Explicit formulation of the shields diagram for incipient motion of sediment

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.