Modelling Wave-Structure-Soil Interactionwith OpenFOAM®
Leichtweiss-Institute, Division of Hydromechanics, Coastaland Ocean Engineering, TU BraunschweigHisham Elsafti and Nils Goseberg, 27.03.2019DANSIS OpenFOAM Seminar, Aalborg University Copenhagen, Denmark
Intro geotechFoam Porous flow Outlook
Outline
Introduction
The geotechFoam solver
Modelling flow through porous media
Concluding remarks and outlook
27.03.2019 Hisham Elsafti and Nils Goseberg Page 2Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
Outline
Introduction
The geotechFoam solver
Modelling flow through porous media
Concluding remarks and outlook
27.03.2019 Hisham Elsafti and Nils Goseberg Page 3Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
Facilities at LWI
Lab area: 140m. X 40m.
3 wave flumes
3D wave basin
www.tu-braunschweig.de/lwi
27.03.2019 Hisham Elsafti and Nils Goseberg Page 4Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
The Large-Wave Flume (GWK)
27.03.2019 Hisham Elsafti and Nils Goseberg Page 5Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
Extension of the GWK
Financial support by BMWi:German Federal Ministry ofEconomy and Energy
The marTech project:€35,526,200
4 years: 01.06.2017 until30.5.2021
New wave machine (maker)
Introduction of curennts
A deeper mid-section of theflume for including soil andfoundations
27.03.2019 Hisham Elsafti and Nils Goseberg Page 6Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
WaSFI concept
The concept of wave-structure-foundation interaction
27.03.2019 Hisham Elsafti and Nils Goseberg Page 7Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
An example of WaSFI: Marine gravity structures
The large wave flume (GWK), the coastal research center (FZK),Hanover
27.03.2019 Hisham Elsafti and Nils Goseberg Page 8Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
Caisson breakwater tests
Oumeraci & Kudella, 2004
27.03.2019 Hisham Elsafti and Nils Goseberg Page 9Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
Displacement-pore pressure relationship
Regular waves H = 0.7m, T = 6.5s u. hs = 1.6m
27.03.2019 Hisham Elsafti and Nils Goseberg Page 10Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
Outline
Introduction
The geotechFoam solver
Modelling flow through porous media
Concluding remarks and outlook
27.03.2019 Hisham Elsafti and Nils Goseberg Page 11Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
The geotechFoam solver
The Finite Volume Method (FVM)Solver of the fully-coupled fully-dynamic (extended) Biot equationsAn approximation is implemented by neglecting the pore fluidconvective accelerationThe u − p approximation is also implemented (neglecting pore fluidacceleration completely)Different material zones: different material properties and/or modelsAn interface for material models (no need to develop a new solver,possible import of developed material models from Abaqus, Flac,plaxis, OpenSees, etc.)A multi-surface plasticity model is implemented for simulating sandcyclic mobilitySoil-structure interaction through frictional contact modellingA single pore fluid (water air mixture with a modified bulk modulus)
27.03.2019 Hisham Elsafti and Nils Goseberg Page 12Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
Extended Biot equations
The mixture momentum balance (equation of motion)
∇ · σ− ρ∂2u∂t2 − c
∂u∂t
− ρf
(∂U∂t
+ U · ∇U
)+ ρb = 0
The momentum balance of the pore fluid
ρf
n
(∂U∂t
+ U · ∇U
)= −∇p − ρf
∂2u∂t2 + ρf b − S
The mass balance equation of the pore fluid
∇ · U +∂εv
∂t+
1Q∂p∂t
= 0
27.03.2019 Hisham Elsafti and Nils Goseberg Page 13Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
The u − p approximation
The mixture momentum balance (equation of motion)
∇ · σ− ρ∂2u∂t2 − c
∂u∂t
+ ρb = 0
The pore fluid mass and momentum balance
∇ ·(
kρf g
(−∇p − ρf
∂2u∂t2 + ρf b
))+∂εv
∂t+
1Q∂p∂t
= 0
27.03.2019 Hisham Elsafti and Nils Goseberg Page 14Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
1D consolidation (Terzaghi)
27.03.2019 Hisham Elsafti and Nils Goseberg Page 15Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
Wave-induced direct seabed response
27.03.2019 Hisham Elsafti and Nils Goseberg Page 16Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
Wave-induced seabed response (validation)
Jeng (1996)
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Intro geotechFoam Porous flow Outlook
Seismic-induced response of an embankment
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Intro geotechFoam Porous flow Outlook
Rocking motion of a plate on seabed
Sumer et al. (2008)
