## 3 Centrifuge Test Results and Discussion
\[f_{t}+f_{ht}\leq f_{ta}\text{ or }-f_{t}+f_{bc}\leq f_{ca} \tag{5}\]  
\[\frac{f_{c}}{f_{ca}}+\frac{f_{bc}}{f_{ba}}\leq 1.0 \tag{6}\]  
here,\(f_{c}\) is the compressive stress of pile (kN m\({}^{-2}\)),\(f_{t}\) is the tensile stress of pile (kN m\({}^{-2}\)),\(f_{bc}\) is the bending compressive stress (kN m\({}^{-2}\)),\(f_{bt}\) is the bending tensile stress (kN m\({}^{-2}\)),\(f_{ta}\) is the allowable tensile stress (kN m\({}^{-2}\)),\(f_{ca}\) is the allowable compressive stress (kN m\({}^{-2}\)),\(f_{ba}\) is the allowable flexural stress (kN m\({}^{-2}\)), and \(f_{a}\) is the allowable stress (kN m\({}^{-2}\)). This study applied the allowable stress (\(f_{ta}=f_{ca}=f_{ba}=185,000\) kN m\({}^{-2}\)) of STK490 steel to the actual prototype structure. As the allowable tensile, compressive, and flexural stresses are the same for STK49 steel, these can be expressed by Equation (7). For the member with \(M\) and \(N\) occurring simultaneously, the combined stress ratio (\(F\)) should not exceed one. \[F=\left|\frac{f_{n}}{f_{a}}\right|+\left|\frac{f_{m}}{f_{a}}\right|\leq\ 1.0 \tag{7}\]  
Figures 15 and 16 show the \(M\)-\(N\) interaction diagrams calculated using the above equations. The \(x\)-axis values were calculated by dividing the bending stress by the allowable stress, and the \(y\)-axis by dividing the axial stress by the allowable stress. Each graph represents the change in bending and axial stresses over time. When the plot is within the area delineated by the dotted lines, the \(F\) value does not exceed one. The bending and axial stresses of each figure are the responses at positions S3 and S4. Figure 16 shows the time history responses when a low input acceleration (0.12-0.15 g) was applied. The plots for the horizontal (Figure 16a) and inclined (Figure 16b) ground models are slightly below the \(x\)-axis as the load on the deck plate acts as the axial stress. In the HA45 model, that is composed of vertical piles, as seen in Figure 16a, the bending stress ratio (\(f_{m}\)/\(f_{a}\)) is relatively large compared with the axial stress ratio (\(f_{n}\)/\(f_{a}\)). This model's derived maximum bending stress ratio and axial stress ratio were 0.67 and 0.15, respectively. The bending stress ratio for the vertical piles (0.14) was greatly reduced for Model HAI55, with the batter piles, the axial force ratio of which was 0.27. The inclined-ground models showed similar trends in Figure 16b because batter piles transmit a lateral earthquake load as an axial force, thereby reducing the moment generated in the pile. The time history responses are shown in Figure 16a for the horizontal-ground model and in Figure 16b for the inclined-ground model when a high input acceleration (exceeding 0.2 g) was applied. Models HA45 and IA62 have relatively large bending stress ratios compared with the axial stress ratios in the vertical piles. Particularly in the IA62 model, a combined stress ratio exceeding one was derived despite the application of a lower input acceleration (0.21 g), compared to that applied to the HA45 model (0.23 g). This was because, for the inclined-ground models, as described above, the kinematic forces of the inclined ground generated additional kinematic forces in the piles. However, batter piles greatly reduced the bending stress ratio of the vertical piles, and the combined stress ratio decreased to less than one. Figure 15: Relationship between bending moment and axial force (input peak acceleration \(\sim\)0.12–0.15 g, scaled to the prototype): (**a**) horizontal ground model and (**b**) inclined ground model. Table 6 compares the combined stress ratio for each model derived using Equation (7). When the batter piles were installed, the combined stress ratio decreased in the vertical pile in both the horizontal and inclined ground models. The combined stress ratios of up to 0.62 in the horizontal ground and one in the inclined ground models decreased. Thus, the batter piles show more efficient performance on inclined ground than on horizontal ground.