## 1 Introduction  
When constructing an expressway or a railway in areas with high mountains and deep valleys, the total length of the route may be shortened by 200 m to 400 m as the height of pier increases 1 m [1]. Therefore, tall-pier bridges are the only design option most times. According to statistics, the number of tall-pier bridges with a pier height over 40 m accounts for more than 40% of the bridges in Western China [2]. However, a worldwide common definition of tall-pier bridge is lacking. AASHTO [3] does not directly provide the definition of the tall-pier bridge, but it regulates that the second-order effect should be considered when the slenderness of the pier is greater than 40. Chinese engineers usually regard the bridge with a pier height no less than 35 m as a tall-pier bridge [4]. This type of highway bridge was investigated in this study. In the middle of the 20 th century, some countries, such as Europe and North America, began the construction of tall-pier bridges. In recent years, the construction quantity and technology of tall-pier bridges in China have developed rapidly. Many bridges in China, such as the Labajin bridge, Hezhang bridge, and so on have continuously broken the record of pier height. However, there are still some challenges and obstacles in the construction of tall-pier bridges. First of all, compared with medium and short piers, the slenderness ratio of tall piers is significantly larger, resulting in instability problems and greater displacement at the top of the piers. To meet the requirements of stability and control the displacement of the piers, double thin-walled or hollow piers are commonly used [5]. These sections can effectively increase the sectional moment of inertia, reduce the slenderness ratio, cut the material consumption of concrete of the tall pier, and improve its stability. Secondly, the methods such as gliding formwork, climbing formwork or turnover formwork [6] to pour concrete on site, are usually adopted in the construction of traditional RC tall piers. These construction methods generally have problems of long construction periods, high labor and site machinery costs, high altitude operations, and other high-risk factors. Furthermore, the seismic design of tall-pier bridges is more complicated than conventional bridges. The mass distribution, high-order modes and second-order effects play significant roles in the structural seismic response. However, there are few relating research on the seismic performance of tall-pier bridges. The difference in the spectral components of different ground motions will result in a varying contribution of different mode in the structural responses. Hence, the ductility of tall piers is different when different ground motions are input. [PERSON] et al. [7] pointed out that the participation factor of higher-order modes in tall piers is too large to be neglected. Otherwise, it would lead to significant errors when performing the displacement-based design. [PERSON] et al. [8] employed the linear-elastic Euler-Bernoulli cantilever beam with a distributed mass and a concentrated mass at the top to simulate the tall pier. The analytical formulation regarding the dynamic behavior and seismic response is proposed, considering the influence of P-\(\Delta\) effect and high-order modes on the dynamic characteristics and seismic response of the pier. The results showed that the mass participation factor of the first mode decreased significantly with the increase of pier height. Meanwhile, the seismic response was strongly influenced by second-order effects and higher modes contributions related to the distributed pier mass. [PERSON] et al. [9; 10] found that the high-order modes significantly contributed to the seismic response of a tall-pier bridge. These modes would result in additional plastic hinges midway up the pier under strong ground motions. Mistakenly using the displacement-based seismic design method for tall piers may result in a seriously unsafe condition. [PERSON] et al.