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Difficulties are often encountered in estimating the bed shear stress in vegetated flows over a sediment bed due to complex interactions of the flow, sediment, and vegetation. Without involving any empirical partition of the bed friction and vegetation resistance, this study presents an analytical approach to evaluate the bed shear stress in the presence of vegetation in light of the phenomenological theory of turbulence. Then, the bed-load transport rate in vegetated flows is computed, with a result that agrees well with the bed-load transport formula developed for unvegetated flows. In addition, it is also shown that the present method is applicable not only to uniformly distributed vegetation but also to vegetation patches. However, further efforts are needed to extend the present model for flexible and submerged vegetation conditions.

By examining the variations in the dimensions of a horseshoe vortex system in front of a pier, the present study proposes a new length scale, called pier hydraulic radius, for the scaling of the maximum scour depth at a bridge pier. It is shown that, in comparison with other length scales, the pier hydraulic radius is more effective for quantifying combined effects of pier width and flow depth on the local scour for both low and high flow conditions. A theoretical formula is finally derived, which agrees well with experimental data reported in the literature.

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