# Flutter Reliability Analysis of Xiangshan Harbor Highway Cable-Stayed Bridges in Service
## 5 Conclusions  
In this research, the Xiangshan Harbor cable-stayed bridge in Ningbo, China was taken as the background, and the flutter instability wind speed was solved by using the finite element model established by ANSYS and the computational fluent dynamic model by FLUENT. Meanwhile, the influence of parameters was analyzed, and the flutter reliability calculation was carried out to obtain the reliability index and failure probability of the flutter of Xiangshan Harbor Bridge. The following conclusions can be drawn:  
(1) The flutter derivative of the bridge can be obtained based on CFD calculation, and the flutter derivative can be effectively time-domainized by combining the rational functions and impulse-response function. The flutter calculation of the cable-stayed bridge in time-domain is realized in Ansys Parametric Design Language (APDL), and the critical flutter wind speed of Xiangshan Harbor bridge at 0\({}^{\circ}\) wind attack angle is calculated, which is 64 m/s. (2) The influence of these four key parameters on the bridge flutter is researched, including the stiffness of main girder, the wire breaking rate, the damping ratio and the cable breakage location. The critical flutter wind speed of Xiangshan Harbor Bridge increases in an S-shape with the increase of main girder stiffness, and the increasing amplitude is slow in the early stage, fast in the middle stage and slow in the late stage. When the wire breaking rate of the cable is less than 10%, the change of the critical flutter wind speed of Xiangshan Harbor Bridge is small. Once the wire breaking rate exceeds 10% the critical flutter wind speed will decrease rapidly, so the cable should be replaced in time, according to the maintenance requirements. When the damping ratio changes from 0 to 1% the critical flutter wind speed increases from 50 m/s to 73 m/s, and the critical flutter wind speed increases faster than that of 0.5-1% during 0-0.5%. Three kinds of cable breakage positions are studied, and the cable breakage in mid-span position has a great influence on the bridge flutter, so special attention should be paid to the wind environment when replacing the stay cables of the bridge. (3) The Latin hypercube sampling method is used to carry out a flutter uncertainty analysis of the bridge considering the influence of parameter uncertainty, and on this basis, the design checking point method is used to calculate the flutter reliability analysis. The flutter reliability indexes of Xiangshan Harbor Bridge for these four parameters, under the most unfavorable conditions such the stiffness of main girder, wire breaking rate, damping ratio and cable breakage location are 2.28, 2.24, 1.96 and 2.08, respectively. (4) The flutter reliability analysis of the bridge for these four parameters in different cases shows that the reliability index is less than 2.2 and the failure probability is greater than 0.01 when the stiffness of main girder is less than 0.5 times initial stiffness of the bridge, the wire breaking rate of the bridge is greater than 20%, the damping ratio is less than 0.3% and the cable breakage location is in the mid-span of the bridge. Once these situations occur during the bridge operation, the corresponding methods should be taken to reduce the risk probability and improve the reliability of the bridge structure. Conceptualization, T.Z. ; Formal analysis, Y.Z. ; Software, X.C. and X.Z. ; Validation, X.Z. ; Writing--original draft, T.Z. ; Writing--review & editing, H.L. All authors have read and agreed to the published version of the manuscript. \begin{table}
\begin{tabular}{c c c c c} \hline Broken cable position & Random location & Bridge tower & Main span 1/4 & Bridge span midpoint \\ \hline Reliability index & 2.31 & 2.42 & 2.32 & 2.08 \\ \hline Failure probability & 0.0103 & 0.0077 & 0.0101 & 0.0189 \\ \hline \end{tabular}
\end{table} 
Table 14: Flutter failure probability corresponding to different cable breakage location.