Slope threshold in rill flow resistance

Rills are small, steep sloping and ephemeral channels, shaped in soils, in which shallow flows move. Rill erosion strictly depends on hydraulic characteristics of the rill flow and for this reason flow discharge Q, rill width w, water depth h, mean flow velocity V, and friction factor are required to model the rill erosion process.

Erosive phenomena strictly depend on the attitude of the soil particles to be detached (detachability) and to be transported (transportability). These properties are affected by soil texture and influence the sediment load G to be transported by flow. The actual sediment load depends on the transport capacity T_c of the flow, which is the maximum amount of sediment, with given sizes and specific weight, that can be transported by a flow of known hydraulic characteristics.

According to Jiang et al. (2018) the hydraulic mechanisms of soil erosion for steep slopes are different from those for gentle slopes. Recent research on T_c equations exploring slopes steeper than 18% (Ali et al., 2013; Zhang et al., 2009; Wu et al., 2016) established that T_c relationships designed for gentle slopes (<18%) are unsuitable to be applied to steep slopes (17–47%). Also Peng et al. (2015) noticed that <<there has been little research concerning rill flow on steep slopes (e.g. slope gradients higher than 10°)>>. In other words, the slope of 18% could be used to distinguish between the “gentle slope” and the “steep slope” case for the recognized difference in hydraulic and sediment transport variables.

The applicability of a theoretical rill flow resistance equation, based on the integration of a power velocity distribution (Barenblatt, 1979; 1987), was tested using measurements carried out in mobile rills shaped on plots having different slopes (9, 14, 15, 18, 22, 24, 25 and 26%) and soil textures (clay fractions ranging from 32.7% to 73% and silt of 19.9% – 30.9%), and measurements available in literature (Jiang et al. (2018), Huang et al. (2020) and Yang et al. (2020)).

The Darcy-Weisbach friction factor resulted dependent on slope, Froude number, Reynolds number and CLAY and SILT percentages, which represent soil transportability and detachability, respectively. This theoretical approach was applied to two different databases distinguished by the slope threshold of 18%. The results showed that, for gentle slopes (< 18%), the Darcy-Weisbach friction factor increases with slope, CLAY and SILT content. Taking into account that for gentle slopes the hydraulic characteristics limit the transport capacity, for this condition T_c and the sediment load G are both limiting factors.

For steep slopes (> 18%), the flow resistance increases with slope and the ratio between SILT and CLAY percentage. Steep slopes determine high values of the transport capacity, which is consequently not a limiting factor. Thus, in this condition the actual sediment load is determined exclusively by the ratio between SILT and CLAY percentage. In other words, the only limiting factor for a steep slope condition is the sediment which can be transported (i.e. the sediment load G), affected by its soil detachability and transportability.