Fatigue analysis of jacket support structure for offshore wind turbines

Journal of Science and Technology in Civil Engineering NUCE 2019. 13 (1): 46–59

FATIGUE ANALYSIS OF JACKET SUPPORT STRUCTURE
FOR OFFSHORE WIND TURBINES
Nguyen Van Vuonga,∗, Mai Hong Quana
a

Faculty of Coastal and Offshore Engineering, National University of Civil Engineering,
55 Giai Phong road, Hai Ba Trung district, Hanoi, Vietnam
Article history:
Received 01 October 2018, Revised 19 November 2018, Accepted 31 January 2019

Abstract
In the past few decades and up to now, the fossil energy has exerted tremendous impacts on human environments and gives rise to greenhouse effects while the wind power, especially in offshore region, is an attractive
renewable energy resource. For offshore fixed wind turbine, stronger foundation like jacket structure has a good
applicability for deeper water depth. Once water depth increases, dynamic responses of offshore wind turbine
(OWT) support structures become an important issue. The primary factor will be the total height of support
structure increases when wind turbine is installed at offshore locations with deeper water depth, in other words
the fatigue life of each components of support structure decrease. The other one will experience more wind
forces due to its large blades, apart from wave, current forces, when makes a comparison with offshore oil and
gas platforms. Summing up two above reasons, fatigue analysis, in this research, is a crucial aspect for design of
offshore wind turbine structures which are subjected to time series wind, wave loads and carried out by aiding
of SACS software for model simulation (P-M rules and S-N curves) and Matlab code. Results show that the
fatigue life of OWT is decreased accordingly by increasing the wind speed acting on the blades, especially with
the simultaneous interaction between wind and wind-induced wave. Hence, this should be considered in wind
turbine design.
Keywords: offshore wind turbine; Jacket structure; fatigue analysis; P-M rules; S-N curves.
/>
c 2019 National University of Civil Engineering

1. Introduction

Wind energy has been utilized for mankind in terms of electricity production for thousands of
years [1]. Wind energy onshore nowadays is a mature industry responsible for meeting a part of the
energy needs in countries around the globe. In the recent few decades, offshore fixed wind turbines
have been all installed in shallow water depth off the coast of Europe (< 30 m) [2], with the typical
gravity-based supports of Mono-pile and Tripod structures. However, there is strong demand that the
application of offshore fixed wind turbine could be extended to deep water where winds are stronger
and steadier than on land [3]. Once water depth increases, dynamic responses of offshore wind turbine
support structures become an important issue. Although there is a potential for more wind turbines to
be erected in offshore locations in order to achieve a greater wind energy harvest, the access to turbines
for maintenance will be restricted. Besides, the fatigue analysis of offshore oil and gas platforms have
been studied in a comprehensive way for ages, but for wind turbine in general and offshore wind
turbine in particular, this issue is still a new field and a restriction to scientists. Thus, the objective of
∗

Corresponding author. E-mail address: (Vuong, N. V.)

46


Vuong, N. V., Quan, M. H. / Journal of Science and Technology in Civil Engineering

the article is to analyze fatigue life of components of wind turbine support structure and eventually
predict the expected lifetime of OWT.
xtended to deep water where winds are stronger and
The paper is carried out by applying the fatigue knowledge for the offshore wind turbine, any
water depth increases, dynamic responses of offshore
computing details
are conducted
by is
MATLAB

code program and SACS software. Applications of the
become an important
issue. Although
there
a potential
method
to
offshore
wind
turbine
with
Jacket
support
ected in offshore locations in order to achieve a greater structure are illustrated in the following sections
up with conclusions
and highlights
for future research.
to turbinesand
forending
maintenance
will be restricted.
Besides,
ore oil and gas platforms have been studied in a
t for wind 2.
turbine
general
and offshore
wind
turbine
Load in

