## 4 Parametric Study
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 square footings, which are resting on silty clay and kaolin-sand soils, are shown in Figure 7. This figure presents the last three cases shown in Table 3, (k), (m), and (n), to study the impact of soil type on the deflection profile. The pile deflection profiles vary with respect to the change in soil type, footing-pile distance, and footing pressure. For a square footing (shape ratio of 1) at a constant footing-pile distance (B\({}_{\text{fp}}\)) of 4.57 m and under footing pressure (P) of 400 kPa in cases (m) and (n) of Figure 7, the change in soil from silty clay to kaolin-sand shows a significant impact on reducing the pile deflections from 0.016 to 0.006 m at its head and from 0.006 to 0.002 m at its toe. In addition, greater impact is observed from changing the soil type from silty clay in Figure 7 (k) to kaolin in Figure 6 (f), where pile deflections are reduced from 0.172 to 0.023 m at its head and from 0.018 to 0.003 m at its toe. The significant reduction in pile deflection due to the change in soil type from silty clay to kaolin and silty clay to kaolin-sand is related to the initial modulus in compression (E\({}_{\text{i}}\)), shown in Table 1, where kaolin-sand and kaolin have higher moduli in compression than silty clay. Based on the profiles of pile deflection in Figures 5-7, the behavior of bent piles confirms that the piles are long, which are chosen based upon the pile embedment length to pile width ratio of greater than 35, which is stated by [PERSON] [3]. Also, the pile bending between depths of approximately 5.0 and 8.0 m is mainly related to the pile embedment length, where the other variables of soil type, footing shape ratio, pile width, and footing-pile distance show a small impact on the depth of pile bending. The profiles of pile lateral pressure (P\({}_{\text{L}}\)) versus depth for the same conditions discussed for the profiles of pile lateral deflection in Figure 4 are shown in Figure 8. Similar to the pile  
Figure 7: \(\delta_{\text{L}}\) versus depth profiles of pile–wall adjacent to square footings resting on silty clay and kaolin–sand soils. deflection profiles, the pressure profiles have different trends between depths of 0.0 and 7.0 m depending on the pile width and footing-pile distance, while the pressure profiles are very close to each other below a depth of 7.0 m. All profiles show an increase from approximately zero lateral pressures at the top to peak values at approximately 2.0 m depth due to the footing pressure, and then, the pressures decrease to a minimum value before they gradually increase with depth, followed by the influence of the geostatic stress. For a constant footing-pile distance (Bfp) of 0.914 m in cases (a) and (c) and between depths of 0.0 and 7.0 m (Figure 8), the pile pressures show a drastic increase at 2.0 m depth, followed by a sharp decrease to negative values at a depth of 2.5 m. The negative portions of the pressure profiles might be the result of the combination of the large pile deflection due to the nearby footing pressure and the unit cohesion, c, of kaolin soil. In these two cases, the increase in pile width (Bp) from 0.254 to 0.356 m increases the peak pressure at 2.0 m depth from 90 to 130 kPa due to a better support from a larger pile. As the footing moves away from the pile-wall from 0.914 to 2.742 m with a constant pile width (Bp) of 0.356 m, as shown in cases (c) and (d) in Figure 8, the peak lateral pressure drops from 130 to 10 kPa at 2.0 m depth due to the lesser influence of the footing. In cases (b) and (d) in Figure 8, the pressure profiles look almost identical regardless of the pile width which reveals that, as the footing moves away from the wall, the influence of the pile width on the interaction behavior also reduces.