Towards unified scaling relationships for gravel-bed and sand-bed rivers

Laboratory flume experiments and field investigations demonstrated the existence of dynamic equilibrium conditions for river channels, according to the hydraulic (flow discharge, water depth) and morphological (bed slope, grain size distribution, cross-section width) characteristics of the channel itself. In the literature, many authors have attempted to find scaling relationships among these quantities based on the different sediment transport mechanisms (i.e., bed load and suspended load) and the threshold for motion of the mean grain size. Recently, authors have proposed to account for an increment of such a threshold when dealing with sand-bed rivers, ultimately suggesting a minimum value (on the order of 5 N m⁻²) for the critical bed shear stress. In this work, we build on this hypothesis and derive scaling relationships for the bed slope, channel width, and water depth of equilibrium channels in bankfull conditions by including the effects of multiple grain sizes of sediment. After calibration, the minimum bed shear stress for sediment motion results in being approximately 70% smaller than the suggested value. Lastly, the validation against two large datasets outperforms the regression statistics of similar relationships available in the literature. As a result, the proposed 1D framework represents an attempt to find universal relationships among the hydro-morphological variables governing the bankfull equilibrium of both gravel- and sand-bed channels.