## 4 Parametric Study
deflections show a significant effect of increasing pile width (B\({}_{\text{p}}\)) from 0.254 to 0.356 m on decreasing the pile head deflection from 0.2 to 0.12 m. For a constant pile width (B\({}_{\text{p}}\)) of 0.254 m in cases (a) and (b) of Figure 5, the increase in footing-pile distance (B\({}_{\text{fp}}\)) from 0.914 to 2.742 m shows a greater impact than pile width (B\({}_{\text{p}}\)) on decreasing the pile head deflection from 0.2 to 0.06 m. For a constant footing-pile distance (B\({}_{\text{fp}}\)) of 2.742 m in cases (b) and (d) of Figure 5, the increase in pile width (B\({}_{\text{p}}\)) from 0.254 to 0.356 m shows a very small impact on the pile deflection, which reveals that, when footing-pile distance increases, the influence of pile width on the pile deflection decreases. For a constant pile width (B\({}_{\text{p}}\)) of 0.356 m in cases (c) and (d) of Figure 5, the increase in footing-pile distance (B\({}_{\text{fp}}\)) from 0.914 to 2.742 m shows a significant impact on decreasing the pile head deflection from 0.12 to 0.06 m.  
The profiles of pile lateral deflection (\(\delta_{\text{L}}\)) versus depth for a constant pile width (B\({}_{\text{p}}\)) of 0.254 m adjacent to rectangle and square footings, which are resting on kaolin soil and loaded by a pressure (P) of 1027 kPa, are shown in Figure 6. This figure presents the second four cases shown in Table 3, (e), (f), (g), and (h), to investigate the effects of footing shape ratio (L\({}_{\text{f}}\)/B\({}_{\text{f}}\)) and footing-pile distance (B\({}_{\text{fp}}\)) on the deflection profile. For a rectangle footing with a shape ratio (L\({}_{\text{f}}\)/B\({}_{\text{f}}\)) of 3 in cases (e) and (g) of Figure 6, the pile deflections show a significant impact of increasing footing-pile distance (B\({}_{\text{fp}}\)) from 0.914 to 2.742 m on decreasing the pile head deflection from 0.063 to 0.038 m, but it shows a small impact on the pile toe deflection. For a constant footing-pile distance (B\({}_{\text{fp}}\)) of 0.914 m in cases (e) and (f) of Figure 6, the decrease in footing shape ratio (L\({}_{\text{f}}\)/B\({}_{\text{f}}\)) from 3 (rectangle) to 1 (square) shows a greater effect than footing-pile distance (B\({}_{\text{fp}}\)) on decreasing the pile deflection from 0.063 to 0.023 m at its head and from 0.006 to 0.003 m at its toe. For a square footing with a shape ratio (L\({}_{\text{f}}\)/B\({}_{\text{f}}\)) of 1.0 in cases (f) and (h) of Figure 6, the increase in footing-pile distance (B\({}_{\text{fp}}\)) from 0.914 to 2.742 m shows a significant influence on decreasing the pile deflection from 0.023 to 0.014 m at its head, but it shows no influence on the pile toe deflection. For a constant footing-pile distance (B\({}_{\text{fp}}\)) of 2.742 m in cases (g) and (h) of Figure 6, the decrease in footing shape ratio (L\({}_{\text{f}}\)/B\({}_{\text{f}}\)) from 3 (rectangle) to 1 (square) shows a great impact on decreasing the pile deflection from 0.038 to 0.014 m at its head and from 0.006 to 0.003 m at its toe. Figure 6: \(\delta_{\text{L}}\) versus depth profiles of pile–wall adjacent to rectangle and square footings resting on kaolin soil. Based upon the pile toe deflections from the different cases in Figures 5 and 6, the pile toe deflection is independent of the footing-pile distance (B\({}_{\text{fp}}\)) and pile width (B\({}_{\text{p}}\)) but particularly sensitive to the footing shape ratio (L\({}_{\text{f}}\)/B\({}_{\text{f}}\)), as shown in Figure 6. This conclusion can be explained by the influence of induced pressure, which is proportional to the footing shape ratio, i.e., the bigger the footing shape ratio is, the greater the pressure is induced at a deeper depth. In addition, the independency of pile toe deflection from the footing-pile distance and pile width is an advantage of using the long piles in this study.