## 2 Self-Centering Rocking Steel Bridge Pier Structure and Its Finite Element Analysis Model  
### The Form and Design Parameters of the Structure  
Currently, mature self-centering rocking bridge pier structures achieve the rocking motion by releasing the bottom constraint with bases, thus extending the natural period of the structure and providing the vibration isolation effect. Meanwhile, under the axial compression from prestressed tendons and the gravity loads, the bridge piers can be self-centering. The structure undergoes cyclic energy dissipation through the plastic deformation of replaceable energy dissipating components. Based on the existing research, this paper designs a single-column self-centering rocking steel bridge pier with a circular cross-section, as shown in Figure 1. The pier material adopts the commonly used Q345 qC steel in bridge engineering. To achieve better self-centering and energy dissipation functions, prestressed tendons and energy dissipating components are placed at the center of the section and outside the base plate, respectively. The prestressed tendons consist of several strands of 1 \(\times\) 7 prestressed steel wires (each strand having a nominal diameter of 15.2 mm) with a yield strength of 1860 MPa. The initial tension is set to 0.4 times of the yield strength. The energy dissipating component is an externally attached buckling-restrained energy dissipating steel plate made of Q235 steel with a low yield point. According to the research on seismic performance of circular-section steel bridge piers [17; 20], the structural parameters that affect the ductility performance of circular-section steel bridge piers are overall slenderness ratio \(\overline{\lambda}\), radius-to-thickness ratio \(R_{t}\) and axial compression ratio \(N/N_{y}\). The formulas for calculating the overall slenderness ratio \(\overline{\lambda}\) and radius-to-thickness ratio \(R_{t}\) are as follows:  
\[\overline{\lambda}=\frac{2h}{R}\cdot\frac{1}{\pi}\sqrt{\frac{\sigma_{y}}{E}} \tag{1}\]  
\[R_{t}=\frac{R}{t}\cdot\frac{\sigma_{y}}{E}\sqrt{3(1-\mu^{2})} \tag{2}\]  
In the above equations, \(h\) represents the pier height, \(R\) represents the radius of the cross section corresponding to the center line of the wall plate, and \(t\) represents the thickness of the wall plate. \(\sigma_{y}\) and \(E\) represent the yield strength and elastic modulus of the steel material, respectively. According to the seismic performance experimental study conducted by [PERSON] et al. [24] on rocking steel bridge piers, the addition of the base plate at the bottom of the rocking steel bridge pier significantly enhances its seismic performance. The enhancement mechanism can be summarized in several aspects. Firstly, the base plate applies tension to the wall plate, counteracting part of the compression force and reducing local deformation effects. Further, the area under shear force at the bottom of the pier increases, making it less prone to elliptical deformation and reducing the effect of stiffness reduction. At the same time, the height of the compression zone decreases. It increases the lever arm for resisting horizontal force and allows the pier to be raised higher. The self-centering effect under the action of prestressed reinforcement is enhanced. However, the influence of base plate thickness and area on the seismic performance is not yet clear. To this end, in this paper, the increasing factors of the base plate thickness \(t_{bp}\) relative to the wall plate thickness \(t\), denoted as \(i_{t}\), and the increasing factors of the base plate radius \(R_{bp}\) relative to the pier section radius \(R\)  
Figure 1: Circular-section rocking steel bridge pier structure. denoted as \(i_{R}\), are considered as design parameters to be investigated. The calculations for \(i_{t}\) and \(i_{R}\) are obtained using Equation (3) and Equation (4), respectively.