A Re-Examination of the Beginning of Movement for Coarse Granular Bed Materials

Certain questions on the Shields entrainment function that require clarification are posed and discussed. It is shown that if the 'beginning of movement' is considered in numerical terms, the logical result is a 3-parameter relationship expressing a dimensionless grain displacement rate as a function of the original Shields parameters.

Flume experiments on low rates of movement of uniformized coal grains, glass spheres and coal mixtures are described and analyzed. It is shown that reasonably consistent results can be obtained if a numerical criterion for beginning of movement is adopted and that for uniform grains little significant difference in Shields' entrainment parameter can be detected for grain Reynolds' numbers exceeding 70 or so. Empirically, the beginning of movement for unimodal mixtures of moderate dispersion can be estimated by inserting the D50 size by weight into the expression for uniform materials.

Suggestions are made for further research on low transport rates of coarse materials that might improve insight into bed-material transport functions. The need for a more fundamental approach to transport of mixtures is recognized. A similarity approach to a transport function, slightly different from previous approaches of the same kind, is outlined briefly.

The analysis and presentation of grain-size distributions for mixtures is discussed in an appendix.