Transcript Ch3BankfullChar.ppt

1D SEDIMENT TRANSPORT MORPHODYNAMICS
with applications to
RIVERS AND TURBIDITY CURRENTS
© Gary Parker November, 2004
CHAPTER 3:
BANKFULL CHARACTERISTICS OF RIVERS
Alluvial rivers construct their own channels and floodplains. Channels and
floodplains co-evolve over time.
Nameless Siberian stream and
floodplain. Image courtesy A.
Alabyan and A. Sidorchuk.
Browns Gulch, Montana
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THE CONCEPT OF BANKFULL DISCHARGE
Let  denote river stage (water surface elevation) [L]
and Q denote volume water discharge [L3/T]. In the
case of rivers with floodplains,  tends to increase
rapidly with increasing Q when all the flow is confined
to the channel, but much less rapidly when the flow
spills significantly onto the floodplain. The rollover in
the curve defines bankfull discharge Qbf.

Minnesota River and
floodplain, USA, during the
record flood of 1965
Qbf
2
Q
1D SEDIMENT TRANSPORT MORPHODYNAMICS
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GRAVEL-BED AND SAND-BED RIVERS
Rivers (or more specifically river reaches) can also be classified according to
the characteristic size of their surface bed sediment, i.e median size Ds50 or
geometric mean size Dsg. A river with a characteristic size between 0.0625 and
2 mm can be termed a sand-bed stream. Two such streams are shown below.
Jamuna
(Brahmaputra)
River, Bangladesh.
Image courtesy J.
Imran.
Fly River, Papua New Guinea.
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GRAVEL-BED AND SAND-BED RIVERS
A river with a characteristic surface size in excess of 16 mm can be termed a
gravel-bed river. Here the term “gravel” is used loosely to encompass cobbleand boulder-bed streams as well. Three such streams are shown below.
Genessee River, New York, USA.
Rakaia River, New Zealand
Raging River, Washington, USA.
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GRAVEL-BED AND SAND-BED RIVERS
A river with a characteristic surface size
between 2 and 16 mm can be termed
transitional in terms of grain size. Such
streams are much less common than
either sand-bed or gravel-bed streams,
but can be found readily enough,
particularly in basins that produce
sediment from weathered granite. An
example is shown to the right.
Hii River, Japan.
Image courtesy H. Takebayashi
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GRAVEL-BED AND SAND-BED RIVERS
Sand-bed
Gravel-bed
Transitional
40
Number of reaches
35
30
25
Alberta
Japan
20
15
(Yamamoto, 1994; Fujita et
al., 1998). Note that most
rivers can be classified as
either gravel-bed or sand-bed.
10
5
12
8
-2
56
28
-1
4
64
-6
2
32
-3
6
16
8
-1
-8
4
-4
2
-2
1
-1
5
0.
-0
.5
5
25
.2
0.
-0
5
12
0.
0.
25
-0
.1
25
0
06
The diagram to the left shows
the frequency of river reaches
with various characteristic
grain sizes within two sets,
one from Alberta, Canada
(Kellerhals et al., 1972) and
the other from Japan
Grain size range in mm
The basic data for the subsequent
plots in this chapter are given in 6
RTe-bookRivers.xls
1D SEDIMENT TRANSPORT MORPHODYNAMICS
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© Gary Parker November, 2004
PARAMETERS USED TO CHARACTERIZE BANKFULL CHANNEL
GEOMETRY
In addition to a bankfull discharge, a reach of an alluvial river with a floodplain also
has a characteristic average bankfull channel width and average bankfull channel
depth. The following parameters are used to characterize this geometry.
Definitions:
Qbf = bankfull discharge [L3/T]
Bbf = bankfull width [L]
Hbf = bankfull depth [L]
S = bed slope [1]
Ds50 = median surface grain size [L]
n = kinematic viscosity of water [L2/T]
R = (rs/r – 1) = sediment submerged specific gravity (~ 1.65 for natural sediment) [1]
g = gravitational acceleration [L/T2]
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DIMENSIONLESS PARAMETERS CHARACTERIZING CHANNEL
BANKFULL GEOMETRY
Qbf
gDs50 Ds250
Q̂ 
Ĥ 
Hbf
Ds 50
B̂ 
Frbf 
= dimensionless bankfull discharge
= dimensionless bankfull depth
Bbf
Ds 50
= dimensionless bankfull width
Qbf
Bbf Hbf gHbf
= bankfull Froude number (dimensionless)
bf 50 
Hbf S
RDs50
Czbf 
Qbf
Bbf Hbf gHbf S = bankfull Chezy resistance coefficient (dimensionless)
Rep50 
RgDs50 Ds50
n
= (estimate of) bankfull Shields number (dimensionless)
= particle Reynolds number (surrogate for grain size:
dimensionless)
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INTERPRETATION OF SOME OF THE DIMENSIONLESS PARAMETERS
Bankfull flow velocity Ubf = Qbf/(HbfBbf)
Frbf 
Qbf
Ubf

