Figure 3.16. Shields' relation for beginning of motion (after Gessler 1971).
Most authors report that Shields determined this relationship (Figure 3.15) by measuring
bed-load transport for various values of τ/(γs - γ) Ds and then extrapolated to the point of
vanishing bed load. Simons and Senturk (1992) state the values of τ/(γs - γ) Ds were at least
twice as large as the critical value. This indirect procedure was used to avoid the
implications of the random orientation of grains and variations in local flow conditions that
may result in grain movement even when τ/(γs - γ) Ds is considerably below the critical value.
However, Buffington (1999) discusses in great detail Shields' research and states the
following:
"Nevertheless, these two passages from Shield's dissertation offer two definitions of incipient
motion (bed-load extrapolation for uniform sizes versus visual observation for mixed grains.
Because Shields neglected to explain which method he used and did not present sufficient
data to recreate his calculations, the matter of his experimental procedure remains open to
debate. However, throughout his dissertation he discussed his approach and results as
being representative of uniform grains (Shields 1936c pp. 11, 14, and 16), suggesting that he
employed bed-load extrapolation (the method he described for uniform sediment."
The Shields Diagram (Figure 3.15) was divided into three regions by Simons and Senturk
(1992) as illustrated in the following.
Region 1: V*D s / ν < 3.63 ~ 5.0
In the region Ds < 3δ, where δ = 11.6ν/V*, and the boundary is considered hydraulically
smooth (δ is the thickness of the laminar boundary layer, Chapter 2). Shields estimated the
portion of the diagram for V*Ds/ν < 2. He did not perform any experiments in that region.
According to Shields, when the value of
τc
≅ 0.1
(3.35)
(γ s - γ)Ds
then (approximately)
3.37
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