## 3 Comparative Analysis of Working Performance of Pile-Raft System
### Numerical Modeling
#### 3.1.3 Material Parameters of Equivalent Reinforcement Zone  
The equivalent reinforcement zone of CFG pile composite foundation was regarded as an anisotropic elastoplastic material and its mechanical behavior was described by using jointed rock model. The model parameters included the stiffness \(E_{1}\) and \(v_{1}\) on the horizontal direction (\(\alpha_{1}=0^{\circ}\)) and the stiffness parameter \(E_{2}\) and \(v_{2}\) on the vertical direction (\(\alpha_{2}=90^{\circ}\)). The strength of the CFG pile was taken as \(c=270\) kPa and \(\varphi=0^{\circ}\). It is key to determine two sets of stiffness parameters during the numerical simulation using the jointed rock model. In this research, assuming \(v_{1}=v_{2}=0.35\), \(E_{1}\) and \(E_{2}\) were determined by trial calculation. The process was as follows: (1) in order to ensure the accuracy of the calculation for pile and cushion, the single-row pile model was established and the meshes of cushion layer and the soil in a certain range of the body of the pile were locally refined to obtain 5-10 elements around each pile; the model mesh is shown in Figure 6; (2) the material parameters of the equivalent composite foundation (\(E_{1}\) and \(E_{2}\)) were acquired by fitting to the vertical deformation (i.e., settlement) and the horizontal deformation outside the pile. Assuming \(v_{1}=v_{2}=0.3\), the first step was to make \(E_{1}=E_{2}\) to fit the vertical deformation, and then to adjust \(E_{1}\) to fit the horizontal deformation. After that, satisfactory fitting results were obtained by adjusting \(E_{2}\) slightly. After three rounds of aforesaid trial calculation, it was established that \(E_{1}=1.0\ \times\ 10^{4}\) kPa, \(E_{2}=1.2\ \times\ 10^{5}\) kPa, and \(G_{2}=0.5E_{2}/(1+v_{2})=4.62\ \times\ 10^{4}\) kPa.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**No.** & \(\rho\) **(kg/m3)** & \(E_{eod}^{ref}\) **(kPa)** & \(E_{50}^{ref}\) **(kPa)** & \(E_{ur}^{ref}\) **(kPa)** & \(m\) & \(v\) & **c (kPa)** & \(\varphi\) **(\({}^{\circ}\))** \\ \hline \⃝1 & 1750 & 6000 & 6000 & 24,000 & 0.5 & 0.35 & 8 & 25 \\ \⃝2 & 1990 & 8000 & 8000 & 24,000 & 0.5 & 0.35 & 8 & 27 \\ \⃝3 & 2000 & 15,000 & 15,000 & 45,000 & 0.5 & 0.30 & 13 & 27 \\ \⃝4 & 2030 & 12,000 & 12,000 & 36,000 & 0.5 & 0.32 & 10 & 29 \\ \⃝5 & 2020 & 45,000 & 45,000 & 135,000 & 0.5 & 0.30 & 5 & 35 \\ \⃝6 & 1960 & 14,000 & 14,000 & 42,000 & 0.5 & 0.25 & 17 & 27 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Physical and mechanical parameters of soil.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Structure** & **Type of Unit** & \(d\) **1 (m)** & \(\rho\) **(kg/m3)** & **E (MPa)** & \(\
u\) & \(T_{\text{skin,top,max}}\) & \(T_{\text{skin,base,max}}\) \\  & & & & & & (kN/m) & (kN/m) \\ \hline Raft plate & Plate & 0.8 & 2500 & 32,500 & 0.15 & — & — \\ Wall & Plate & 0.3 & 2500 & 30,000 & 0.15 & — & — \\ Floorslab & Plate & 0.2 & 2500 & 30,000 & 0.15 & — & — \\ Pillar & Beam & 0.6 & 2500 & 30,000 & — & — & — \\ Concrete-bored pile & Embedded pile & 0.8 & 2500 & 28,000 & — & 166 & 200 \\ CFG pile & Embedded pile & 0.4 & 2500 & 28,000 & — & 83 & 100 \\ \hline \hline \end{tabular}  
* \(d\) is the thickness or diameter. \({}^{2}\)\(T_{\text{skin,max}}\) is the limit value of lateral frictional resistance of the pile, assuming linear distribution along its depth.  
\end{table}
Table 2: Material parameters of structure. CFG—cement/fly ash/gravel.  
The comparisons of vertical deformation and horizontal deformation of the bottom cushion between the above equivalent model and the embedded pile model are shown in Figures 7 and 8, respectively. It was shown that the numerical results obtained using the equivalent model were very close to those obtained using the embedded pile model, and the equivalent parameters were reasonable.  
Figure 6: Model mesh of single-row pile: (**a**) integral model diagram; (**b**) partial enlarged detail.  
Figure 7: Comparison of vertical deformation of the bottom cushion: (**a**) embedded pile model; (**b**) equivalent reinforcement zone model.