Transcript Slide 1

1D SEDIMENT TRANSPORT MORPHODYNAMICS
with applications to
RIVERS AND TURBIDITY CURRENTS
© Gary Parker November, 2004
CHAPTER 12:
BULK RELATIONS FOR TRANSPORT OF TOTAL BED MATERIAL LOAD
Sediment-laden meltwater emanating from a glacier in Iceland. The flow
is from top to bottom. The flow to the left is braided, whereas that to
the right is meandering. Image courtesy F. Engelund and J. Fredsoe. 1
1D SEDIMENT TRANSPORT MORPHODYNAMICS
with applications to
RIVERS AND TURBIDITY CURRENTS
© Gary Parker November, 2004
QUANTIFICATION OF TOTAL BED MATERIAL LOAD
The total bed material load is equal to the sum of the bedload and the bed material
part of the suspended load; in terms of volume transport per unit width, qt = qb +
qs. Here wash load, i.e. that part of the suspended load that is too fine to be
contained in measurable quantities in the river bed, is excluded from qs. Total bed
material load is quantified in various ways in addition to qt
Flux-based volume concentration Ct = qt/(qt + qw)
Flux-based mass concentration Xt = sqt/(sqt + qw)
Flux-based mass concentration in parts per million = Xt106
Concentration in milligrams per liter = sqt/(qt + qw)106, where qt and qw are in m2/s
and s is in tons/m3.
In the great majority of cases of interest qt/qw << 1, so that the concentration in
milligrams per liter is accurately approximated by the mass concentration in parts
2
per million.
1D SEDIMENT TRANSPORT MORPHODYNAMICS
with applications to
RIVERS AND TURBIDITY CURRENTS
© Gary Parker November, 2004
RELATION OF ENGELUND AND HANSEN (1967)
A variety of relations are available for the prediction of bulk total bed material load.
Most of them are based on the regression of large amounts of data. Five such
relations are reported here. Although the data bases for some of them include
gravel, they are not designed for gravel-bed streams. As such, their use should be
restricted to sand-bed streams.
Perhaps the simplest of these relations is that due to Engelund and Hansen (1967).
It takes the form
qt 
0.05  5 / 2
( )
Cf
where
qt
q 
RgD 50 D50

t
b
u2
,  

RgD 50 RgD 50

The relation is designed to be used in conjunction with the formulation of
hydraulic resistance of Engelund and Hansen (1967) presented in Chapter 9.
Brownlie (1981) has found the relation to perform very well for field sand-bed
streams.
3
1D SEDIMENT TRANSPORT MORPHODYNAMICS
with applications to
RIVERS AND TURBIDITY CURRENTS
© Gary Parker November, 2004
RELATION OF BROWNLIE (1981)
The formulation of Brownlie (1981) can be expressed as:
qt 
Xt
1
qw
(R  1) (1  X t )

ˆ U
ˆ
X t  7.115  10 c F U
c
3
ˆ
U
U
RgD 50
ˆ  4.596 ( )0.5293 S0.1405 0.1606
U
c
c
g

1.978
ˆ 0.3301
S0.6601 H
H
ˆ
, H
D50

c
  0.22 Re
0.6
p
 0.06  10
( 7.7 Re p0.6 )
In the above relations g is the geometric standard deviation of the bed sediment
and cF takes the value of 1 for laboratory conditions and 1.268 for field conditions.
The relation is designed to be used in conjunction with the Brownlie (1981)
formulation for hydraulic resistance.
4
1D SEDIMENT TRANSPORT MORPHODYNAMICS
with applications to
RIVERS AND TURBIDITY CURRENTS
© Gary Parker November, 2004
RELATION OF YANG (1973)
The formulation of Yang (1973; see also 1996) can be expressed as:
Xt
1
qt 
qw
(R  1) (1  X t )
u 
og10 ( X t  106 )  5.435  0.286og10 (R f Re p )  0.457og10    
 vs 

 u 
 US Uc S 




1
.
799

0
.
409

og
(
R
Re
)

