## 5 Parametric Study  
For the fully penetrated column foundation, there are two key parameters influencing the settlement, including the ratio of elastic modulus between the column and the surrounding soil, \(E_{c}\)/\(E_{s}\), the ratio between the radius of the column, and the radius of the model \(r_{c}\)/\((d_{e}/2)\). To study the effect of these parameters on the ground settlement, a series of parametric studies were conducted. The properties of the column and the surrounding soil are shown in Table 3. The pressure on the surrounding soil, \(\sigma_{s}\), is 500 kPa, and the pressure on the stone column, \(\sigma_{c}\), is 4000 kPa. Figure 12 shows the ground settlement profiles for the fully penetrated column with various elastic modulus ratios. With an increasing elastic modulus ratio, the ground settlement becomes smaller. However, with the rate of the elastic modulus ratio increasing faster, the rate of settlement decrease becomes slower. In addition, by increasing the elastic modulus ratio, the supporting effect from the column to the soil becomes weaker as the settlement level increases more with the distance from the column. Figure 11: Effect of the area ratio (Ar) on the load intensity-settlement of composite specimens: (a) Ar = 5%, (b) Ar = 10%, (c) Ar = 15%, (d) Ar = 20%. Figure 13 shows the ground settlement profiles for the fully penetrated column with various ratios between the radius and the spacing of the columns. With the increasing ratio between the radius and the spacing of the columns, the ground settlement becomes smaller. However, contrary to the previous phenomenon, the supporting effect is more obvious as the settlement does not increase with distance as much as in Figure 12.  
The Poisson's ratio of the soil also plays an important role in the ground settlement of the column-reinforced foundation. As shown in Figure 14, the Poisson's ratio has a very big impact on the ground settlement. With an increase in Poisson's ratio of soil, the ground settlement decreases very quickly. Compared with the Poisson's ratio of the soil, the Poisson's ratio of the column has a smaller effect on the ground settlement, as shown in Figure 15. The reason is that the area replacement ratio is only 0.36%. Therefore, the changing of the Poisson's ratio of the column produces a much smaller effect. With the increase in the area replacement ratio, the effect of Poisson's ratio of the column will be more pronounced. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Material** & **Property** & **Value** \\ \hline \multirow{3}{*}{Surrounding soil} & Modulus of elasticity, \(E_{c}\): kPa & 4000 \\ \cline{2-3}  & Poisson’s ratio, \(v_{s}\): & 0.3 \\ \hline \multirow{6}{*}{Stone column} & Modulus of elasticity, \(E_{c}\): kPa & 400,000 \\ \cline{2-3}  & Poisson’s ratio, \(v_{c}\): & 0.2 \\ \cline{2-3}  & Length, \(H\): m & 10 \\ \cline{2-3}  & Radius of stone column, \(r_{c}\): m & 0.3 \\ \cline{2-3}  & Radius of model, \(d_{e}\)/2: m & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The reference parameters. Figure 12: Ground settlement of the unit cell for the fully penetrated column with various elastic modulus ratios. Figure 14: Ground settlement of the unit cell for the fully penetrated column with different Poisson’s ratios of the soil. Figure 13: Ground settlement of the unit for the fully penetrated column with various ratios between the radius and the spacing of columns. According to the previous results, with increasing [PERSON]'s modulus and Poisson's ratio, the ground settlement decreases. The reason is that, for the limited lateral deformation and mainly the deformation caused by axial compression, the constraint modulus plays a major role.