## 1 Introduction  
Seismic damage of bridge structures will cause not only serious economic losses but also significant difficulties in disaster relief and post-disaster reconstruction. The bridge vulnerability model can evaluate the damage probabilities of bridge structures during an earthquake, which can be used not only for the seismic risk assessment, but also for the sorting of the bridge structure reinforcements. The wall pier girder bridge is a universal bridge type of municipal bridges in China. So far, few studies about wall pier bridges have been published [1; 2]. There are some gaps to be filled: (1) Formerly used finite elements such as fiber-based beam-column element are not quite suitable for the simulation of wall piers, and some newly-developed finite elements have not been applied to this field; (2) The seismic capacity models of common pier columns developed in previous studies cannot be applied to the wall pier, a parameter-dependent capacity model is worth further developing. In this study, these problems are analyzed and discussed, and a seismic vulnerability model of the wall pier girder bridge is proposed. There are significant differences between the wall piers and common column piers in seismic behavior and failure mode due to their distinguishing geometric details. Haroun [3] and Aboutaha [4] conducted experimental studies on wall piers in 1993 and 1999, respectively. Haroun studied the wall pier bridges built before 1971 in California, then established experimental components of wall piers and found out that in-plane shear failure and out-of-plane flexural failure occurred in the wall piers under cyclic load. Aboshadi investigated the wall pier girder bridges in the United States and established seven wall pier experimental components that were subjected to out-of-plane cyclic loading, with the result that flexural failure occurred in all experimental components. The results reported here reflect that different failure modes may appear in both the in-plane and out-of-plane of the wall piers under the action of loads. In view of this mechanical property of the wall pier, finite element models of the wall piers are established by the layered shell element in this study, and their accuracy is verified. Since few studies were focused on wall piers, this study refers to several experimental studies of shear walls considering the similarity between the structures of the wall pier and the shear wall. Greifenhagen [5] conducted an experimental study on four shear walls with insufficient vertical reinforcement. None of these components suffered a complete brittle failure, and the strength of these components was controlled by bending strength. The axial compression ratio had a significant influence on the displacement capacity of the components. Hidalgo et al. [6] studied the seismic performance of the low-rise shear wall and conducted hysteresis analysis on the components with different shear span ratios, reinforcement ratios and compressive strengths of concrete, then found that all the structural parameters had a significant influence on displacement drift ratios of the components under various damage states. Based on the studies above, this article proposes an in-plane probabilistic capability model of wall piers with structural parameters and other information. Utilizing the sample points obtained by numerical simulation, estimate and filter the unknown parameters of the capability model by Bayesian parameter estimation method. For a wall pier girder bridge as a reference bridge, 120 wall pier girder bridge samples were obtained by Latin hypercube sampling by considering the uncertainty of the chosen parameters. One hundred and twenty finite element models of these samples are subjected to one earthquake event, respectively, by means of time-history analysis. On this basis, the seismic demand of each vulnerable component is obtained. The in-plane capacity models of the wall piers are used to determine its damage state.