## 3 Results of the Parametric Study
### Number of Piles in a Pile Group  
Figure 13a-f show the results of the shaft shear stress mobilisation with pile groups of different depths (single pile, 2 \(\times\) 2, 3 \(\times\) 3, 5 \(\times\) 5, 9 \(\times\) 9, and 15 \(\times\) 15 pile groups, respectively) and different pile slenderness ratios (L/D of 50, 40, 30, 20, and 10) at a load level of 30% of the ultimate load. In a general sense, the 2 \(\times\) 2 and 3 \(\times\) 3 pile groups display responses very similar to that of a single pile. The 5 \(\times\) 5 pile groups can be considered a transitional case. The behaviours of the 9 \(\times\) 9 and 15 \(\times\) 15 pile groups are substantially different from those of the smaller pile groups. The shaft shear stresses for the larger pile groups are mobilised more uniformly and increase gradually with depth. The behaviours for the large pile groups are very similar to those of the short and stubby single piles. This can be explained by following the logic suggested by [PERSON] et al. in which the interaction effects along the pile shaft in a large pile group transfer more loads into the end-bearing strata of the group. Since the end-bearing pressure is much greater than the average skin friction, block failure occurs only when the increase in the base area is offset by a large decrease in the surface zone of a pile group shaft. As a result, pile groups with large numbers of long slender piles at a specific spacing are more likely to fail as a block than groups of multiple short stubby piles that fail at the same spacing. [PERSON] (2018) also found that as the number of interaction piles increases, the shear stress distribution along the shaft decreases and more pile loads are transferred to the bottom of the pile groups. Figure 12: Load ratios developed at the pile shaft and the pile base with load levels for a 9 \(\times\) 9 pile group and a single pile. (**a**) _L/D_ = 10; (**b**) _L/D_ = 20; (**c**) _L/D_ = 40. The behaviours of the small pile group and the large pile group are illustrated in Figure 14a-c. These figures show the degrees of the mobilisation of the base load, which is represented by the ratio of the average total base load, \(P_{\textit{flavg}}\), and the ultimate total base load, \(P_{\textit{fl(all)}}\), for different pile slenderness ratios (\(L\)/\(D\) = 10 to 60) and different numbers of piles in the pile groups (single pile, 2 \(\times\) 2, 3 \(\times\) 3, 5 \(\times\) 5, 9 \(\times\) 9, and 15 \(\times\) 15 pile groups) under different load levels (30, 50, 80% of the ultimate capacity of the pile group). These figures indicate that the contribution of the base load of the group varies with the size of the pile group, the pile slenderness ratio, and the level of load mobilisation. In short pile groups, the contribution of the base loads of the pile groups are very similar to that of the single pile regardless of the size of the pile group. This is consistent with the relatively uniform trends of the shaft shear stress profiles for short pile groups (\(L\)/\(D\) = 10) under different group sizes as indicated in Figure 13a-f. However, for longer pile groups with higher \(L\)/\(D\) values, the contribution of the base load for the large pile groups is very different from that of the single pile behaviours. For a single pile, the importance of the base capacity of the pile decreases with the pile length, which indicates that the pile shaft becomes more effective in providing the load capacity of the single pile. Although there are substantial amounts of pile-shaft interactions in large pile groups, the importance of the pile shaft in large pile groups diminishes quickly with the pile length. Thus, more loads are transferred to the base of the group and the total contributions of the base capacity of the group increase substantially. Large pile groups thus behave similar to a large rigid block embedded in the soil. The 5 \(\times\) 5 pile group (with the conditions undertaken in this study) can be considered the transition group size to delimit small-group from large-group behaviours.