Effects of Boulder Arrangement on Flow Resistance Due to Macro-Scale Bed Roughness

Abstract

Flow resistance in gravel-bed channels is not only affected by the shape and size of the roughness elements, but also by their arrangement on the channel bed surface (position to flow streamlines, spacing between elements, and their protrusion from the channel bed). Many investigations proved that open channel flow resistance can be obtained by integrating the power velocity profile. For a macro-scale roughness condition, this study aims to investigate the effect of different boulder arrangements on flow resistance. First, for each arrangement, the equation relating Γ function of the power velocity profile, the Froude number, and the channel slope was calibrated using available measurements performed in a flume covered by pebbles with “Random”, “Transversal stripe”, and “Longitudinal stripe” arrangements. For each arrangement, the experimental datasets were divided to consider the effects of boulder concentration Ch. Moreover, the relationship obtained for the “Random” arrangement and element concentration lower than 48% was tested using literature measurements performed in a flume covered by coarse elements randomly arranged. Finally, the effects of the different boulder arrangements on the flow resistance law were investigated by imposing a concentration threshold. The results demonstrated that (i) the Darcy–Weisbach friction factor can be accurately estimated by the proposed flow resistance equation, (ii) the flow resistance increases with Ch for low values (<48%) of concentration, while it does not depend on Ch for high concentrations (≥48%), and (iii) the effect of the boulder arrangement on flow resistance law is more evident for low element concentrations.