Bbf Hbf gHbf
gHbf
Qbf
Ubf
Czbf 

Bbf Hbf gHbf S
gHbf S
bf 50 
Rep50
Hbf S
RDs50
Bankfull Froude number characterizes a ratio of
momentum force to gravity force. When Froude
number Fr < 1 the flow is subcritical, or tranquil:
when Fr > 1 the flow is supercritical, or swift. Here
Fr  U/ gH where U and H are cross-sectionallyaveraged flow velocity and depth, respectively.
The relation can be rewritten as Ubf  Czbf gHbf S
so that a high value of Czbf implies a low
bed resistance.
As explained in Chapter 5, for the case of steady, uniform (normal) flow,
the bed shear stress b is given as b = rgHS where H = depth. A
dimensionless measure of the ability of the flow to mobilize sediment is

the Shields number, * = b/(rRgD). Here bf 50 denotes an estimate of
value of * for bankfull flow based on a surface median size for D.
RgDs50 Ds50

n
Since in most cases g = 9.81 m/s2, R  1.65 and n  1x10-6 m92/s,
Rep50 is a surrogate for median surface grain size ~ Ds503/2.
1D SEDIMENT TRANSPORT MORPHODYNAMICS
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DIMENSIONLESS CHARACTERIZATION OF BANKFULL STREAM GEOMETRY
While each river has its own unique characteristics, alluvial rivers show a
considerable degree of commonality. This can be made apparent in terms of
dimensionless plots of bankfull characteristics. This is illustrated here with several
sets of data.
Gravel-bed rivers with Ds50 (surface median size) ranging from 27 mm to 157.5 mm
from three compendiums are used: Britain (Charlton et al., 1978), Alberta, Canada
(Kellerhals et al., 1972) and Idaho, USA (Parker et al., 2003). In addition, a subset
of sand-bed streams with Ds50 < 0.5 mm, including single-thread streams and
multiple-thread streams, selected from the compendium of Church and Rood (1983)
by Parker et al. (1998), are used. The bankfull characteristics of these streams are
studied in the following slides.
Transitional grain-size streams have been purposely excluded in order to illustrate
the similarities and differences between sand-bed and gravel-bed streams. Two of
the slides also include, however, data from Japan (Yamamoto, 1994; Fujita et al.,
1998), which includes many transitional grain-size streams.
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DIMENSIONLESS WIDTH VERSUS DIMENSIONLESS DISCHARGE
Each of the two stream types plots in a consistent way. The Alberta gravelbed streams are consistently a little wider than their British counterparts.
This may reflect, e.g. differences in vegetation density.
1.E+07
1.E+06
1.E+05
1.E+04
Grav Brit
Grav Alta
Sand Mult
Sand Sing
Grav Ida
B̂ 1.E+03
1.E+02
This plot, subsequent plots
in this chapter and the basic
data for them are given in
