Study on Horizontal Displacement Response of Bridge Pier Tops Under Bidirectional Seismic Excitation

The near‐field vertical seismic action not only causes an increase in the pressure endured by the bridge pier but also exerts a remarkable influence on the horizontal deformation at the top of the pier. To deeply explore this complex phenomenon, this research has constructed a set of control differential equations depicting the vibration characteristics of the tall piers of double‐span bridges. To precisely simulate the dynamic response of the tall piers under vertical seismic action, we have adopted the variable‐step Runge–Kutta numerical integration method. The research results indicate that the vertical seismic excitation not only intensifies the degree of horizontal deformation of the bridge pier but also might lead to an underestimation of the dynamic response when the coupling effect between the horizontal and vertical directions is disregarded. Particularly importantly, this study also discovers that under intense seismic action, a separation phenomenon may occur between the bridge pier and the bridge. Such separation will result in the failure of the horizontal constraint of the bridge support, thereby altering the horizontal dynamic response characteristics of the bridge pier and significantly enhancing the risk of instability of the bridge structure.