A sediment transport equation for interrill overland flow on rough surfaces

A model for predicting the sediment transport capacity of turbulent interrill flow on rough surfaces is developed from 1295 flume experiments with flow depths ranging from 3-4 to 43·4 mm, flow velocities from 0·09 to 0·65 m s^-1, Reynolds numbers from 5000 to 26949, Froude numbers from 0·23 to 2·93, bed slopes from 2·7° to 10°, sediment diameters from 0·098 to 1·16 mm, volumetric sediment concentrations from 0·002 to 0·304, roughness concentrations from 0 to 0·57, roughness diameters from 1·0 to 91·3 mm, rainfall intensities from 0 to 159 mm h^-1, flow densities from 1002 to 1501 kg m^-3, and flow kinematic viscosities from 0·913 to 2·556 × 10^-6 m² s^-1. Stones, cylinders and miniature ornamental trees are used as roughness elements. Given the diverse shapes, sizes and concentrations of these elements, the transport model is likely to apply to a wide range of ground surface morphologies. Using dimensional analysis, a total-load transport equation is developed for open-channel flows, and this equation is shown to apply to interrill flows both with and without rainfall. The equation indicates that the dimensionless sediment transport rate ø is a function of, and therefore can be predicted by, the dimensionless shear stress χ, its critical value χ_c, the resistance coefficient u/u*, the inertial settling velocity of the sediment w_i, the roughness concentration C_r, and the roughness diameter D_r. The model has the form ø = aθ^1·5 (1 - θ_c - θ)^3·4 (u - u*)^c (wi - u *)^-0·5 where log a = -0·42 C_r/D⁰·20_r and c = 1 + 0·42 C_r/D⁰·20_r. Testing reveals that the model gives good unbiased predictions of ø in flows with sediment concentrations less than 0·20. Flows with higher concentrations appear to be hyperconcentrated and to have sediment transport rates higher than those predicted by the model.