Impact force-damage depth model for ship-bridge collision

The impact force-damage depth model, i.e., P-a model, provides a feasible approach to design and evaluate bridge resistance under ship collisions, which is inadequately addressed in the existing specifications and literature. In the present study, based on an 18500 DWT (deadweight tonnage) bulbous bow bulk carrier and the main tower of cable-stayed bridges, the P-a model for shipbridge collision is established with consideration of pile cap, bridge pylon and striking ship. Firstly, the refined finite element (FE) model of prototype ship was established with detailed modeling of both the main and stiffening components. The material model parameters and FE analysis approach were validated through the existing tensile tests on marine steel coupons and crush tests on ship bow specimens. It is found that the modeling of stiffening components has rationality in predicting the impact force and asymmetrical folding collapse of ship bow. Then, concerning two collision scenarios with the main tower of cable-stayed bridges, i.e., only bulbous bow-pile cap collision and sequential bulbous bow-pile cap and bow overhang-bridge pylon collisions, the influences of nine critical parameters from pile cap (height, curvature and water level), bridge pylon (width, curvature, angle and bow overhang-bridge pylon distance) and striking ship (mass and velocity) on the impact forces and failure patterns of ship bow were comprehensively discussed. It indicates that: (i) the larger impact forces of bulbous bow and bow overhang appear with increased pile cap height, decreased bridge pylon curvature and inward inclined pylon angle; (ii) the loading paths of P-a relationships are approximately identical with different striking ship masses and velocities. Finally, the P-a model for ship-bridge collision was established by response surface methodology, and the corresponding calculation procedure was further given and validated.