# Comprehensive Evaluation of Lateral Performance of Innovative Post in Sand
## 6 Parametric Study
### Effect of Plate Width  
In this section, we examine the influence of plate width on the lateral capacity of SP and DP posts. The plate width was systematically altered in 25% increments, ranging from 0.25 to 2.25 times the initial width of S16. Figure 13 depicts an incremental increase in the pile capacity by 57%, 29%, and 21% for \(\mathrm{W_{p}}/\mathrm{W_{f}}\) equal to 1.6, 2.4, and 3.1, respectively, indicating that at low width of plate-to-pile ratio the size of the plate significantly affects the lateral capacity of the double-paddled pile.  
In contrast, the single-paddled pile's capacity experiences a relatively minor impact from an increase in plate width, showing a 35% capacity increase for a plate width of 250 mm and a 19% increase for a width of 375 mm. Notably, it becomes evident that as the plate-pile flange width ratio rises, the influence of the plate width on displacement diminishes. Figure 11 further illustrates that when the plate is four times the width of the pile's flange in a double-paddled pile system and three times the width in a single-paddled pile system, the effect of plate width on lateral displacement becomes negligible. Additionally, the lateral deflection of double-paddled piles consistently measures approximately 5 mm, indicating a stiffness 25% to 30% greater than that of a single-paddled pile across all \(\mathrm{W_{P}}/\mathrm{W_{f}}\) ratios.  
The effectiveness of the innovative posts was also assessed through a stiffness efficiency parameter, denoted as \(\eta_{S}\). This parameter is defined as the enhancement in the lateral stiffness of the pile under a specific lateral load when compared to an equivalent plain pile.  
\[\eta_{S}=\frac{s_{PP}-s_{P}}{s_{P}} \tag{3}\]  
where \(S_{PP}\) and \(S_{P}\) are the lateral stiffness corresponding to the lateral head displacement at a given load for paddled pile and plain pile, respectively.  
Figure 14 shows the stiffness efficiency curve, which indicates that the variation of the paddled H-pile lateral stiffness with the plate width. It is clear that \(\eta_{S}\) increases as the plate width increases. This indicates that stiffening the pile with one or two plates substantially enhances the stiffness of the foundation system and can provide from 121% to 318% more rigidity (with a plate width of 500 mm) than the corresponding plain pile. As expected, the double-paddled piles demonstrate greater stiffness than single-paddled piles for the same plate width. Figures 13 and 14 show that a double-paddled pile can provide up to more  
Figure 13: Relationship between lateral deflection and plate width normalized by pile width.  
than 100% stiffness than the corresponding single-paddled pile. This significant increase is related to the increase in the geometry of the innovative post and due to the confined soil between the two plates. However, it is anticipated that the double plate would be more expensive. Hence, single-paddled posts may have an economic advantage.  
Figure 15 illustrates the variation in the maximum bending moment along the pile shaft. The outcomes reveal a reduction in the maximum bending moment due to the presence of plates, with a noticeable decrease as the plate width increases. However, for \(W_{p}/W_{t}\) values equal to or exceeding 5.4, the reduction in bending moment becomes negligible. The plates play a role in resisting a portion of the bending moment, thereby reducing the overall bending moment in the H-pile. Additionally, it is observed that the depth of the maximum bending moment decreases with an increase in plate width. These observations align with the findings reported by [PERSON] and [PERSON] [18], [PERSON] [16] and [PERSON] [17].