2007-2008

1

Loads, dynamics and structural design

Offshore Wind Farm Design

Michiel Zaaijer

DUWIND

2007-2008 2

Overview

• Introduction

• Modelling offshore wind turbines

• Types of analysis and tools

• Loads and dynamics in design

2007-2008 3

2007-2008

4

IntroductionLoads, dynamics and structural design

2007-2008 5

Harmonic loading

( ) ( )ϕω +⋅⋅= tFtF sinˆ

0 1 2 3 4 5 61

0

1

Simple Harmonic Loading

Time

Loa

ding

- Gravity loads on blades- Mass imbalance rotor (1P)- Aerodynamic imbalance (1P)- Small regular waves

27 RPM = 0.45 Hz

2007-2008 6

Non-harmonic periodic loading

0 1 2 3 4 5 61

0

1

Complex Cyclic Loading

Time

Lo

adin

g

- Wind-shear- Yaw misalignment- Tower shadow- Rotational sampling of turbulence

0 1 2 3 4 5 60.5

0

0.51st Signal (0.5 Hz)

Time

Lo

adin

g

0 1 2 3 4 5 60.5

0

0.52nd Signal (1 Hz)

Time

Lo

adin

g

0 1 2 3 4 5 60.5

0

0.53rd Signal (1.5 Hz)

Time

Lo

adin

g

( )

( )0ˆ sink k

k

F t

a a F k tω ϕ∞

=

+ +∑

(all 2P or 3P and multiples)

3P

2007-2008 7

Non-periodic random loading

0 1 2 3 4 5 6

1

0

1

Random Load

Time

Loa

din

g

- Turbulence (small scale)- Random waves

2007-2008 8

Other (non-periodic) loading

Transients

0 1 2 3 4 5 61

0

1

Step Load

Time

Loa

ding

Short events

0 1 2 3 4 5 61

0

1

Impulsive Load

Time

Loa

ding

- Start/stop- Turbine failures- Storm front

- Extreme gust- Extreme waves

2007-2008

9

IntroductionLoads, dynamics and structural design

2007-2008 10

The effect of dynamics

km

k = 1 [N/m]

-2

-1

0

1

2

1F

Force [N]

-2

-1

0

1

2

1

xResponse [m]

?

2007-2008 11

The effect of dynamics

-2

-1

0

1

2

1

-2

-1

0

1

2

1

m= 0.0005 [kg]

-2

-1

0

1

2

1

m= 0.1 [kg]

Force [N]

-2

-1

0

1

2

1

m= 0 [kg]

(Static)

2007-2008 12

-2

-1

0

1

2

1

-2

-1

0

1

2

1

The effect of dynamics

km

FSystem

Fintern = k · x

Force [N]

m= 0.0005 [kg]

Response [m]Internal forces ≠ external forcesdue to dynamics

Internal forces drive the design,not external forces!

2007-2008 13

Dynamic amplification factor

0 1 2 3 4 50

1

2

3

4

5

damping ratio = 0.1damping ratio = 0.2damping ratio = 0.5

Frequency RatioD

yna

mic

Am

plif

ica

tion

Fa

cto

r (D

AF

)

Note: the DAF is defined for harmonic excitation

DAF = Dynamic amplitudeStatic deformation

fexcitation

fnatural

Resonance

2007-2008 14

Character of resonance

• Excitation frequency ≈ natural frequency

• Large oscillations

• Fatigue damage (due to severe cyclic loading)

• Generally not destructive (anticipated in design)

Natural frequencies of wind turbine (-components) are close to several excitation frequencies

