Lateral dynamic response of a vertical pile under ice impact: linking ice fragmentation, pile-soil interaction and displacement demand

Vertical piles in ice-prone waters may experience short-duration dynamic demand when drifting level ice crushes and fragments against the pile surface. This study investigates the dynamic response of a single vertical pile by using a coupled cohesive-element/finite-element framework that resolves ice fragmentation, pile deformation and seabed restraint within the same explicit analysis. The model is validated against the Norströmsgrund lighthouse benchmark and then applied to a vertical pile subjected to head-on ice impact. The baseline response shows localized ice fragmentation, a single-peak pile-head displacement history and a critical bending region below the mudline. Parametric analyses demonstrate that cantilever length mainly amplifies post-peak vibration, pile diameter controls lateral deformation resistance, and load application height governs the bending-moment distribution. An ice element damage ratio is introduced to quantify the local fracture state and is shown to correlate positively with maximum pile-head displacement across 180 orthogonal numerical cases. A simplified regression equation is calibrated for preliminary estimation of the maximum pile-head displacement, achieving R² = 0.981 within the investigated medium-long and elastic-long pile cases. The results provide a mechanism-based interpretation of how ice fragmentation translates into displacement demand for vertical pile structures in cold marine environments.