The initiation or ceasing of motion of sediment particles is involved in many geomorphic and

hydraulic problems including stream stability and scour at highway bridges, sediment

transport, erosion, slope stability, stable channel design, and design of riprap. These

problems can only be handled when the threshold of sediment motion is fully understood.

Beginning of motion can be related to either shear stress on the grains or the fluid velocity in

the vicinity of the grains. When the grains are at incipient motion, these values are called the

critical shear stress or critical velocity. The choice of shear stress or velocity depends on: (1)

which is easier to determine in the field; (2) the precision with which the critical value is

known or can be determined for the particle size; (3) the type of problem. In sediment

transport analysis most equations use critical shear stress. In stable channel design either

critical shear stress or critical velocity is used; whereas, in riprap design critical velocity is

generally used.

Equations for determining the shear stress on the bed of a stream are given in Chapter 2,

Section 2.4.5. The average shear stress on the boundary is given by τ0 = γ RS. Where γ is

the unit weight of water, R is the hydraulic radius and S is the slope of the energy grade line.

In wide channels (width equal to or greater than 10 times the depth) R ≈ y, the depth. Other

relations give the shear stress in terms of the velocity of flow.

It may not be sufficient to determine the average value of the critical shear stress or velocity

because both quantities are fluctuating. For the same mean values, they may have larger

values that act for a sufficiently long enough time to cause a particle to move. In addition,

the forces on the particle resulting from the flowing water, waves, and seepage into or out of

the bed or banks affect the beginning of motion.

In this section, the following topics are discussed: theory of beginning of motion, Shields

experimental relationship and its modifications, equations to determine the relation between

flow variables (depth, velocity or discharge) and sediment size, tables giving observe values

between flow variables and sediment size, and figures for determining the flow or sediment

variables at beginning of motion.

When the force of the flowing water (as measured by the shear stress or velocity) is less than

some critical value, the bed material of a channel remains motionless. Then, the alluvial bed

can be considered as immobile. But when the shear stress or velocity over the bed attains or

exceeds its critical value, particle motion begins. In general, the observation of particle

movement is difficult in nature. The most dependable data available have resulted from

laboratory experiments.

The beginning of motion is difficult to define. This difficulty is a consequence of a

phenomenon that is random in time and space. When the shear stress is near its critical

value, it is possible to observe a few particles moving on the channel bottom. The time

history of the movement of a particle involves long rest periods. In fact, it is difficult to

conclude that particle motion has begun. Kramer (1935) and Buffington (1999) proposed

four levels of motion of bed material.

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