]. Correspondingly, stress reduction areas are also observed at the top and bottom of the pile, as illustrated in Figure 2c,d. As demonstrated by [PERSON] et al. [35], tensile-induced dilation of the soil leads to a reduction in volumetric stress (or strain), with tensile stress being positive in FLAC\({}^{3\text{D}}\) \begin{table}
\begin{tabular}{c c c} \hline \hline
**Material** & **Saturated Clay** & **Pile** \\ \hline Constitutive model & Mohr–Coulomb & Linear elasticity \\ Elastic modulus [\(E/\left(\text{GPa}\right)\)] & 0.01 & 30 \\ Poisson’s ratio [\(\
u\)] & 0.45 & 0.27 \\ Density [\(\rho\) (kg/m\({}^{3}\))] & 1800 & 2500 \\ Internal friction angle [\(\phi/\left({}^{5}\right)\)] & 20 & — \\ Cohesion [\(c/\left(\text{kPa}\right)\)] & 15 & — \\ Earth pressure coefficient at rest [\(K_{0}\)] & 0.5 & — \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material parameters of pile and clay. \begin{table}
\begin{tabular}{c c} \hline \hline
**Contact Type** & **Frictional Contact** \\ \hline Normal stiffness [\(k_{\text{a}}\) (Pa/m)] & \(1\times 10^{9}\) \\ Shear stiffness [\(k_{\text{S}}\) (Pa/m)] & \(1\times 10^{9}\) \\ Contact surface cohesion [\(c^{\prime}/\left(\text{kPa}\right)\)] & 4 \\ Contact surface friction angle [\(\phi^{\prime}/\left({}^{5}\right)\)] & 8 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Soil–pile surface parameters. \begin{table}
\begin{tabular}{c c} \hline \hline
**Fluid Type** & **Isotropic** \\ \hline Fluid bulk modulus [\(K_{f}/\left(\text{Pa}\right)\)] & \(2\times 10^{9}\) \\ Modified fluid bulk modulus [\(K_{f}^{a}/\left(\text{Pa}\right)\)] & \(1.5\times 10^{6}\) \\ Permeability coefficient [\(k\) (cm/s)] & \(1\times 10^{-7}\) \\ Fluid density [\(\rho_{f}/\left(\text{kg/m}^{3}\right)\)] & \(1\times 10^{3}\) \\ Fluid tensile strength [\(c_{f,t}/\left(\text{kPa}\right)\)] & 10 \\ Porosity [\(P\)] & 0.5 \\ Main process calculation step [\(m\)] & 10 \\ Slave process calculation step [\(n\)] & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Fluid parameters. Hence, it can be inferred that the occurrence of stress reduction and negative pore pressure around the pile top and bottom are caused by tensile-induced dilation of the soil under undrained conditions. Additionally, Figure 2d illustrates the variation in soil volumetric stress at pile penetration depths of 5 m and 10 m. The results show that the volumetric stress at the pile bottom is lower than the initial stress, while the volumetric stress around the pile top decreases as the penetration depth increases. From the perspective of cavity expansion theory, the expansion of a cylindrical cavity is typically simplified to a plane problem, where soil displacement varies only with radial distance. Although theoretical solutions ignore the influence of depth, they provide a good approximation for estimating the radial displacement of soil caused by pile installation. According to [PERSON] et al. (2018), the radial displacement of soil at a distance \(x\) from the center of the cylindrical cavity is given by  
\[S_{x}=d_{\mathrm{e}}\bigg{(}\sqrt{1+\left(x/d_{\mathrm{e}}\right)^{2}}-x/d_{ \mathrm{e}}\bigg{)} \tag{2}\]  
where \(S_{x}\) is the radial displacement of soil at a distance \(x\) from the cylindrical cavity center point, and \(d_{\mathrm{e}}\) is the equivalent pile radius.