## 3 Validation of Proposed Model  
To improve the reliability and minimize the error of the proposed numerical model, a validation procedure was carried out by comparing the dynamic pile internal responses calculated by the numerical model with those measured by the dynamic centrifuge model tests ([PERSON] et al., 2013) [20]. The centrifuge model tests were performed with the KAIST dynamic centrifuge facility in Korea, which has a 5 m radius, 2.5 ton payload and a up to 100 g centrifugal acceleration. All tests were performed at a centrifugal acceleration of 40 g and similitude factor was 40, also. In order to analyze dynamic behavior of soil-pile interaction using centrifuge tests, the model structure should be manufactured considering reasonable similitude law. The model piles and ground were simulated by dynamic centrifuge similitude law which was verified by many preceded researches ([PERSON] et al. (1980) [32], [PERSON] (1995) [33]). Two aluminum model pile were used with 2.5 cm (1 m in prototype scale) and  
Figure 3: Acceleration-amplification ratio of soil according to the distance from pile. 1.8 cm (0.72 m in prototype scale) external diameters and a 0.1 cm (0.04 m in prototype scale) thickness, and embedded depth was 57 cm (22.8 m in prototype scale). Joomunjin sand, characterized as clean and uniform sand, was used in these tests. The primary properties of model soil and pile are summarized in Tables 2 and 3. The layout of the test is shown in Figure 4. Eight pairs of strain gauges were attached on both sides of the pile to calculate the bending moment in the pile during vibration. Eight accelerometers were installed in the soil at the same depth as each strain gauge to calculate the displacement of soil and one accelerometer was attached to the pile head to measure the acceleration responses of the pile. In order to compare centrifuge model tests and numerical analysis results, all results from the centrifuge tests were expressed at the prototype scale. Figure 5a depicts an example of the acceleration-time history of a sinusoidal event with a maximum acceleration of 0.4 g and frequency of 1 Hz. Two kinds of real earthquake events (Ofunato and Nisqually earthquakes) were scaled into various input motions with different amplitudes of peak base accelerations (0.06 g, 0.13 g, 0.25 g, 0.36 g, 0.51 g). Figure 5b,c depict the representative acceleration-time histories of those two real-earthquake events, which have a maximum amplitude of 0.51 g. \begin{table}
\begin{tabular}{c c} \hline \hline
**Property** & **Value** \\ \hline Friction angle (degree) & 42 \\ Dry density (kN/m\({}^{3}\)) & 15.80 \\ Poisson’s ratio & 0.3 \\ Void ratio & 0.677 \\ Relative density (\%) & 80 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Input properties of model soil. Figure 4: Layout of test (in prototype). For the first stage of the validation procedure, the internal pile responses calculated from the numerical model and those measured from centrifuge tests using the test case of Model 1 in Table 3 were compared and discussed. Figure 6a,b shows measured and calculated peak bending moment profiles for different input frequencies under input acceleration of 0.13 g. It was identified that the peak bending-moment profiles predicted by the proposed numerical method showed similar trend for various input frequencies with those observed in centrifuge tests. The peak bending moment of the pile obtained in both approaches sharply increased as input frequency approaches to 1 Hz. Figure 7a-c shows the maximum values of the pile bending moments for various input earthquake frequencies and amplitudes. As shown in Figure 7, the maximum values calculated by numerical model and measured by the centrifuge test show good agreement for various input earthquake conditions.