RTe-bookRivers.xls
1.E+01
1.E+00
1.E+00 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10 1.E+12 1.E+14
Q̂
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DIMENSIONLESS DEPTH VERSUS DIMENSIONLESS DISCHARGE
Again, each of the two stream types plots in a consistent way.
1.E+05
1.E+04
1.E+03
Ĥ
Grav Brit
Grav Alta
Sand Mult
Sand Sing
Grav Ida
1.E+02
1.E+01
1.E+00
1.E+00
1.E+02
1.E+04
1.E+06
Q̂
1.E+08
1.E+10
1.E+12
1.E+14
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BED SLOPE VERSUS DIMENSIONLESS DISCHARGE
The relation for slope versus dimensionless bankfull discharge shows general
consistency but much more scatter. This probably reflects the fact that much
more time is required to change a river’s bed slope than its width or depth;
indeed so much time that tectonics becomes a factor in the scatter.
1.E-01
Grav Brit
Grav Alta
Sand Mult
Sand Sing
Grav Ida
1.E-02
S
1.E-03
1.E-04
1.E-05
1.E+02
1.E+04
1.E+06
1.E+08
Q̂
1.E+10
1.E+12
1.E+14
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BANKFULL FROUDE NUMBER VERSUS BED SLOPE
Sand-bed and gravel-bed streams mesh together smoothly in this plot, but the sandbed streams generally have lower bankfull Froude numbers Fr. All but one of the
streams are in the subcritical range (Fr < 1) at bankfull flow. This does not mean that
supercritical flow is dynamically impossible in alluvial streams. Rather, the sediment
transport capacity is typically so high that alluvium cannot usually be supplied at a
fast enough rate.
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Grav Brit
Grav Alta
Grav Ida
Sand Mult
Sand Sing
FrFr
bfbf
1
0.1
0.00001
0.0001
0.001
0.01
S
0.1
1
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DIMENSIONLESS CHEZY FRICTION COEFFICIENT VERSUS SLOPE
Again, the sand-bed and gravel-bed sets mesh together smoothly, but the
resistance coefficient is generally larger in the sand-bed streams. This
probably reflects the effect of dunes.
100
Grav Brit
Grav Alta
Grav Ida
Sand Mult
Sand Sing
Czbf
10
1
0.00001
0.0001
0.001
S
0.01
0.1
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DIMENSIONLESS CHEZY FRICTION COEFFICIENT VERSUS
DIMENSIONLESS DEPTH
The sand-bed and gravel-bed sets plot in different regions, largely because
in sand-bed streams resistance is more dependent on bedform
characteristics.
100
Czbf
10
Grav Brit
Grav Alta
Grav Ida
Sand Mult
Sand Sing
1
1
10
100
1000
Ĥ
10000
100000
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BANKFULL SHIELDS NUMBER VERSUS DIMENSIONLESS DISCHARGE
Gravel-bed streams maintain a bankfull Shields stress that is loosely about
0.05. Sand-bed streams maintain a bankfull Shields stress that is loosely
about 1.9.
1.E+01
1.E+00


