Effect of moving load due to irregularity in ice sheet floating on water

Abstract

The present paper is concerned with the stresses produced due to a load moving on the irregular surface of an ice sheet floating on water. The irregularity of the ice medium is of parabolic type, and a rectangular irregularity has also been considered as a special case. The mathematical formulation of this physical problem gives rise to a boundary value problem with the specified boundary conditions. The perturbation method is applied to find the displacement field. Closed-form expressions of the normal and shear stresses developed in the ice medium and semi-infinite water medium due to moving load and irregularity have been derived using the boundary conditions. The variations of dimensionless normal and shear stresses with different depth below the surface are computed for a realistic numerical model and discussed. The same numerical data are used for surface plots to analyze the combined variation of non-dimensional stresses and velocity ratio against depth. From the outcome of the numerical study, the normal and shear stresses developed in both the ice and water media are found to be very sensitive to the changes in frictional coefficient, dimensionless wave number and irregularity factor present in the medium.