## 2 Modeling Methodology and Estimation of Input Parameters
### Modeling of Far-Field Boundary  
One of the most important points in dynamic analysis for a soil-pile system is proper simulation of semi-infinite boundary. If soil elements are generated without limit for accurate simulation of the infinite boundary in a field, the effectiveness of the analysis is significantly decreased by the long analysis time. Therefore, setting up the boundary condition at a proper distance is very important. It must be considered carefully because inaccurate results can be induced due to reflected waves that are generated at the model boundary when the boundary condition is not properly modeled. In this study, a simplified continuum modeling method, which was proposed by [PERSON] et al. (2012) ([PERSON] et al., 2012), was adopted to simulate the soil-boundary responses accurately and effectively.  
Figure 2 depicts the 3D schematic view of the model mesh used in this study. The entire region is divided into two parts: near-field and far-field zones. As shown in this figure, only the near field, which is directly affected by the soil-pile dynamic interaction, was physically modeled, whereas the far field, which is considered to be unaffected by the soil-pile dynamic interaction, was not modeled. The acceleration-time histories along depth in far-field zone were then obtained independently by preliminary site-response analysis and input at the outer boundary of near-field zone. This kind of boundary is advantages in that it can reduce the analysis time remarkably and is very effective for the simulation of the boundary for a semi-infinite soil condition compared with the full modeling of the two zones. [PERSON] et al. (1992) ([PERSON] et al., 1992), [PERSON] et al. (1998), [PERSON] et al. (1999) ([PERSON] et al., 1999), and [PERSON] (2008) ([PERSON] and [PERSON], 2008) carried out similar approaches, relating it with p-y elements; however, most of those were performed with one- or two- dimensional simplified approaches. Application of this method to the 3D continuum model using the finite-element or finite-difference method is needed to reach a straightforward analysis of the prototype system. [PERSON] et al. (2012) ([PERSON] et al., 2012) applied this kind of method to finite-difference analysis, and the applied model was calibrated by 1g shaking table tests, which cannot reproduce the confining pressure of field conditions.  
In this method, the boundary extent of the near-field zone, where the soil motion becomes the same as the far-field motion, should be determined. The acceleration amplification ratio, which is the ratio of the maximum acceleration at the surface to the base input acceleration, was analyzed to determine the optimum boundary extent of the near-field zone. Figure 3 shows the amplification ratio with respect to the distance from the pile center. The dynamic excitation of the pile increases the surface acceleration; hence, the ratio decreases as the distance from the pile is increased. The optimal distance, at which the ratio is constant, was determined as 10D, where D is the pile diameter. Finally, the boundary applied as the extent of the near-field zone was determined as 10D from the pile center.  
Figure 2: Three-dimensional schematic view of model mesh.