River ice cover flexure by an incoming wave

A riverʹs ice cover can be broken up by unsteady flows that may result from a sudden increase in discharge resulting from a dam break event, an ice jam release event or a flash-flood. As the resulting wave (surge or ‘jave’) travels downstream, if it is not strong enough to break the cover, its amplitude and celerity will be dampened whereas if it is, they may be amplified. It is therefore important to know what rise in levels is required to break an intact ice sheet. In this paper, 1D and 2D numerical models are used to investigate the wave–ice cover interaction in order to formulate simple river ice sheet breakup criteria. The 1D model (based on the theory of beams on an elastic foundation) uses an iterative, in-house, finite difference method to converge on a solution that correctly models the limiting effect that the ice sheetʹs freeboard has on the imposed load. The analyses show the importance of non-linear ice sheet response to increasing wave amplitudes and/or water surface slopes as a function of ice sheet thickness. The paper also presents an analysis of water shear effects on axial and bending stresses. Lastly, a finite element method (FEM) is used to resolve the 2-D problem. For ice sheets frozen into or simply attached to the river banks, computed stresses are shown to be significantly different from the 1-D solution.