Moving load in an ice channel with a crack

Abstract

The effect of a crack in the ice cover of a channel on strains and deflections of the ice sheet, which are caused by a load moving along the channel, is investigated. The crack is at the center of the channel. The problem is symmetric with a load moving along the crack at constant speed. The problem is formulated within the linear hydroelastic theory. The fluid in the channel is inviscid and incompressible and its motion is potential. The ice sheets are modeled as viscoelastic thin plates clamped to the walls of the channel. The coupled hydroelastic problem is solved by using the Fourier transform along the channel and the normal mode method across the channel. The effects of the load speeds, depth of the channel, ice thickness and characteristics of the load on the hydroelastic response of the ice sheet are investigated. It is shown that the deflections and strains in the ice sheet strongly depend on the speed of the load with respect to the critical speeds of the hydroelastic waves propagating along the channel. The maximum ice deflection occurs at the critical speed of long waves for relatively large values of the retardation time of ice, and at the critical speed of the lowest hydroelastic wave with minimum phase speed for small retardation time of ice. The strain along the center plane of the channel peaks at the critical speed of long waves for ice sheet without a crack. However, it peaks near the critical speed of the lowest hydroelastic wave with minimum phase speed for ice sheet with a crack. The moving load causes larger strains in the ice cover if the load is elongated along the channel for a given total load and load length. The moving load causes smaller strains in the ice cover if the load is elongated along the channel for a given total load and load width.