## 5 Conclusions  
This paper investigates the impact of creep deformation at the main girder on the operational capability of high-speed trains, taking a large-span continuous beam bridge on a high-speed railway as the background. Midas software was used to establish the creep model of this bridge, then the long-term deformation of the bridge was calculated under a constant load. The coupled vibration equations of the train bridge were established using the set-in-right-position rule and the principle of Total Potential Energy with Stationary  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Vehicle**} & \multicolumn{3}{c}{**Criteria of Sperling Comfort Index**} \\  & **Excellent** & **Good** & **Accepted** \\ \hline motor cars & \(\leq\)2.75 & 2.75–3.10 & 3.10–3.45 \\ trailers car & \(\leq\)2.50 & 2.50–2.75 & 2.75–3.00 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Criteria of Sperling comfort index in HSR Code.  
Figure 13: Sperling comfort index of train.  
Value in Elastic System Dynamics. The long-term bridge creep, as a form of track irregularity excitation, is imported into the train-bridge coupling system. Finally, this complex system is solved by a self-designed program to analyze the dynamics index of the train and the bridge. The following conclusions are drawn:  
1. When long-span continuous beam bridge is completed, the main girders will have large deformation due to the shrinkage and creep of the concrete. After three years, the main beam's deflection growth rate gradually decreases with shrinkage creep development. For this bridge, the camber deformation reaches the maximum at ten years.
2. There is no significant effect of creep deformation on the dynamic responses of the bridge as a high-speed train passes through. The displacement and acceleration responses of key sections are below the limits of the design code under all work conditions. The results show that long-term creep deformation of the bridge has no significant effect on the stiffness of the bridge.
3. The creep deformation of the main girder also has no noticeable impact on the train running safety of high-speed trains. However, the criteria for train running safety, for example, the car body acceleration, derailment factor, Sperling comfort index and offload factor, have increased to a certain extent. Under the influence of long-term creep, the deformation will not cause significant problems to the safety of train operations. However, it also has an impact on the comfort of passengers traveling.  
Conceptualization, Funding acquisition and Investigation, H.L.; Conceptualization, Visualization and Writing--original draft, C.X.; Data curation and Formal analysis, X.G. ([PERSON]); Writing--review & editing, M.L.; Software, Methodology and Resources, X.G. ([PERSON]); Supervision, H.G. 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. 51408217) and The National Natural Science Foundation of Hunan Province (Grant No. 2021)30258, 2015 JJ3066).  
The study did not require ethical approval.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors declare no conflict of interest.