effects
analysis
of offshore
wind
turbine
a new field and a restriction to scientists. Thus, the
load
yze fatigue2.1.
lifeWind
of components
of wind turbine support
he expected
lifetime
of
OWT.
a. Wind profiles and turbulence
applying the fatigue
knowledge
for the offshore
wind
The wind
velocity measured
in the field
shows variations in space, time and direction and is
are conducted by MATLAB code program and SACS
composed by two parts: a mean (or slowly variable) and a stochastic part (turbulence) as showing in
method to offshore wind turbine with Jacket support
Fig. 1. The
wind up
velocity

any points of
structure is the sum of the average wind velocity and
ollowing sections
andtotal
ending
with in
conclusions
and
turbulent wind velocity [4]:
(1)
{V (z, t)} = {¯v (z)} + {v (t)}
hore wind turbine
where v¯ (z) is average wind velocity; v(t) is turbulent wind velocity.
The geometric parameters in Fig. 2 conclude: the water mean depth (h), the hub height above
the mean water level (H) and the blades length (or rotor radius) (R). Accepting approximately the
ed in the field shows variations in space, time and
component
of the wind
according
to the Weibull distribution law. Weibull probability diswo parts: adynamic
mean (or
slowly variable)
and
a stochastic
tribution
(the
so-called
probability
distribution
Rosin-Rammler) is a common form used to describe

Fig. 1. The total wind velocity in any points of structure
occurrence
of velocity
extreme quantities
in meteorology, hydrology and weather forecasts such as floods,
elocity andthe
turbulent
wind
[4]:
waves and winds. In this paper, the Weibull probability distribution is used to calculate the cumulative
velocity
any velocity;
directions.k (1)
)} = {v
̅ (z)}frequencies
+ {v(𝑡)} of wind
where
U is in
wind
is the shape parameter; U is the rate parameter. The
o

distribution curve of Weibull function with different wind speed as shown in Fig. 2.
c)
Correlation
between
significant wave height, period and
wind speed
Wind blowing time tx,u is in
accordance to wind fetch X, and

wind velocity u [5], the time to a
state of fully developed sea:

wind
elocity.
Figure
pth (h),
n water
or rotor
imately
e wind
ribution
X0.67
ribution
t x,u = 77.23 0.34 0.33
(3)
𝑢
g
ribution
Significant wave height in
n form
Figure 1. Wind, accordance
wave and current
actions
Figure 2. Distribution curve of wind speed
with
windconfiguration
velocity u:[14]
of
Figure 1. Wind, wave and current actions

Figure
2. Distribution curve of wind speed
2
ogy, hydrology and weather forecasts such as floods,
𝑢∗
configuration [5]
(4)
Hz = Ho
the Weibull probability distribution is used to calculate
g
nd velocity in any directions.
where according
b. Cumulative
distributionto
function
of wind velocity according to Weibull
ribution function
of windfrequency
velocity
Weibull
𝑘
g𝑋
𝑈
m1
H
=
λ
𝑥
;
𝑥

=
o
1
(2)
 U 𝑢k 2
= 1 − exp [− ( ) ]
∗
𝑈o
P (u) = 1 − exp −
(2) (5)
U0 

1 rate parameter. The distribution curve
where U is wind velocity; k is the shape parameter; U0 is the
2 m1 =
λ1 = 0.0413;
; 𝑢 = √Cd u10
of Weibull function with different wind speed as shown in Fig.
2 2.∗
Zero-crossing average period Tz47
in accordance with wind velocity u:
Tz = To

where

𝑢∗
g

(6)

Vuong, N. V., Quan, M. H. / Journal of Science and Technology in Civil Engineering

c. Correlation between significant wave height, period and wind speed
Wind blowing time t x,u is in accordance to wind fetch X, and wind velocity u [6], the time to a
state of fully developed sea:
X 0.67
(3)
t x,u = 77.23 0.34 0.33
u g
Significant wave height in accordance with wind velocity u:
Hz = H0

u2∗
g

where
H0 = λ1 xm1 ;

x=

2

(4)

gX
u2∗

(5)
4

Ag
g
(8)
exp
(−B
(
) )
1
λ1 = 0.0413; m𝑓15= ; u∗ = 𝑓UCd u10
2
𝐻𝑠 2
𝑈 4
3 u:
Zero-crossing average period T z in
accordance
with
wind
velocity
(9)
A = 4𝜋 ( 2 ) ; B = 16𝜋 (
)
𝑔𝑇𝑧
𝑔𝑇𝑧
u∗
where U is wind speed at the
(6)
T z height
= T 0 of 19.5m above sea level; A, B are constants,
and P-M spectra with wind speed U19.5 =g15m/s is shown in Fig.5.