2007-2008 15

Classification for wind turbines

1P 3P

soft-soft soft-stiff stiff-stiff

1

DAF

f0

Excitation

Response

2007-2008 16

Soft-stiff example

1P = 0.45 Hz

fnatural= 0.55 Hz

3P = 1.35 Hz

2007-2008 17

Reduced response to loading

DAF

1

f0

Alleviation of (wind) loading by shedding loads through motion

soft-softstructure

Typical rotor loadingfrequencies

1P 3PTypical wave loading

frequencies

2007-2008 18

Increased response to loading

1-P *-P

Quasi-static or amplified response to wave loading

2007-2008 19

Single degree of freedom system

xk ⋅+

k

xc &⋅+

c

xmF &&⋅=

m

F

x

2007-2008 20

Wind turbine characteristics

• Stiffness• Material properties / soil properties• Buoyancy of a floating structure

• Damping• Material properties / soil properties• Aerodynamic loading• Control• (Viscosity of water / radiation in soil)

• Inertia• Material properties• Hydrodynamic loading (water added mass)• Entrained water mass

2007-2008 21

Linear / non-linear systems

x(t) y(t)

a·x1(t) + b·x2(t) a·y1(t) + b·y2(t)

Linear system:

Non-linear system:

x(t) + x0 y(t) + y0Initial condition x0:

• No superposition possible• Possible dependency on initial conditions• Possible variation in output statistics for the same input (statistics)

2007-2008 22

Non-linearities for wind turbines

• Aerodynamic loading

• Hydrodynamic loading

• extreme waves

• waves and currents

• Speed and pitch control

• some algorithms

• settings for various wind speeds

• Extreme deformations (2nd order effects)

2007-2008

23

IntroductionLoads, dynamics and structural design

2007-2008 24

Lifelong response signal

Response(loading + dynamics)

Time �

Extreme events

Lifelong variations

2007-2008 25

Effects of loads and dynamics

• Ultimate limit state (ULS)(maximum load carrying resistance)

• Yield and buckling

• Loss of bearing / overturning

• Failure of critical components

• Fatigue limit state (FLS)(effect of cyclic loading)

• Repeated wind and wave loading

• Repeated gravity loading on blade

2007-2008 26

Effects of loads and dynamics

• Accidental limit state (ALS)(accidental event or operational failure, local damage or large displacements allowed)

• Ship impact

• Serviceability limit state (SLS)(deformations/motion, tolerance for normal use)

• Blade tip tower clearance

• Vibrations that may damage equipment

• Tilt of turbine due to differential settlement

2007-2008 27

Design drivers of wind turbinesComponent Design drivers

Ultimate Fatigue

Tower top top mass -

Tower - wind/wave

Submerged wind/wave/current wind/wavetower

Foundation wind/wave/current -

2007-2008 28

Importance of dynamics in design

• Increase or decrease of maximum load

• Affects Ultimate Limit State conditions

• Increase or decrease of number of load cycles and their amplitudes

• Affects Fatigue Limit State / Lifetime

2007-2008 29

Effect on structural design

Monopilesoft-soft

Monopilesoft-stiff

Support structure costSoft-stiff monopile≈ 100 % Soft-soft monopile≈ 80 %

Energy costSoft-stiff monopile≈ 100 % Soft-soft monopile≈ 95 %

2007-2008 30

Use of dynamic models

Analyse system properties

Avoid resonance and instabilities

Assess lifelong loading

Reduce internal loads and match resistance

Make lightest and cheapest structural design

1. 2. 3.

Validate reliability and technical lifetime

2007-2008

31

Modelling of offshore wind turbines

Structural models of rotor, nacelle and support structure

2007-2008 32

Flexibility of wind turbines

Drive train - Torsion

Blades - Flapwise bending- Edgewise bending- Torsion

Tower - Bending- Torsion

Rotor - Rotation

Foundation- Rotation- Horizontal- Vertical

2007-2008 33

Integrated dynamic model

Wind

Wave

Grid

Controllers

Rotor Drive train Generator

Offshore wind turbine

Support structure

2007-2008 34

Rotor model

Aerodynamic properties

Distributed mass-stiffness

Beam theoryFEM

µ, EIx,y,pTablesCl – αCd – α

2007-2008 35

Drive train model

Ihub+low speed shaft

Igenerator

Stiffness torsion in transmission and main shaft; main shaft bending

Damping transmission suspension and generator torque control

Transmission ratio

2007-2008 36

Generator model

n0

generator

motor

00

Tk,g

n

synchronous generator:

n0 2n0

induction generator:

