## 4 Parametric Study
### Effect of Thickness of Liquefiable Soil Layer  
Dynamic pile responses obtained from repetitive analysis for varying thickness of liquefiable soil layer (i.e., 3, 6, and 9 m) were discussed. Figure 12 shows the peak envelopes of the bending moment and the pile lateral displacement according to the thickness of the liquefiable layer when input acceleration of 0.13 g is applied. Pile foundation with superstructure is usually exerted by two kinds of dynamic forces representatively under earthquake. One is inertial force induced by superstructure, the other is kinematic force induced by ground movement. These forces induce complex dynamic interactions to the pile, and combination mechanism of the two forces acting on the pile depends on the site condition. The way of combination mechanism can govern overall performance of the pile foundation under earthquake. [PERSON] et al. (2004) [52] reported that, if the natural period of the superstructure is less than that of the ground, the ground displacement tends to be in phase with the inertial force from the superstructure. In contrast, if natural period of the superstructure is greater than that of the ground, the ground displacement tends to be out of phase with the inertial force, restraining the pile stress from increasing. In Figure 12, when the thickness of liquefiable layer is increased, larger soil deformation is induced. The maximum displacement decreased by approximately 34% as the thickness of liquefiable layer decreased from 9 m to 3 m. Peak bending moment value also increased as thickness of liquefiable layer increased. If soil layer is liquefied, natural period of the ground increased because soil stiffness decreased (natural period and stiffness are inverse proportion). Therefore, the natural period of the liquefied soil is always greater than that of the superstructure, resulting in kinematic force due to ground movement in phase with the inertial force in this case. In this  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Parametric Study** \\ \hline Thickness of upper liquefiable layer & 3 m, 6 m, 9 m \\ D\({}_{\text{r}}\) of liquefiable soil & 30 \%, 50 \% \\ Superstructure weight & 0, 300 kN, 600 kN, 900 kN \\ \hline \hline \end{tabular}
\end{table}
Table 3: Selected parameters in a parametric study.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Property** & **D\({}_{\text{r}}\) = 30\%** & **D\({}_{\text{r}}\) = 50\%** \\ \hline Porosity & 0.445 & 0.415 \\ Saturated unit weight (kN/m\({}^{3}\)) & 19.27 & 19.75 \\ Friction angle (\({}^{\circ}\)) & 32 & 34 \\ Poisson’s ratio & 0.32 & 0.31 \\ Volume change constants & \(C_{1}\) = 1.54, \(C_{2}\) = 0.26 & \(C_{1}\) = 0.43, \(C_{2}\) = 0.93 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Input properties of the model soil for parametric study.  
situation, as the thickness of liquefiable layer increased, larger kinematic force is exerted with inertial force to the pile structure. On the other hand, the bending moment profile reached the maximum at the interface between the liquefied and non-liquefied layers regardless of analysis case. The pile with the upper liquefied sand behaved like a cantilever beam embedded below the non-liquefied layer. [PERSON] (2002)[PERSON] (2002) reported that many pile damages were observed at the interface between the liquefied and non-liquefied layers from the investigations of past earthquakes. It can be demonstrated that this kind of destruction pattern was caused by sharp increase of bending moment at the interface and captured by proposed numerical model. Also, it is confirmed that critical seismic design section with the bending moment is the interface between liquefied and non-liquefied regions by numerical simulation.