Statistical Analysis of Ice Forces

Abstract

Statistics offer a method for quantifying unmanageable complexity. During impact of large ice masses with structures, a vast number of local failure events take place. These local failure events may themselves be straightforward to understand, at least in principle, but understanding of their gross effect is an exercise in statistics. Simple statistical models based on non-simultaneous failure of discrete independent zones provide a realistic picture of observed force histories at, for instance, Hans Island (1980, 1981 and 1983). This is illustrated by an example numerical simulation using constant sized failure zones and stochastic occurrence of events. The treatment can be further generalized using fractal geometries. These models of non-simultaneous failure provide a plausible explanation of the exceptionally low forces measured at Hans Island. Observations since 1986 on the Molikpaq structure, however, show strikingly regular periodic force records, indicating that local zone failure may be coherent rather than stochastic and independent. The regularity of these records appears to be associated with structural response characteristics, but it is likely that pulverised ice at the contact zone plays an essential role in enabling apparently simultaneous failure to be observed over a wide front. The forces observed during such failure at Molikpaq are, nonetheless, low, and conform to the broad trend evident froril the “pressure-area” diagram. Non-simultaneous failure may not be the appropriate explanation of the Molikpaq data, but the trend still apparently provides a basis for statistically based design load calculation.