3-D Simulation of Iceberg Towing Operations: Cable Modeling and Frictional Contact Formulation Using Finite Element Analysis

Ice management in regions of offshore development with icebergs present includes re-direction of icebergs by means of towing. The prevention of tow-rope slippage and iceberg rolling due to hydrostatic instability are essential for an effective and safe operation. The ability to simulate any particular towing operation in the field, prior to attempting it, would provide some measure of assurance of its feasibility. In addition, such a model will allow optimization of towing configuration and application by showing optimal tow direction, maximum force and rate of force application; selection of single tow line or net; and optimum net configuration. The objective of the described work is to develop a simulation tool that can be used for such application. A previous project funded by Hibernia Management and Development Company Ltd. (HMDC) gathered 3-dimensional profile data on 29 icebergs off the East coast of Canada; and further data collection has been ongoing. The present project utilizes these profiles as valuable input in the development of the model for simulating single-line and net tows. This paper presents the first phase of development of a 3-D dynamic iceberg towing model that evolved from an earlier 2-D static version. The current iteration applies the ‘Total Lagrangian’ Finite-Element Method (FEM) to model the cable-and-rope structure between the towing vessel and iceberg, and a contact model that includes sticking and sliding friction between the rope/net and iceberg. The iceberg is modeled as a rigid surface mesh and is fully constrained against motion during the current phase of development, while the cables and ropes are modeled as elastic bar elements with translational inertia and velocity-squared fluid drag. The contact elements consist of penalty springs with proportional damping, and appropriate values of these are found to be critical for numerical stability of the solution. As well, due to the large difference in stiffness values between the heavy tow cable and buoyant ropes, special attention is given to obtaining the initial tangent stiffness matrix of the cable-and-rope structure. The FE dynamic equations of motion are solved implicitly in the time domain using a combination of full and modified Newton-Raphson iteration. Simulations of contact initiation between the rope and iceberg for single-loop and net configurations are presented, as well as slipping during particular single-loop tows. Current challenges and opportunities for further development are discussed, including improving computational speed, implementing iceberg motion, adding wind and wave forces, and validating rope-ice friction characteristics through small-scale iceberg towing response in a laboratory.