# Seismic Performance Assessment of Wide Pile-Supported
## 3 Results and Discussion
### Bending Moment of Piles  
Figures 15-20 illustrate the bending moment distributions of the piles due to the SDW and LDW, respectively. The distributions are the snapshots when the bending moment of each pile becomes maximum at a certain point in the pile. The piles are numbered sequentially from the left (smallest number) to the right (largest number) side. The \(\mathcal{O}\)1000, \(\mathcal{O}\)1100, and \(\mathcal{O}\)1200 mm piles are labeled P1-P17, P1A-P12A, and P1B-P3B, respectively. Figure 14: Horizontal residual ground displacement due to the LDW. (**a**) Scenario 1; (**b**) Scenario 2. Figure 13: PSW horizontal displacement due to the LDW. (**a**) Scenario 1; (**b**) Scenario 2. Figure 16: Bending moment distribution of \(\mathcal{O}1100\) mm pile due to the SDW. (**a**) Scenario 1; (**b**) Scenario 2. Figure 15: Bending moment distribution of \(\mathcal{O}1000\) mm pile due to the SDW. (**a**) Scenario 1; (**b**) Scenario 2. Figure 17: Bending moment distribution of \(\mathcal{O}1200\) mm pile due to the SDW. (**a**) Scenario 1; (**b**) Scenario 2. Figure 18: Bending moment distribution of \(\mathcal{O}1000\) mm pile due to the LDW. (**a**) Scenario 1; (**b**) Scenario 2. Figure 19: Bending moment distribution of \(\mathcal{O}1100\) mm pile due to the LDW. (**a**) Scenario 1; (**b**) Scenario 2. Figure 20: Bending moment distribution of \(\mathcal{O}1200\) mm pile due to the LDW. (**a**) Scenario 1; (**b**) Scenario 2. In all the cases, the maximum bending moments were observed at pile heads. The maximum bending moments in the \(\mathcal{O}1200\) mm piles were significantly large. In Scenario 1, there was no pile that reached the plastic bending moment when the SDW was applied, but the plastic bending moment was reached in the \(\mathcal{O}1200\) mm pile when the LDW was applied. In Scenario 2, the plastic bending moments were reached at the \(\mathcal{O}1000\), \(\mathcal{O}1100\), and \(\mathcal{O}1200\) mm piles for any action of SDW and LDW. The reason why the bending moment of the \(\mathcal{O}1200\) mm pile was large in Scenario 1 is that the \(\mathcal{O}1200\) mm pile shared the largest inertia force because of its highest rigidity among the piles. In Scenario 2, in addition to the above, the \(\mathcal{O}1000\) mm piles were strongly affected by the ground displacement at the slope, resulting in a large bending moment, particularly in the piles close to the top of the slope. Regarding the bending moment distribution below the ground surface, the results of Scenario 1 showed the maximum bending moment at shallow points in the underground. This bending moment profile is consistent with that generated in the beam on the Winkler foundation [41]. On the other hand, the results of Scenario 2 did not produce the maximum bending moment at shallow points in the ground. The explanation is that the ground stiffness and subgrade reaction were lowered in the shallow part of the ground due to the effect of the slope displacement. In contrast, large bending moments occurred at the boundary between Clay 2 and Clay 3 in Scenario 2 results. This is the same mechanism that caused buckling to occur at deep underground locations of the piles of the PSW at Kobe Port during the 1995 Kobe Earthquake because of the strong impedance contrast in soil layers [42]. Since the slope was gentle in the target wharf of this study, the plasticization of the pile did not occur in the underground part, but care should be taken that seismic design practice ignoring slope displacement may lead to the design results being on the dangerous side even for points in the underground. Figures 21 and 22 illustrate the time histories of bending moments at the \(\mathcal{O}1200\) mm pile head due to the SDW and the LDW, respectively. The comparison between the bending moment time history of the piles and the acceleration and displacement time history of the PSW in Scenario 1 shows a correlation in amplitude patterns; large acceleration and displacement correspond to a large bending moment and vice versa.