Discrete-element modelling of ship interaction with unconsolidated ice ridges: ridge resistance and failure behaviour

Abstract

Safe and efficient shipping in ice-covered waters requires the consideration of multiple sea ice features. Ice ridges can significantly increase the resistance of a ship; understanding this resistance requires knowing the failure mechanism of ice ridges. Traditionally, this failure mechanism has been studied using analogies to soil mechanics. This thesis provides a new approach to studying ice ridge resistance using a three-dimensional discrete element method to calculate the kinetic responses of an unconsolidated ice ridge interacting with a ship. The proposed approach is used to analyse the effect of ice ridge dimensions (width and depth) and ship hull form on ridge resistance and ridge failure behaviour. The analysis indicates that ridge width plays an essential role in ridge resistance—the peak resistance increases with ridge width until the width is of the same order as the ship's length. The analysis further indicates that, for wide ridges, peak ridge resistance increases exponentially with ridge depth following a power-law function with an exponent of 1.5. With regard to hull form, the analysis indicates that the peak ridge resistance and the work needed to penetrate a ridge increase linearly with any of the three main bow angles (waterline angle, stem angle and flare angle). This finding is obtained using a simplified wedge-shaped bow model, which has been shown to yield results similar to those using a realistic reference ship model. A ship-ice ridge interaction is a dynamic ridge failure process involving irreversible ridge deformation. The deformed domain is defined by ice blocks accelerated by and moving with the ship. The deformation force, as part of the ridge resistance, is found to relate to the mass of ice blocks in the deformed domain. The ice ridge failure behaviour at local scale is described by the kinetic responses of individual ice blocks within the deformed domain. The velocity field of the rubble shows that fast-moving ice blocks are in the near-bow field and stationary ice blocks at the far end of the ridge until the entire ridge fails to sustain the ship's penetration. No well-defined shear plane could be observed. Loads within the ice rubble are transmitted through force chains, which develop with the ship's penetration and form into an arch-like pattern normal to the bow. In addition, the ice ridge failure behaviour at large scale is analysed by the average stress and strain state of the ridge in the deformed domain. The ratio of horizontal to vertical normal stresses is less than half the value often used in previous analytical models based on Rankine theory and appears to be related to the ridge width.