# Transient Response of Bridge Piers to Structure Separation under Near-Fault Vertical Earthquake
## 1 Introduction  
As a transportation hub, bridges cause serious damage to the road network when an earthquake occurs, which brings great difficulties to rescue work in the disaster-stricken areas. Simultaneously, this greatly affected the post disaster recovery and reconstruction work and significantly reduced the traffic function between regions [1, 2]. In the past, the research on pier failure mainly focused on horizontal excitation, ignoring the influence of vertical earthquake [3, 4, 5]. However, with the progress of monitoring level in recent years, increasingly monitoring data show that the near-fault earthquake which has a sizeable vertical excitation amplitude, may cause landslides and damage to the bridge foundation [6, 7, 8, 9]. In addition, the pier will suffer more tremendous vertical pressure, or even cause the pier axial compression damage [10, 11, 12]. Moreover, the fluctuation of axial force may also change the flexural and shear performance of the pier. In this regard, many experimental studies have been carried out [13, 14, 15, 16]. For the main girder, the vertical seismic excitation will also increase the mid-span bending moment and even cause the bending failure of the structure [13, 17]. In order to reduce the response of bridges under earthquake, a series of research have been carried out in the field of energy dissipation, such as the performance of rubber-bearing isolators under seismic events [18, 19].  
For the ratio of vertical and horizontal seismic acceleration, many codes simply set it as 2/3. However, these years, monitoring data show that V/H was far more than 2/3 or even 2. For example, in the Northridge earthquake, the ratio of vertical acceleration to horizontal acceleration reached 1.79, and the amplitude of vertical acceleration reached 1.18 g [20]. Under the Kobe earthquake, the peak acceleration ratio V/H is as high as 2 [21].  
Analyzing nine pieces of data collected within 20 km of the Wenchuan earthquake source, the average acceleration ratio V/H is 0.89, and the maximum value is 1.2 [22].  
Unlike foreign rigid frame bridges, most bridges in China use rubber bearings. The main beam is directly placed on the pier, and the structure lacks a tensile connection [23; 24]. When the vertical seismic excitation is too large, the main beam and pier may be separated. In the 1989 Loms Prieta earthquake [25], a highway bridge is divided under the vertical quake, and the girder is thrown up. When the bridge collides again, the pier directly passes through the bridge deck. Besides, [PERSON] [26] considered that the impact force caused by separation might damage the bearing and local pier.  
In the past, the collision of bridge mainly focused on the longitudinal beam to beam collision [27], and the research on the vertical collision was less. In addition, the damping measures are set in the horizontal direction [28; 29], but the effect of the vertical separation on the horizontal seismic response is ignored. Previous studies on bridge failure assumed that the structure always kept in contact and did not consider the possibility of structural separation caused by the near-fault vertical earthquake. In this study, a double-span continuous beam bridge model is established, and the forced resonance response of the bridge is calculated by using the transient wave function method [30]. The structural displacement response caused by the collision force is calculated by using the indirect modal function method [31]. The force and displacement response of the bridge are calculated by the theoretical approach, and the bending conditions of the bridge pier under different conditions are obtained.