Tk,g

0 0

generator

motor

n

Slip

2007-2008 37

Tower model

Distributed mass-stiffness

Beam theoryFEM

µ, EIx,y,p

Modal representation

Deflection 1st mode

+

Deflection 2nd mode

=

“Total”deformation

Effective reduction of DOFs

2007-2008 38

Foundation model

⋅

=

θθθθ

θ u

kk

kk

M

H

x

xxx

2007-2008

39

Modelling of offshore wind turbinesDeriving parameters for foundation models

2007-2008 40

Importance of foundation model40

.0m

5.0m

15.0

m21

.0m

3500

Ø x

75

250

0Øx

100

2800

Ø x

60

280

0Ø x

32

280

0Ø x

25

2800

Ø x

20

37.0m

(25.0m Penetration)

3.0m

6.0m

280

0Ø x

60

15.4m

12.0m

12.0m

12.0m

6.0m

Pile

Tower

Flange

Boat Landing

J-Tube

MSL

x 30

3.0m

3.5m

5.0m

Scour Protection

4.6m

x10

0

Rotor/nacelle mass 130,000 kg

First natural frequency (Hz)without foundation 0.34627with foundation 0.29055with scour 0.28219

Second natural frequency (Hz)without foundation 2.2006with foundation 1.3328with scour 1.2508

2007-2008 41

Enhanced foundation model

External shaft friction(t-z curves)

Internal shaft friction(t-z curves)

Pile plug resistence(Q-z curves)

Pile point resistance(Q-z curves)

Lateral resistance(p-y curves)

Use:Standards (API/DNV)Existing software(In exercise: ANSYS Macro’s)

2007-2008 42

Scour

General scour depth

Local scour depth

Overburden reduction depth

No scour condition

General scour only

Local scour condition

Vertical effective soil pressure0

Pile

Seabed

Typically 6 times pile diameter

Typically 1-1.5 times pile diameter

2007-2008 43

Effective fixity length

Seabed

Effective fixity

length

3.3 D – 3.7 DExperience with offshore turbines

6 DGeneral calculations

7 D – 8 DVery soft silt

3.5 D – 4.5 DStiff clay

Effective fixity length

Configuration

2007-2008 44

Uncoupled springs

Tower

Seabed

Rotation

Translations

Forced displacement/rotation

Ignore M Ignore F

Method A

θF M

u

Ignore θ

Applied force/moment

Ignore uMethod B

θF M

u

In exercise: Use ANSYS Macro’s and method B for a monopile

2007-2008 45

Stiffness matrix

Stiffness matrix

Seabed

Tower

Run two load cases with FEM model with py-curves(See next slide)

⋅

=

θθθθ

θ u

kk

kk

M

H

x

xxx

2007-2008 46

FEM-based pile-head stiffness

4. Check assumption with another FEM solution

111 θθ ⋅+⋅= xxx kukF

111 θθθθ ⋅+⋅= kukM x

1. Solve FEM for F1, M1

(F1, M1 near loading situation of interest)

222 θθ ⋅+⋅= xxx kukF

222 θθθθ ⋅+⋅= kukM x

2. Solve FEM for F2, M2

(F2, M2 near loading situation of interest)

3. Scratch one equation and solve kxx, kxθ, kθθ(kθx = kxθ, assume matrix equal for both loads)

2007-2008 47

Selection of pile foundation models

• Foundation flexibility significant enough to require close consideration of modelling

• Effective fixity length model dissuaded

• Stiffness matrix much more favourable than uncoupled springsFor exercise: Monopile in Bladed modeled with uncoupled springs (unfortunately)

