# Numerical Analysis of the Settlement Behavior of Soft Soil Improved with Stone Columns
## 3 FE Analysis Results  
### Effect of Stone Column Spacing  
The influence of the stone column spacing, s, upon the settlement performance of the pad footings is investigated for trial Footings 1 and 2, with column spacings of 1.5 m and 2 m, respectively (Figure 2). It is observed that the widely spaced stone columns (Footing 2) attracted more stresses than the closely spaced stone columns (Footing 1), as shown in Figure 5, which agrees with the measured settlement at the Bothkennar site by [36]. The predicted settlements found with PLAXIS 3D were compared to the monitored settlement values in Table 4 for the two load increments with average bearing pressures of 33 kPa and 70 kPa. It can be seen in Table 4 that the predicted settlement in Footing 1 is less than the predicted settlement in Footing 2, which contradicts the measured settlement during the field trials for the two footings. The former is what would be expected due to the effect of the closely spaced columns on the column-soft clay composite stiffness within the treated depth. The less measured settlement of Footing 1 compared to Footing 2 may be attributed to the disturbance of soft soil between the closely spaced stone columns and remouding of Bothkennar soft clay due to the higher vibration associated with the stone column installation. The higher stiffness (reinforcing effect) per unit area of foundation in Footing 1 may also explain the settlement performance during the field trials. The predicted load-settlement curves for Footings 1 and 2 are illustrated in Figure 6 under drained and undrained conditions. It appears that the short-term settlement is less than the long-term settlement by about 10% to 25% at applied pressures higher than 70 kPa for Footings 1 and 2. It is evident that both analyses predict similar settlement magnitudes at lower pressures up to 40 kPa. For Footing 2, the drained analysis predicts slightly higher settlement up to an applied pressure of 110 kPa, beyond whi \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Vertical**} & \multicolumn{3}{c}{**Normalized \(u_{z}\)**} & \multicolumn{3}{c}{**Mean Effective**} & \multicolumn{3}{c}{**Normalized \(p^{\prime}\)**} & \multicolumn{3}{c}{**Normalized \(p^{\prime}\)**} \\
**Boundary** & \multicolumn{3}{c}{**Displacement,**} & \multicolumn{3}{c}{**Error (\%)**} & \multicolumn{3}{c}{**Stress,**} & \multicolumn{3}{c}{**Error (\%)**} & \multicolumn{3}{c}{**Error (\%)**} & \multicolumn{3}{c}{**Error (\%)**} & \multicolumn{3}{c}{**Normalized Error for**} \\
**Distance (m)** & \multicolumn{3}{c}{\(u_{z}\) (mm)**} & \multicolumn{3}{c}{**Error (\%)**} & \multicolumn{3}{c}{**\(p^{\prime}\) (kPa)**} & \multicolumn{3}{c}{**Error (\%)**} & \multicolumn{3}{c}{**Error for**} \\  & **A** & **B** & **C** & **A** & **B** & **C** & **A** & **B** & **C** & **A** & **B** & **C** & \\ \hline
4 L = 12 & 31.0 & 22.0 & 12.3 & 3.2 & 0.5 & 1.6 & 12.3 & 13.0 & 17.5 & 0.0 & 0.8 & 0.6 & 4 L–6 L \\
6 L = 18 & 30.0 & 21.9 & 12.1 & 2.3 & 0.9 & 2.5 & 12.3 & 12.9 & 17.6 & 4.1 & 0.0 & 0.6 & 6 L–8 L \\
8 L = 24 & 29.3 & 21.7 & 11.8 & 2.2 & 1.4 & 2.5 & 11.8 & 12.9 & 17.7 & 1.7 & 0.0 & 0.6 & 8 L–10 L \\
10 L = 30 & 28.67 & 21.4 & 12.1 & & & & 11.6 & 12.9 & 17.8 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Influence of the bottom boundary distance upon footing settlement. Figure 5: Vertical stress ratio at stone column base level for Footings 1 and 2 (drained conditions). shows that the stone column starts yielding and the plastic deformation becomes more pronounced with higher applied pressures, greater than 130 kPa. For a typical factor of safety in the range of 2.5 to 3.0, the allowable pressure would be in the range of 43 kPa to 52 kPa. A working applied pressure of 50 kPa is deemed acceptable to avoid excessive settlement at the Bothkennar site. However, the relevant settlement at 50 kPa is about 35 mm, which exceeds typical tolerances (25 mm) of a narrow strip footing supporting lightly loaded brick masonry structures [46].