Local pressures for ships in ice: Probabilistic analysis of full-scale line-load data

Abstract

Ships operating in ice might be exposed to significant ice loading. Using a probabilistic semi-empirical method known as the event-maximum method, the long-term maximum level of ice loading on a ship can be estimated based on parent distributions of short-term full-scale ice load measurements. The event-maximum method is used to model the relationship between extreme local ice pressures and impact area by estimating parameters corresponding to the inverse slope (α) and intercept (x0) for the line of best fit for the tail of ranked peak pressure data versus the natural logarithm of the Weibull plotting position. These best-fit lines are assumed to follow an exponential distribution and associated α and x0 values are produced for different local design areas. This allows for the determination of α-area curves, which reflects the relationship between ice pressure and the local design area. Previous studies have determined α-area curves for different geographical areas such as the Beaufort Sea and South Bering Sea, representing different ice types including both first-year and multi-year ice. In this study, two separate sets of full-scale ice load measurements having been considered, namely measurements from the Kara Sea and the Barents Sea, as well as measurements from the Antarctic Ocean. Using these two datasets, two new α-area curves have been generated that represent among other operating areas (the Kara Sea and the Barents Sea), operating modes (icebreaker assisted operation) and impact areas (aft shoulder) not covered by other curves. Earlier formulations of the event-maximum method are based on local design areas in which the width and height of areas are defined by the size of instrumented rectangular panel areas (or combinations of those areas) on the bow of the vessel from which the data were collected. In that approach, ice thickness is not directly considered since the height of individual panels is based on the dimensions of instrumented areas and moreover, detailed ice thickness records were not available for those data sets. In the present study, an alternative approach has been developed to extend the event maximum method for use with ship line-load data. In this approach ice pressures are calculated by dividing the ice force measured on frames by the corresponding line-load area (ALL), which is the product of the width (W) that is based on frame spacing and an assumed line-load height (H) corresponding to 30% of the maximum prevailing ice thickness, as per best design practice, along the lines of the Finnish-Swedish ice class rules. Data already presented as line-loads (in units of force per unit width), are converted to pressures by dividing line-loads by height H. The event definition used in the present approach is defined as the maximum pressure corresponding to 10- or 20-min intervals, as opposed to the impact event definition used in earlier works. In applying this extended method to develop new α-area curves, valuable insights into the relationship between local peak ice pressure and prevailing ice thickness have been gained for the above-mentioned full-scale measurements. The determined curves indicate a negative correlation between prevailing ice thickness and maximum local nominal ice pressure. Finally, it has been demonstrated that it is feasible to apply such curves in combination with the principle of the event-maximum method to estimate the maximum nominal ice pressure expected for a ship given a specified transit distance in sea ice with different prevailing thicknesses.