Discussion of “Hydrodynamic Loading on River Bridges” by Stefano Malavasi and Alberto Guadagnini

Abstract

The authors have made a very useful contribution to the understanding of hydrodynamic forces acting on submerged bridge decks approximated as rectangular cylinders. Based on their experimental findings and dimensional analysis, they provided relationships relating hydrodynamic loading coefficients to deckFroude number and geometric-similarity parameters. In particular, an explicit form of the functional relationship between these parameters and the overall drag coefficient was developed from linear-momentum conservation considerations. This discussion is intended to supplement the authors’ contribution by a closer examination of the behavior of drag loading when the circular cylinders interact with the free surface. As pointed out by the authors, results obtained for circular cylinders are not directly applicable to rectangular bridge decks. Nevertheless, the following analysis is useful in that it reveals the intrinsic wave-origin of that interaction, and highlights an alternate hydrodynamic path for arriving at the same parametric relationship developed by the authors. A horizontal cylinder positioned beneath a free surface creates differences in the water-surface level around the body resulting in the formation of standing surface deformations. Lamb ~1945! presented the first analysis of this phenomenon for the case of a two-dimensional, circular, stationary cylinder beneath the free surface of a steady, uniform, potential flow. He assumed the existence of an irrotational ~potential! flow around a circular cylinder with diameter D,z, where z is the distance from the cylinder’s axis to the undisturbed free surface. The free-surface displacement hsx , t.0d about the undisturbed free surface, hsx ,0d=0, where x is the streamwise distance from the vertical passing through the cylinder’s axis and t is time, as developed by Lamb and normalized by the discusser, is given by