3.5 BEGINNING OF MOTION
3.5.1 Introduction
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.
3.5.2 Theoretical Considerations
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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