Extreme responses and associated uncertainties for a long end-anchored floating bridge

Abstract

Very-long floating bridges represent an innovative marine structure for crossing wide and deep fjords. During the design of a floating bridge, extreme structural responses at a specified probability of exceedance are required to be properly evaluated for ultimate limit state (ULS) design check. This study addresses the estimation of extreme structural responses due to wind and wave loads and associated uncertainties. An end-anchored floating bridge, about 4600 m, is considered in a case study. The long-term extreme responses are estimated by using a simplified engineering approach, in which the long-term extreme response is approximated by the one-hour short-term extreme responses at a high fractile (90% in this study) for selected short-term sea states. The extreme responses are expressed as μ+κ·σ, where μ and σ are the ensemble mean and standard deviation, and κ is a multiplying factor. Statistical analyses indicate that the structural responses, including axial force, strong and weak axis bending moments of the bridge girder, are close to follow a Gaussian distribution. A simplified analytical method, the Gumbel method and the mean upcrossing rate (MUR) method are employed to estimate the multiplying factor κ and extremes. The κ estimated by these three methods are generally close, varying in the vicinity of 4. The κ and extremes estimated by the simplified method have a much smaller variation than the Gumbel and MUR methods. Statistical uncertainties and model uncertainties in the extreme value prediction are also addressed. Based on the results of 10 sets of 10 1-h ensembles, the mean and coefficient of variation (CoV) of μ,κ,σ and extremes of structural responses of 10 1-h simulations under two selected sea states are evaluated. The CoV of σ is less than 0.045, but the CoV of κ is relatively large, mainly between 3.5×10-2 and 6.5×10-2. The CoV of extremes estimated by the simplified analytical method is fairly small, less than 0.035. While the CoV of extremes estimated by the Gumbel and MUR methods are much larger and can reach 0.137 and 0.158, respectively. In practical design of floating bridge, only a limited number of simulations (e.g. 10 1-h) are conducted to predict the extreme structural responses. This will introduce statistical uncertainties and should be corrected by a factor for a conservative estimate. A simplified procedure to derive the correction factor is presented in this study. For the floating bridge considered with 10 1-h simulations, the correction factor is recommended to be 1.1 when the absolute value of mean μ is smaller than σ, and be 1.2 when the absolute value of mean μ is larger than σ, in order to achieve a 90% conservative estimation of extreme.