# Performance Analysis of Pile Group Installation in Saturated Clay
## 2 Numerical Modeling and Validation
### Model Validation
Figure 2: Soil response caused by single pile installation: (**a**) radial displacement, (**b**) excess pore pressure, (**c**) volumetric stress, and (**d**) variation in volumetric stress with depth. The variation in EPP within the soil caused by single pile installation can be calculated using the formula derived by [PERSON] [12] based on cylindrical cavity expansion theory:  
\[\frac{\Delta u}{C_{u}}=\left\{ \begin{array}{l}\left[2\ln\left(\frac{R_{\rm p}}{ x}\right)+1.733A-0.578\right],\ x\leq R_{\rm p}\\ \left(1.733A-0.578\right)\left(\frac{R_{\rm p}}{x}\right)^{2},\ x>R_{\rm p} \end{array} \right. \tag{3}\]  
\[\frac{R_{\rm p}}{d_{\rm e}}=\sqrt{\frac{E}{2(1+v)C_{u}}} \tag{4}\]  
in which \(R_{\rm p}\) is the radius of the soil plastic zone, \(d_{\rm e}\) is the equivalent radius of the pile, \(E\) is the elastic modulus of the soil, \(v\) is the Poisson's ratio of the soil, and \(A\) is the pore pressure coefficient, with \(A\) ranging from 0.7 to 1.3 for normally consolidated soil and from 1.5 to 2.5 for sensitive soil. In this study, the soil is normally consolidated, so \(A\) is taken as 1.2, and \(C_{u}\) is the undrained shear strength of the soil. Since the undrained shear strength of saturated clay shows an approximately linear or piecewise linear relationship with depth, \(C_{u}\) is taken as \(C_{u}=22.5+2.5\,z\) in this study. In Figure 2(a), the \(y\)-axis stands for the normalized radial soil displacement by the pile diameter. It can be observed that the computed curve agrees well with the theoretical and measured curves: the radial soil displacement decreases rapidly with increasing radial distance, and the influence region for the radial soil displacement is 0-10 \(D_{\rm e}\). As shown in Figure 2(b), the EPP normalized by the effective vertical stress (\(\sigma^{\prime}v_{0}\)) decreases rapidly with increasing radial distance. The EPP obtained from the analytical method is generally higher than the measured data. These results may be due to the theoretical solution not including the pile-soil friction effect. The influence region is 0-10 \(D_{\rm e}\). However, the computed EPP obtained from the proposed numerical method aligns well with the measured values, thus further validating that the established numerical model is feasible for simulating the pile installation process. As soil consolidation progresses, the EPP dissipates gradually over time. This study calibrates the actual seepage time using the fluid bulk modulus, with the modified fluid bulk modulus denoted as \(K_{f}^{a}\). [PERSON] et al. [33] measured the dissipation of EPP around the pile shaft after installation and obtained the pile's load-displacement (\(L\)-\(D\)) curve through centrifuge testing. The material parameters for the calculated model are consistent with centrifuge tests, as listed in Table 4. As shown in Figure 4, the EPP decreases over time, and the calculated results are in good agreement with the measured data. Figure 5 presents the \(L\)-\(D\) curve of the pile after 8.65 days of consolidation, showing distinct elastic and plastic  
Figure 3: Comparison of calculated (**a**) radial soil displacement [3; 36] and (**b**) excess pore pressure with test results along the radial distance [3; 12; 37; 38]. stages consistent with the measured trend. Therefore, this method is suitable for analyzing the installation, consolidation, and bearing capacity of jacked piles.