# Numerical Analysis of the Settlement Behavior of Soft Soil Improved with Stone Columns
## 3 FE Analysis Results
### Effect of Stone Column Length  
The influence of the stone column length upon the settlement performance of the pad footings is investigated for trial Footings 3, 4, and 5, with column lengths of 3.7 m, 5.7 m, and 7.7 m, respectively (Figure 2). The predicted settlement with increasing applied pressure for Footings 3 to 5 is depicted in Figure 8 under drained and undrained conditions. The calculated settlement with PLAXIS 3D is less that the measured settlement during the application of the first load increment with an average pressure of 33 kPa (Table 4), which suggests that the FE analysis overpredicts the stiffness response of the pad footings at low loads. The predicted settlement values agree with the monitored magnitudes during the field trials after the application of the second load increment (average pressure of 70 kPa).  
Figure 7: Influence of column spacing on the footing and ground surface settlement in drained conditions (a) Footing 1; (b) Footing 2.  
It is evident that the undrained analysis initiates a larger settlement beyond a yield point compared to the drained analysis, and the rate of settlement increases between the short-term and the long-term behaviors with increasing pressure (Figure 8). Both the drained and undrained analyses reached failure at pressures over 180 kPa for Footings 3 to 5. The predicted settlement with undrained analysis is higher than the one with drained analysis at applied pressure of 130 kPa for Footing 3 and 170 kPa for Footings 4 and 5. This  
Figure 8: Load-displacement response for (**a**) Footing 3; (**b**) Footing 4; (**c**) Footing 5.  
can be attributed to the lateral bulging occurring at shallow depths, where the undrained analysis predicts significantly higher lateral bulging in the y-direction (perpendicular to the footing length) compared to the drained analysis (Figure 9). The calculated settlement of Footing 4 is marginally higher than the settlement of Footings 3 and 5 under the second load increment which is consistent with the field measurements. This can be explained as the applied pressure on top of Footing 4 is slightly more than Footings 3 and 5, and Footing 4 bulged slightly more than the other two footings.  
A critical column length of 5.5 m was calculated by [36] for the Bothkennar field trials based on work by [5] who concluded that increasing the column length beyond the critical length does not enhance the bearing capacity performance but will contribute to reducing the column settlement. Footing 4 was installed to a length of 5.7 m (close to the critical column length) and Footing 5 was installed to a length of 7.7 m; therefore, the calculated settlement of Footing 5 was relatively lower than that of Footing 4, which is in close agreement with findings by [5].  
The ground surface settlement profile from the centerline of the foundation for the two load increments of interest is shown in Figures 10-12 for Footings 3, 4, and 5, respectively. Footing 5 over the longer stone columns settled the least at the first load increment \(\approx\)33 kPa (9.5 mm) compared to Footing 3 (16 mm) and Footing 4 (14 mm). Footing 4 was further examined as its length is close to the design treatment depth (5.5 m) [36]. It is evident that no surface settlement occurs at distances of 2 L and 2.6 L (L = footing length = 3 m) from the centerline of the footing for the undrained and drained analyses, respectively. The calculated ground surface settlement is slightly less for the undrained analysis compared to the drained analysis, which may be attributed to the improvement of the soft soil strength during the consolidation phase in the undrained analysis. It is worthy of note that a very small amount of heave (\(\approx\)1 mm) is observed at a distance of 2 L in undrained conditions.  
Figure 9: Column bulging of (**a**) Footing 3; (**b**) Footing 4; (**c**) Footing 5 at applied pressure of 190 kPa.