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.

中文翻译：

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长端锚浮桥的极端响应和相关不确定性

摘要 超长浮桥是跨越宽阔峡湾的创新海洋结构。在浮桥设计过程中，需要正确评估特定超出概率的极端结构响应，以进行极限状态 (ULS) 设计检查。这项研究解决了由于风和波浪载荷以及相关不确定性引起的极端结构响应的估计。案例研究中考虑了一座约 4600 m 的端锚式浮桥。长期极端响应是通过使用简化的工程方法估计的，其中长期极端响应近似于选定的短期高分位数（本研究中为 90%）的一小时短期极端响应。术语海洋状态。极端响应表示为 μ + κ · σ ，其中 μ 和 σ 是整体均值和标准差，κ 是乘法因子。统计分析表明，桥梁的轴力、强弱轴弯矩等结构响应接近于高斯分布。一种简化的分析方法，Gumbel 方法和平均上交率 (MUR) 方法被用来估计乘法因子 κ 和极值。这三种方法估计的κ一般比较接近，在4附近变化。简化方法估计的κ和极值的变化比Gumbel和MUR方法小得多。还解决了极值预测中的统计不确定性和模型不确定性。基于 10 组 10 个 1-h 集合的结果，μ、κ、σ 和在两种选定海况下 10 次 1 小时模拟的结构响应的极端值进行了评估。σ 的 CoV 小于 0.045，但 κ 的 CoV 比较大，主要在 3.5 × 10 - 2 和 6.5 × 10 - 2 之间。通过简化分析方法估计的极端情况的 CoV 相当小，小于 0.035。而 Gumbel 和 MUR 方法估计的极端情况的 CoV 要大得多，分别可以达到 0.137 和 0.158。在浮桥的实际设计中，只进行了有限数量的模拟（例如 10 1-h）来预测极端结构响应。这将引入统计不确定性，并应通过保守估计的系数进行校正。本研究介绍了推导出校正因子的简化程序。对于用 10 个 1 小时模拟考虑的浮桥，