Integrated River Management - River Dynamics and Integrated River Management - page 742

oo
' M ( Vi )

e u (11.11)

P P

' t

in where u P is the average velocity of the bed load particle, e P is the energy consumption per time for one
bed load particle. Because the horizontal vector component is against the flow direction,

' G is
positive. There are N bed load particles moving over the bed per area. The sum of e P for all bed load
particles, N e P , is the total energy consumption of the water flow on bed load motion.

o

Vi

Fig. 11.26 The dispersive force as a result of collisions between moving particles

Almost all of the energy consumed during bed load motion comes from the water flow. The potential
energy exerted on the bed by the water body is P=ȡghUs , in which U is the average velocity of the water
flow, ȡ is the density of water, g is the gravitational acceleration, h is the water depth, and s is the bed
slope. The bed load motion consumes a part of the water energy, thus

oo
' ( Vi )

NM u EU ghUs (11.12)

P

' t

in which ȕ is a coefficient. The equation may be rewritten as:

oo
' NM ( V i ) u

J E s

P

(11.13)

b

U hgt ' U

where J b is the energy slope due to bed load motion. The rate of bed load transport per width is
g b gNMu p , thus J b is proportional to the rate of bed load transport.
Bed load motion in river flow plays a role of protecting the bed from erosion. As shown in Fig. 11.27,
particle P collides with the particles on the channel bed, which results in the dispersive force acting on
the bed load particle. In the meantime the particles on the bed are acted upon by a reactionary force F

o

.
The vertical component of the force, F y plays an important role in protection of the bed from erosion. It
is well known that the initiation of motion of sediment particles on the river bed is mainly related to the
lift force of the flow. F y counterbalances a part of the lift force, and, thereby, prevents the particles from
entering into motion. With bed load movement increasing with increasing flow velocity, there comes an
instant when the average value of F y equals the lift force. The channel bed cannot be eroded further and
the bed load motion reaches equilibrium. The bed load layer acts like a protective coating, which protects
the bed against continuous erosion. The higher the flow velocity and the larger the tractive shear stress,
the more the bed load and the thicker the protective coating, so that the channel bed can remain stable (i.e.
not being continuously eroded) at different hydraulic conditions.
Bed structures create high resistance and consume flow energy. The energy consumption due to bed
structures, such as step-pool systems, can be estimated using the formula of water head loss due to sand