Date of this Version
Jichao Jiang (2019).THEORETICAL MODEL FOR SHIELDS DIAGRAM AND ITS APPLICATION (M.S. Thesis).
The transition from the condition of “no motion” to initial sediment moment, defined as sediment initiation, has been related to practical engineering (channel degradation, stable channel design), oceanographic (dredging, pipelines, cables), sedimentologic (sediment mobility, transport rates), geologic (the hydraulic interpretation of paleoenvironments), geochemical (pollutant transport), and gained considerable interest since nineteenth century.
Shields diagram for sediment initiation in terms of critical shear stress is a classic problem in sediment transport, but it is still an empirical law without a simple and practical theory despite extensive research since the 1930s. Hence, this research presents a simple theoretical model for critical shear stress, which has four lumped parameters determined analytically and fits data from various references in the Shields diagram. Specifically, it first describes the hydrodynamic drag on a bed particle with Forchheimer's law from porous media flow; it then models the cohesive force between sediment particles by considering the effects of attached water film and electrostatics. The resulting dimensionless critical shear stress (or the critical Shields parameter) is a rational function of particle Reynolds number, which reproduces the Shields diagram by tending to two constants for small and large particle Reynolds numbers, respectively, and having a minimum value in the transitional regime. For applications, the proposed rational function can be solved for a critical shear stress or a critical sediment size analytically without numerical iterations.