Erosion depth and concentration profile formulae for graded sediment transport in asymmetric oscillatory sheet flow

The transport of graded sediments is much more complex and universal compared with that of uniform sedi-ments. This paper proposes formulae of erosion depth and concentration profile for graded sediments in asymmetric oscillatory sheet flow. The erosion depth is obtained by taking the summation of each size fraction whilst considering the phase residual, phase shift and acceleration modification. The erosion depth includes a hiding-exposure factor of exposure height and a phase shift correction of gradation, which represent the selective transport (promotion or inhibition) of graded sediments. The sediment concentration for each size fraction is proposed using the idealised exponential or power function, which is based on erosion depth considering mass conservation. The upper sheet flow boundary and sheet flow layer thickness are further identified from the erosion depth and concentration profile. Experimental data for validation are recalculated by an improved method that considers mass conservation and actual stationary bed. The proposed formulae demonstrate a better performance in predicting the erosion depth and concentration profile of graded sediments compared with previous uniform and graded sediment formulae. The proposed formulae are able to identify the selective transport and grade recombination on mobile sediment bed. The hiding-exposure effect and phase lag discrep-ancy for different size fractions are also discussed.