Since static analysis procedures in the vessel impact-resistant design codes neglect dynamic amplification effects related to bridge mass, ship-impact responses of bridges may be potentially underestimated. For this reason, several dynamic vessel-impact analysis techniques had been recently proposed, where a force-deformation curve was employed to model the vessel bow stiffness. Most of the recent works mainly focused on the force-deformation curves of the barge bows rather than the ship bows. In this paper, a high-resolution finite element model is developed to obtain the ship bow force-deformation curves. The global and local characteristics of the ship bow force-deformation curves are discussed based on the finite element crush analyses between the ship bows and the rigid walls. Effect of pile-cap depth on the force-deformation curves (rather than only impact forces) is studied in detail, and the corresponding empirical equations are developed using an energy ratio method. Finally, a practical example of ship-bridge collision is investigated to validate the force-deformation curves considering the effect of pile-cap depth. It is found from the case study that the effect of pile-cap depth plays an important role in quantifying structural demand under impact loads. The case study also indicates that the developed equations are reasonable in practical applications. 1. Introduction With the rapid growths in the numbers of merchant ships and bridges over navigable waterways, the frequency and severity of vessel-bridge collisions have markedly increased [1–3]. From 1951 to 2000 (over a 50-year period), 617 bridge failures in the United States were investigated by Harik et al. [4] and Wardhana and Hadipriono [5]. Out of the total reported failures, 29 (about 5%) bridge failures were due to vessel collision, which was one of the most likely causes. In China, one of the recent catastrophic accidents is the collapse of the Jiujiang Bridge over the Xijiang River. It was hit by a fully loaded cargo ship (about 2000 tons) in June 2007, resulting in the loss of nine lives and the collapse of 200-meter bridge deck. In March 2008, the Jintang Bridge connecting Jintang Island to Ningbo was struck by an empty bulk carrier (about 10,000？DWT), causing 4 fatalities and the collapse of a 60-meter span. Therefore, the need is evident for bridges crossing navigable waterways to minimize their vulnerability to damage from vessel collisions. Compared with well-established seismic and wind-resistant designs, vessel impact-resistant design of bridges is still in its infancy
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