Sediment Movement in Alluvial Rivers - River Dynamics and Integrated River Management - page 285

in which Ȧ' is the group fall velocity, Ȧ is the fall velocity of a single particle in pure water, and m is a
exponent varying within the range of 2-8 For fine sediment, m is large, e.g., D 0.1 mm, m 8; for
coarse sediment, m is small, e.g. D 2 mm, m 2. Generally, m is a function of the particle Reynolds
number, as shown in Fig. 5.24

Fig. 5.24 The exponent m in the group fall velocity equation (5.45) as a function of particle Reynolds number, Re p

5.2.2 Sediment Transportation

5.2.2.1 Initiation Velocity
Incipient motion is an important critical condition, under which sediment starts to move through the
action of flow. In 1753, Brahms suggested that the velocity for incipient motion is proportional to the
grain weight raised to the one-sixth power. This concept agreed quite well with the knowledge of
incipient motion of sediment at that time. At the end of the nineteenth century, people began to study the
problem from the concept of a balance of forces acting on the grains. In 1914, Forchheimer systematically
summarized and evaluated the knowledge that had accumulated by that time, and he discussed the
influence of sediment gradation, sorting, and armoring on the incipient motion of sediment. In 1936,
Shields applied the method of dimensional analysis, prevalent at that time to sediment motion and
developed the well-known Shields (1936) diagram, which is still used widely. In the 1950s, Lane (1953)
applied the concept of drag force in canal design and proposed a design of regime canals that is more
soundly based on theoretical grounds. More recently, investigations of the incipient motion of the
sediment have focused on conditions for non-uniform and cohesive sediments. For the former, the
armoring process at the bed should be included as part of the process of erosion, and for the latter, the
sediment motion is related to the physico-chemical properties at the surface of fine grains. Both of these
cases are quite complex. After long experience, people gradually began to conceive of incipient motion
of sediment as a stochastic phenomenon. Its study must use an approach that combines the theories of
probability and fluid mechanics if one is to understand the physical essence of the incipient motion of
sediment.
The Shields (1936) equation for incipient drag force for non-cohesive uniform sediment can be used.
Shields found that the dimensionless critical shear stress (Shields number) depends only on the grain
Reynolds number, Re * = U * D/ Q.

W
JJ

UD

§ ·

c

f (5.46)

¨ ¸

( ) D Q

© ¹

s

where W is the critical value of shear stress needed to initiate sediment motion, and U * is the shear