0
.
314

og

og



10
f
p
10 
10 

vs 
 v s 
 vs

2.5


uD
Uc  og10   50

 
vs 



  0.06

 0.66 , 1.2 
uD
2.05 , 70   50

uD50
 70

Rf 
Re p 
vs
RgD 50
RgD 50 D50

In the above relations vs is the fall velocity associated with sediment size D50.
5
1D SEDIMENT TRANSPORT MORPHODYNAMICS
with applications to
RIVERS AND TURBIDITY CURRENTS
© Gary Parker November, 2004
RELATION OF ACKERS AND WHITE (1973)
The formulation of Ackers and White (1973) can be expressed as:
Xt
1
qt 
qw
(R  1) (1  X t )
 Fgr

R 1
Xt 
(Cz )n Caw 
 1
ˆ
H
 A aw



m
1n


1

1n


Fgr   (Cz ) 
ˆ)
32

og
(
10
H
10


1.00  0.56 og10 Re p2 / 3 , 1  Re p2 / 3  60
n
0 , 60  Re p2 / 3

 9.66
2/3
 2 / 3  1.34 , 1  Re p  60
m  Re p

1.50 , 60  Re p2 / 3

U
Cz 
u
0.23 Re p1/ 3  0.14 , 1  Re p2 / 3  60
A aw  
0.17 , 60  Re p2 / 3

2.86 og10 ( Re p2 / 3 )  [og10 ( Re p2 / 3 )]2  3.53 , 1  Re p2 / 3  60
og10 Caw  
 1.60 , 60  Re p2 / 3

H
ˆ
, H
D50
6
1D SEDIMENT TRANSPORT MORPHODYNAMICS
with applications to
RIVERS AND TURBIDITY CURRENTS
© Gary Parker November, 2004
RELATIONS OF KARIM AND KENNEDY (1981) AND KARIM (1998)
The formulation of Karim and Kennedy (1981) can be expressed as:



qt
U
  2.2786  2.9719 og10 
og10 
 RgD D 
 RgD
50
50 
50


 H
 0.2989 og10 
 D50
 u  uc

 og10  
 RgD

50



U
  1.0600 og10 

 RgD
50




 og10  u  uc

 RgD
50










where u*c can be evaluated from Brownlie’s (1981) fit to the original Shields curve:

c
  0.22 Re
0.6
p
( 7.7 Re p 0.6 )
 0.06  10
, Re p 
RgD D

The above relation may be used in conjunction with their relation for hydraulic
resistance presented in Chapter 9. Karim (1998) also presents a total bed material
load equation that is fractionated for mixtures;
 U 
qti

 0.00139


Fai RgD i Di
 RgD i 
 D
i  C1 i
 D50



C2
v
, C1  1.15 s50
 u
2.97
1.47
 u 
 
 v si 
i

v
 , C2  0.60 s50

 u
Fai 



Fi / Di 
n
 Fi / Di 
i 1
7
1D SEDIMENT TRANSPORT MORPHODYNAMICS
with applications to
RIVERS AND TURBIDITY CURRENTS
© Gary Parker November, 2004
REFERENCES FOR CHAPTER 12
Ackers, P. and White, W. R., 1973, Sediment transport: new approach and analysis, Journal of
Hydraulic Engineering, 99(11), 2041-2060.
Brownlie, W. R., 1981, Prediction of flow depth and sediment discharge in open channels, Report
No. KH-R-43A, W. M. Keck Laboratory of Hydraulics and Water Resources, California
Institute of Technology, Pasadena, California, USA, 232 p.
Engelund, F. and E. Hansen, 1967, A Monograph on Sediment Transport in Alluvial Streams,
Technisk Vorlag, Copenhagen, Denmark.
Karim, F., 1998, Bed material discharge prediction for nonuniform bed sediments, Journal of
Hydraulic Engineering, 124(6): 597-604.
Karim, F., and J. F. Kennedy, 1981, Computer-based predictors for sediment discharge and
friction factor of alluvial streams, Report No. 242, Iowa Institute of Hydraulic Research,
University of Iowa, Iowa City, Iowa.
Yang, C. T., 1973, Incipient motion and sediment transport, Journal of Hydraulic Engineering,
99(10), 1679-1704.
Yang, C. T., 1996, Sediment Transport Theory and Practice, McGraw-Hill, USA, 396 p.
8