Geoscience Reference
In-Depth Information
Wu
et al
. (2000b) compared their bed-load transport formula (3.80) and the
formulas of Meyer-Peter and Mueller (1948), Bagnold (1966), and Engelund and
Fredøse (1976) against 1,345 sets of uniform bed-load data. These data were selected
from Brownlie's (1981) compilation by limiting the standard deviation of bed mate-
rial
2.5.
They were observed in several decades by many investigators, covering flow dis-
charges of 0.00094-297 m
3
s
−
1
, flow depths of 0.01-2.56 m, flow velocities of
0.086-2.88 m
σ<
1.2, the Shields number
>
0.055, and the Rouse number
ω
/κ
u
∗
>
s
s
−
1
, surface slopes of 0.0000735-0.0367, and sediment sizes of
0.088-28.7 mm. None of them was used to calibrate the Wu
et al
. formula. As shown
in Table 3.3, the Wu
et al
. formula provides the best results.
Many other investigators, such as Yang (1984) and van Rijn (1984a), have also
compared bed-load transport formulas. The conclusions are usually different because
different data have been used. However, it has been shown that the existing formulas
have better predictions for flume data than for field data. The reasons are that the bed-
load transport is more complex and the measurement instruments are less efficient in
natural rivers. As recognized by van Rijn (1984a), it is hardly possible to predict the
bed-load transport rate with accuracy less than a factor of 2. Perhaps his remark is
useful for sediment engineers to judge the prediction capability of the existing sediment
transport formulas.
·
Table 3.3
Calculated versus measured transport rates of uniform bed load
Error range
% of calculated transport rates in error range
Engelund-Fredøse
Bagnold Meyer-Peter-Mueller Wu et al.
0.8
≤
r
≤
1.25
21.4
21.4
21.3
38.7
0.667
≤
r
≤
1.5
37.4
38.9
39.4
59.3
0.5
≤
r
≤
2
54.1
57.2
66.2
80.1
Note:
r
is the ratio of calculated and measured transport rates.
Comparison of bed-load formulas using multi-fraction data
Ribberink
et al
. (2002) tested the performances of several multi-fraction bed-load
transport formulas, including the Parker (1990) formula, the Wu
et al
. (2000b) for-
mula, the Ackers-White (A&W, 1973) formula with the hiding-exposure correction
factors of Day (1980) and Proffitt and Sutherland (P&S, 1983) (to be introduced in
Section 3.6.2), and the Meyer-Peter-Mueller (MP&M, 1948) formula with the hiding-
correction factors of Egiazaroff (1965) and Ashida and Michiue (A&M, 1972). The
“single-size” Engelund-Hansen (E&H, 1967) and van Rijn (1984a) formulas without
any hiding and exposure correction were added as reference. The data used cover the
bed-load transport of widely graded sediment mixtures in the lower Shields regime.
The results are summarized in Table 3.4 and expressed in mean under- or overesti-
mation scores (factor
n
over/underestimation gives a score of 1/
n
). Separate scores are
made for the predicted total transport rate and mean transported diameter, and an
average score for both.
Of all the compared multi-fraction formulas, the Wu
et al
. (2000b) formula gives
the highest scores, followed by the Ackers-White formula with the hiding-exposure
