Evaluating the effects of soil grain roughness and rill cross-section shape on flow resistance

The knowledge of the hydraulic characteristics of rill flows is needed to improve the understanding and the accurate modelling of upland erosion processes. Flume investigations are developed to schematize conditions useful to analyze the influence of a unique variable significant for modelling rill hydraulics, while field investigations are used to simulate morphological and hydraulic conditions of natural cases. The main aim of this investigation is to compare flow resistance measurements carried out using a rectangular rill channel (flume data) and manually generated and naturally shaped rills (plot data) for the same soils and hydraulic conditions. The two data sets allowed for establishing how the soil grain roughness and rill cross-section shape affect flow resistance using a theoretical equation deduced by applying dimensional analysis and self-similarity theory. The analysis developed for a fixed-bed channel with a rectangular cross-section demonstrated that the influence of different soil roughness on the Darcy-Weisbach friction factor is approximately equal to ±1%, while for a rill with an irregular cross-section the same effect is almost equal to ±2%. Therefore, for an open-channel flow on a fixed bed, the effect of the grain size roughness on the friction factor is limited. For each examined soil, the investigation also demonstrated that the rill cross-section shape leads to a variability of the friction factor from −20% to +30%. This result highlights that, for a fixed-bed channel, the effect of the cross-section shape on the Darcy-Weisbach friction factor is much greater than that due to the soil grain size roughness. The main implication of this work is that the results deduced by laboratory measurements with regular cross-sections, thus neglecting a complex geometry, can be affected by relevant discrepancies from those obtained by the field measurements, which better simulate natural conditions.