## 1 Introduction  
Batter piles are widely used to resist lateral loads from such as earthquakes, wind, and waves. Batter piles are advantageous as they can transmit lateral load partly in the form of axial force, rather than shear and bending alone. In contrast, vertical piles carry the lateral load through shear and bending [1]. Additionally, when the batter pile is installed, it is possible to secure an effective bearing capacity by supporting it on the bedrock. However, certain historical cases have highlighted their potential negative effects in supporting structures during earthquakes [2]. In the US, the 1989 Loma Prieta earthquake damaged the whart at the Port of Oakland, and the Northridge earthquake, in 1994, damaged the Los Angeles whart. In both cases, tensile failure occurred at the head of the batter piles. In Japan, the 1995 Kobe earthquake buckled the batter piles in a whart in the Sumiyoshihama region, causing horizontal displacement of about 1 m, tilting the structure was \(\sim\)2-5\({}^{\circ}\)[3; 4]. In the Philippines, the 1990 7.8 magnitude earthquake damaged the Port of San Fernando, opening many gaps in the longitudinal direction of the concrete deck, including one that was 0.7 m in size. Additionally, the cracks and chopping were observed on the vertical and batter pile caps, that exposed the reinforcing steel bars [4]. Several reports have identified the following problems of batter piles during earthquakes. A large force at the pile cap can undesirably, and permanently, rotate it due to the asymmetry of the pile. Additionally, the bending moment capacity can be reduced by the seismically induced tensile forces [1]. Thus, certain codes do not recommend the application of batter piles in seismic design. For instance, the French Seismic Code [5] suggests that batter piles should not be used to resist seismic loads, and the Eurocode [6] recommends not to use them to transmit lateral loads to the soil. The Korean Ministry of Ocean and Fisheries [7] also recommends that batter piles should not be installed as they are easily damaged at their connection with the top plate. However, some researchers have reported the positive role of batter piles. Numerical analysis by [PERSON] et al. [8] demonstrated satisfactory seismic performance of both the superstructure and the foundation when batter piles are properly designed. [PERSON] [9] argued that the past seismic damage of batter piles was caused by the lack of engineering knowledge and numerical modeling techniques and that it is possible to secure positive performance by applying advanced numerical analysis and appropriate design methods. Recently, several studies have been conducted using dynamic experimentation to evaluate the performance of batter piles considering multiple variables, such as bottom condition, input motion, and structure size. [PERSON] et al. [10] conducted dynamic centrifuge model tests on pile groups consisting of one by two vertical piles, and one by two pile group with one batter pile. The bottom was classified as end-bearing, or a floating pile group, to evaluate the performance of batter piles with respect to the conditions at the bottom of the pile. Horizontal cyclic loading and horizontal impact tests were performed on each pile. The installation of the batter piles reduced the moments of both piles. [PERSON] [11] also performed a dynamic centrifuge model test by applying repeated earthquake and sinusoidal inputs to the model, previously used by [PERSON] et al. [10]. The soil response, pile cap response, and stresses in the piles were comprehensively reviewed. The test results showed that the batter piles were significantly affected by the frequency characteristics of the input wave. [PERSON] et al. [12] conducted dynamic centrifuge model tests to evaluate the behavior of vertical and batter piles. They analyzed the characteristics of the batter piles corresponding to their natural frequency and size of structures.