PSI - Issue 61

Igor Gribanov et al. / Procedia Structural Integrity 61 (2024) 89–97

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I.Gribanov et al. / Structural Integrity Procedia 00 (2024) 000–000

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Fig. 9. Comparison of the waterfall crossing for floes of varying thickness. (a) 3 cm, (b) 10 cm, (c) 50 cm. Color indicates separate fragments.

Fig. 10. Simulation result of an ice sheet measuring 100 × 50 m that breaks up under the action of the waves. There are 847 fragments spread out by the wind, each fragment consisting of 650 elements on average.

with the experimental observations at the initial stages of fragmentation. The width of the formed strips is equal to approximately half of the wavelength, with the fractures initiating at the peaks of the waves.

4.3. Waterfall

This scenario is inspired by the naturally observed events that occur during spring ice breakup on rivers. Large floes break up into smaller fragments when crossing a waterfall or an artificial dam. When a floe reaches a waterfall, an initial crack is formed under a bending load at a certain distance away from the edge. The disconnected portion then crosses the waterfall, breaking up into several more fragments. The formation of such cracks is explained by the location of the maximal bending moment during the approach of the floe. For the laminar flows the main forces acting on the floes are drag and buoyancy. The water surface is modeled with a smoothstep function f s ( x ). The simulation is performed in the reference frame of the floe, and the evolution of the water level with time is described as L w ( x , t ) = − A w f s ( x − x f + v w t ) , where A w is the height of the waterfall, v w is the velocity of the stream, and x f is the initial position of the front. The vertical velocity of the water is inferred by taking the time derivative of the water level. The resulting quantity is used as the velocity of the medium in the damping term of the equation of motion (1). The buoyancy force is applied vertically per node. For this test, the stream velocity v w is set to 1m / s, the height of the waterfall A w is 10 cm, the span of the fall is one meter. The same rectangular floe is used for this test, measuring 20 × 5 m, and 10 cm thick. Compared with the naturally observed phenomenon, the suggested model lacks variability in ice strength and the loading along the y -axis, so it underestimates the level of fragmentation. However, it is interesting to compare the resulting fragmentation for di ff erent thickness parameters. As expected, thinner floes produce more fragments. In thicker floes, the bending moment’s distribution along the length is smoother, leading to fewer, more regular, fragments (Figure 9).

4.4. Landfast ice

The wave and wind loads can be combined to model the breakup of a large floe. The current example shows a floe measuring 100 × 50 m and 10 cm thick. The wave pattern consists of two waves oriented at 90 degrees to one another, with a wavelength of 4 m, and a propagation speed of 1 m / s. The waves’ amplitude gradually increases for five seconds, reaching the maximum of 12 cm, and then subsides for another five seconds. The amplitude at the bottom of the sheet is attenuated to match the scenario of landfast ice. After the breakup completes, the wind force is applied