2007-2008 48

Vertical

Horizontal

Rocking

InertiaViscous damping

Spring stiffness

( )ν−⋅⋅13

3DG

( )ν

ν87

116

−−⋅⋅ DG

ν−⋅

1

2 DG

( )νρ−⋅

⋅⋅132

65.04 GD

( )νρ−⋅

⋅⋅24

6.42 GD

( )νρ−⋅

⋅⋅14

4.32 GD

( )νρ

−⋅⋅132

64.05D

( )νρ

−⋅⋅28

76.03D

( )νρ

−⋅⋅18

08.13D

GBSLumped springs and dashpots for:- Horizontal- Vertical- Rocking

Documented GBS model parameters

2007-2008

49

Types of analysis and toolsNatural frequency and mode analysis

2007-2008 50

FEM modal analysis

FEM analysis provides:

• Natural frequencies

• Mode shapes

• (Pre-processed) matrices of structural properties:

• Mass

• Stiffness

• Damping

1

XYZ

Parametric support structure model generation

2007-2008 51

Natural frequencies

0

0.5

1

1.5

2

2.5

3

3.5

Monopile Monopod Tripod Truss

Nat

ura

l fre

qu

enci

es

2007-2008 52

Modes of the support structure

Monopile 1st mode 2nd mode

2007-2008 53

Rayleigh's method

=

Z Velocity:

Maximumstrain energy

2ˆ~ Z

( )2max ˆ2

1

:

xkV

SDOF

=

Maximumkinetic energy

22ˆ~ ω⋅Z

( )( )

( )22

20max

ˆ2

12

1

:

xm

xmT

SDOF

ω=

= &

( ) ( ) ( )tZxtxv ωsinˆ, ⋅Ψ=

2007-2008 54

Rayleigh's method

• To estimate first natural frequency (lowest)

• Based on energy conservation in undamped, free vibration: Exchange of energy between motion and strain

• Mode shape must fit boundary conditions

• Best estimate of mode shape results in lowest estimate of natural frequency

• (Deflection under static top-load gives educated guess of mode shape)

2007-2008 55

Rayleigh’s method for stepped tower

( )2 322

2 4

44 48

3

top eq

found

eq

m m L LT C

EI

ππω π

+= ≈ ⋅ +

See document on Blackboard for:• Derivation of this equation• Explanation of EIeq, meq, Cfound

2007-2008 56

Free vibration of cylinder in water

( ) ( )cwcwDcMwM xvxvDCxDCaDCf &&&& −−⋅⋅+⋅⋅−−⋅⋅= ⊥⊥⊥ ,,2

,2

2

1

41

4ρπρπρ

Inertia force Drag force

Inertia force due to moving cylinder

• Still water � remaining inertia term is called ‘water added mass’

• With CM ≈ 2 � water added mass ≈mass of replaced waterBut related to water surroundingthe cylinder!

• Use water added mass in analysis of natural frequency and modes

2007-2008

57

Types of analysis and toolsResponse analysis

2007-2008 58

Types of response analysis

• Static analysis with dynamic response factors

• Time domain simulation

• Frequency domain analysis

• Mixtures

All approaches can also be divided in:

• Integrated combined loading

• Superposition of effect of load components (wind, wave, current, gravity)

2007-2008 59

Static + dynamic response factors

• Calculate static response for several loading conditions (separate wind, wave, g)

• Estimate a dynamic response factor per condition (comparison of characteristic frequencies) Typical 1.2-1.5

• Superimpose results (including partial safety factors per loading type)

2007-2008 60

Superposition of forces

SuperpositionWaves +current

Windon tower

ThrustGravity

2007-2008 61

Time domain simulation

• Generate realisations of external conditions

• Integrate equations of motion numerically

• Analyse response (extremes, probability distribution, fatigue, …)

• Repeat until statistically sound information is obtained

The tool used in the exercise to do this is ‘Bladed’.See Blackboard item ‘Assignments’ for a tutorial and manuals.

