## 3 Centrifuge Test Results and Discussion
\[N=EA\cdot\frac{\varepsilon_{1}+\varepsilon_{2}}{2} \tag{1}\]  
\[M=\frac{EI}{y}.\frac{\varepsilon_{1}-\varepsilon_{2}}{2} \tag{2}\]  
here, \(EA\) is the pile axial stiffness (kN), \(EI\) is the pile bending stiffness (kN m\({}^{2}\)), \(\varepsilon_{1},\ \varepsilon_{2}\) is the pile strain value at both sides, and \(y\) is the pile diameter (m). Figure 8: Pile moment and axial force time histories of horizontal ground model (0.15 g) (scaled to the prototype). Figure 8 shows the responses of models HA45 and HAI55 (0.15 g), and Figure 9 shows those of models IA62 and IAI58 (0.12 g). As shown in Figure 7, the installation of batter piles to the horizontal-ground model significantly reduced the moments of the vertical piles (S1-S3), whose maximum moment was reduced by 88%, 73%, and 79%, respectively. The axial forces (S4, S5) of the batter piles were large, up to a maximum of 1744 kN. Figure 9 shows similar results wherein the batter piles reduced the maximum moments of the vertical piles (S1-S3) by 70%, 74%, and 79%, respectively, and the axial forces (S4, S5) of the batter piles were very large, up to a maximum of 1499 kN. Figure 10 (models HA45 and HAI55; 0.15 g) and 11 (IA62 and IAI58; 0.12 g) show the vertical pile moment and the batter pile axial force along the depth of each model. The vertical pile moment responses were derived according to the direction of the pile movement (toward the sea or land). The batter-pile axial force responses were derived according to tension and compression. The figures show the responses by the depth at the time of the maximum response. The moment in the lower part of pile three, in model HAI55 (Figure 10), was not measured due to an instrumentation error. The vertical pile moments, presented with respect to the depth for piles one to three in Figure 10, show that the maximum moment occurred mostly at the top of the pile, and the greatest moment with the opposite sign occurred at a depth of 10 m. The moment converged to zero at a depth of 16 m.  
Figure 11: Depth profiles of maximum moment and axial force of inclined ground model (0.12 g) (scaled to the prototype). Figure 10: Depth profiles of maximum moment and axial force of horizontal ground model (0.15 g) (scaled to the prototype). The batter piles reduced the maximum moment of the vertical piles by 88% and encountered large axial forces. The vertical pile moment reduced as the lateral load of the earthquake was transmitted to the axial force in the batter pile. This finding is similar to that of the dynamic centrifuge model test for pile groups by [PERSON] et al. (2010) and [PERSON] et al. (2012). [PERSON] et al. (2010) found that using batter piles reduced the maximum moment of the vertical piles and increased the axial force by 1.7 times in the front (batter) pile, and doubled it in the rear (vertical) pile. [PERSON] et al. (2012) reported that the pile moment and axial force depended on the size of the structure and the applied frequency. Under a 3.5 Hz sine wave, the maximum moment was reduced in the batter pile group regardless of the structure size. The axial force decreased for a small structure with a batter pile group (about 7 m depth) and increased for a large structure (about 16 m depth). The results obtained from this study for a pile-supported structure with sufficiently long piles were similar to those obtained by [PERSON] et al. (2012). Figures 12 and 13 plot the peak acceleration of the deck plate (A3), the horizontal residual displacement of the deck plate (L1, PM6), the maximum moment of the vertical piles (S3), and the maximum axial force of the batter piles (S4), corresponding to the input acceleration for each model. The vertical pile moments were derived at the pile top (S3), where the maximum moment was observed. The plotted axial forces of the batter piles were also derived at the pile top (S4). As four to five datasets were derived per test in this study, regression analysis curves were also plotted to obtain the intermediate value. Quadratic polynomials were derived using the least square method.