A Modified Matlock–Duffing Model for Two-Dimensional Ice-Induced Vibrations of Offshore Structures With Geometric Nonlinearities

Oil and gas exploration and production have been expanding in Arctic waters. However, numerical models for predicting the ice-induced vibrations (IIV) of offshore structures are still lacking in the literature. This study aims to develop a mathematical reduced-order model for predicting the two-dimensional IIV of offshore structures with geometric coupling and nonlinearities. A cylindrical structure subject to a moving uniform ice sheet is analyzed using the well-known Matlock model, which, in the present study, is extended and modified to account for a new empirical nonlinear stress–strain rate relationship determining the maximum compressive stress (MCS) of the ice. The model is further developed through the incorporation of ice temperature, brine content, air volume, grain size, ice thickness, and ice wedge angle effects on the ice compressive strength. These allow the effect of multiple ice properties on the ice–structure interaction to be investigated. A further advancement is the inclusion of an equation allowing the length of failed ice at a point of failure to vary with time. A mixture of existing equations and newly proposed empirical relationships is used. Structural geometric nonlinearities are incorporated into the numerical model through the use of Duffing oscillators, a technique previously proposed in vortex-induced vibration studies. The model is validated against results from the literature and provides new insights into IIV responses including the quasi-static, randomlike chaotic, and locked-in motions, depending on the ice velocity and system nonlinearities. This numerical Matlock–Duffing model shows a potential to be used in future IIV analysis of Arctic cylindrical structures, particularly fixed offshore structures, such as lighthouses, gravity bases, and wind turbine monopiles.