SEDIMENT TRANSPORT RATES DURING
UNSTEADY FLOW EVENTS
Joanna Crowe Curran, Ph.D. and Kevin A. Waters, Ph.D.
water resource specialists
Goals
• Quantify impact of repeated unsteady flows on sediment yield, transport rate, and bed
structure
• Connect unsteady flow induced hysteresis with sediment yield, transport rates, and bed structure
• Adjust sediment transport models for hysteresis during unsteady flows
Channel bed adjusts under steady, low flow
Sediment transport alters bed surface
Unsteady, flood flow occurs
Hysteresis affects sediment transport
Unsteady Flow Experiments
Developed from the NRCS curvilinear dimensionless unit hydrograph
30% gravel / 70% sand
D50 = 0.55 mm
Hydrograph work and unsteadiness both varied over an order of magnitude
70% sand/ 30% silt
D50 = 0.27 mm
0.10
High Flow
Low Flow
0.08
Q (cms)
0.078 m3/s
0.06
0.044 m3/s
0.04
0.017 m3/s
0.02
0.00
0
50
100
150
200
250
300
Total Flow Sequence Run Time (min)
350
400
450
500
Sediment transport hysteresis
Sand / Gravel (7)
Clockwise
Figure 8
Counter‐Clockwise
None
100
Sand / Silt (12)
Clockwise
Figure 8
Counter‐Clockwise
Single‐value + Loop
100
100
10
10
qs (g/m/s)
qs (g/m/s)
qs (g/m/s)
10
1
1
1
0.1
0.1
RL
0.01
0.02
CW
CCW
FL
0.04
0.06
q
(m2/s)
0.08
0.1
0.02 0.04 0.06 0.08 0.10 0.12 0.14
q (m2/s)
0.01
0.02
Figure 8
0.04
0.06
q
(m2/s)
0.08
Sand/Gravel Bed Structure
Low flow hydrographs
• Surface sand content decreased by 14% • No bedforms
Steady flow
First hydrograph
Final hydrograph
High flow hydrographs
• Surface sand content increased by 18%
• Limited bedforms
Steady flow
First hydrograph
Final hydrograph
Sand/Silt Bed Structure
Surface sand and bedform steepness increased with successive
hydrographs
Steady flow
Low flow hydrographs
• Ripples formed
First hydrograph
Final hydrograph
Steady flow
High flow hydrographs
• Ripples and patches developed
First hydrograph
Final hydrograph
Hysteresis and Sediment Yield
Combine flow data with channel width and D50 to estimate sediment yield
.
∗
∗
22762
1.0E+06
1.0E+05
Ys*
1.0E+04
1.0E+03
0.0
2.0
4.0

6.0
8.0
Peak flow
70
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
qs (g/m/s)
60
50
40
30
20
10
0
1
9
17
Rising Limb
25
33 41
Time
49
57
65
Q (m3/s)
Hysteresis and Sediment Transport Rate
Separate calculations are for the rising limb and falling limb of the hydrograph
73
Falling Limb
1. Using estimates of bed slope and depth during the flow, separate data from rising and falling limbs of the hydrograph
2. Calculate 
3. With grain size, convert to *
4. Use in Parker‐Einstein equation with W*=0.002 to find r*
5. With *, r*, velocity, depth, and bed slope, calculate qs
∗
1
1
0.8531
∗
∗
Connect Bed Structure with Transport
Sand/Gravel
Sand/Silt
0.10
∗
0.01
White boxes: rising limb only
Grey boxes: falling limb only
Diamonds: total hydrograph
Clockwise
Counter‐
Clockwise
Clockwise
Counter‐
Clockwise
Transport Equations: Sand/Silt Sediment
Equation
Ackers‐White (1973)
Einstein and Brown (1950)
Engelund and Hansen (1967)
Laursen (1958)
Van Rijn (1984)
Yang (1973)
0.5 DR 2.0
33%
19%
39%
49%
42%
58%
Equation
Method Calculating Rising and Falling Limbs Separately
1000
100
100
Measured qs (g/m/s)
Measured qs (g/m/s)
68%
1000
Yang, 1973
10
1
0.1
Greater under‐
prediction at low flows
0.01
0.001
0.001
0.5 DR 2.0
0.01
0.1
1
10
Predicted qs (g/m/s)
100
New method with RL and FL separated
10
1
0.1
0.01
1000
0.001
0.001
0.01
0.1
1
10
Predicted qs (g/m/s)
100
1000
Transport Equations: Sand/Gravel Sediment
Equation
Einstein and Brown (1950)
Ackers‐White (1973)
Yang (1973, 1984)
0.5 DR 2.0
22%
33%
33%
Equation
Method Calculating Rising and Falling Limbs Separately
1000
Yang, 1984
100
Measured qs (g/m/s)
Measured qs (g/m/s)
68%
1000
100
10
1
0.1
0.01
0.001
0.001
0.5 DR 2.0
0.1
1
10
Predicted qs (g/m/s)
100
10
1
0.1
0.01
Over‐predicts qs
0.01
New method with RL and FL separated
1000
0.001
0.001
0.01
0.1
1
10
100
Predicted qs (g/m/s)
1.08 kg/m/s . . . On a river 5 m wide (16.4 ft) over 15 minutes of full sediment mobility, this is 4890 kg / 10,780 pounds / 5.4 tons
1000
Impact of Unsteady Flows
Unsteady flow alters the bed surface structure
Accounting for hysteresis improves sediment yield and transport rate predictions, especially at low flows
Transport rates vary with hydrograph limb creating hysteresis
Bedforms develop and sediment yield increases Surface fines or coarsens
Structure develops over successive hydrographs
Reference shear stresses adjust with changes in bed surface and slope What is ‘good enough’ in sediment transport?
Only need an estimate of the amount of sediment that will be / has been moved during a storm? – Use storm variables (depth, velocity, duration), channel width, and bed D50 to predict yield for the event
Have a sand bed and ok with half transport estimates between 0.5‐
2 times actual and not concerned with low flow rates? Have a gravel and sand bed and ok with 1/3 between 0.5‐2 times actual?
– Use the standard sediment transport equations
Is there sensitive habitat or infrastructure and a need to evaluate bed structure response to a storm? Want to do better?
– Spend the time to calculate transport rates over hydrograph rising and falling limb separately
~70% within 0.5‐2 times actual
not consistently overpredicting gravel/sand transport
Questions
[email protected]
[email protected]
Watch for the paper:
Waters, K.A. and J.C. Curran, “Linking bed morphology changes of two sediment mixtures to sediment transport predictions in unsteady flows,” Water Resources Research. In Review.
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