Sloping-sided structures have been used in ice-infested waters to reduce ice loads by inducing flexural failure in the incoming level ice, which can be a fraction of the crushing load of the same level ice on vertical walls [1]. Croasdale’s model [2] has been widely used to predict this type of ice loading, which compares well with available field data, such as that measured at the Confederation Bridge [3]. In Croasdale’s formulation, the problem is idealized as a semi-infinite beam on an elastic foundation and neglects the effects of second-order bending and the edge moment arising from eccentricity of axial loadings, i.e. the distance between the point of ice-structure contact and the centroidal axis of the beam. For thin ice, the edge moment effect is indeed negligible due to the small moment arm. However, the edge moment influence on the structural load increases with the ice thickness, as reported in [4]. This suggests that Croasdale’s model may be inadequate for ice thickness beyond a certain threshold. In this paper, we focus on the plane breaking load of thick ice, taking into account the second order bending of the beam as well as the edge moment effect. We also account for the local crushing of level ice that comes into contact with the sloping structure, which creates a surface parallel to the slope prior to the bending failure of ice sheet. This local crushing is assumed to occur until a sufficient surface area is created to provide the bearing capacity required to induce bending failure in the beam. As a result, the eccentricity of axial loading is reduced, lowering the effects of the edge moment and consequently, the predicted load. Taking the above effects into account, the governing equation and the corresponding deflection equation of the refined model are reformulated, and the system of non-linear equations solved with numerically with the Newton-Raphson method. Additionally, the competition between different failure modes, i.e. flexural, crushing and shear, of a level ice encountering a sloping structure is briefly investigated. It is shown that flexural failure remains the dominant mode of failure even for thick ice, for various practical slope angles, ice material properties and ice-structure contact properties.
Numerical Simulation of a Polar Ship Moving in Level Ice Based on a One-Way Coupling Method