Modelisation of suspended sediment transport in rivers Master thesis Véronique Briguet 2011 Alain Recking, Oldrich Navratil, Nicolle Mathys.

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