Size Effect on Strength of Floating Sea Ice under Vertical Line Load

The size effect on the nominal strength of a floating ice plate subjected to a vertical uniform line load is analyzed. The cracks produced by the load, which are parallel to the load line, are treated as softening inelastic hinges. The problem is one dimensional in the direction normal to the load line, equivalent to a beam on elastic foundation provided by buoyancy of ice in water. The softening moment-rotation diagram of inelastic hinges is simplified as linear and its dependence on structure size (ice thickness) is based on the energy dissipated by fracture. For thick enough plates, no two hinges (on one side of the line load) can soften simultaneously, in which case a simple analytical solution is possible. In that case, the load-deflection diagram has multiple peaks and troughs and consists of a sequence of spikes that get progressively sharper as the plate thickness increases. In terms of a dimensionless nominal strength, the effect of a finite fracture process zone at ice surface leads to an up-and-down size effect plot, such that each load peak decreases with the size at first but then asymptotically approaches a rising asymptote of the type $(\mathrm{thickness}{)}^{1/4}$ (which implies a reverse size effect, caused by buoyancy). The energy dissipation when the crack in the hinge gets deep causes a strong monotonic size effect, such that the dimensionless troughs between two spikes, in the case of thick enough plate, decrease asymptotically as $(\mathrm{thickness}{)}^{-1/2}\text{.}$ For thin enough plates, more than one hinge soften simultaneously and, in the asymptotic case of vanishing ice thickness, the plasticity solution, which has no size effect, is approached. In the intermediate size range with hinges softening simultaneously, the exact solution is complicated and only approximate formulas for the size effect are possible. They are constructed by asymptotic matching.