## 4 CEL Modelling
### Simulation of Forced Replacement Method  
As mentioned above, the subsurface deposit from 0.0 to 16.0 m consists of very soft soil, having SPT \(N\) value of 0/30. Thus, it was planned to improve a soil strength through the forced replacement method in this site, in order to build the temporary road embankment for the construction. For the forced replacement method, the lateral deformation and the heave in nearby the range occurring forced replacement would occur together. These effects are closely related to the constructability and economics for construction. However, the existing approaches for replacement depth could not predict the height and range of soil heave. Therefore, the CEL analyses are performed to investigate the replacement depth, height and range of soil heave of this site. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Model** & \begin{tabular}{c} **Soil Cohesion** \\ **(kPa)** \\ \end{tabular} & \begin{tabular}{c} **Internal Friction** \\ **Angle (deg.)** \\ \end{tabular} & \begin{tabular}{c} **Effective Unit** \\ **Weight (kN/m3)** \\ \end{tabular} & \begin{tabular}{c} **Elastic** \\ **Modulus (MPa)** \\ \end{tabular} & \begin{tabular}{c} **Poisson’s** \\ **Ratio** \\ \end{tabular} \\ \hline \begin{tabular}{c} Organic soil \\ (very soft soil) \\ \end{tabular} & \({}^{*}\) M.C. & 2.4 & 0 & 1 & 0.24 & 0.49 \\ \
\begin{tabular}{c} Embankment \\ Deep mixing soil \\ \end{tabular} & M.C. & 15.0 & 25 & 9 & 20 & 0.33 \\
\begin{tabular}{c} Deep mixing soil \\ \end{tabular} & M.C. & 21.6 & 0 & 3 & 4.3 & 0.49 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Input parameter for Coupled Eulerian–Lagrangian (CEL) analyses (Korea Institute of Gotechnology [28]). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Name** & \(s_{m}\)/\(B_{0}\) & \begin{tabular}{c} **Replacement** \\ **Depth \(D_{z}\) (m)** \\ \end{tabular} & \
\begin{tabular}{c} **Computation** \\ **Time (s)** \\ \end{tabular} &
\begin{tabular}{c} **Number of** \\ **Elements** \\ \end{tabular} \\ \hline Mesh 1 & 0.0833 & 5.0 & 6.5 & 3243 \\ Mesh 2 & 0.0417 & 4.5 & 44.6 & 32,586 \\ Mesh 3 & 0.0167 & 4.2 & 204.3 & 69,786 \\ Mesh 4 & 0.0083 & 4.1 & 930.5 & 163,416 \\ Mesh 5 & 0.0042 & 4.1 & 7260.1 & 471,516 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Convergence study for mesh. Figure 7: Relationship between replacement depth and computation time. Figure 8 shows a CEL model for the simulation of forced replacement method. The overall dimensions of the domains comprise a width of 16 times the embankment width (\(B_{0}\)) in \(x\)-direction, in order to minimize possible boundary effect on the predicted replacement depth, height, and range of soil heave. In addition, the width of the domain in \(y\)-direction is 1 m, because the replacement depth and soil heave are mainly important in this analysis. The height of the domains in \(z\)-direction is 16.0 m, and the width and height of embankment are modelled on 6.0 m and 2.0 m, respectively, which is identical with the site condition. Zero horizontal displacements are predefined at the lateral boundaries and full fixities at the bottom boundary. The domain is divided into two parts, i.e., the soft soil part and the void part where the soil could be heaved and moved into the empty element. Especially, the void part have no properties, indicating zero strength and stiffness. The input parameters for analyses are summarized in Table 2, based on the geotechnical investigation. To verify the CEL modelling qualitatively, the instantaneous velocity vector plot in a velocity field is illustrated, as shown in Figure 9. We could investigate the mechanism of the forced replacement method in terms of the sequences, representing the soil flow. As shown in Figure 9, the soil flow as dotted lines comprise wedge zone, radial shear zone, and passive zone. It is very similar to the general bearing capacity theory for a strip foundation proposed by [PERSON] [22]. As the replacement occurs, the magnitude of vertical flow decreases, whereas the magnitude of lateral and heave flow increases.