Encyclopedia of Environmental Science and Engineering, Volume I and II

SEDIMENT TRANSPORT AND EROSION 1069

Initial Motion

White, in 1940, 20,21 using an analytical approach, showed

that, for sufficiently turbulent flow over a granular bed, the

critical shear or shear to initiate grain movement is

t c  k c g f^ ( S s –1) d, (5)

in which k c ; 0.06; g f  fluid specific weight; S s  specific

gravity of sediment grain; d  grain diameter.

Shields,^21 using an experimental approach, obtained the

more general equation

t c  g f ( S s –1) d f ( R * ), (6)

in which R *  U * d
 n; U *  friction velocity; n  kinematic

viscosity; and f ( R * ) is defined in Figure 7.

Permissible or allowable tractive stresses for use in chan-

nel designs with granular or cohesive boundaries are given

by Chow.^7

Bed Load Formulae

When the bed shear, t o , due to the flowing stream exceeds the

critical shear, t c , a part of the bed material starts to move in a

layer of the stream near the bed, i.e. the bed layer. Experimental

0 0.2 0.4 0.6 0.8 1.0 1.2

Median Fall Diameter in mm.

0.001

0.002

0.004

0.006

0.008

0.01

0.02

0.04

0.06

0.08

0.1

0.1

0.2

0.4

0.6

0.8

1.0

1.0

10

4.0

2.0

Stream power,

tV, lbs/ft

-^

sec.

Stream power,

tV, gms/cm

sec.

Upper Region

Transition

Dunes

Ripples

Plane

FIGURE 6 Relation of stream power and median fall diameter to bed form (after

Simons).

TABLE 2

Chézy C in sand channels

Regime Bed Form Cl √g (where C is Chézy C)

Lower regime

ripples d 50  0.6 mm 7.8 to 12.4

dunes 7.0 to 13.2

transition 7.0 to 20

Upper regime plane bed 16.3 to 20

anti-dune {standing wave 15.1 to 20

{breaking wavechutes and

pools“slug” flow

10.8 to 16.3

9.4 to 10.7

—

C019_001_r03.indd 1069C019_001_r03.indd 1069 11/18/2005 11:06:00 AM11/18/2005 11:06:00 AM