Empirical Model for Shields Diagram and Its Applications

The Shields diagram is a classic method for quantifying sand incipient motion in sediment transport. It is often expressed by empirical or semiempirical equations. This research applies the Padé approximant to the data in the extended Shields diagram and presents a simple generalized empirical model for the critical shear stress. The resulting dimensionless critical Shields parameter is a fractional function of the critical grain Reynolds number, which reproduces the extended Shields diagram by tending to two constants for lower and higher critical grain Reynolds numbers, respectively, and having a minimum value in the transitional regime. The proposed function results in an explicit Shields diagram in terms of grain Reynolds number and has an analytical solution for critical sediment diameter given a bed shear stress.