## 2 Materials Employed
### Geotextile as an Encasement Material  
Under vertical loads, the vertical displacement of the stone column must occur with lateral swelling near the head of the column. Because of this swelling/expansion, the geotextile encasement stretches and develops a circumferential stress that is tensile, providing additional confining stress on the column. Because of this lateral expansion, the geotextile encasement stretches and develops a circumferential tensile stress, adding confining stress on the column. Considering that a geotextile enclosure behaves linearly elastically, and also disregarding the shear stresses in the circumferential direction between the column and the geotextile, the hoop tensile force T in the geotextile undergoes conversion into a state of horizontal tension \(\sigma_{\text{rego}}\), which is given to the geotextile, i.e.,  
\[\sigma_{\text{r,geo}}=\frac{\text{T}}{\text{r}_{\text{c}}} \tag{1}\]  
\[\text{T}=\text{T}^{0}+\Delta\text{T} \tag{2}\]  
\[\Delta\text{T}=\text{J}\;\varepsilon_{\text{r}}=\text{E}_{\text{g}}\;\text{t} _{\text{g}}\;\frac{\Delta\text{r}_{\text{c}}}{\text{r}_{\text{c}}} \tag{3}\]  
The variable \(\text{r}_{\text{c}}\) is the radius of the column, \(\text{T}^{0}\) represents the initial tensile tension exerted on the encasement due to the installation of the column; \(\Delta\text{T}\) means that the column has increased tensile tension due to lateral bulging; \(\text{E}_{\text{g}}\), \(\text{J}\), and \(\text{t}_{\text{g}}\) are the elasticity modulus, tensile modulus, and the measurement of the geotextile's thickness, respectively; and \(\text{J}=\text{E}_{\text{g}}\text{t}_{\text{g}}\). The value of \(\text{T}^{0}\) is typically non-zero, and its size is contingent upon the specific installation method [32]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Characteristics** & **Value** \\ \hline Specific gravity (SG) & 2.56 \\ \hline Plastic limit (PL) & 27\% \\ \hline Liquid limit (LL) & 50\% \\ \hline Plasticity limit & 23\% \\ \hline Shrinkage limit (SL) & 10\% \\ \hline Maximum dry unit weight & 17.16 kN/m\({}^{3}\) \\ \hline Optimum moisture content & 19.23\% \\ \hline Bulk unit weight at 26.13\% water content & 18 kN/m\({}^{3}\) \\ \hline Unified classification system & CL \\ \hline Undrained shear strength & 20 kPa \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Clay’s characteristics. \begin{table}
\begin{tabular}{c c} \hline \hline
**Characteristics** & **Value** \\ \hline Specific gravity & 2.5 \\ \hline Maximum dry unit weight & 16.4 kN/m\({}^{3}\) \\ \hline Bulk unit weight for the test at 68\% relative density & 15.8 kN/m\({}^{3}\) \\ \hline Minimum dry unit weight & 14.4 kN/m\({}^{3}\) \\ \hline Internal friction angle (\(\varphi\)) at 68\% relative density & 42\({}^{\circ}\) \\ \hline Curvature coefficient (\(C_{\text{c}}\)) & 1.10 \\ \hline Uniformity coefficient (\(Cu\)) & 2.14 \\ \hline Unified classification system & GP \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Stone column properties. When Equations (1)-(3) are combined, the calculation of the supplementary restraining force induced through the geotextile is contingent upon the encasement properties and the lateral expansion of the column, i.e.,  
\[\sigma_{\text{r,geo}}=\frac{\text{T}^{0}}{\text{r}_{\text{c}}}+\text{J}\;\frac{ \Delta\text{r}_{\text{c}}}{\text{r}_{\text{c}}^{2}} \tag{4}\]  
The material used for encasement was a geotextile made of woven polypropylene, designed to handle a large amount of weight while having low permeability. The data presented in Table 3 illustrate the tensile strength values of the geosynthetics under consideration, as determined by typical wide-width tensile test methods. Geotextiles are employed in several applications, including but not limited to roads, airport runways, storage locations, and retaining walls.