## 4 Numerical Analysis Using Plaxis 3D  
In order to enhance the comprehension of the performance of the OSC and ESC, numerical simulations were run. The failure mechanism and footing settlement were  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{ \begin{tabular}{c} **Type of** \\ **Column** \\ \end{tabular}  } & \multirow{2}{*}{**Test Description**} & \multirow{2}{*}{ \begin{tabular}{c} **Length of** \\ **Reinforcement** \\ \end{tabular}  } & \multicolumn{3}{c}{**Column Diameter**} & \multicolumn{1}{c}{\multirow{2}{*}{\ \begin{tabular}{c} **Total Number** \\ **of Tests** \\ **Performed** \\ \end{tabular}  }} \\  & & & **S0 mm** & & **S0 mm** & **100 mm** \\ \hline \multirow{4}{*}{ \begin{tabular}{c} Solitary Stone \\ Column \\ \end{tabular}  } & \multirow{2}{*}{Clay} & \multirow{2}{*}{✓} & \multirow{2}{*}{✓} & \multirow{2}{*}{✓} & \multirow{2}{*}{✓} & \multirow{2}{*}{3} \\  & & & & & \\ \cline{1-1} \cline{5-5}  & &  
investigated. We also examined how the column and encasement length (both VESC and HRSC) affected the results. The code for finite elements Plaxis 3D was used to create the entire 3D model. Clay and stone columns were modelled as a continuum element consisting of 10-noded tetrahedral elements. The geosynthetic encasement was simulated as discrete elements possessing solely normal stiffness, exhibiting solely translational degrees of freedom at their nodes and the capacity to endure solely tensile stresses. The numerical simulations employed a conservative strain formulation, and a hierarchical construction process was simulated. The inherent softness of the soil was initially modelled as a horizontal surface with a consistent depth. Geostatic initial stresses were created by the soil unit weight and the coefficient of lateral earth pressure at rest, K\({}_{0}\). Subsequently, the placement of the columns and footings, collectively with their encasements, was carried out without considering the potential variations in the underlying soil resulting from the building of the columns. Finally, the settlement of the footing of 50 mm was simulated, and the analysis was run to obtain the results. The Mohr-Coloumb model was used to model the clayey soil and the stone columns. Soil and column simulations were performed using the soil parameters given in Tables 1 and 2. The various parameters needed to assign the properties were E, \(\gamma_{\text{bulk}}\), \(\gamma_{\text{sat}}\), c, v, and \(\varphi\). To precisely mimic the boundary constraint pertaining to the mode tank, the model's bottom was constrained in the x, y, and z directions. However, in order to allow for stone column settlement under the influence of weight, vertical bounds in the z-direction were not restricted. The study by [PERSON] and [PERSON] [26] emphasized the examination of unreinforced columns of stone without an interface element. Their findings indicated that the primary deformation mode in these columns was radial bulging, with minimal shear deformation observed. Geotaxile encasement was modelled for reinforced stone columns using the Plaxis code's geogrid element. The material under consideration, referred to as an \"elastic\" substance, requires the incorporation of axial stiffness (EA) to represent its stiffness properties. In this context, \"E\" denotes the modulus of elasticity of the geotextile, while \"A\" represents the cross-sectional area of the geotextile. The discretization of the earth and stone columns was accomplished with the help of 15-noded triangular elements (Figure 3). A medium mesh type was used to generate a mesh in all the analyses. The total number of soil elements varied between 4000 and 8000. For a reference case of \(D=75\) mm, when \(Lr=L\), the average element size was found to be 0.1031 m. For the same case, the maximum and minimum element sizes were 0.1885 m and 0.01212 m, respectively. Similarly, the element size, nodes, and other discretization properties could be observed.