## 3 Input Seismic Motion  
In this study, the effects of the duration of seismic motion were evaluated by selecting two types of seismic records from recent damaging earthquakes and using an input seismic motion whose amplitude was adjusted to obtain the same acceleration response spectrum (for L2 seismic motion settings). Figure 9 shows the two input seismic motions. Seismic motions (A) and (B) were set as the strong ground motion waveforms of the \"NS-direction seismic record at the Muroran Port during the 1993 southwest-off Hokkaido earthquake\" [29] and the \"NS-direction seismic record at the Hanshin Expressway East-Kobe Bridge (GL-35 m) during the Hyogo-ken Nanbu earthquake\" [30], respectively, whose amplitudes were adjusted with the spectrum used to set the JGA L2 seismic motion  
Figure 8: Pile M–N failure diagram. Figure 7: Analysis model. (Figure 10). As shown in Figure 10, the original waveforms of both seismic motions differ significantly in magnitude. The original waveform used for seismic motion (A) was small in magnitude; thus, the amplitude was significantly adjusted in the wide period band from the short -to long-period components. However, the waveform used for seismic motion (B) had minor adjustments because it was an L2 earthquake close to the design spectrum. Seismic motion (B) was the seismic wave used in a previous study [13]. Both seismic motions were strong ground motions that included long-period components. In each case, the amplitude was adjusted without changing the duration. The duration was defined by the \"bracketed duration\" of [PERSON] [31] and the duration based on the power accumulation time of [PERSON] and [PERSON] [32]. The \"bracketed duration\" is defined as the length of time between the first and the last time when the amplitude of the seismic record exceeds a \"given level\". This level was defined as \"10% of the maximum amplitude\", as in Kamiyama [33] (hereinafter referred to as \"b-duration t\({}_{\text{b}}\)\"). The definition by [PERSON] and [PERSON] is to calculate the duration as the length of the interval containing 90% (5-95%) of the total power of the earthquake record (hereafter referred to as \"p-duration t\({}_{\text{p}}\)\"). The duration t\({}_{\text{b}}\) and t\({}_{\text{p}}\) calculated from these definitions were shown in Table 4 for both adjusted and original waves. The table shows that the duration of earthquake motion (A) is about 9 times longer than that of earthquake motion (B) in terms of t\({}_{\text{b}}\). The seismic response analysis used a bottom viscous boundary [22; 34; 35] corresponding to shear wave velocity Vs = 420 m/s and density \(\rho\) = 2.0 g/cm\({}^{3}\) in the horizontal direction of all the nodes on the ground bottom, and the seismic waves were input equally in the horizontal direction of all the nodes on the ground bottom. Figure 10: Acceleration response spectrum. Figure 9: Input seismic motion for analysis: seismic motions (A) and (B). In this study, the seismic response of the ground was specifically discussed. Therefore, 1D analysis was conducted to examine the response of the ground itself when two different seismic motions were input to the target ground. Figures 11 and 12 show the settlement amount during and after the earthquake when seismic motions (A) and (B), respectively, were input to the horizontal ground using the FE mesh and boundary conditions in Figure 1c and when the structure was not installed for each (i.e., ground surface settlement amount and stratified settlement amount). The ground surface settlement amount was 0.44 m and 0.21 m for seismic motions (A) and (B), respectively. The mean effective stress of the surface sandy soil layer (B layer/Yus layer) decreased during the earthquake (i.e., excess pore water pressure accumulated); consolidation settlement began as a result of the dissipation of the excess pore water pressure during the earthquake for the B layer and immediately after the earthquake for the Yus layer.