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