2. Weak movement: Only a few particles are in motion on the bed. The grains moving on
one square centimeter of the bed can be counted.
3. Medium movement: The grains of mean diameter begin to move. The motion is not local
in character but the bed continues to be plane.
4. General movement: All the mixture is in motion; the movement is occurring in all parts of
the bed at all times. It is sufficiently vigorous to change the bed configuration.
Whether or not a plane bed can exist with weak sediment motion is debated; though positive
evidence of its existence has been presented by Liu (1957) and Senturk (1969). Liu's
observations may have involved such shallow flow that the Froude number was larger than
1, which would indicate antidunes not ripples. Many researchers such as Kramer (1935),
Shields (1935), White (1940), Tison (1953), Simons and Richardson (1966), Gessler (1971),
Vanoni (1977), have studied the problem of initiation of motion. Buffington (1999) provides
an excellent review of Shields research. The studies involve both theory and
experimentation. The complexity of the problem explains the diversity of experimental
results. In reality, there is no truly critical condition for initiation of motion for which motion
begins suddenly as the condition is reached. Data available on critical shear stress are
based on arbitrary definitions of critical conditions and most definitions used have relied on
subjective visual observations. Also, no evidence has shown that the mean diameter
represents the composition of a mixture correctly. The engineer facing this dilemma of
dealing with beginning of motion in a mixture of sediment sizes should analyze the problem
very carefully. However, the equations presented in this section are theoretically sound and
have proven to give reliable results. This is true, even though there is a diversity in the
experimentally determined coefficients.
Water flowing over a bed of sediment exerts forces on the grains. These forces tend to
move or entrain the particles. The forces that resist the entraining action of the flowing water
differ depending upon the properties of bed material. For coarse sediments such as sands
and gravels, the resisting forces relate mainly to the weight of the particles, but also are a
function of shape of particle, its position relative to other particles, and the form of bed
roughness. For cohesive bed material (generally silts and clays), chemical bonding between
particles resists the beginning of motion.
When the hydrodynamic forces acting on a grain of sediment have reached a value that, if
increased even slightly the grain will move, critical or threshold conditions are said to have
been reached. Under critical conditions, the hydrodynamic forces acting upon a grain are
just balanced by the resisting force of the particle.
3.5.3 Theory of Beginning of Motion
The forces acting on an individual particle on the bed of an alluvial channel are:
1. Body force Fg due to the gravitational field,
2. External forces Fn acting at the points of contact between the grain and its neighboring