Geoscience Reference
In-Depth Information
Alonso (1980) tested eight formulas, including those of Ackers and White (1973),
Engelund and Hansen (1967), Laursen (1958), Yang (1973), Bagnold (1966), Meyer-
Peter and Mueller (1948), Yalin (1972), and the combination of the Meyer-Peter-
Mueller bed-load formula and the Einstein (1950) suspended-load formula (denoted
as MPME), using 225 sets of flume data and 40 sets of field data. Alonso limited
his comparisons against those field data where bed-material load could be measured
by special facilities to avoid the uncertainty of unmeasured load. Table 3.7 shows
the discrepancies of the selected formulas. The Yang (1973), Ackers-White (1973),
Engelund-Hansen (1967), and Laursen (1958) formulas are more reliable.
Table 3.7
Comparison of sediment transport formulas (Alonso, 1980)
Formula
Ratio of predicted and measured discharges
Flume data with
Flume data with
Field data
h
/
d
≥
70 (177 sets)
h
/
d
<
70 (48 sets)
(40 sets)
Mean
σ
% in 0.5-2 Mean
σ
% in 0.5-2 Mean
σ
% in 0.5-2
Ackers-White
1.34
1.29
73.0
1.12
0.52
89.6
1.27
0.68 87.8
Engelund-H.
0.73
0.68
51.1
0.75
0.50
66.7
1.46
0.56 82.9
Laursen
0.81
0.51
71.4
1.04
0.99
79.2
0.65
0.48 56.1
MPME
3.11
2.75
42.1
1.34
1.04
66.7
0.83
1.02 58.5
Yang
0.99
0.60
79.8
0.90
0.51
85.4
1.01
0.39 92.7
Bagnold
0.85
2.50
20.8
1.53
1.14
45.8
0.39
0.26 32.0
Meyer-Peter-M. 0.40
0.49
18.5
1.03
0.83
72.9
0.24
0.09 0
Yalin
1.62
4.08
32.6
1.92
1.65
64.6
2.59
1.62 46.3
Note:
σ
=
standard deviation, and % in 0.5-2 means percentage of data in error range of 0.5-2.
Brownlie (1981) compared fourteen formulas. The discrepancies resulting from
these formulas are shown in Fig. 3.24. The median and 16th and 84th percentile values
in the figure are based on the approximation of a log-normal distribution of errors.
The Brownlie (1981), Ackers-White (1973), and Engelund-Hansen (1967) formulas
provide good results for the data sets used in the comparison.
Woo and Yoo (1991) tested ten sediment transport formulas using the data carefully
selected from Brownlie's (1981) compilation. Fig. 3.25 presents the discrepancy ratios
of the calculated and measured sediment discharges. The Engelund-Hansen (1967),
Ackers-White (1973), and van Rijn (1984a & b) formulas are more reliable than
other compared formulas.
The author compared the Engelund-Hansen (1967), Ackers-White (1973), Yang
(1973, 1984), and Wu
et al
. (2000b) formulas as well as the SEDTRA module (Gar-
brecht
et al
., 1995) against 1,859 sets of uniform bed-material load data selected from
Brownlie's (1981) compilation by limiting the standard deviation of bed material
σ<
>
1.2 and the Shields number
0.055. These data cover flow discharges of 0.00094-
297 m
3
s
−
1
, flow depths of 0.01-2.56 m, flow velocities of 0.086-2.88 m
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
. formulas (3.80) and (3.102). The discrepan-
cies between the calculated and measured bed-material transport rates are listed in
Table 3.8. All these five formulas have comparable reliability for uniform bed-material
load transport rate.
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