Environmental Engineering Reference
In-Depth Information
a number of formulas for bed load transport and suspended load transport. These formulas are based on
different modes of motion and use different parameters, including shear stress, flow velocity, and stream
power. Although the formulas have been widely used in hydraulic engineering and numerical modeling
of fluvial processes, the relative error is quite high. Several tens to thousand times difference between the
calculated and measured rates of sediment transportation are found in some cases. Very briefly the
Meyer-Peter and Muller (1948) formula for bed load transport and WIHEE (1961) formula for suspended
load transport are introduced as examples.
Bed load is the sediment load that moves in the vicinity of the bed and at least intermittent contact
with the bed. In many rivers, the bed load motion and deposition largely determines channel morphology.
Bed load is critical in maintaining ecological diversity and habitat in stream channels. Therefore, bed
load transport has become a focal point of research for a century, although bed load is only a very small
portion of the total load. Since 19
th
century many scientists have studied the phenomenon and proposed a
number of formulas for the rate of bed load transport. They used different parameters, including shear
stress, flow velocity and stream power. The formulas of Meyer-Peter-Mullër, Einstein, Bagnold, Engelund
and Yalin are the most widely applied (Chien et al., 1998). In the following the Meyer-Peter and Muller
formula is introduced. Other formulas may be found in the literatures (Chien et al., 1998).
Since the 1970s, many researchers tested, analyzed and compared these formulas with measured data
and flume experiments. All the bed load formulas can not accurately give the rate of bed load transport.
For bed load motion in mountain streams, the relative error of the calculated results with all current
formulas is too great to be applied and new approaches are needed, which is discussed in the last part of
this chapter.
Meyer-Peter and Muller (1948) developed a simple empirical bed load formula by using a similarity
law and data from their preliminary experiments. The formula involved only a few simple parameters.
Then they applied the formula to more complex cases involving the variation of additional parameters
and found a systematic difference between the measured data and the formula. They analyzed the difference
and determined its cause. They studied the effect of each new parameter by separating it from the others
in additional experiments and then incorporated the parameter into the formula. In this way, they studied
the effects of density, size composition of the sediment, and bed form step by step and eventually obtained a
comprehensive bed load formula. This approach required a long time to develop, but it is effective for
studying problems involving numerous parameters.
For bed load motion in a steady and uniform flow, Meyer-Peter and Muller (1948) obtained the following
formula:
3/2
ª
3/2
º
§
·
§
2/3
1/3
·
K
J
R J
0.047
JJ
§
·
«
»
1/ 2
3/ 2
¨
¸
g
8
g
J
D
b
b
s
(5.47)
¨
¸
¨
¸
b
s
«
¨
¸
»
c
JJ
D
J
K
©
¹
©
¹
©
¹
s
¬
¼
b
where
g
b
is the rate of bed load transport per unit width in weight,
D
the diameter of the bed load and is
usually represented by the median diameter,
R
is the hydraulic radius as affected by the bed resistance,
K
c
is the ratio of the roughness coefficient duo to grain resistance to that of the total resistance.
The Meyer-Peter and Muller Formula is based on a large quantity of experimental data. The main
variables in their experiments varied within the following ranges:
Width of flume
:
/
b
b
. 5 - 2 m
Flow depth
:
. 1 - .2 m
Energy slope
:
. % - %
1.25 - 4 g/cm
3
Density of sediment
:
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