## 5 Conclusions  
The overall performance of viaducts with different kinds of viscous dampers and different stopper values is evaluated during serious earthquakes in this study. Application of viscous dampers and stoppers to reduce some kinds of viaduct damage is also proven. Stopper value plays a more important role in pier damage than viscous damper. The analysis results provide sufficient evidence for the following conclusions:  
(1) Calculated results demonstrate that a stopper could effectively reduce the possibility of deck unseating. However, the possibility of deck unseating could also be significantly reduced in the case of D2000 because of its large resistance force and stiffness;  
(2) Maximum closing relative displacement could be greatly reduced in the case of viscous dampers. Maximum closing relative displacement also obviously decreases as the resistance force and stiffness of damper increase. However, a stopper could greatly reduce maximum opening relative displacement;  
(3) Viaducts with less stopper value present less residual pier inclination. As stopper value increases, residual pier inclination rises.ounding force between roller bearing and stopper is much larger than fixed bearing force. Thus, P1 with fixed bearings on top of it exhibits the least residual pier inclination compared with other piers. Viaducts with viscous dampers present less residual pier inclination than those without viscous dampers. However, the resistance force and stiffness of a damper do not obviously affect the residual pier inclination. Residual pier inclination and residual curvature at pier bases present similar trend for all cases;  
(4) Plastic deformations at pier bases appear in X and Y directions during earthquakes. Maximum bending moment and maximum curvature at pier bases in X direction are larger than those in Y direction. Thus, maximum bending moment and maximum curvature at pier bases in X direction play a more important role in the damages of pier bases. In the case of same viscous damper, maximum bending moment and maximum curvature at pier bases obviously increase with the rise in stopper value. A viaduct equipped with a viscous damper presents less maximum bending moment and less maximum curvature at pier bases than those without viscous dampers. However, the type of viscous dampers does not affect the maximum bending moment and maximum curvature at pier bases. Stopper value plays a more important role in maximum bending moment and maximum curvature than viscous dampers.  
Conceptualization, Q.T.; methodology, C.K. and Q.T.; software, C.K. and Q.T.; validation, L.Z.; formal analysis, Q.T.; resources, Q.T.; data curation, C.K. and Q.T.; writing--original draft preparation, C.K., Q.T. and L.Z.; writing--review and editing, C.K.; project administration, Q.T.; funding acquisition, Q.T. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Natural Science Foundation of China, grant number 52168023; the National Science Foundation for Young Scientists of Jiang Xi, grant number 20161 BAB216113; the Natural Science Foundation of Jiang Xi, grant number 20171 BAB206050; and the China Postdoctoral Science Foundation, grant number 2017M611993.  
The authors declare no conflict of interest.