2007-2008 62

Frequency domain analysis

Fourier transforms and linear systems

Time domain Frequency domain

( ) ( ) ( )thtytx ,, ( ) ( ) ( )ωωω HYX ,,

( ) ( ) ( ) ( ) ( )*y t x h t d x t h tτ τ τ= ⋅ − =∫ ( ) ( ) ( )ωωω HXY ⋅=

( ) ( )( ) ( )tybtya

txbtxa

21

21

⋅+⋅→⋅+⋅ ( ) ( )

( ) ( )ωωωω

21

21

YbYa

XbXa

⋅+⋅→⋅+⋅

2007-2008 63

Frequency domain analysis

• Determine transfer function per load sourceLinearise system or use small harmonic loads

• Multiply spectrum of load source with transfer function

• Superimpose response spectra of different sources

Due to non-linearity in the system, this procedure must be

repeated for different average wind speeds

2007-2008 64

Time domain - frequency domain

Time domain Frequency domain

• Comprehensive non-linear structural model

• Simplified linear structural model

•Very time consuming • Very rapid calculation• Careful choice of time signal

• Well documented wind turbulence spectra

• Able to model control system dynamics

• Able only to model linear control system

• Established fatigue prediction tools

• Fatigue prediction tools relatively new

2007-2008 65

TD simulation:- Transfer function tower top

loading (linearisation)- Aerodynamic damping

FD analysis:- Transfer function for wind loading- Aerodynamic damping as extra

structural damping- Linear wave loading

+ ≈

Mixing time- and frequency domain

2007-2008 66

U(1-a)

Aerodynamic damping

Tower for-aft motion

Blade motion

Vblade

Angle of attackdecreases/increases

-Vblade

αLift/thrust force

diminishes/increases

δL

δL opposite Vblade

2007-2008 67

Aerodynamic damping

0

1

2

3

4

5

6

5 10 15 20 25

wind speed at hub height [m/s]

aero

dyn

. dam

pin

g a

s fr

ac. o

f cr

it.

dam

p. [

%]

soft-soft monopile

soft-stiff monotower

stiff-stiff lattice tower

Function of wind speed, turbine design (aerodynamic and control) and support structure!

2007-2008 68

Some relevant analysis tools

ANSYSSesamAdams WTPhatasBladedFlexTurbu

FEM Time Freq Rotor OffshoreXX X X XX X X XX X X XX X X XX X X XX X X X

2007-2008

69

Loads and dynamics in designOverview of the process

2007-2008 70

Suggested steps

• Choose a limited set of load cases

• Make preliminary design based on static loads

• Check for resonance*

• Check extreme loads with time domain simulations*

• Check fatigue damage*

* Adjust design when necessary

2007-2008 71

Partial safety factor method

• Apply load and resistance factors to:

• loads on the structure or load effects in the structure

• resistance of the structure or strength of materials

• Fulfill design criterion:

• Combined loading with non-linear effects:

• Apply one safety factor to combined load effect, determined from structural analysis of simultaneous loading

RS

RS

γγ ≤⋅

2007-2008 72

Values for safety factors

• Importance of structural component w.r.t. consequence of failure considered

• Typically between 0.7 and 1.35

• ≤ 1.0 for favourable loads!

• Load factor 1.0 for fatigue (safety in resistance)

• See e.g. Offshore standard DNV-OS-J101Design of offshore wind turbine structures

2007-2008

73

Loads and dynamics in designChoose load cases

2007-2008 74

Fundamental problems in evaluation

Response(loading + dynamics)

Time �

More realisationsat the same site

What is the true extreme?

Long time span (20 year)

2007-2008 75

Load cases: Combine conditions

extreme

normal

external conditions

stand-by

operational conditions

normal conditions

start-up

power production

normal shut-down

fault conditions

condition after occurrence of a fault

erection

The number of combinations that is required in the standards is enormous!

