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

L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations 3

Dynamic stiffness and damping of

wind-turbine foundations

Measured damping and fundamental frequencies,

influence of pore water seepage

L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations 4

• Logarithmic decrement histograms for the four wind parks

Estimation of damping in four wind parks

L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations 5

Wind Park I

29 Turbines have been investigated

Wind Park II

27 Turbines have been investigated

Wind Park III

78 Turbines have been investigated

Wind Park IV

34 Turbines have been investigated

• 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

L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations 6

• 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

L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations 7

• 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

Effects of pore water seepage

L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations 8

x x

xx

Effects of pore water seepage

• 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

L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations 9

Effects of pore water seepage

• Pore water effect on shear modulus and loss factor

• Viscous damping model calibrated from poroelastic model

• Damping only in transition phase (typically in sand)

L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations 10

Stochastic model for prediction of

fundamental frequencies

Monopile foundation, random soil properties

L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations 11

• 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

L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations 12

• Spatial variation for the undrained shear strength of soil

Random soil properties: Monopile in clay

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

Random soil properties: Monopile in clay

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

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

Lognormal distribution

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

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

bab

ilit

y D

ensi

ty

(b)

Histogram

Lognormal distribution

14

• Sample random field simulation results for a monopile

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

Random soil properties: Nonlinear FEA

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

Mapping of the three-dimensional random field

in the finite-element model

Plastic strains at fully developed failure

mechanism

15

Lumped-parameter models for

wind-turbine foundations

Formulation of consistent lumped-parameter models,

time-domain analysis with few degrees of freedom

L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations 16

Consistent lumped-parameter model (LPM)

L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations 17

• Rational approximation of the frequency-response

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

•

•

Consistent lumped-parameter model (LPM)

L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations 18

• Foundation with more than one reference point (RP)

where

•

•

• Six degrees of freedom per RP

Consistent lumped-parameter model (LPM)

L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations 19

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

Consistent lumped-parameter model (LPM)

L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations 20

• 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)

Consistent lumped-parameter model (LPM)

L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations 21

Probabilistic model for evaluation of

fatigue loads

Random soil properties, linearized model, load

evaluation by aero-hydro-elastic code

L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations 22

• 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

L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations 23

Random linearized model for the soil

L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations 24

• 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

L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations 25

• 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

L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations 26

• 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

L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations 27

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

L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations 28

• 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

L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations 29

• Uncertainties in the soil

properties have a large

impact on side–side ΔMeq

1 Hz equivalent fatigue moment in two directions

L. V. Andersen: Modelling considerations for dynamic soil–structure interaction of OWT foundations 30

Thank you

la@civil.aau.dk