modelling considerations for dynamic soil structure ... · l. v. andersen: modelling considerations...

Modelling considerations for

dynamic soil–structure interaction of

offshore wind turbine foundations

Lars Vabbersgaard Andersen

Department of Civil Engineering, Aalborg University, Denmark

ISCOG 2017 & GeGe 2017

Zhejiang University | Hangzhou | China | 5–7 July 2017

• Dynamic stiffness and damping of

wind-turbine foundations

• Stochastic model for prediction of

fundamental frequencies

• Lumped-parameter models

for wind-turbine foundations

• Probabilistic model for evaluation

of fatigue loads

Acknowledgement: The work has to large

extent been carried out by my PhD students:

Mohammad Javad Vahdatirad, Mehdi Bayat,

Mads Damgaard, and Paulius Bucinskas

Outline of presentation

L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations 2

• The fatigue limit state (FLS) is the design driver for many

modern offshore wind turbines

• Three possible structural design regimes

• Soft–soft ( f1 < 1P) f1: First natural frequency

• Soft–stiff (1P < f1 < 3P) 1P: Rotor rate

• Stiff–stiff (3P < f1) 3P: Blade passage rate

Overall design approach


Dynamic stiffness and damping of


Measured damping and fundamental frequencies,

influence of pore water seepage


• Logarithmic decrement histograms for the four wind parks

Estimation of damping in four wind parks


Wind Park I

29 Turbines have been investigated

Wind Park II


Wind Park III


Wind Park IV


• Calculated natural frequencies are systematically too low

• Lowest natural frequencies recorded for each wind turbine

in a wind park are higher than the calculated value

• The calculation is based on a linear Winkler model

Measured and calculated eigenfrequencies


• A part of the difference may be caused by the typical but

erroneous assumptions about drained conditions

• Even at the frequency related to the first mode of an OWT

on a monopile, drained response is not obtained in sandy

soil around the foundation

Effects of pore water seepage


• Calculated natural frequencies are updated (x)

• Still the computed natural frequencies are too low

• Improved models of soil–pile interaction are needed

• Current models are subject to high bias and uncertainty



x x

xx


• Pore water effect on shear modulus and loss factor

• Stiffness of poroelastic model determined from two-phase model

• Equivalent partially undrained Poisson’s ratio for solid model



• Pore water effect on shear modulus and loss factor

• Viscous damping model calibrated from poroelastic model

• Damping only in transition phase (typically in sand)


Stochastic model for prediction of

fundamental frequencies

Monopile foundation, random soil properties


• Calibration of the structural properties:

Natural frequency close to 0.285 Hz

• Modelling of the pile as a beam

• Soil behaviour: p–y curve (clay)

• Soil–pile interaction: Winkler model

• Undrained shear strength modelled as

stochastic process

• Monte Carlo Simulation

Random soil properties: Monopile in clay


• Spatial variation for the undrained shear strength of soil


L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations

0

5

10

15

20

25

30

350 200 400 600 800

Undrained shear strength (kN/m2)

Lay

er d

epth

(m

)

Random field

Mean value

13

Random field for undrained

shear strength

- Mean value increasing

linearly with depth

- Coefficient of variation:40 %

- Correlation length: δ = 0.5 m

- Distribution type: lognormal

• Eigen frequency obtained from p–y curves



0 5 10 15

x 107

0

0.5

1

1.5

2

2.5

3

3.5x 10

-8

Impedance (horizontal), N/m

Pro

babil

ity D

ensi

ty

(a)

Histogram

Lognormal distribution

0 1 2 3 4 5 6 7

x 1010

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

x 10-10

Impedance (rotational), N.m/rad

Pro

babil

ity D

ensi

ty

(b)

Histogram


0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.310

10

20

30

40

50

60

70

80

Natural frequency (fn), Hz

Probabil

ity D

ensit

y

Histogram

0 5 10 15

x 107

0

0.5

1

1.5

2

2.5

3

3.5x 10

-8

Impedance (horizontal), N/m

Pro

bab

ilit

y D

ensi

ty

(a)

