Extreme ice forces on offshore structures appear to be proportional to the square root of the projected contact area. An analogy in indentation of brittle foam suggests a simple theory, which explains the size effect in ice through non-simultaneous failure.
Offshore production structures in the Arctic will have to be able to resist large forces from moving ice. It is not hard to make a rough estimate of how large the forces might be. Imagine a 20 km square ice mass 2 m thick, with a 65 knot wind blowing across it, lodged against a production island 150 m across. The wind force on the ice is about 1700 MN (170,000 tonnes). An idea of the "strength" of the Ice can be got by crushing a sample cube in compression it will turn out to be about 5 Mn/m2, somewhat less if the ice is warm (only just below freezing point) or highly saline. Tie estimated maximum force that can applied to the island before the ice begins to crush is t en 1500 MN (150,000 tonnes), given by the projected contact area multiplied by the strength. In that, instance, the wind driving force is greater than the crushing force, and so it is the crushing force that determines the maximum force that can be applied to the island. In other instances, though, the driving force is the limiting factor (Croasdale(l)).
This simple calculation can be criticised in many ways, and is almost certainly incorrect, but indicates the seriousness of the problem. However, it is also important not to exaggerate the forces involved: 1500 MN is the same order of magnitude as the design wave force on a typical offshore platform, and that can be designed for routinely. Only larger ice features (such as pressure ridge sand icebergs) raise the ice forces by an order of magnitude, to 15,000 MN, and introduce much more severe design problems.
Research into the prediction of horizontal ice forces on structures has generally adopted a slightly more sophisticated version of the simple calculation outlined above. One complication is that the measured compressive strength of ice depends on how fast it is loaded. This is a consequence of creep, and indeed the concept of "strength" has no meaning in the creep range : the ice simply creeps to keep up with the strain rate a plied by the testing machine. The product of the strength and the area is multiplied by an indentation factor, which in most applications is close to 1. The effect of creep can be accounted for by reference stress theory (2, 3).
There is an increasing amount of new evidence that the received theory outlined above is seriously incomplete, and that it may overpredict ice forces on production structures, perhaps by as much as a factor of 10. One source of evidence is full-scale measurements. Hans Island is a small island in Kennedy Channels between Greenland and Ellesmere Island.