## 1 Introduction
They confirmed that the performance of the batter piles degraded when the applied sinusoidal wave was in the region of the structure's natural period, and improved when the structure's natural period was in the region of that of the soil. Similarly, [PERSON] et al. [13] analyzed the behavior of batter piles relative to the size of the structures by applying earthquake excitation. The batter piles had positive effects on the structure in terms of displacement and force and, overall, showed positive performance, especially in short structures. [PERSON] et al. [14] conducted field tests on structures with vertical and batter piles, analyzing the effects of the batter piles on the frequency and the number of piles. A mechanical oscillator was installed on the pile cap to apply a sinusoidal load. The batter piles significantly reduced the displacement with increasing load. Overall, various studies have considered the seismic performance of batter piles corresponding to a range of variables and have found that excellent seismic performance can be observed when an appropriate design method is applied. Recently, several studies have been conducted in this dynamic domain using numerical analysis. [PERSON] et al. [1] assessed variables using a three-dimensional numerical analysis to evaluate the effects of batter piles. They found that the overturning moment varied depending on the size of the structure, and the impact of the batter piles depended on parameters such as structure size, pile rake, and pile-cap connection. [PERSON] and [PERSON] [15] performed three-dimensional analysis using FLAC 3D (Fast Lagrangian Analysis of Continua in 3 Dimensions) to understand the behavior of batter pile foundations subjected to lateral soil movement. Numerical analysis was performed on a three by three group pile combined with vertical piles of batter piles. The response of the group pile to soil movement was analyzed and revealed that the maximum moment of the batter piles was smaller than that of the vertical piles in sand, but was five to eight times higher than in clay. Similarly, [PERSON] et al. [16] performed three-dimensional analysis to evaluate the seismic behavior of batter pile groups. The seismic behavior of a two by two vertical and batter pile, with a batter angle of 15\({}^{\circ}\), was compared using a full three-dimensional finite element code, developed in MATLAB. The comparison of the response of the frame structures of the five stories showed that the response in the structure with a batter pile foundation was reduced by \(\sim\)12%-50%, compared to the structure with a vertical pile foundation. Batter piles are widely used in whaves, piers, and jetties. Whaves are generally built on inclined ground, and piers and jetties, on horizontal ground [17] (Figure 1). A structure's performance during an earthquake can vary greatly depending on the slope of the ground. [PERSON] and [PERSON] [18] conducted a dynamic centrifuge model test to examine structural responses corresponding to the ground slope and explained that the kinematic force of the slope causes an additional response in the pile. However, they evaluated the seismic performance of only vertical piles. This highlights that current research on the seismic performance of batter piles with respect to the ground slope is insufficient. In this study, dynamic centrifuge model tests were performed to evaluate the seismic performance of batter piles with respect to the ground slope. Four test models were selected according to the presence or absence of batter piles and the ground slope. When designing the batter pile of a pile-supported structure, an inclination between 3:1 and 5:1 was used with respect to the positional constraints of the other piles and the constructional constraints, such as the driving machine [19]. The inclination of 3:1 (18\({}^{\circ}\)) was used so that the batter pile could properly support the lateral force.