## 3 Validation of Proposed Model
Based on Figures 6 and 7, it can be identified that resonance occurred in both results when the frequency  
Figure 5: Acceleration–time history of input motion: (a) Acceleration-time history of base input for sine wave (1 Hz, 0.4 g); (b) Acceleration-time history of base input for Ofunato earthquake (a\({}_{\text{max}}\) = 0.51 g); (c) Acceleration-time history of base input for Nisqually earthquake (a\({}_{\text{max}}\) = 0.51 g). of the input earthquake approached 1 Hz, meaning that the natural period of the system appeared to about 1 s in both results. This kind of behavior was also captured in sweep analysis as shown in Figure 8. Therefore, it is demonstrated that proposed numerical model can simulate the important dynamic characteristics of the soil-pile-structure system, such as resonance. Figure 6: Measured and calculated peak bending moment profiles under input acceleration of 0.13 g (Model 1, sinusoidal wave): (**a**) Calculated by proposed model; (**b**) Measured by experiment. Figure 7: _Cont._  
Figure 9 and 10 show the peak bending moment profiles for different input accelerations when the Nisqually and Ofunato earthquakes were applied as input excitations, respectively. The peak bending moment according to the depth predicted by the numerical model matched well with those observed in dynamic centrifuge tests for both real earthquake events. It is shown that the proposed  
Figure 8: Result of sweep analysis. Figure 7: Maximum values of bending moments for various input motions (Model 1, sinusoidal wave): (**a**) Input frequency:1 Hz; (**b**) Input frequency:2 Hz; (**c**) Input frequency:3 Hz. numerical model has the capability to properly simulate seismic pile behavior for various input earthquake conditions. Figure 10(a),b shows the comparison between the analysed and observed maximum values of pile bending moments for various input amplitudes of both real-earthquake events. And, in this figure, discrepancies between two results were also showed for quantitative discussion. It depicts that all results show good agreement with discrepancy rate of less than 20%, which indicates that the predicted dynamic-pile responses agree reasonably well with the observed values for both the Nisqually and  
Figure 10: Measured and calculated peak bending moment profiles (Model 1, Ofunato earthquake): (**a**) Ofunato, 0.13 g; (**b**) Ofunato, 0.51 g.  
Figure 9: Measured and calculated peak bending moment profiles (Model 1, Nisqually earthquake): (**a**) Nisqually, 0.13 g; (**b**) Nisqually, 0.51 g.  
Ofunato earthquakes. In particular, the numerical model predicted the pile bending moments well in conservative manner with good accuracy, which means that the proposed numerical model can simulate the dynamic pile behavior in dry sand with safety and economic margins under various kinds of earthquake conditions. The above results identified the viability of the proposed model for simulating the dynamic behavior of piles under earthquake conditions. However, the validation was performed only for a single test pile case, which was carried out using Model 1. Additional verification is necessary to validate the applicability of the proposed model for various site conditions. For this reason, further verification was conducted by comparing the internal pile responses of Model 2. In this part, only the test case in which the Nisqually earthquake was applied as an input excitation was used because test results obtained from the test case applying Ofunato earthquake as an input excitation were unreasonable due to defects in the measuring instruments during the test. Figure 12 shows the comparison between the observed and predicted maximum values of pile bending moments for various input amplitudes in a single graph. It can be seen that the calculated bending  
Figure 4:0 Measured and calculated maximum values of bending moments for various input amplitudes (Model 1): (**a**) Nisqually earthquake; (**b**) Ofunato earthquake. moments agree quite well with the values recorded during the experiment.