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Intro geotechFoam Porous flow Outlook
Breaking wave impact on a caisson breakwater
27.03.2019 Hisham Elsafti and Nils Goseberg Page 20Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
One-way coupling (caisson breakwater)
One way (semi-) coupling
Separate time and space discretisation
Can also be used to introduce inputfrom experimental results
Overlap zones of CFD and CSDsolvers for realistic flow through porousmedia
27.03.2019 Hisham Elsafti and Nils Goseberg Page 21Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
One-way (semi) coupling validation
27.03.2019 Hisham Elsafti and Nils Goseberg Page 22Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
Outline
Introduction
The geotechFoam solver
Modelling flow through porous media
Concluding remarks and outlook
27.03.2019 Hisham Elsafti and Nils Goseberg Page 23Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
Water flow through granular materials
Resolved solid particles
Flow modelled more accurately
More difficult, more expensive
Averaged domain
Flow meets resistance
More convenient, much faster
27.03.2019 Hisham Elsafti and Nils Goseberg Page 24Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
Averaged models of granular materials
Resistance to flow: drag force + inertial force
Drag force: resistance to unidirectional flow (velocity constant)
Inertial force: resistance to transient flow (velocity changes)
Further, drag force: linear component (Darcy) + nonlinearcomponent (Forchheimer)
More elaborate models: e.g. Lin and Karunarathna (2007)
Darcy (simplest drag model):
U = −KI
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Intro geotechFoam Porous flow Outlook
Drag resistance
Drag resistance force (sink term):
Fd = −∇p = −ρgI
Linear model (Darcy):
Fd = ρgUK
= ρgUK
–> isotropic
Nonlinear model (Darcy-Forchheimer):
Fd = ρg(aU + bU∣∣U∣∣)
Nonlinear model (Lin and Karunarathna, 2007):
Fd = ρg(aU + cU√∣∣U∣∣+ bU
∣∣U∣∣)27.03.2019 Hisham Elsafti and Nils Goseberg Page 26Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
New proposed drag model
Based on the concept of effective viscosityEffective viscosity is a concept used for turbulence modelling (eddyviscosity)An artificial (higher) viscosity is given to water to model resistanceThe drag force (simplified):
Fd = ∇ · τ(porous drag)
Fd = µeff ((∇U + (∇U)T ) −23(∇ · U)I)
µeff = max [δl , δtReP ]µwater
New parameters:δl : linear drag parameterδt : nonlinear drag parameterReP : Particles Re
Drag is either linear or nonlinear Rep
μr
�t
�l
laminar turbulent
1
27.03.2019 Hisham Elsafti and Nils Goseberg Page 27Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
Inertial resistance model
Inertial resistance force: with added mass coefficient (cA)
Fi = cA∂U∂t
cA = γ(1 − n)
nTypically in porous flow models γ = 0.34Van Gent et al. (1995):
γ = max
(0.85 − 0.015
ngTAU
, 0
)b = 1.1
(1 +
7.5KC
)1 − n
n3
1nD50
where: KC =AUT
nD50
T and AU are period and amplitude of oscillatory flowVan Gent’s model cannot be generalized to transient flow
27.03.2019 Hisham Elsafti and Nils Goseberg Page 28Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
New fluid momentum balance equations
Applying VAT and adding pore fluid viscous stresses, addedviscous stresses due to turbulence, sink term for drag resistanceand inertial resistance
ρf
((1 + cA)
n∂U∂t
+1n2 U · ∇U
)=−∇p +
1n
(∇ ·(τ+
Rn
))− ρf
∂2u∂t2 + ρf b − S
Viscosity ratio µr to represent effective viscosity (new model)
ρf
((1 + cA)
n∂U∂t
+1n2 U · ∇U
)=−∇p +
µr
n
(∇ ·(τ+
Rn
))− ρf
∂2u∂t2 + ρf b
where: µr =µeff
(µ+ µt)> 1
27.03.2019 Hisham Elsafti and Nils Goseberg Page 29Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
Van Gent (1993) physical model tests
27.03.2019 Hisham Elsafti and Nils Goseberg Page 30Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
Recalibration of van Gent’s model
For a –> 1732 instead of 1000
a = 1732(1 − n)2
n3
ν
gD250
For b –> 0.665 instead of 1.1
b = 0.6651 − n
n3
1gD50
The model results and recalibration make it clear that an additionalterm for transitional flow conditions (Lin and Karunarathna, 2007) isobsolete
These models superpose linear and nonlinear drag componentsinstead of using either linear or nonlinear drag
27.03.2019 Hisham Elsafti and Nils Goseberg Page 31Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
Calibration of proposed eff. viscosity model
0
1
2
3
4
5
6
7
0 0.1 0.2 0.3 0.4 0.5 0.6
I/U
[s/m
]
U [m/s]
Rock type R3Proposed model
Van Gent (1995) exp.
0
0.5
1
1.5
2
2.5
3
3.5
4
0 0.1 0.2 0.3 0.4 0.5
I/U
[s/m
]
U [m/s]
Rock type R4Proposed model
Van Gent (1995) exp.
