Efficient Modeling of Ship–Bridge Collisions: Simplified Bow Impact Force–Deformation Relationships

The impact force–deformation relationship of vessels is a critical aspect in the design of bridges against vessel collisions. This paper begins by reviewing existing research on barge impact force–indentation relationships. Using a 1,000 deadweight tonnage (DWT) ship and a 1,000 DWT barge as examples, the fundamental differences in impact force–deformation relationships between ships and barges were elucidated through numerical simulations, followed by a comparative analysis with existing barge impact models. Motivated by these comparisons, finite-element models of five ships ranging from 500 to 5,000 DWT were developed. Through numerical simulations of ship-rigid wall collisions, 45 samples of ship impact force–deformation relationships were obtained, leading to the proposal of a simplified power-function-based model for ships. During the model development process, a shock spectrum analysis method was employed to conduct parametric studies on the effects of curve shape and residual deformation on structural impact response, with recommended values for model parameters provided. To validate the computational accuracy and advantages of the proposed model, a comparative analysis was performed using a cable-stayed bridge and a continuous girder bridge, evaluating the solution accuracy of the proposed model against full ship–bridge collision models, equivalent ship impact forces, and the ship impact force time-history model. Finally, the applicability of the proposed methodology was assessed using the shock spectrum analysis method.