Histogram


0 1 2 3 4 5 6 7

x 1010

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

x 10-10

Impedance (rotational), N.m/rad

Pro

bab

ilit

y D

ensi

ty

(b)

Histogram


14

• Sample random field simulation results for a monopile

• Can be used for code-calibration but not direct analysis

Random soil properties: Nonlinear FEA


Mapping of the three-dimensional random field

in the finite-element model

Plastic strains at fully developed failure

mechanism

15

Lumped-parameter models for


Formulation of consistent lumped-parameter models,

time-domain analysis with few degrees of freedom


Consistent lumped-parameter model (LPM)


• Rational approximation of the frequency-response

functions for each non-zero component of C(ω)

•

•



• Foundation with more than one reference point (RP)

where

•

•

• Six degrees of freedom per RP



x

y

z

16

13

11 14

1215

26

23

21 24

2225

Footing 1 Footing 2

)()()( FFF FZC

,)()()()(Ff,2f,1f,F

TTN

TT ZZZZ

,)()()()(Ff,2f,1f,F

TTN

TT FFFF

nznynxnznynxT

n UUU ,,,,,,f, Z

nznynxnznynxTn MMMPPP ,,,,,,f, F

• Not all terms should be included in the LPM

• Dynamic flexibilities relative to maximum flexibility



• Three typical examples of dynamic stiffness compontents

• Direct stiffness related to one degree of freedom (sliding)

• Coupling term for two d.o.f. of one footing (sliding–rocking)

• Cross-coupling term for two d.o.f. of two footings (rocking–rocking)



Probabilistic model for evaluation of

fatigue loads

Random soil properties, linearized model, load

evaluation by aero-hydro-elastic code


• The soil is regarded as viscoelastic

• Nonlinear behaviour of soil is partly accounted for

• A representative shear strain level in the ground is estimated

• The shear modulus and loss factor are changed accordingly for

each design load case

• Assumptions

• Shear strain is directly

proportional to load

• Load is directly proportional

to mean wind speed

• Notes on assumptions

• Regards the mean values

• Ideally a backbone curve

should be used

Random linearized model for the soil


Random linearized model for the soil


• Soil modelled as

viscoelastic layer

• Monopile modelled

as beam fixed at the

bottom

• Pile cap is rigid

• LPM with 2 internal

d.o.f. for each non-

zero component

Lumped-parameter model for the pile


• Metocean data for a site in the North Sea are used

• Conditional probabilities of wave directions are given for

each mean wind speed interval and mean wind direction

• 12 x 12 x 13 x 6 x 10 minutes = 6,739,200 s simulations

should be done for one realization of the soil properties

Design load cases in aero-hydro-elastic analysis


• The number of design load cases (DLCs) is reduced

• 4–24 m/s and 4 simulations per DLC: 6,729,200 s → 3,801,600 s

• Opposing wind/wave directions lumped: 3,456,000 s → 950,400 s

• DLCs with same fatigue contribution lumped: 950,400 s → 113,400 s

Design load cases in aero-hydro-elastic analysis


All DLCs within one cell

are represented by one

DLC that is extended to

cover the full time event

Must hold for

the 10%, the

50% and the

90% quantile

• Lognormal distributions of soil properties are recovered

PDFs for soil properties at various wind speeds


• Natural frequency

• Upper limit ~ bottom fixed

solution

• Beta distribution provides a

good fit

• COV is generally small but

increasing with increasing

mean wind speed

• Damping

• Lognormal distribution

• Large COV—especially at

low mean wind speeds

• High influence on fatigue in

the side–side direction

PDFs for natural frequencies and damping


• Uncertainties in the soil

properties have a large

impact on side–side ΔMeq

1 Hz equivalent fatigue moment in two directions


Thank you

[email protected]

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