Safety aspects of floating ice sheets under moving loads

Winter roads on frozen lakes are an important part of the transportation infrastructure in several Northern countries. Authorities follow various plans for opening and closing roads, maintaining safety by checking ice thickness and instructing drivers. Many of these plans are based on Gold’s formula which relates the thickness of the ice cover to the allowable load based largely on empirical observations of ice failure or non-failure under various loading conditions.

In the case of moving loads such as motorized vehicles, the speed of the load is an important factor in addition to ice strength considerations. Indeed, experience has shown that under certain conditions of speed, ice thickness and water depth, the deflection under a vehicle travelling on a floating ice sheet may be amplified considerably.

Indeed, it was shown in [1] that a decelerating load can lead to constructive interference of waves which could exceed the critical stress for crack formation. Ice roads are particularly treacherous near the shore as the critical speed gets smaller due to decreasing depth. In addition, due to existing blowouts, traffic may have to be rerouted to avoid broken ice. In the present contribution, we consider the waves created by a load moving in a circular path. Following [2], we show that curved paths may also lead to constructive interference which may be more severe than the waves created by a decelerating load.

[1] Dinvay, E., Kalisch, H. & Părău, E.I. Fully dispersive models for moving loads on ice sheets. J. Fluid Mech. 876, 122–149 (2019).

[2] Johnsen, K., Kalisch, H. and Părău, E.I. Ship wave patterns on floating ice sheets. Scientific Reports, 12, 1-10 (2022).