Planar multi-body model of iceberg free drift and towing in broken ice

There are no full-scale data on iceberg towing in ice. However, there is a great interest in such an operation. Simulating the interaction between icebergs and surrounding ice floes during towing may help with choosing iceberg management strategies and design criteria for icebreakers and tug vessels. Broken ice has a discontinuous nature; therefore, it is proposed to model the interaction using a discrete element method (DEM) and known approximations of wind and water drag, wave, and Coriolis forces. The DEM is used to simulate the contacts between rigid, polygon-shaped ice floes. The floes are prevented from interpenetration by applying contact impulses tending to separate the bodies. Depending on the relative velocity of the contacting bodies, the contacts can be classified into two categories: collisions at non-zero relative velocity and resting contacts where the contacting bodies have the same velocity. Converting the calculated impulses into contact forces is straightforward for resting contacts but not for collisions. First, the applied impulses for collisions depend on the choice of restitution coefficient. Second, the collision duration must be estimated in order to convert collision impulses into forces. This paper discusses the choice of the restitution coefficient for ice and proposes an approach to estimate the collision force using the collision duration, which appears to be roughly proportional to the square root of the reduced mass. Additionally, the paper presents an innovative method to generate the ice field through which the iceberg is towed. The field is represented by a domain filled with randomly shaped rigid ice floes. The algorithm is capable of creating an ice field of given concentration and size distribution of the ice floes. The power law size distribution, obtained from aerial and satellite image analysis, is reproduced with high accuracy. The new approach to estimate the collision forces is subjected to a simple test on isolated floe impacts showing a good agreement with experimental and full-scale data. Finally, the simulation of iceberg towing is demonstrated and compared to experimental data. The results of the simulation were found to be in satisfactory agreement with the experiment.