The Shields diagram remains the most widely used criterion for incipient motion of sediment. However its implicit nature makes applications rather inconvenient. By deploying Guo’s logarithmic matching method twice, this technical note develops an explicit formulation of the Shields diagram, enabling the critical Shields parameter to be determined directly from fluid and sediment characteristics without resorting to any trial and error procedure or iteration. An extended application of the logarithmic matching method is demonstrated.

Dam-break flows over mobile bed are often sharply stratified, comprising a bedload sediment-laden layer and an upper clear-water layer. Double layer-averaged (DL) models are attractive for modelling such flows due to the balance between the computing cost and the ability to represent stratification. However, existing DL models are oversimplified as sediment concentration in the sediment-laden layer is presumed constant, which is not generally justified. Here a new DL model is presented, explicitly incorporating the sediment mass conservation law in lieu of the assumption of constant sediment concentration. The two hyperbolic systems of the governing equations for the two layers are solved separately and simultaneously. The new model is demonstrated to agree with the experimental measurements of instant and progressive dam-break floods better than a simplified double layer-averaged model and a single layer-averaged model. It shows promise for applications to sharply stratified sediment-laden flows over mobile bed.