## 5 Results and Discussion  
### Failure Mechanism--Experimental Result  
At a displacement of 50 mm, the failure of all the columns was considered. The surrounding clay from the loading setup was removed, and the stone columns were excavated. Uncased stone columns with distorted shapes were studied. The cause of the failure was determined to be the deformation of the stone columns, resulting in bulging. Bulging failure occurred for a single OSC for a distance of \(D\) to 2.5 \(D\) from the crest of the stone columns. Furthermore, apart from the prominent failure in bulging, the stone columns without casing also demonstrated lateral displacement. Figure 5a shows the bulging failure in the case of an OSC. The lateral deformation seen in the current tests exhibited similarities to the lateral displacement documented by [PERSON] et al. [33]. As each column was uniformly subjected to the vertical load, there were hoop stresses developing inside the stone column. This caused the stone column to bulge laterally. Stone columns possess the ability to endure a substantial magnitude of hoop stress due to their encapsulation within a material characterised by notable tensile strength. The test findings demonstrated that all reinforced stone columns (for various \(Lr\)) had less bulging and lateral deformation than unreinforced stone columns. The entirely encased column (\(Lr=L\)) failed the punching test as there was no bulging throughout its whole length (Figure 5b(i)). Bulging was modest for the  
Figure 4: Comparison of vertical load intensity settlement behaviour of end-bearing column. 50% encasement length column (\(Lr\) = 0.5 L). Under the enclosed zone, only slight lateral distortion was seen (Figure 5b(iii)). A comparable finding was obtained for a 75% encased length, i.e., \(Lr\) = 0.75 L (Figure 5b(ii)). For \(Lr\) = 0.25 L, bulging was visible slightly beneath the encasement length in the case of VESCs, as illustrated in Figure 5b(iv). The bulging level and location were demonstrated to be equivalent to those of the OSC example (Figure 5a). In the scenario involving HRSCs, it was observed that the placement of horizontal strips at uniform intervals throughout the column's length (specifically, at intervals of 100 mm) resulted in the collapse of the column. This collapse occurred as a consequence of localised swelling at distances ranging from 1.5 times to 2.5 times the column's diameter (referred to as \(D\)), which was analogous to the behaviour observed in OSCs (Figure 5c(i)). This suggests that there was not sufficient space between the geotextiles' horizontal layers. Figure 5c(ii) depicts modest bulging when reinforced for the top half (0.5 L from the column top), observed at the intersection of the column length's reinforced and unreinforced portions. The bulging failure was similar to an unreinforced case when the reinforcement was used for the lower portion, particularly within a distance of 0.5 L from the centre to the foot. For columns having a length greater than the critical length and irrespective of whether it was end-bearing or floating, it failed by bulging [17]. However, columns shorter than the critical length are likely to fail in general shear if it is end-bearing on a rigid base and  
Figure 5: Multiple failure mechanisms for a column with a 100 mm diameter: (**a**) OSC, (**b**) VESC (**i**) \(Lr\) = \(L\) (**ii**) \(Lr\) = 0.75 L (**iii**) \(Lr\) = 0.5 L (**iv**) \(Lr\) = 0.25 L, (**c**) HRSC (**i**) Equal interval throughout the depth (**ii**) Top half—0.5 L from head (**iii**) Bottom half—from centre to bottom. punching if it is a floating column. The critical column length is the shortest column that can carry the ultimate load regardless of settlement [31]. In various research works, a different L/\(D\) ratio was found for the critical length of the column. Moreover, in the current study, the L/\(D\) ratio ranged between 5 and 10, the bulging failure was predominant. Its study is significant as it can further lead to the instability of the foundation.