Modelisation of suspended sediment transport in rivers
Master thesis Véronique Briguet 2011
Alain Recking , Oldrich Navratil, Nicolle Mathys
Contents
2
1. Introduction
2. Data set
3. Data analysis
4. Modelling
5. Perspectives
6. Conclusion
3
Suspension versus bedload
Data set
4
Data set
Fraser River at Yale Lochsa River
2 mm
d50 du lit
GBR
SBR
Sand Bed River versus Gravel Bed River
5
Connexion with hillslopes processes:
Head Water Streams HWS versus Lowland Rivers LR
Erosion on the Draix Catchment
Data set
Data set
0.03 mg/L < C < 29 g/L; 0.01% < S < 18%;
0.012 <Q< 3770 m3/s ; 0.08 < A < 31313 km².
Measurement Nbr of value
Rivers Source
1 Instantaneous Bedload + susp
3186 88 reaches, 76 rivers, 15 SBR, 62 GBR
USGS, USDA…
2 Instantaneous susp
150 5 SBR Brownlie 1985..
3 Annual load 139 1 SBR and 8 GBR, 139 years
ORE Draix, McLean, Church et al 1999…
4 Event load 213 5 HWS ORE Draix
Log(A) Log(C) Log(d50) Log(H) Log(P) Log(q) Log(qb) Log(qs) Log(S) Log(U) Log(W)
Log(C) 0.185 1.000 -0.174 0.302 0.364 0.450 0.630 0.859 -0.168 0.518 0.106
Log(qs) 0.553 0.859 0.036 0.708 0.729 0.831 0.711 1.000 -0.513 0.838 0.471
Correlation coefficient R
A: Watersherd area
D50: median diameter
H: depth
P: power QS
U: Velocity
C: Suspended load concentration
qs: Suspended load / unit width
qb: bedload / unit width
q: Q/W
W: Width
S: Slope
qs=Cq => autocorrelation
Correlation between qb and C
Data Analysis
7
8
Dispersion du ratio instantané Qs / QT
Suspension versus bedload in the total load
Data Analysis
Instantaneous measurements
9
Event scale
Data Analysis
Bedload (t)
Suspension (t)
10
Data Analysis
Annual load
Bedload (t)
Suspension (t)
11
Suspension – bedload interactions: some hypothesis
1 : bedload 2 > 1 : progressive suspension concentration
SBR
1 : weak suspension
2 > : Sharp suspension concentration with bedload
GBR
Data Analysis
HWS Inconsistencies in Qs/Qt between event and volumes
Possible bias in instantaneous measurements with bedload absent for the flood conditions considered
Modelling
Deterministics : Bagnold (1966), Einstein (1950), Celik et Rodi (1991)…
Empirical models : Lefort (1990) , Abrahams (2001)…
12
Equations of fluid mechanics
Constants calibration with
experimental data
Deterministic Model
Identification of representative
variables
Fit equations with experimental data
Empirical model
SUSPENSION Qs OR TOTAL TRANSPORT QT
13
Limits of deterministics and empirical models:Most of them calibrated in flumeWith uniform materialsFine sands
Modelling
Correlation analyses with field
data
Fit equations « black box » models
Statistical models qs=f(q): Turowski & Rickenmann (2010)
Use generally limited to the river used to built the data set (Prosser & Rustomji 2000)
14
Confluence Galabre - BèsHaute Bléone à PradsBès à Sivan
Modelling
Width? Bed diameter? Transported diameter? Fall velocity?...
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Modelling
Discrepancy ratio r =qs calculated
qs measured
Scores = % of r values obtained in a given interval
Tested in the interval [0.1 – 10]
Ex: a scores of 30% significates that 30% of the predictions are correct within plus or minus one order of magnitude
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Modelling
Score when 0
Model Output
Nbre of values
Data set % of
0 0.1<Qc/Qm<10 R²
Comments (input, intermediate calculation…)
Einstein (1950) Qs 2860 1 et 2 5% 31% 0.01 Fall velocity
Bagnold (1966) QT 2658 1 0% 22% 0.61 Fall velocity Bagnold (1966) Qs 2725 1 0% 46% 0.85 Fall velocity Engelund et Hansen (1967) QT 2629 1 0% 57% 0.81 Measured Flow velocity Engelund et Hansen (1967) QT 2629 1 0% 55% 0.65 Calculated flow velocity Ackers et White (1973) QT 2629 1 85% 45% 0.71 Threshold formula Engelund et Fredsoe (1976) Qs 2860 1 et 2 5% 14% 0.1 Fall velocity
Van Rijn (1984) Qs 2658 1 et 2 79% 58% 0.51 Threshold formula, Fall velocity Lefort (1990) QT 2629 1 68% 53% 0.6 Threshold formula Celik et Rodi (1991) Qs 2658 1 et 2 15% 82% 0.85 Fall velocity Abrahams (2001) QT 2629 1 62% 37% 0.19 Threshold formula, Fall velocity
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Modèle de Bagnold (1966)
Modèle de Celik et Rodi (1991)
Modelling
Auto correlation !qs=Cq
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Modelling
1.E-09
1.E-07
1.E-05
1.E-03
1.E-01
1.E+01
1.E-09 1.E-07 1.E-05 1.E-03 1.E-01 1.E+01
Qs meas
Qs
cal
qs=Cq with C randomly choosen
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=> An accurate concentration model is required
Modèle de Celik et Rodi (1991)
Modelling
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Perspectives ?
Tested with a new bedload model specifically developed for gravel beds (Recking 2010)
21
C calculated with qb
measured
C calculated with qb
computed
Perspectives ?
22
Perspectives ?
Conclusion
23
No tool is really efficient in the field, especially
in gravel bed rivers
Strong correlation between suspended load and
bedload, especially in gravel bed rivers
Necessity to develop a new concentration model
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Thank you for your attention