## 3 Results and Discussions
### Results of the Parametric Study  
The concepts of studying the effects of varying different parameters for single helical piles are already well established and found in much literature, as discussed earlier. Still, for this study to validate the predicted FEA results with the analytical data results and experimental results, a comparison was made by varying the embedment depth ratio and the spacing ratio of the helical pile. However, the pile shaft diameter, helical plate diameter, pitch of the helical plate, and length of the pile are kept constant for all the cases. The load-displacement curve obtained from the numerical analysis for the helical pile subjected to uplift and lateral loads is depicted in Figures 7 and 8, respectively. The load-displacement behavior seen in all of the repetitions appears to be consistent. As previously discussed, the ultimate uplift capacities are defined as the load that causes an uplift displacement of 10% of the helical plate's diameter, that is 10% of 40 mm (4 mm). The ultimate lateral capacities are measured as half of the load that causes the pile head to displace laterally by about 25 mm from its original position. From Figures 8 and 9 it is clear that the capacities are significantly increased with an increase in embedment depth ratio  
Figure 8: Load–displacement curve for lateral capacity of helical pile. Figure 7: Load–displacement curve for uplift capacity of helical pile. and number of helical plates. Experimental investigations conducted by [PERSON] et al. [8] for the uplift capacity and [PERSON] and [PERSON] [22] for the lateral capacity for a pile embedded in marine clay also obtained a similar behavior. However, the influence of soil consistency, moisture content, and soil strength also affect the tensile and lateral capacity, which is kept constant in this study. The results of uplift and lateral capacity for a helical pile obtained using theoretical, numerical, and experimental investigations are given in Table 3.  
Figures 9 and 10 show the comparison between theoretical and numerical results for the uplift and lateral capacities, respectively. It is observed that in the case of uplift loading, the increase in the embedment depth ratio has less effect on capacity increase. In addition, the model underpredicts the capacity in most cases. However, in the case of lateral capacity the model over-predicts the capacity values while comparing them with the theoretical results. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Pile Type**} & \multicolumn{3}{c}{**Uplift Capacity (kN)**} & \multicolumn{3}{c}{**Lateral Capacity (kN)**} \\ \cline{2-7}  & **Theoretical** & **Numerical** & **Experimental** & **Theoretical** & **Numerical** & **Experimental** \\ \hline SHP-1-12 &  
The maximum percentage variation is found to be 5% and 8% in the cases of uplift and lateral tests, respectively. In the case of lateral loading, the embedment depth ratio and the number of plates influence the capacity values significantly. In addition, increasing the eccentricity of loading decreases the lateral capacity substantially. When comparing the lateral capacity of the four-plated helical pile to that of the one-plated helical pile, a maximum of a 48% increase is observed. The reason behind this may be that increasing the number of helical plates increases the bearing resistance and uplift resistance, which leads to an increase in capacity. Figure 11a,b show the comparison of the load-displacement curve for experimental and numerical results of uplift loading. Figure 12 shows the load-displacement curve obtained experimentally for helical piles subjected to lateral loads. A similar behavior is seen from the load-displacement behavior graph for all pile types. Figure 11: Comparison between Experimental and Numerical results—Uplift loading, (**a**) \(\mathrm{H/D}=6\); and (**b**) \(\mathrm{H/D}=8.75\). Figure 10: Comparison between theoretical and numerical results—Lateral loading.