# Numerical Study on Track-Bridge Interaction of Integral Railway Rigid-Frame Bridge
## 6 Conclusions  
In this paper, a series of refined FE integrative models were proposed to investigate the characteristics of additional forces on CWRs of a novel HSR bridge structure system. The representative additional forces were illustrated and discussed in detail. Specifically, the influences of different design parameters, such as suitable types of rail fasteners, optimal layout schemes of adjacent bridges and the reasonable stiffness of piers, were studied. Several major conclusions can be drawn from this work as follows:  
1. The additional expansion force accounts for the largest proportion of the additional force of integral rigid-frame bridges, followed by the additional braking force. Due to the large vertical stiffness of this kind of bridge, the additional bending force is small and can be ignored.  
Figure 21: Total additional stress of the rail under different pier stiffness.  
Figure 20: Additional braking stress of the rail under different pier stiffness.  
2. Through comparative studies of two types of fasteners with different longitudinal resistances, this study verified that a decrease of resistance weakens the various additional forces caused by the interaction between track and bridge; notably, the additional expansion stress of the rail decreased by 55%. However, the rail broken gap increases greatly. 3. For this \(3\times 70\) m integral rigid-frame bridge, adopting the widely-used WJ-8 fasteners, the total additional stresses reached \(-143.1\) MPa and 151.7 MPa, which both exceed the standard limit in the UIC code. If no rail expansion joints are arranged, small resistance fasteners are suggested to be adopted for this new HSR line to reduce the additional stress of the CWR. 4. By adopting \(4\times 32\) m simply supported beams as the adjacent span arrangement scheme, the additional expansion stress and the additional braking stress of the rails in the integral rigid-frame bridge were less than the corresponding stresses in other schemes. 5. The minimum threshold value of the pier stiffness for integral rigid-frame bridges is closely related to the longitudinal resistance of HSR lines. With an increase of the longitudinal resistance between the CWR and the bridge, the minimum threshold value of the pier stiffness increases accordingly.  
Conceptualization, W.L. and G.D.; methodology, S.R.; formal analysis, H.L.; validation, W.L., S.R. and H.L.; data curation, H.L.; writing--original draft preparation, W.L.; writing--editing, H.L.; writing--review, G.D.; project administration, D.W. and B.W. All authors have contributed to the whole paper. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (Grant No. 51708560); the Natural Science Foundation of Hunan Province (Grant No. 2018J3672); the Science and Technology Research and Development Program of China Railway Corporation (Grant No. K2018C017); and the Science and Technology Research and Development Program of China Railway Siyuan Survey and Design Institute Group Co., Ltd. (Grant No. 2018K002).  
Not applicable.  
The authors would like to express their gratitude for the support from China Railway Siyuan Survey and Design Group Co., Ltd. and China Southeast Coast Railway Group (Fujian) Co., Ltd. The second author would also like to acknowledge the support of the Fundamental Research Funds for the Central Universities of Central South University (2019 zzts627).  
The authors declare no conflict of interest in this work.