Long-term extreme response analysis of cable-supported bridges with floating pylons subjected to wind and wave loads
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A suspension bridge with floating pylons is a possible solution to cross a fjord with a large width and great depth. This new concept is a combination of a slender suspension bridge and tension-leg platforms supporting the pylons. Very limited information is available for the design of such a new bridge concept. To contribute to a better understanding of the wind and wave resistance ability of the bridge, this research work aims at investigating the following features: (1) the stochastic dynamic behavior of the bridge under combined wind and wave actions, and (2) the extreme wind- and wave-induced load effects over a long-term period. Considering that slender structures are susceptible to wind- or wave-induced vibrations, geometrical nonlinearities and nonlinear wind and wave actions can be very important. Therefore, a state-of-the-art state-space time-domain method is applied. The research first addresses the wind actions, and thus, the single-span suspension bridge, Hardanger Bridge, is used for the case study. The flutter stability limit and buffeting response of the structure obtained using the time-domain method are compared with those obtained using the power spectral density frequency-domain method. The results are found to correspond very well when nonlinear effects are not considered. Thereafter, the time-domain method is generalized by including wave actions and then applied to the suspension bridge with floating pylons. This method is again first validated by comparing with a power spectral density approach using a linear analysis. Meanwhile, the nonlinear effects analysis shows that geometric nonlinearities and the second-order wave force have only a minimal influence on the particular bridge being considered. However, the one parameter Pierson-Moskowitz spectrum has been applied in this study, and the influence of the second-order wave loads should be further investigated considering several wave height and peak period combinations. Another important topic investigated is the long-term extreme load effects. It is discovered that the nonlinearities constitute a difference of approximately 20% in the extreme values of the bending moment due to vertical deformation at the most important position along the girder in the specific case that was considered. This means that time-domain simulations, which require substantial computational effort, have to be performed for the prediction of extreme responses. A simplified full long-term method, environmental contour method and inverse first-order reliability method are three of the computationally efficient alternatives to the full long-term method. The accuracy of the three approximate methods is validated by the full long-term method based on the response statistics obtained by frequency-domain simulations. Considering that the simplified full long-term method is still quite time-consuming and that the environmental contour method requires an empirically determined correction factor or percentile to compensate for the inaccuracy induced by disregarding the uncertainties of the short-term extreme response values, the inverse first-order reliability method is selected as the first choice in these case studies. It is noticed that most of the iterations in the inverse first-order reliability method are concentrated in a small area. The iterations are proposed to be performed based on the combined frequency- and time-domain simulation results. The time-domain simulation results are only used in the small area where the several last iterations are concentrated, while the frequency-domain results are used outside of this area. Consequently, the inverse first-order reliability method becomes more computationally efficient. Attracted by the computational efficiency of machine learning approaches in the application of reliability analysis, we investigated the feasibility of such novel methods in the prediction of long-term extreme wind- and wave-induced load effects. By using the simulation results under a small number of environmental conditions as the training data, the approximated limit state function matches very well with the exact one. Monte-Carlo simulation is then connected with the trained artificial neural network and support vector machine to calculate the cumulative distribution function of the extreme load effects over a long-term period. The accuracy and efficiency of this method are proven to have better performance than the first- and second-order reliability methods in the case studies of Hardanger Bridge under wind actions and the suspension bridge with floating pylons under combined wind and wave actions.