## 4 Parametric Study
### Effect of Superstructure Weight on Dynamic Behaviour of Pile  
Inertial force induced by superstructure and kinematic force induced by soil movement is representative in dynamic soil-pile-structure interaction. Therefore, in this section, influence of these two representative dynamic forces on model pile used in this study was investigated. For the first step, numerical analyses using proposed numerical model were performed for four systems which have different weight of superstructure. Figure 13a,b depicts maximum lateral displacement profiles of pile for various input accelerations and four different weights of superstructure, which was 0 kN, 300 kN, 600 kN, 900 kN. Resonance effect was excluded in this section because natural frequency of each system was about 1.5\(\sim\)3 Hz according to the sweep analysis. It is identified that weight of superstructure significantly affected on dynamic lateral responses of pile. When weight of superstructure decreases from 900 kN to 0 kN, maximum lateral displacement of pile decreases about 90%. This kind of behavior was observed regardless of input acceleration level. Because test condition was identical in all cases except weight of superstructure, this phenomenon is responsible for difference of inertial force induced by superstructure and exerted kinematic force is identical for all analysis cases. It can be noted that inertial force induced by superstructure significantly governs seismic behavior of soil-pile-structure system in dry sand.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Property** & **Values for D\({}_{\text{r}}\) = 35 \%** & **Values for D\({}_{\text{r}}\) = 55 \%** & **Values for D\({}_{\text{r}}\) = 80 \%** \\ \hline Friction angle (\({}^{\circ}\)) & 39 & 40.5 & 42 \\ \hline Dry density (kN/m\({}^{3}\)) & 14.2 & 14.8 & 15.8 \\ \hline Poisson’s ratio & 0.32 & 0.31 & 0.30 \\ \hline Void ratio & 0.851 & 0.782 & 0.677 \\ \hline \end{tabular}
\end{table}
Table 4: Input properties of model soil for parametric study.  
Figure 13: Maximum lateral pile displacement envelopes obtained from four different weight of superstructure. (**a**) Input acceleration: 0.13 g; (**b**) Input acceleration: 0.45 g.  
Figure 14 depicts variation of maximum lateral displacement of pile for different input acceleration. As weight of the superstructure increases and input acceleration increases, maximum value of lateral pile displacement also increases. Additionally, relationship between weight of superstructure and maximum value of lateral pile displacement shows linear with high correlation coefficient for various input acceleration conditions. It can be demonstrated that lateral displacement of pile under specific axial load can be properly predicted if proposed model is adopted in practice. Finally, critical damage of entire structure as well as pile foundation can be prevented by estimating dynamic lateral responses of pile foundation under any earthquake level by proposed numerical model.  
Figure 14: Relationship between weight of superstructure and maximum lateral pile displacement. (**a**) Input acceleration: 0.13 g; (**b**) Input acceleration: 0.25 g; (**c**) Input acceleration: 0.45 g.