Background Soil erosion by water in red soil hilly region in tropical and subtropical zones of central China cause severe soil quality degradation and environmental issues. Soil erosion is primarily controlled by large volumes of surface runoff in this region due to abundant rainfall. Previous studies show that hydraulic characteristics are important in elucidating the mechanisms of erosion and sediment yield on slope. So far several laboratory and field experiments had conducted to understand the correlations between hydraulic parameters and soil erosion. However, most researches showed diversified results on those correlations due to various types of soils and different conditions in different experiments. The objectives of this study are to assess the difference in hydraulic parameters and sediment yield under red soil hilly-slope.

Methods In order to simulate the surface runoff erosion process, an indoor experiment, involving four slopes (5°, 8°, 10°, and 12°), three flow rates (5, 7.5, and 10 L/min) was carried out in a red soil flume (3-meter length and 0.5-meter wide). The bulk density and initial moisture for the soil sample was 1.35 g/cm³ and 30%, respectively. Experimental indices were measured by different approaches, the staining method was utilized to measure the flow velocity; the flow width was measured using a ruler at 3 positions; the sediment yield rate and discharge rate were deduced and calculated from the water bottle collected the runoff samples at the bottom of the flume during a set time interval. A single trial lasted 15 min. The hydraulic characteristics mainly used were Reynolds number (Re), Froude number (Fr), and other two different expressions of flow resistance Manning roughness coefficient (n) and Darcy-Weisbach friction (f).

Results 1) Water erosion of red soil slope presented obvious periodic development process. There was short time sheet flow at the beginning, and soon transformed to rill flow. The sheet flow regimes generally indicated in transitional-sub-critical zone, and rill flow regimes indicated in transitional-super-critical zone. The unit discharge, mean flow velocity, mean flow depth, Re and Fr of sheet flow were larger than those of rill flow, while the n and f exhibited inversely in a same period. 2) The n and f of the flow varies between 0.038-0.092 and 0.73-4.41, respectively. Both n and f showed a power function with Fr (R²=0.49; R²=0.52), and besides this, f also showed a power function with Re of transitional flow (R²=0.29). 4) A composition hydraulic parameter JRe, which was define as the product of Re and J (J was water surface slope), was an appropriate indicator for soil erosion. Sediment yield rate in the red soil slope could be estimated by JR_e with an exponential function in both sheet flow phase and rill flow phase (R²=0.93; R²=0.51).

Conclusions The results are conducive to the comprehensive understanding flow hydraulic characteristics and provide a reference for further studies on rill erosion in red soil hilly region.