## 1 Introduction  
Curved bridges are commonly used for highway interchanges and have become an important component of modern transportation systems. Curved composite steel I-girder viaducts with steel bearings are a viable option for complicated interchanges or river crossings, where geometric restrictions and site space limitations cause extreme complication of the adoption of standard straight viaducts. During the 1995 Kobe earthquake, the failure of steel bearings resulted in the unseating of decks [1]. Another representative example includes a curved steel girder bridge located 49 km from the epicenter of the 1992 Petrolia earthquake that suffered severe damage [2]. This damage occurred at the cross-frames and shear connections between the steel girder and concrete deck, which resulted in large lateral deformations at the bearings. Damage of pounding between adjacent viaduct segments has also been observed in earthquakes. Pounding phenomenon could amplify the relative displacement between adjacent superstructures [3, 4, 5]. Pounding could transfer large seismic lateral forces from one deck to the other, which obviously increases reaction forces at the pier bases [6]. The other problem is that pounding could increase the opening gap between adjacent superstructures, which may result in the deck falling down [7]. Roller bearings equipped with stopper are installed on top of piers to mitigate the abovementioned damage [8, 9]. Stoppers are known to prevent large roller bearing displacement and could thus mitigate roller bearing damage [10]. [PERSON] et al. studied the hysteretic performance and isolation effect of the steel reinforced elastomeric bearing [11, 12]. Although a seismic isolation device, such as a lead rubber bearing and steel-reinforced elastomeric bearings could be used to reduce viaduct damage, the price is more expensive [11, 12, 13]. A stopper will have a good application prospect due to its cheap price and simple installation. [PERSON] et al. [9] used the linear spring model to simulate multipoint pounding for simulating the pounding phenomenon of a steel stopper, but the model ignored the energy consumption in the pounding process, which would underestimate the bounding damage. Another structural measure to reduce seismic damage is a viscous damper, which has been developed since the late 1980s [14; 15]. It provides an adaptable damping force by adjusting the size of the orifice through which a viscous fluid flows when a piston moves in a hydraulic cylinder. The major advantage of viscous dampers is that they show no resistance forces under slow relative movements of segments due to thermal changes, creep, and shrinkage effects. It only begins to work when an earthquake occurs. Recent research shows that the viscous damper effectively controls the relative displacement and helps self-centering of the superstructure by reducing the potential residual displacement to near zero [16]. Therefore, application of viscous dampers to viaducts has gained considerable attention in recent years [17; 18; 19]. A steel stopper and a viscous damper will have good application prospects because they have the abovementioned advantages. At present, there is much research on lead rubber bearing or friction pendulum bearing combined with a viscous damper to reduce bridge earthquake damage [20; 21]. However, the research on a steel stopper combined with a viscous damper to reduce bridge seismic damage is lacking. Therefore, this study aims to analyze the overall performance of curved viaducts with different kinds of viscous dampers and different stopper values. Different kinds of viscous dampers have different stiffness and resistance forces. Thus, the relationship between different kinds of viscous dampers and curved viaduct damage could be explored. The effect of stopper value combined with viscous dampers on seismic damage is also studied. According to the relationship and the mitigating effect, advice for the seismic design of a curved viaduct could be proposed.