# Seismic Performance of Curved Bridges with Longitudinal Slope
## 1 Introduction  
In recent years, with the development of traffic construction, curved bridges have been used widely in expressway and urban transportation systems [1; 2; 3] due to their various characteristics, such as flexible linetype (which can select different curvature radii and longitudinal slopes), adaptability to terrain (they can be used in mountainous areas), and connection to traffic routes (they can be connected to different transportation hubs). Curved bridges have a curvature and longitudinal slope, which enable the structure to have bending-torsion coupling, and their internal force is complicated. The structural response of a curved bridge under seismic excitation is different from that of an ordinary bridge; thus, the curved bridge is prone to earthquake damage [4; 5; 6]. Currently, numerous researchers have analyzed the structural response of curved bridges under seismic action via numerical simulation and theory. [PERSON] et al. [7] investigated the dynamic characteristics of curved bridges under the action of earthquakes and found that seismic excitation remarkably affects the in-plane response of horizontally curved bridges. [PERSON] et al. [8] evaluated the influence of different seismic input angles on the response of curved girder bridges and emphasized that the seismic response is closely related to the seismic input angle. [PERSON] et al. [9] established a set of brittle analysis curves of horizontally curved highway bridges and conducted the probabilistic vulnerability assessment of curved girder bridges on the basis of OpenSees finite element software. [PERSON] et al. [10] developed the fault rupture-response spectrum analysis method, which effectively validated a curved bridge. [PERSON] et al. [11] examined the structural response characteristics of acurved reinforced concrete bridge under directivity pulse ground motions. Results showed that the effect of directivity pulses remarkably amplifies the response of curved bridges, which is maximized when the structural period is close to half of the main pulse cycles. [PERSON] et al. [12] analyzed the seismic performance of the curved bridge by considering the soil-abutment superstructure and discussed the influence of different factors on the seismic performance of structures. [PERSON] et al. [13,14] used the transfer matrix method to analyze the mechanical characteristics of curved bridges. [PERSON] et al. [15] adopted the general coordinate method, Hamilton theory, and energy theory to derive the motion equation of the curved bridge. [PERSON] et al. [16] proposed a simplified model for studying the stiffness eccentricity parameters of curved bridges and presented the formula for calculating the seismic response of curved bridges. A shaking table test is more advantageous than numerical simulation due to the reappearance of the destruction process of the earthquake. Several researchers have conducted a shaking table test on curved bridges with the improvement of test equipment and technology. [PERSON] et al. [17] analyzed the structural response of curved bridge under the action of traveling wave effect and local site effect ground motion through the shaking table test. Results showed that the structural response of a curved bridge is evident under the action of the traveling wave effect and local site effect earthquake. [PERSON] et al. [18] conducted a comparative study of the shaking table test and finite element analysis of the S-shaped curved bridge. [PERSON] et al. [19] performed a seismically isolated test of the curved bridge via a shaking table test. They found that the seismic response of the curved bridge is asymmetric and the rotation of the superstructure presents a non-linear increase with the earthquake level. [PERSON] et al.