2007-2008 76

Reducing number of load cases (extremes)

Select a few independent extreme conditions that might be design driving, e.g.:

• Extreme loading during normal operation

• Extreme loading during failure

• Extreme wind loading above cut-out

• Extreme wave loading

And combine these with reduced conditions for the other aspects (wind, wave, current)

2007-2008 77

Reducing number of load cases (fatigue)

Hs \ \ Tz 0 - 1 1 - 2 2 - 3 3 - 4 4 - 5 5 - 6 6 - 7 7 - 8 8 - 9 total5.5 - 6 0.05 - 5.5 0.08 0.14.5 - 5 0.04 0.3 0.34 - 4.5 0.3 0.08 0.43.5 - 4 lumped sea state 0.7 0.73 - 3.5 0.7 0.72.5 - 3 0.6 0.04 0.72 - 2.5 0.2 0.21.5 - 2 0.01 - 1.5 3.4 0.4 3.80.5 - 1 19 58 0.7 77.70 - 0.5 0.68 1.0 65 12 0.1 0.11 79.0

total 0.7 0.0 1.0 84.2 73.4 2.0 1.9 0.5 0.0 164

Idling: Vw > Vcut_out

Idling: Vw < Vcut_in

Normal operation:Vcut_in < Vw < Vcut_out

Lump states in 3D scatter diagram

Use normal operation and idling

2007-2008 78

T

VVrated Vcut-out

‘Ideal’ pitch

Stall

Responseto gust/failure

Vextreme

~V2

~V-1

~V2

Knowledge about load case selection:Thrust curves

2007-2008 79

Extreme and reduced conditions

• Hmax ≈ 1.86 · Hs

• Hreduced ≈ 1.32 · Hs

• Vgust,max ≈ 1.2 · V10 min

• Vgust,reduced ≈ (1.2 / 1.1) · V10 min

2007-2008

80

Loads and dynamics in designMake preliminary design

2007-2008 81

Preliminary support structure design

• Determine largest loads at several heights• Estimate wind, wave, current and gravity loads

e.g. CD,AX = 8/9 (Betz) at Vrated & linear wave & DAF & safety

• Superimpose and determine largest at each height

• Dimension tower (moments / section modulus)

• Rule of thump D/t• 200 tower section

• ~60 driven foundation pile (see e.g. API on BB)

• Estimate pile size with Blum’s method(See document on Blackboard!)

2007-2008

82

Loads and dynamics in designCheck for resonance

2007-2008 83

Campbell diagram

‘forbidden’area

margin

Cha

ract

eris

tic fr

eque

ncy

Rotor speed

1e lead-lag

3-P

1-P

1e flap

1st tower frequency1st tower frequency 1st tower frequency

Soft-stiff

Soft-soft

Stiff-stiff

Wave-excitation

Soft-stiff

Soft-soft

2007-2008 84

Design adaptations

• Change diameters and/or wall thicknesses

• Shift massese.g. move transformer from nacelle to platform

• Adjust rotor speed controle.g. skip resonance in partial load region

• Change concepte.g. to braced tower / tripod

2007-2008

85

Loads and dynamics in designCheck lifetime fatigue

2007-2008 86

Fatigue

Fstatic

F

time

failure

σ

number of cycles

fatigue test

Fatigue: after a number of cycles of a varying load below static strengthfailure occurs.

2007-2008 87

S-N curves

log N

log σamp

UTS

1:20? Carbon-Epoxy

1:10

Glass-Polyester

Steel (Welded)

1:3

2007-2008 88

Variable amplitude loading

σamp

log N

n1

n2

n3

n4n5

N1

N2

N3N3

N4

N5

Miner’s Damage Rule:5

5

4

4

3

3

2

2

1

1

N

n

N

n

N

n

N

n

N

n

N

n

i

i ++++=∑

Damage < 1.0

2007-2008 89

Stochastic loadingStress history can be converted to blocks of constant amplitude loadings (using counting method)