0
5
10
15
20
0 0.1 0.2 0.3 0.4 0.5 0.6
I/U
[s/m
]
U [m/s]
Rock type R5Proposed model
Van Gent (1995) exp.
0
2
4
6
8
10
12
0 0.1 0.2 0.3 0.4 0.5
I/U
[s/m
]
U [m/s]
Rock type R8Proposed model
Van Gent (1995) exp.
27.03.2019 Hisham Elsafti and Nils Goseberg Page 32Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
New model parameters
µr = max [1, δl , δtReP ]
ReP =D50|U |
ν
- Linear and nonlinear parameters
δl = 720798.65
+ 241929.15× D85/D15× n
+ 270422446.46 ∗ ×D250
− 53815452.76× DEQ × n
δt = 503.33 + 9184.52× D50
− 25.40× n − 28.04× l/t
− 191.35× D85/D15 − 14355.29× D15
0
50
100
150
200
250
300
350
0 50 100 150 200 250 300 350
Pred
icte
d x
10-3
Calibrated x 10-3
r2 = 0.998
0
20
40
60
80
100
120
140
160
180
0 20 40 60 80 100 120 140 160 180
Pred
icte
d
Calibrated
r2 = 0.999
27.03.2019 Hisham Elsafti and Nils Goseberg Page 33Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
Approximate model link to Darcy permeability
The proposed eff. viscositymodel laminarizes the flow
Sink term: uniform velocityprofile - eff. viscosity: paraboliccurve 0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.2 0.4 0.6 0.8 1
Y [m
]
Velocity [m/s]
Van Gent modelThe presented model
The viscous shear stresses canbe approximated and equalizedto Darcy’s dragδl
n∇ · τ =
ρgK
U
δl =nρgψµK
Fully developedlaminar flow
U
27.03.2019 Hisham Elsafti and Nils Goseberg Page 34Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
Oscillatory flow: Van Gent (1993) results
Results from experiences vary in conforming to a harmonic functionExperiments with higher periods and higher amplitudes give betterresultsPeriod and pressure amplitude are measured from curves for inputto the numerical simulations
27.03.2019 Hisham Elsafti and Nils Goseberg Page 35Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
Oscillatory flow: Fitted numerical results
-0.3
-0.2
-0.1
0
0.1
0.2
12 13 14 15 16 17 18
Ave
rage
d fl
ow v
eloc
ity [m
/s]
Time [s]
Numerical model with constant γ = 0.34Numerical model with constant γ = 2
Experiments from van Gent (1993) -0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
12 13 14 15 16 17 18
Ave
rage
d fl
ow v
eloc
ity [m
/s]
Time [s]
γ for Re dependant cA; = 0.0006γ for constant cA; γ = 2
Experiments of van Gent (1993)
Fitted two types of cA: typical form and ReP dependant form:
cA = γReP(1 − n)
nFor constant cA a value of 0.34 is not universal (see example)
Fitting results to a ReP dependant cA is possible
27.03.2019 Hisham Elsafti and Nils Goseberg Page 36Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
Oscillatory flow: γ value
For the van Gent tests, fittingthe value of γ
The range of available results isnot sufficient
γ is definitely not 0.34
Adding ReP is better, maybemore variables are needed
More experiments are reallyneeded
0
5
10
15
20
0 0.05 0.1 0.15 0.2 0.25 0.3
γ (f
or c
onst
ant c
A)
Averaged flow velocity amplitude [m/s]
Period = 2sPeriod = 3sPeriod = 4s
0
0.001
0.002
0.003
0.004
0.005
0 0.05 0.1 0.15 0.2 0.25 0.3
γ (R
e de
pend
ant c
A)
Averaged flow velocity amplitude [m/s]
Period = 2sPeriod = 3sPeriod = 4s
27.03.2019 Hisham Elsafti and Nils Goseberg Page 37Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
Outline
Introduction
The geotechFoam solver
Modelling flow through porous media
Concluding remarks and outlook
27.03.2019 Hisham Elsafti and Nils Goseberg Page 38Modelling Wave-Structure-Soil Interaction with OpenFOAM®
Intro geotechFoam Porous flow Outlook
Concluding remarks and outlook
Hydro-geotechnical modelling with OpenFOAM: the geotechFoamsolver
Download from repository on BitBucket, visitwww.geotechfoam.com
Tutorials + "draft" documentation
Use of numerical modelling as a virtual lab to work in tandem withphysical modelling
Uplift pressure on structures –> flow through porous media –>cyclic/transient flow???
OpenFOAM® is a registered trademark of OpenCFD Ltd.
27.03.2019 Hisham Elsafti and Nils Goseberg Page 39Modelling Wave-Structure-Soil Interaction with OpenFOAM®