1.E-01
bf 50
Grav Brit
Grav Alta
Sand Mult
Sand Sing
Grav Ida
1.E-02
1.E-03
1.E+02
1.E+04
1.E+06
1.E+08
1.E+10
1.E+12
1.E+14
Q̂
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SOME REGRESSION RELATIONS FOR BANKFULL GEOMETRY
The regression relations below are based on the same data as those in the
previous slides of this chapter.
 4.87 Q̂0.461 , gravel  bed
B̂  
0.565
, sand  bed
0.274 Q̂
0.368 Q̂0.405 , gravel  bed
Ĥ  
0.321
, sand  bed
 3.01Q̂
0.0976Q̂ 0.341 , gravel  bed
S
0.397
, sand  bed
 6.42 Q̂
0.049 , gravel  bed
bf 50  
 1.86 , sand  bed
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Rf  [
4
]1/ 2
3c D (Re p )
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REVIEW FROM CHAPTER 2: MODES OF TRANSPORT OF SEDIMENT
Bed material load is that part of the sediment load that exchanges with the bed
(and thus contributes to morphodynamics).
Wash load is transported through without exchange with the bed.
In rivers, material finer than 0.0625 mm (silt and clay) is often approximated as
wash load.
Bed material load is further subdivided into bedload and suspended load.
Bedload:
sliding, rolling or saltating just above bed
role of turbulence is indirect, ballistic
trajectory
Suspended load:
feels direct dispersive effect of eddies
may be wafted high into the water column
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SHIELDS REGIME DIAGRAM
The concepts in this diagram are explained more in Chapter 6. The thick solid line
approximately divides the regimes of no motion versus motion (normally as
bedload) of Ds50 of the surface material at bankfull flow. The thin solid line plays the
same role in regard to significant suspension of the size Ds50 of the surface material.
10
suspension
no suspension
1
suspension
bf 50
motion
0.1
motion
no motion
silt
0.01
1.E+00
sand
1.E+01
gravel
1.E+02
1.E+03
Rep50
1.E+04
1.E+05
1.E+06
20
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SHIELDS REGIME DIAGRAM WITH DATA FOR GRAVEL-BED AND
SAND-BED STREAMS
The two stream types plot in very different places: sand-bed streams can normally
easily suspend their dominant bed material at bankfull flow: gravel-bed streams
normally cannot do so (but do, on the other hand, suspend sand).
10
suspension
no suspension
suspension
1

motion
Brit

bf 50
Alta
Ida
Sand mult
0.1
Sand sing
motion
no motion
silt
0.01
1.E+00
sand
1.E+01
gravel
1.E+02
1.E+03
Rep50
1.E+04
1.E+05
1.E+06
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SHIELDS REGIME DIAGRAM WITH DATA FOR STREAMS WITH VALUES
OF D50 BETWEEN 0.5 mm AND 16 mm ADDED
The extra data are for the Japanese streams of Yamamoto (1994): the discharge
used is a characteristic flood flow that is probably close to bankfull flow, and for the
gravel-bed streams, the characteristic D50 is based on a bulk bed material sample
rather than a surface sample. The sand-bed Japanese streams plot with the other
sand-bed streams; likewise with the gravel-bed streams. The transition between the
two types is seen to be smooth, with a paucity of streams in the transitional range.
10
suspension
motion
ripples
Brit
Alta
Ida
Sand mult
Sand sing
Japan
Yamamoto
1
bf 50
0.1
0.01
1.E+00
1.E+01
1.E+02
1.E+03
Rep50
1.E+04
1.E+05
1.E+06
22
1D SEDIMENT TRANSPORT MORPHODYNAMICS
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REFERENCES FOR CHAPTER 3
Charlton, F. G., Brown, P. M. and Benson, R. W. , 1978, The hydraulic geometry of some gravel
rivers in Britain, Report INT 180, Hydraulics Research Station, Wallingford, England, 48 p.
Church, M. and Rood, K., 1983, Catalogue of alluvial river data, Report, Dept, of Geography,
University of British Columbia, Vancouver, B. C., Canada.
Fujita, K., K. Yamamoto and Y. Akabori, 1998, Evolution mechanisms of the longitudinal bed
profiles of major alluvial rivers in Japan and their implications for profile change prediction,
Transactions, Japan Society of Civil Engineering, 600(II-44): 37–50 (in Japanese).
Kellerhals, R., Neill, C. R. and Bray, D. I., 1972, Hydraulic and geomorphic characteristics of
rivers in Alberta, River Engineering and Surface Hydrology Report, Research Council of
Alberta, Canada, No. 72-1.
Parker, G., Paola, C., Whipple, K. and Mohrig, D., 1998, Alluvial fans formed by channelized
fluvial and sheet flow: theory, J. Hydraul. Engrg., 124(10), 1-11.
Parker, G., Toro-Escobar, C. M., Ramey, M. and Beck, S., 2003, Effect Of Floodwater Extraction
On Mountain Stream Morphology, J. Hydraul. Engrg., 129(11), 885-895.
Yamamoto, K., 1994, The Study of Alluvial Rivers, Sankaidou (in Japanese).
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