# Comprehensive Evaluation of Lateral Performance of Innovative Post in Sand
## 6 Parametric Study
### Effect of Plate Length  
The effect of plate length on the lateral response of the innovative post is assessed in this section. Figure 16 displays the effect of plate length normalized by its width, \(L/W_{p}\), on the lateral capacity of the innovative post for two cases: plates are connected to an H-pile with a fixed embedded length of 3.5 m; and a post with identical pile and plate lengths.  
Figure 14: Stiffness efficiency for various \(W_{p}/W_{t}\) values.  
Figure 15: Bending moment versus depth of double-paddled piles with various plate width.  
For a fixed-length pile, the computed maximum lateral deformations are 17.8 mm and 19 mm for the double-paddled and single-paddled piles with L\({}_{\text{p}}\) = 550 mm, respectively. Generally, as the plate length increases, there is a corresponding decrease in lateral displacement. However, the increase in lateral capacity becomes negligible for single-paddled piles with L/W\({}_{\text{p}}\geq\) 3.5 and for double-paddled piles with L/W\({}_{\text{p}}\geq\) 4.5. The disparity in lateral capacity between double- and single-paddled piles is insignificant for L/W\({}_{\text{p}}\leq\) 1.5 and escalates as this ratio increases. At L/W\({}_{\text{p}}\) = 3.5, the calculated difference in lateral displacement is approximately 5 mm; as L/W\({}_{\text{p}}\) continues to rise, the impact of adding a second plate remains constant. Stiffness efficiency analyses were conducted across various L/W\({}_{\text{p}}\) values to ascertain the percentage increase in capacity for design optimization. Double- and single-paddled piles with a plate length of 0.25 L (550 mm) exhibit higher capacity than the plain pile by 21% and 16%, respectively, as depicted in Figure 17. It is expected that \(\eta_{\text{S}}\) increases with L. For a plate length of 2325 mm, the stiffness efficiency rises by 341% and 119% for double- and single-paddled piles, respectively. In the studied configuration, the increase in stiffness efficiency becomes negligible for L/W\({}_{\text{p}}\geq\) 4 for both single- and double-paddled piles.  
The effect of plate length for double-paddled piles was also investigated considering a system with identical lengths for the pile and plate. The results indicate significantly higher lateral displacement (64.1 mm) than the first system (6.2 mm), for the pile with a length of 1.74 m. Nevertheless, a sufficient lateral capacity was obtained for an embedded pile-plate length of 2.20 m with L/W\({}_{\text{p}}\) = 4.7, and with approximately 1 mm less than the recorded value for the 3.5 m long pile. The effect of increasing the pile length becomes negligible as L/W\({}_{\text{p}}\) increases.  
The lateral displacement profiles for both examined systems are presented in Figures 18 and 19. In a system where plates are welded to an H-pile with a fixed embedded length of 3.5 m, the observed behavior aligns with that of a flexible pile. Conversely, the behavior resembling that of a short pile becomes apparent in a system where the plate-pile length is identical and the ratio of length to plate width (L/W\({}_{\text{p}}\)) is \(\leq\)6. Piles with a ratio of length to plate width (L/W\({}_{\text{p}}\)) \(\geq\) 7 demonstrate the behavior of a fixed pile. The results further suggest that the depth at which fixation occurs, marked by zero lateral deflection and slope, is approximately \(-\)2.8 m (equivalent to 5 to 6 W\({}_{\text{p}}\)). As a result, the soil characteristics within the top 5 to 6 W\({}_{\text{p}}\) significantly impact the lateral behavior of the proposed H-pile. These results are consistent with those reported by [PERSON] and [PERSON] [18] for PHPs in clay soil. Thus, there exists an optimal range of plate width that balances the load-bearing capacity of the post with the width ratio, ensuring an efficient design for the innovative post. These outcomes provide valuable insights for optimizing the design of innovative posts in engineering applications.  
Figure 16: Relationship between lateral deflection and the length of the plate normalized by the width of the pile.