## 4 Case History Study  
[PERSON] and [PERSON] (2018) conducted a series of large-scale laboratory model experiments to explore the behavior of Compacted Lime-Well-graded Soil (CL-WS) rigid stone columns in soft soils. These tests were performed on composite specimens to evaluate the effect of different parameters, such as column diameter, slenderness ratio, area ratio, etc. To simulate the actual behavior of the CL-WS column-treated ground in the field, loads were applied over the entire area of the composite specimen to evaluate the increase in stiffness of the treated ground. When the entire area is loaded, settlement levels up to 15 mm were achieved at the top of the unit cell confinement, as shown in Figure 8.  
Figure 7: Settlement profile of the composite ground by three different methods. The properties of the soil and the columns were well recorded. However, the properties of the sand pad were not provided. When simulating the performance of column-reinforced soil using the proposed model, the deformation of the sand pad cannot be ignored. However, the deformation of the sand pad in the proposed method is relatively small since the sand is assumed to be in one-dimensional compression, and the stiffness of sand is assumed to be relatively large while the thickness is very small. The parameters of sand were calibrated from the back-analysis of the experiment. The properties of the materials are shown in Table 2.  
Firstly, the effect of the slenderness ratio, _H/D_, (the ratio between length, \(H\), and diameter, \(D\), of column) on the composite specimens is compared, as shown in Figure 9.  
The results of laboratory model experiments, the proposed method, and FEM are quantitatively compared regarding the settlement up to 15 mm corresponding to the load intensity in the laboratory tests for different slenderness ratios. The results from the finite element analyses and experiments are very close, with differences ranging from 9.4 to 12%. This dissimilarity arises probably due to the overestimation of the stiffness of the sand pad. Throughout the derivation, the soil layer was assumed to be homogeneous and isotropic. This assumption no longer holds due to the presence of the sand pad. At the same time, the deformation of the sand pad cannot be ignored. Therefore, the deformation of the sand pad is assumed to be axial compression deformation, which increases the stiffness of the sand pad, resulting in the calculated settlements of the proposed method being smaller than those of the FEM and the experiments. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Material** & **E (kPa)** & **v** \\ \hline Clay & 12,000 & 0.41 \\ \hline Sand & 20,000 & 0.3 \\ \hline Column & 200,000 & 0.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Physical and mechanical properties of materials used. Figure 8: Laboratory test setups. The experimental procedure was also extended to evaluate the effect of model size on CL-WS column performance by changing the column diameter from 50 mm to 150 mm. Figure 10 shows the relationship between load intensity \(L\) and settlement \(S_{t}\) of a column with an area ratio equal to 10% and \(H\)/\(D\) = 6. A comparison of the results shows that the differences between them vary from 5.5% to 17%. Figure 10: Effect of the diameter of the column on the load intensity—settlement of composite specimens: (**a**) \(D\) = 150 mm, (**b**) \(D\) = 125 mm, (**c**) \(D\) = 100 mm, (**d**) \(D\) = 75 mm, (**e**) \(D\) = 50 mm. Figure 9: Effect of the slenderness ratio on the load intensity—settlement of composite specimens: (**a**) \(H\)/\(D\) = 8, (**b**) \(H\)/\(D\) = 6, (**c**) \(H\)/\(D\) = 4 (for 10% area ratio between the area of the column (Ac) and the total area within the unit cell (A) of 10%, and 100 mm column diameter). Figure 11 shows the variation of load intensity \(L\) versus settlement \(S_{t}\) for different area ratios, \(H\)/\(D\) = 6 and \(D\) = 100 mm. A comparison of the results reveals that the differences between them vary from 0.02 to 21.2%.