Empirical Model for Shields Diagram and Its Applications

Junke Guo

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


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.

Original languageEnglish (US)
Article number04020038
JournalJournal of Hydraulic Engineering
Issue number6
StatePublished - Jun 1 2020


  • Bed load
  • Channel stability
  • Critical shear stress
  • Incipient motion
  • Sediment threshold
  • Sediment transport
  • Shields diagram
  • Shields parameter

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Water Science and Technology
  • Mechanical Engineering


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