# Comprehensive Evaluation of Lateral Performance of Innovative Post in Sand
## 6 Parametric Study
### Effect of Plates on Surrounding Soil  
The capacity of piles subjected to lateral loads is controlled by the rigidity of the pile, as well as the stiffness and strength of the surrounding soil. It is assumed that the influence zone of a laterally loaded pile takes the form of a three-dimensional inverted cone near the ground surface, centered on the pile [43]. The key factor affecting the lateral resistance of the pile is the deformation of the soil within this influence zone [41]. Consequently, this analysis focuses on evaluating the interaction between paddled piles and the soil within the zone of influence.  
Figure 21 displays the typical patterns of lateral displacement for the pile and surrounding soil due to a lateral load applied at the pile head. The extent of the influence zone for different plate widths is shown in Table 7. It is observed that the size of influence zone increases significantly as the plate width increases, ranging from 1.9 m to 2.7 m along the load direction (Y-direction) and from 1.0 m to 1.7 m perpendicular to load direction (X-direction).  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{\(\mathbf{W_{p}}\) (mm)} & \multicolumn{2}{c}{**Disturbed Zone (m)**} \\ \cline{2-3}  & \multicolumn{2}{c}{**Y-Direction**} & \multicolumn{2}{c}{**X-Direction**} \\ \hline
250 & 1.88 & 1.03 \\
375 & 2.36 & 1.31 \\
500 & 2.37 & 1.33 \\
625 & 2.4 & 1.42 \\
750 & 2.62 & 1.60 \\
875 & 2.64 & 1.62 \\
1000 & 2.67 & 1.64 \\
1125 & 2.67 & 1.66 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Extent of soil influence around double-paddled piles.  
Figure 20: Comparison of load-displacement curves considering different manufacturing methods.  
Figure 22 presents the variation of influence zone factor with the plate width. The influence zone factor is defined as the extent of influence zone normalized by the plate width for both horizontal directions. The influence zone extends from 2.4 W\({}_{\text{P}}\) and 1.5 W\({}_{\text{P}}\) to 7.5 W\({}_{\text{P}}\) and 4.1 W\({}_{\text{P}}\) for X and Y directions, respectively.  
The data were curve fitted and the following equations can be obtained:  
\[\text{Y}\left(\text{m}\right)=-6\times 10^{-9}\;\text{W}_{\text{P}}{}^{3}+2 \times 10^{-5}\;\text{W}_{\text{P}}{}^{2}-0.0232\;\text{W}_{\text{P}}+12.374\]  
\[\text{X}\left(\text{m}\right)=-6\times 10^{-12}\;\text{W}_{\text{P}}{}^{4}+1 \times 10^{-8}\;\text{W}_{\text{P}}{}^{3}-3\times 10^{-6}\;\text{W}_{\text{P}}{}^{2}-0.0069\;\text{W}_{\text{P}}+5.916\]  
where Y, X, and W\({}_{\text{P}}\) are the influence zone along the load direction, perpendicular to the load direction, and width of the plate, respectively.  
Illustrating the behavior of both the pile and soil, Figure 23 displays iso-surface plots of phase shear strain \(P\gamma_{s}\), highlighting the scope of the soil influence zone at various W\({}_{\text{P}}\)/W\({}_{\text{f}}\) values based on the original S16 dimensions. The introduction of plates to the flanges of the H-pile results in a reduction of shear strain development in the loading direction when  
Figure 21: Typical total lateral displacement (Uy) behavior of soil and pile under lateral load: (**a**) horizontal cross-section; (**b**) vertical cross-section.  
Figure 22: Influence zone factor (influence distance/plate width) considering different plate widths.  
compared to the traditional H-pile. This impact becomes less pronounced as WP increases (e.g., \(\mathrm{W_{p}}/\mathrm{W_{f}}=750\)). With a small plate width (e.g., \(\mathrm{W_{p}}/\mathrm{W_{f}}=250\)), the soil influence zone mobilizes rapidly, encompassing the entire plate width, involving the entire paddle in soil resistance mobilization. Conversely, for \(\mathrm{W_{p}}/\mathrm{W_{f}}\) values of 650 or higher, the development of the mobilized soil influence zone is slower, and the contribution of the plate to lateral load resistance becomes insignificant. As a result, part of the plate is excluded from the mobilized influence zone.