modelling wave-structure-soil interaction with...

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 Modelling Wave-Structure-Soil Interaction with OpenFOAM®


Facilities at LWI

Lab area: 140m. X 40m.

3 wave flumes

3D wave basin

www.tu-braunschweig.de/lwi


www.tu-braunschweig.de/lwi


The Large-Wave Flume (GWK)



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



WaSFI concept

The concept of wave-structure-foundation interaction



An example of WaSFI: Marine gravity structures

The large wave flume (GWK), the coastal research center (FZK),Hanover



Caisson breakwater tests

Oumeraci & Kudella, 2004



Displacement-pore pressure relationship

Regular waves H = 0.7m, T = 6.5s u. hs = 1.6m



Outline

Introduction







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)



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



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



1D consolidation (Terzaghi)



Wave-induced direct seabed response



Wave-induced seabed response (validation)

Jeng (1996)



Seismic-induced response of an embankment



Rocking motion of a plate on seabed

Sumer et al. (2008)



Breaking wave impact on a caisson breakwater



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



One-way (semi) coupling validation



Outline

Introduction






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



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



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 Modelling Wave-Structure-Soil Interaction with OpenFOAM®


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



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



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



Van Gent (1993) physical model tests



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



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]



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]



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]





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



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



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



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



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



Outline

Introduction







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.


www.geotechfoam.com

Thank you for your attention!

Dr.-Ing. Hisham Elsafti+49 (0)531 / [email protected]

mailto:[email protected]

modelling wave-structure-soil interaction with...

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