σamp

log N

stress histogramσ

Time

Stress history

Information about sequence lost

2007-2008 90

Rainflow counting

• Two parametric method: Range and mean

• Display series of extremes with vertical time axis

• Drip ‘rain’ from each extreme, stop at a larger extreme

• Start and stop combine to one stress cycle

2007-2008 91

Rainflow counting

• Established method

• Several equivalent algorithms exist

• Reservoir method

• Intermediate extremes in groups of 4

• Principle based on stress-strain hysteresis loops:

2007-2008 92

Frequency domain approach

Rayleigh:Theoretical, narrow band signals:

Dirlik: Empirical, wide band signals:

Used for spectra of random, Gaussian, stationary processes

2007-2008 93

Lifetime fatigue analysisHs \ \ Tz 0 - 1 s 1 - 2 s 2 - 3 s 3 - 4 s 4 - 5 s 5 - 6 s 6 - 7 s 7 - 8 s 8 - 9 s total5.5 - 6 m 0.05 - 5.5 m 0.08 0.14.5 - 5 m Idling, high: Vw >= Vcut_out 0.04 0.3 0.34 - 4.5 m 0.3 0.08 0.43.5 - 4 m lumped sea state 0.7 0.73 - 3.5 m 0.7 0.72.5 - 3 m 0.6 0.04 0.72 - 2.5 m 0.2 0.21.5 - 2 m idling, low: Vw < Vcut_in 0.01 - 1.5 m 3.4 0.4 3.80.5 - 1 m 19 58 0.7 77.70 - 0.5 m 0.68 1.0 65 12 0.1 0.11 79.0total 0.7 0.0 1.0 84.2 73.4 2.0 1.9 0.5 0.0 164

Do the following for all load cases(scatter diagram, operational and idle)

σ

Time

Determine stress time series or PSD(PSD = Power Spectral Density)

Determine stress histogram(Rainflow counting – Dirlik)

σamp

log N

2007-2008 94

Lifetime fatigue analysisn1 N1Apply Miner’s rule to histogram

(damage per load case) σamp

log N

∑=i

i

N

nD

Apply Miner’s to all load cases:Damage of each load case (normalised to 1 unit of time) *

Probability of load case * Total lifetime

0.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Idle

,low

1

Idle

,low

2

Idle

,low

3

pro

d. 8

m/s

pro

d. 1

0 m

/s

pro

d. 1

4 m

/s

pro

d. 1

5 m

/s

pro

d. 1

7 m

/s

pro

d. 1

9 m

/s

pro

d. 2

0 m

/s

pro

d. 2

1 m

/s

Idle

, hig

h 1

Idle

, hig

h 2

Idle

, hig

h 3dam

age

for

load

cas

e w

ith

un

ity

pro

bab

ility

[-]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

pro

bab

ility

of

load

cas

e [-

]PP wind & waves

II, IP: waves

PP: wind

PP: waves

probability

Load case typePile 5.5 m below mudline

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

Idle

,low

1

Idle

,low

2

Idle

,low

3

pro

d. 8

m/s

pro

d. 1

0 m

/s

pro

d. 1

4 m

/s

pro

d. 1

5 m

/s

pro

d. 1

7 m

/s

pro

d. 1

9 m

/s

pro

d. 2

0 m

/s

pro

d. 2

1 m

/s

Idle

, hig

h 1

Idle

, hig

h 2

Idle

, hig

h 3

(ab

solu

te)

dam

age

per

load

cas

e [-

]

No.1: wind & waves (full avail.)

No. 2: waves & no aerodyn. damping

No. 4: pure wind

No. 5: waves & aerodyn. damping

Fatigue analysis typePile 5.5 m below mudline

2007-2008 95

Integrated system dynamics

0

10

20

30

40

50

Equ

ival

ent b

endi

ng m

omen

t

wind

wave

windloading

waveloading

super-position

separate analyse

combinedloading

integratedanalysis

combined