## 3 Numerical Analysis Calculation Mode
### Gridding  
Based on the soil layer distribution map of the calculation section, a single sand drain consolidation model grid was established. To convert the plastic drain board into a sand drain with a radius of 0.05 m, the formula \(r_{w}=\alpha(a+b)/4\) (where \(a\) is the width of the drain board, \(b\) is the thickness of the drain board, and \(\alpha\) is the conversion factor) was used. The smear layer radius was taken as 3 times 0.15 m, and the affected area radius was taken as 7 times 0.35 m. The thickness of the clay layer is 1 m. The thickness of the muddy silty clay layer is 17 m. The bottom of the sand drain is flush with the bottom of the muddy silty clay layer, and the depth of the sand drain is 18 m. The thickness of the silty clay layer is 5 m.  
This paper defines each soil layer as a group, the sand drain as a group, and the smear layer near the sand drain in different soil layers as a group. A total of six groups are defined: clay, muddy silty clay, silty clay, smear layer of clay, smear layer of muddy silty clay, and sand drain.  
As the single sand drain foundation was axisymmetric, only one-quarter was taken for calculation. A cylindrical peripheral gradient radial grid was applied in the clay layer and muddy silty clay layer. A cylindrical peripheral gradient radial grid, cylindrical shell grid, and cylindrical grid were applied in the silty clay layer. A cylindrical grid was applied in the sand drain. A cylindrical shell grid was applied in the smear layers. The calculation model was 1.4 m wide and 23 m deep, divided into 2576 units and 3346 nodes, as depicted in Figure 3.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Series**} & \multirow{2}{*}{**Clay**} & \multirow{2}{*}{\begin{tabular}{c} **Smear Layer** \\ **of Clay** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Muddy** \\ **Silty Clay** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Smear Layer of** \\ **Muddy Silty** \\ **Clay** \\ \end{tabular} } & \multirow{2}{*}{**Silty Clay**} & \multirow{2}{*}{**Sand Drain**} \\  & & & & & & \\ \hline Compressive modulus, & & & & & \\ \(E_{s}/\text{MPa}\) & 4.61 & 4.61 & 4.35 & 4.35 & 8.77 & 11.66 \\ Poisson’s ratio & 0.47 & 0.47 & 0.55 & 0.55 & 0.49 & 0.3 \\ Cohesion, \(c/\text{kPa}\) & 14 & 14 & 3.7 & 3.7 & 4 & 0 \\ Internal friction angle, \(\varphi/^{\circ}\) & 15.5 & 15.5 & 18.9 & 18.9 & 26.7 & 36 \\ Bulk density, \(\gamma/\text{kN-m}^{-3}\) & 19.2 & 19.2 & 17.8 & 17.8 & 18.8 & 19 \\ Water content, \(\omega/\%\) & 31.9 & 31.9 & 44.4 & 44.4 & 35 & / \\ \hline \hline \end{tabular}
\end{table}
Table 1: Calculation parameters of the constitutive model.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Series**} & \multirow{2}{*}{**Clay**} & \multirow{2}{*}{\begin{tabular}{c} **Smear Layer** \\ **of Clay** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Muddy Silty** \\ **Clay** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Smear Layer of** \\ **Muddy Silty** \\ **Clay** \\ \end{tabular} } & \multirow{2}{*}{**Silty Clay**} & \multirow{2}{*}{**Sand Drain**} \\  & & & & & & \\ \hline Horizontal permeability & & & & & \\ coefficient, \(k_{\text{100-200}}/\text{cm/s}\) & & & & & & \\ Vertical permeability & & & & & & \\ coefficient, \(k_{\text{6100-200}}/\text{cm/s}\) & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Calculation parameters of the seepage model.