## 1 Introduction  
The integral abutment jointless bridge (IAJB) has many advantages including beneficial integrity, durability, comfortable driving and favorable seismic behavior. The pile foundations of IAJBs may be subjected to cyclic longitudinal deformations due to expansion and contraction of girders induced by ambient temperature and earthquakes, which result in a remarkable soil-pile interaction [1; 2; 3; 4; 5]. Therefore, ductile piles are commonly used in IAJBs to sustain the cyclic deformations.  
Currently, various piles with different sections and materials such as the reinforcement concrete (RC) pile, prestressed concrete (PC) pile, H-shaped steel pile, steel tubular pile, and concrete-filled steel tubular (CFST) pile are widely adopted in the IAJBs. Several IAJBs supported on H-shaped steel piles have been constructed in North America and Europe, and researchers showed that the H-shaped steel pile is the best type of pile foundation for the IAJBs [6; 7; 8; 9; 10]. [PERSON] et al. [11], [PERSON] et al. [12], [PERSON] et al. [13] and [PERSON] et al. [14] studied the mechanical behaviors of a H-shaped steel pile subjected to ambient temperature and earthquake loadings. The test results indicated that the H-shaped steel pile had good plastic deformation capacity and was widely adopted in IAJBs. Nevertheless, in some countries, the concrete pile and other types of piles are also used to support the IAJBs because of economy, habitual principle, etc. Germany, Sweden and China [15; 16] collaboratively evaluate the feasibility of employing the concrete pile in the IAJBs. [PERSON] et al. [17; 18] and [PERSON] et al. [19] used finite element models to investigate the mechanical behaviors of a concrete pile supporting a IAJB. It was found that the pile-abutment connections significantly affect the mechanical behavior of IAJBs and when a reinforcement concrete pile was designed appropriately, its concrete cracking resistance was substantially improved. [PERSON] et al. [20] used the computer program LPILE to analyze the behavior of concrete piles in various types of soil for the IAJB. It was found that concrete piles had limited flexibility under lateral loads and can be only used in short-span IAJBs. [PERSON] et al. [21] and [PERSON] et al. [22] proposed a displacement-based simplified calculation method to analyze the soil-pile interaction of reinforced concrete and PHC pipe piles for IAJBs. It was shown that results obtained from the simplified method had a good agreement with the test results. In addition, several studies on PC piles were carried out and indicated that they can be used to support IAJBs [23; 24; 25]. The application of the rectangular concrete piles was also studied for the IAJBs [26; 27]. [PERSON] et al. [28] conducted a pseudo-static low-cycle experiment on the PHC pipe piles buried in sand type soil to investigate their failure modes and seismic behaviors, considering the soil-pile interaction. It is shown that the PHC pipe pile can support the foundation of IAJBs. [PERSON] et al. [29; 30] and [PERSON] et al. [31] carried out the full-scale pile test to obtain similar understanding about pile mechanics.  
Most of the aforementioned studies were concentrated on the behavior of one type of pile foundation for the IAJBs and, clearly, there is a lack of comparative study on the seismic performance of various types of pile for the practical engineering of IAJBs. Therefore, in this research, a pseudo-static low-cyclic test was conducted on various types of pile having different cross-sections, materials, reinforcement ratios, prestressing levels and buried length. A comparative study was performed to find their behaviors in terms of damage mechanism, deformation shape, bearing capacity, strain and bending moment distribution, etc. Finally, new seismic design criteria of three-stage seismic fortification and five damage level for the concrete piles of integral bridges were put forward based on the seismic design criteria of piers, which can be provided as a reference for the design specifications.