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Modelling fast transient flows and
morphological evolution in rivers
Sandra Soares-Frazão
Civil Engineering
Université catholique de Louvain
1
Contents
• Mathematical models
• Open questions
– 1D approach
– Steep slopes
– Sediment transport
• Application to breaching
2
Depth-averaged models
• Clear Water Layer (CWL)
– Saint-Venant – Exner
• Mixture Layer(ML)
– Variable density
• Two Phases (2P)
– Distinct velocities
• Two Layers (2L)
4
Numerical resolution
• Saint-Venant – Exner 2D
• Unstructured mesh
• Finite-volume scheme
• HLLC flux solver
5
(Soares-Frazão and Zech 2010)
tLt
i
nb
j
jj*jj
i
ni
ni Δ
Ω
Δ
1
11SUFTUU
Closure equations
• Sediment transport
• Formules empiriques, calibrées dans
des conditions limitées
6
References Non-dimensional bed-load Calibration conditions
d (mm) S0 τ*
Meyer-Peter &
Müller (1948) 0.4-29 <0.02 <0.25
Wong and
Parker (2006) 0.4-29 <0.02 <0.25
Wu et al. (2000) 0.062-128 <0.016 -
Smart & Jäggi
(1983) 0.4-29 0.073-0.2 0.1-3.3
Camenen &
Larson (2005) 0.084-200 0.03-0.2 0.1-3.3
Wilson (1987) 13 - >0.8
Abrahams
(2003) 3-10.5 0.03-0.21 0.6-1.83
2/3
,* 8 cMPMsq
2/3
,* 97.3 cWPsq
)(2.4 0**
5.0
*
6.0
*,* cfSJs Suuq
5.1
*,* / uuq As
cCLsq 5.4exp125.1
,*
2.2
**
5.1
,* 1'0053.0 cWus nnq
5.1
,* 8.11 Wisq
Numerical model for bank erosion
• Slope break
– Tilting of local slope in each element
– Designed to ensure mass conservation
8
(Swartenbroekx et al 2010)
Contents
• Mathematical models
• Open questions
– 1D approach
– Sediment transport: bed shear stress
– Steep slopes
• Application to breaching
9
11
Brembo river (Italy)
• Bed profile
0 5 10 15 20 25 30 35 40 45 50100
150
200
250
300
350
400
450
500
x (km)
zb
(m
)
12
Brembo river
• Bed profile
0 5 10 15 20 25 30 35 40 45 50100
150
200
250
300
350
400
450
500
x (km)
zb
(m
)
13
Brembo river (Italy)
• Bed profile
0 5 10 15 20 25 30 35 40 45 50100
150
200
250
300
350
400
450
500
x (km)
zb
(m
)
14
Water level predictions
200
250
300
350
400
450
5 10 15 20 25 30x (km)
z (m) Bed elevation
ORSA1D
SV1D
SANA1D
SOBEK
• Results very close for all models
15
Discharge predictions
• Apparent significant variations
0
200
400
600
0 10 20 30 40 50x (km)
Q (m³/s) ORSA1D
SV1D
SANA
SOBEK
16
Discharge prediction
• Saint-Venant equations
f
z
SAgx
IggI
A
Q
xt
Q
x
Q
t
A
11
2
0 Q = Discharge
Q = Momentum
17 x
t
Analysis of discharge variations
niQ
1niQ
*2/1iQ
*2/1iQ
*2/1
*2/1
1
ii
ni
ni QQ
x
tAA
tSx
tQQ ii
ni
ni
*2/1
*2/1
1SgIA
Q
xt
Q
x
Q
t
A
1
2
0
18
Discharge prediction
• Mass flux instead of Q
0
200
400
600
0 10 20 30 40 50x (km)
Q (m³/s) ORSA1D
SV1D
SANA1D
Open questions
• 1D approach: improved models
– HLLS
– Augmented-Roe with energy balance
19
Adaptation to irregular
cross-sections
Fabian Franzini,
PhD research
Open questions
• Sediment transport: bed shear stress
– Manning?
– Extension to
transient flow?
20
Ilaria Fent
PhD research
Open questions
• Sediment transport on steep slopes
– Gravity projection?
– Adapted transport formula?
21
Contents
• Mathematical models
• Open questions
– 1D approach
– Steep slopes
– Sediment transport
• Application to breaching
23
Breaching
24
Elbe (Germany), June 2013 (www.independent.ie/world-news/europe/villages-evacuated-as-german-floods-worsen-29334727.html)
Breaching
• By overtopping
25
Visser (1998)
Vertical erosion Lateral erosion
Sediment transport
Geotechnical
instability
Experimental test case
• Dispositif expérimental
26
(Spinewine et al 2004)
Sand: d50 = 1.8 mm, ρs = 2615 kg/m³, ε0 = 42%
1:2
1:3
Numerical results
• Model parameters
– Manning: n = 0.0167 s m–1/3
– CFL: 0.9
– zw,upstream = 0.45 m
– Mesh:
27
Dike
l = 2 cm
Sand layer
h = 10 cm
Downstream
l = 1 m
Upstream
l = 1 m
Sylvie Van Emelen
PhD 2014
Dike:
variable mesh
Numerical results: mesh influence
30
t = 70 s
l =10 cm ~45 000
meshes
l =5 cm ~90 000
meshes
l =3 cm ~200 000
meshes
l =2 cm ~420 000
meshes
Numerical results
• Comparaison des formules de charriage
31
MPM
CL
WP Wu
SJ
Wi+MPM A+MPM
EXPE
t = 175 s
Numerical results
• Comparaison des formules de charriage
32
MPM
CL
WP Wu
SJ
Wi+MPM A+MPM
EXPE
t = 175 s
Underestimated vertical erosion
Breach narrow and shallow!
Numerical results
• Comparaison des formules de charriage
33
MPM
CL
WP Wu
SJ
Wi+MPM A+MPM
EXPE
t = 175 s
Fast crest lowering
Important vertical erosion
Influence of transport formula
35
• Discharge hydrograph
• Peak
discharge:
mean and
standard
deviation