## 3 Centrifuge Test Results and Discussion
However, when the batter piles were installed, the system response significantly reduced in the inclined-ground model (IAI58), compared to that in the horizontal-ground model (HAI55) because the lateral resistance greatly increased when the batter piles were installed to the former model. However, installing the batter piles to the horizontal-ground model increased the lateral resistance and the asymmetry of the system. Hence, the response reduction was not significant. Thus, the batter piles performed better in the inclined-ground model than in the horizontal-ground model. The member stress of the pile is calculated by combining pile moment (\(M\)) and axial force (\(N\)). Installing batter piles can degrade the bending capacity of a member due to the increase in the axial force [1]. Therefore, it is important to consider both the bending moment and the axial force of the pile to evaluate the member performance. \(M\)-\(N\) curves are widely used to evaluate the cross-sectional member force when \(M\) and \(N\) occur simultaneously in monolithic beam [30]. They are also called the \(M\)-\(N\) interaction diagrams because the two cross-sectional forces influence each other and are a crucial method for evaluating the seismic performance of bridges. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Horizontal Ground Model**} & \multicolumn{4}{c}{**Inclined Ground Model**} \\ \hline \multirow{4}{*}{Peak acc. of deck plate (g)} & Input acc. (g) & 0.09 & 0.13 & 0.17 & 0.21 & Input acc. (g) & 0.09 & 0.13 & 0.17 & 0.21 \\  & HA45 & 0.21 & 0.31 & 0.39 & 0.44 & IA62 & 0.25 & 0.36 & 0.49 & 0.62 \\  & HAI55 & 0.22 & 0.26 & 0.29 & 0.32 & IAI58 & 0.20 & 0.26 & 0.30 & 0.32 \\  & Diff. (\%) & 4 & –17 & –25 & –27 & Diff. (\%) & –19 & –30 & –40 & –48 \\ \hline Horizontal residual displacement of deck (mm) & HA45 & 1.20 & 1.06 & 2.30 & 4.94 & IA62 & 5.12 & 19.69 & 40.99 & 69.02 \\  & HAI55 & 3.75 & 7.91 & 12.34 & 17.03 & IAI58 & 6.59 & 15.81 & 25.13 & 34.57 \\  & Diff. (\%) & 212 & 650 & 436 & 245 & Diff. (\%) & 29 & –20 & –39 & –50 \\ \hline \multirow{4}{*}{Maximum moment of vertical pile (kN-m)} & HA45 & 571 & 892 & 1134 & 1297 & IA62 & 754 & 1103 & 1473 & 1863 \\  & HAI55 & 160 & 209 & 256 & 303 & IAI58 & 190 & 230 & 268 & 304 \\ \cline{1-1}  & Diff. (\%) & –72 & –77 & –77 & –77 & Diff. (\%) & –75 & –79 & –82 & –84 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Difference in system response with and without the batter pile. The MOF [7] proposes a method for evaluating the performance of the pile-supported structure with batter piles under static load. However, a method to properly evaluate the seismic performance of a structure with a batter pile has yet to be formulated as its use has been avoided in seismic design. Therefore, this study used the performance evaluation method, under static load, proposed by the MOF [7] in seismic design. Accordingly, an \(M\)-\(N\) interaction diagram was derived during an earthquake to evaluate the member force of the structure with batter piles. The code first explains that axial force and bending moment are converted into sectional stresses. Equations (3) and (4) show the axial stress (\(f_{n}\)) and the bending stress (\(f_{m}\)), respectively. \[f_{n}=\frac{N}{A} \tag{3}\]  
\[f_{m}=\frac{M}{Z} \tag{4}\]  
here,\(f_{n}\) is the axial stress of pile (kN m\({}^{-2}\)),\(f_{m}\) is the bending stress of pile (kN m\({}^{-2}\)), \(A\) is the cross-sectional area of pile (m\({}^{2}\)), and \(Z\) is the section modulus of pile (m\({}^{3}\)). For a member with \(M\) and \(N\) occurring simultaneously, the sectional stress should not exceed the allowable stress. Equations (5) and (6) explain the relationship between sectional stress and allowable stress divided into cases where the tensile and compressive forces occur, respectively.