## 5 Concluding Remark  
A numerical modeling methodology was proposed to analyze the dynamic soil-pile-structure interactive behavior embedded in liquefiable sand. The applicability of the proposed method was verified by comparing with the dynamic responses from the centrifuge tests performed by [PERSON] (1998) [16]. A parametric study was conducted to provide better discernment into the dynamic behavior of pile foundation under liquefaction. Detailed conclusions are as follows:  
Figure 17: Effect of superstructure weight on lateral displacement of a pile in dry soil: (a) Input acceleration: 0.25 g; (b) Input acceleration: 0.25 g.  
Figure 18: Effect of kinematic force in different soil condition under earthquake.  
1. The proposed methodology includes the liquefaction model, which can simulate pore pressure generation and soil strength reduction under strong earthquake in real time. Simplified continuum modeling was adopted firstly for liquefaction related soil-pile-structure system to accurately simulate boundary condition and to improve analysis efficiency. Damping and interface models were proposed to properly consider soil nonlinearity, and various dynamic soil properties such as initial shear modulus, interface friction angle, etc. were carefully determined.
2. Based on the verification, it was confirmed that time histories of the excess pore pressure ratio, pile bending moment, and pile head lateral displacement by depth derived using the proposed modeling method effectively simulated those observed in centrifuge test.
3. In a parametric study, the bending moment reached its maximum at the interface between the liquefied and non-liquefied layers, and the lateral pile displacement remarkably decreased as the thickness of liquefiable layer was decreased. As the liquefiable layer became denser, the liquefied depth became shallower and dynamic pile responses significantly decreased. The kinematic force induced by soil deformation was dominant in liquefiable sand, whereas the inertial force induced by superstructure was relatively insignificant. These kinds of important dynamic characteristics for different soil conditions were clarified by full-scale numerical simulation.
4. Based on the results from a series of parametric studies using the proposed numerical model, several recommendations can be drawn in design stage of pile foundation. Additional careful consideration should be made when constructing piles in multi-layered ground condition because unexpected unusual sharp increase of dynamic response can be occurred at the interface between soil layers. Even under similarly liquefied conditions, significant differences in the dynamic responses of pile can occur due to differences in ground relative density because kinematic force is dominant in liquefied condition. Therefore, when the liquefiable layer is distributed to a deep depth, a more rational design is possible if an effective soil improvement method such as dynamic compaction is used in combination with a pile, rather than massive reinforcement or the addition of a pile.  
[PERSON] organized the paperwork, made a analysis plan, performed numerical analysis and suggested the numerical analysis method; [PERSON] supported the numerical model verification by comparing test results helped the data analysis; all authors contributed to the writing of paper. All authors have read and agreed to the published version of the manuscript.  
This research was supported by (1) a grant (code: 20 SCIP-C151438-02) from Construction Technologies Program funded by Ministry of Land, Infrastructure and Transport of Korean government and (2) Review of Strategic Environmental Assessment funded by Korea Environment Institute.  
The authors declare no conflict of interest.