## 3 Centrifuge Test Results and Discussion  
Many researchers have considered pile bending moment, axial force, and horizontal displacement to evaluate the seismic performance of such structures [12; 13; 28]. Seismic design codes for pile-supported structures consider the lateral load. PIANC [4] evaluated the residual tilting of piles to account for the horizontal displacement of a structure during an earthquake, and the MOF [19] evaluated member performance using the maximum moments and axial force during an earthquake. Therefore, this study derived the acceleration of the ground and the structure, residual displacement of the structure, pile moment, and the axial force from the dynamic centrifuge model test. The relationship between the moment and the axial force was analyzed to assess the performance of the member. Figures 6 and 7 compare the acceleration time history and response spectrum curves of each model; all the test data show the prototype response. Figure 6 shows the responses of the horizontal-ground models (HA45 and HAI55) for a peak input acceleration of 0.15 g. Results for the bedrock and ground surface acceleration (A1, A2) show a similar trend for the two models, despite a 10% difference in their ground relative densities. In contrast, their deck plate accelerations (A3) were varied significantly. \begin{table}
\begin{tabular}{c c} \hline
**Soil Type** & **Silica Sand** \\ \hline USCS & SP \\ \(C_{c}\) & 1.16 \\ \(C_{u}\) & 1.96 \\ \(G_{s}\) & 2.63 \\ \(\gamma\)_4.max_ (kN\(\cdot\)m\({}^{-3}\)) & 16.5 \\ \(\gamma\)_4.min_ (kN\(\cdot\)m\({}^{-3}\)) & 12.4 \\ \hline \end{tabular}
\end{table} 
Table 4: Properties of silica sand. \begin{table}
\begin{tabular}{c c c c c} \hline  & **Horizontal Ground Model** & \multicolumn{2}{c}{**Inclined Ground Model**} \\ \hline Model & HA45 & HAI55 & IA62 & IAI58 \\ Relative density (\%) & 45 & 55 & 62 & 58 \\  & 0.09 & 0.07 & 0.05 & 0.08 \\  & 0.14 & 0.12 & 0.12 & 0.12 \\ Input peak acceleration (g) & 0.15 & 0.15 & 0.18 & 0.14 \\  & 0.18 & 0.2 & 0.21 & 0.19 \\  & 0.23 & 0.26 & - & 0.24 \\ \hline \end{tabular}
\end{table} 
Table 3: Seismic motion input for each model. Particularly, when the batter piles were installed, the response decreased in the long-period region (\(\geq\)0.45 s) as the stiffness of the system increased. Figure 7 shows the responses of the inclined-ground models, IA62 and IA158, to a peak input acceleration of 0.12 g. The results for the bedrock and ground surface acceleration (A1, A2) show no  
Figure 6: Acceleration time histories of horizontal ground model (0.15 g) (scaled to the prototype). Figure 7: Acceleration time histories of inclined ground model (0.12 g) (scaled to the prototype). significant difference in model responses. In contrast, their deck plate accelerations (A3) were varied greatly. Even in the case of the inclined ground model, when batter piles were installed, the response decreased in the long-period region (\(\geq\)0.35 s) as the stiffness of the system increased. Figures 8 and 9 show the time history curves of the moments and axial forces along the piles for each model. The strain gauges were placed in pairs on the exterior of the piles to derive the pile moments and axial forces (Figure 4a). When a pile bends, tensile force is generated on one side, and compression force on the other, such that strains having opposite signs are derived from both strain gauges. When the axial force occurs in the pile, strains having the same signs are derived. Therefore, the sum of the strains on each side was divided by two to calculate the axial force, and the difference between each side strains was divided by two to calculate the moment. Equations (1) and (2) show the calculation process of the pile axial force (\(N\)) and the pile bending moment (\(M\)), respectively.