# Flutter Reliability Analysis of Xiangshan Harbor Highway Cable-Stayed Bridges in Service
###### Abstract  
With the development of bridge structures towards being light weight and having a large span, the overall flexibility, and, hence, wind sensitivity, of the bridge increases. Flutter is one of the pivotal factors considered in the design and operation stage for long-span cable-stayed bridges due to its devastating impact, often intrigued by relatively low instability caused by wind speed. This paper presents a reliability theory-based numerical analysis on bridge flutter stability and its influence law of key parameters using a real bridge, the Xiangshan Harbor highway cable-stayed bridge in China. The analysis starts with creating a full scale of finite element model for the bridge in service to calculate the flutter derivative and time-dominated combining rational function in order to obtain the critical-flutter wind speed, and then the aerodynamic self-excited forces on the bridge and flutter time-history response are calculated to identify the flutter critical wind speed. Further, the influence of key parameters for flutter reliability, including the stiffness of the main girder, wire breaking rate, damping ratio and cable breakage location are analyzed comprehensively to achieve the change law of critical flutter wind speed with these parameters. Considering the uncertainty of the actual parameters, these parameters are taken as random variables, and the reliability index and failure probability of bridge flutter are calculated according to their probability distribution and the Latin hypercube sampling method. On this basis, a few suggestions are put forward for flutter risk-control during the service of this cable-stayed bridge, which can further enhance the design theory for long-span flexible bridges. long-span cable-stayed bridge in service; flutter instability; parameter influence analysis; Latin hypercube sampling; flutter reliability +
Footnote †: journal: Applied Sciences  
[PERSON] [17; 18; 19] and [PERSON] [20] used the first-order second-moment reliability method to evaluate the flutter safety of long-span cable-stayed bridges. However, the flutter test wind speed and flutter critical wind speed were calculated by the Van der Put formula instead of by a wind tunnel test or finite element simulation. In addition, because of the limitations of the first-order second-moment method, the evaluation result is more conservative. [PERSON] [21], [PERSON] [22], [PERSON] [23; 24] and [PERSON] [25] analyzed the flutter reliability of long-span suspension bridges, but the flutter reliability of the bridges in their analyses was not comprehensive because only the probability distribution of flutter critical wind speed was considered, and the flutter reliability study on the Messina Bridge was conducted based on the modified FORM. At the same time, another general method for the probabilistic flutter analysis of bridges is the sampling method, such as the Monte Carlo simulation (MCS). [PERSON] and [PERSON] [12; 13] analyzed the single-mode torsional flutter reliability, containing the randomness of the flutter derivatives and critical wind speed by using MCS and FORM. [PERSON] [26] studied flutter reliability by MCS, considering the randomness of structural parameters and flutter derivatives. Similarly, [PERSON] [14] obtained the distribution type of flutter derivatives. Based on the sampling approach, a framework of the uncertainty quantification of bridge flutter is proposed. After these studies, some in-depth explorations have emerged for the flutter reliability analysis of long-span bridges, such as [PERSON] [27], who used the finite element reliability method to calculate the static wind reliability and flutter reliability for the Xihoumen Bridge. The research results show that the ignoring of the uncertainty of parameters may lead to the unsafe flutter reliability of bridge structures.