Numerical Simulations of Ice Interaction with a Moored Structure
Authors: Sayed Mohamed , Barker Anne 
Published: December 2011

Abstract
The paper describes a numerical model of floating ice interaction with a moored structure. The model is based on solving the equations for conservation of mass and momentum together with the constitutive equations for the ice cover, as well as the equations of motion of the moored structure. The ice cover is considered to follow a cohesive Mohr-Coulomb yield criterion with a tension cut-off. The structure is treated as a rigid body supported by a linear spring that can move in the horizontal plane. Vertical movements are neglected. A depth averaged version of the ice model is used, whereby stresses and velocities are averaged over the depth. The model accounts for variations of ice thickness and clearing around the structure, but not clearing under the structure.
The simulations addressed cases resembling conditions of the Kulluk deployment in the Beaufort Sea during the 1980s. The data of the Kulluk was examined in order to determine the stiffness of the mooring system. Simulations produced distributions of ice concentration, thickness and pressures, and forces on the structure, as well as the resulting velocities and displacements of the structure. The resulting forces increased with increasing ice thickness and with increasing ice velocity. The predicted forces show good agreement with measured peak forces.
The role of the mooring stiffness was also examined. The mooring system causes a moderate reduction of forces below those obtained for a fixed structure. A relatively low stiffness was shown to reduce the transient forces. The forces eventually rise to approach those for stiffer mooring as ice continues to impinge on the structure.

Introduction
The performance of moored drilling ships in ice is of significant current interest. Safe and efficient operation of such vessels requires reliable knowledge of the magnitude of ice forces, and the resulting displacements. However, the interaction between a moored vessel/structure and ice remains poorly understood. Predicting ice forces, even on fixed structures, involves many complexities and uncertainties. The mooring system introduces more substantial complexties and uncertainties.
Field observations, though, are available from the deployment of the moored Kulluk structure at a number of sites in the Beaufort Sea during the 1980s. Wright (1999) gave a comprehensive analysis of the available Kulluk data and experience learned during its deployment. He provides the best available information on the behavior of moored structures in ice. The report of Wright (1999) includes estimates of the forces and the corresponding ice and environmental conditions. Ice basin tests of the dynamic hehavior of the Kulluk were also carried out by Matsuishi and Ettema (1985), and by Nixon and Ettema (1988). Comfort et al (1999) reviewed those studies along with other ice basin tests of moored structures. That review indicates that the ice basin tests give some insights into the manner in which compliance of the structure (or mooring system) may affect ice forces. There are many issues with scaling and interpretation, and even conflicting measurements that make it difficult to develop predictive tools that can apply to new structures or to full scale conditions.
The renewed interest in the subject prompted several recent investigations. Asknes et al (2008) and Bonnemaire et al (2008) carried out ice basin tests of moored structures. Asknes also developed a semi-empirical method (2010a) and (2010b) based on the ice basin results. That method can be incorporated in probabilistic models. Asknes also developed a one dimensional model based on an idealized ice failure scenario. These recent models and tests provide insight into the role that the mooring system plays in ice-vessel interaction. For example, it is evident that a soft mooring system is likely to reduce ice forces. The drawback in that case is the relatively large displacements of the structure.