## 1 Introduction  
Liquefaction, which generally occurs in loose sandy soil, is one of the major causes of damage to facility structures during earthquakes because many structures, such as civil infrastructure systems and plant facilities, are currently constructed on liquefiable soft ground, such as reclaimed area. In particular, in the magnitude 5.4 Pohang earthquake in November 2017, liquefaction was firstly observed in South Korea, raising concerns for the safety of foundations embedded in liquefiable ground. As the pile behavior in liquefiable sand has a more complicated mechanism than that in non-liquefiable soil, it exhibits much more uncertain and unpredictable characteristics. Not only do the inertial force of the upper structure and the kinematic force due to soil deformation apply different dynamic loads on the pile, but the stiffness and shear strength of the soil also decreases over time due to the nonlinear behavior of soil and development of excess pore pressure. Recently, owing to the development of physical model tests, such as the centrifuge test and 1-g shaking table test, and establishment of the numerical analysis method, several studies have evaluated the dynamic behavior of pile foundations in liquefiable sand. In particular, owing to the temporal, economic, and spatial limitations of physical model tests, increasing attention is being given to the efficiency of numerical analysis for simulating the liquefaction phenomenon. [PERSON] (2006) [1], [PERSON] et al. (2012) [2], [PERSON] et al. (2015) [3], and [PERSON] et al. (2018) [4] performed physical model tests and showed that pile behavior is significantly influenced by factors, such as the resonance between the foundation and superstructure, inertia force from the superstructure, kinematic force from soil deformation, and characteristics of input earthquake motions. [PERSON] et al. (2006) [5], [PERSON] & [PERSON] (2005) [6], [PERSON] et al. (2007) [7], [PERSON] et al. (2014) [8], [PERSON] & [PERSON] (2015) [9], and [PERSON] & [PERSON] (2014) [10] presented the simplified approach of a one-dimensional (1D) or two-dimensional (2D) numerical model, which was developed for the analysis of piles founded in liquefying soil, and showed that the simplified 1D or 2D model was capable of predicting the maximum lateral displacement and the peak bending moment of piles with relative accuracy. However, such approach requires making numerous assumptions. Moreover, it is difficult to estimate accurate values of soil stiffness and damping, which change significantly over time. With advances in the capacity of computers and analysis methods, straightforward three-dimensional (3D) numerical analysis has been conducted by [PERSON] & [PERSON] (2002) [11], [PERSON] et al. (2004) [12], [PERSON] & [PERSON] (2009) [13], [PERSON] et al. (2014) [14], and [PERSON] et al. (2017) [15]. While fully-coupled formulation (u-P or u-P-U formulation) was applied in some of these studies, uncoupled formulation was typically applied, in which the deformation of soil particles and development of excess pore pressure were calculated separately. This analysis method has a limitation in simulating direct pore pressure development as well as a reduction of shear strength due to the shear deformation of soil. This study aims to overcome this limitation by proposing a model which is capable of more directly and accurately simulating soil deformation and subsequent pore pressure development for more reasonable predictions of the dynamic pile behavior in liquefiable sand. Therefore, in this study, the seismic behavior of pile foundations during liquefaction was simulated using FLAC3D (Fast Lagrangian Analysis of Continua in 3 Dimensions), which was used as an analysis tool, and the detailed modeling methodology and determination of complex dynamic soil parameters were established independently.