Estimating Long Term Extreme Slamming From Breaking Waves

Abstract

Characteristic loads for design are defined in terms of their annual exceedance probability, q. For ultimate limit state (ULS) q = 10−2, while q = 10−4 for accidental limit state (ALS). In principle a full long term analysis is required in order to obtain consistent estimates. This is straight forward for linear response problems, while it is a challenge for non-linear problems in particular if they additionally are of an on-off nature. The latter will typically be the case for loads due to breaking wave impacts. The Contour line approach is an alternative convenient method to estimate the long term extreme response, based on short term statistics from an appropriate sea state. The consequence of very large short term variability (large coefficient of variation for 3-hour extreme value) on the application of the contour method will be discussed. The long term integral is carried out over all sea state combinations. The lowest sea states will of course not affect the extremes. However, for the impact problem the short term variability is much larger than for most response cases. The coefficient of variation of the 3-hour maximum impact pressure is often between 0.5 and 1, while for a typical response process it is between 0.1 and 0.2. Due to the large variability, lower sea states than normal will contribute to the long term response. In this paper the irregularity of the response surface, and the uncertainties related to the number of seeds used in each sea state is looked into. The focus is on slamming loads from breaking waves, and some results from a model test are presented. The uncertainties in long term response from slamming loads are compared to a more common response process. The effect on the long term response when integrating over a reduced area of sea states in the scatter diagram is discussed.