c) JONSWAP Spectra
where
(ω − ωm )2
ag 2
5 ω −4
T 0 = λ(2 xm2) ) γ exp (−
(7) (10)
Sηη (𝑓) =
exp
(−
)
(2π)4 𝑓 5
4 ωm
2σ2 ωm
1
−0.22
λ1 = 𝑋0.751;
m2 =
16.04
3
(11)
a = 0.046 ( 2 ) ; ωm =
(XU10 )0.38
𝑈10
2.2. Wind-induced
wave
where
X isload
fetch; U10 is wind speed at the height of 10m above sea level; γ = 0.3; σ =
a. Sea-state0.08.

model
For the by
purpose
of primarily
Waves are generated
wind blowing
over the
analyzing
fatigue
of
offshore
surface of the sea and are the major source of loadP-M spectra
is posian
ing for moststructures,
offshore structures.
At any fixed
appropriate
model
in
the
study
that
tion in the open sea, the level of the water surface
deals with the state of sea with
varies randomly due to the passing waves and may
maximum wind speed (generating
be modeled as a steadily stochastic process, stanwaves under the infinite wind
dard distribution, Ergodic nature [8]. The wave
fetch). The most glaring difference
height H of single wave is normally defined as

between JONSWAP and P-M
the total range of η(t) in the time interval T 0 beFigure 3. Description of single wave [15]
spectrum with the same wind speed
Figure 3. Description of single wave [7]
tween two consecutive zero up-crossing by η(t),
can be seen in Fig. 4.
Sηη (𝑓) =

see Fig. 3.
Recent research has led to a number of semi-empirical expressions for the form of the spectra
S ηη (ω) of water surface elevation η(t), (generally called wave spectra). Two commonly used spectra
are the Pierson-Moskowitz (P-M) [9] and the JONSWAP [10].
b. Pierson-Moskowitz Spectra (P-M Spectra)


Ag2
g
S ηη ( f ) = 5 exp −B
fU
f

4





(8)

48

Figure 4. Pierson-Moskowitz and JONSWAP spectrum

Figure 5. P-M spectrum, wind speed u19.5=15m/s


ectrum

For the purpose of primarily
analyzing fatigue of offshore
structures, P-M spectra is an
appropriate model in the study that
Vuong, N. V., Quan, M. H. / Journal of Science
and Technology
deals
with thein Civil
stateEngineering
of sea with
maximum wind speed (generating
2
4 the infinite wind
waves 3 under
Hs
U
A = 4π
;
B
=
16π
(9)

fetch). The
gT z most glaring difference
gT z2
between JONSWAP and P-M
where
is wind speed
at thewave
height
sea level; A, B are constants, and P-M spectra
Figure U
3. Description
of single
[15]of 19.5 m above
spectrum
with the same wind speed
with wind speed U19.5 = 15 m/s is shown in Fig. 4.
can be seen in Fig. 4.

Figure 4. Pierson-Moskowitz and JONSWAP spectrum

Figure 5. P-M spectrum, wind speed u19.5=15m/s

Figure 5. P-M spectrum, wind speed u19.5 = 15 m/s

Figure 4. Pierson-Moskowitz and JONSWAP
spectrum

3.1 The fundamental equation of the stochastic dyn
Differential equation that describes stochastic



structure
system is as 2following:
 5 ω −4 
ag2
 γ exp − (ω − ωm )
MÜ + CU̇ + (10)
KU = F(𝑡)
exp (12)
−
2
4 5

he stochastic
dynamic problem
c. JONSWAP Spectra
ibes stochastic oscillation of the offshore fixS ηη ( f ) =

Figure

3. Stochastic dynamics of wind turbine in freq

d turbine in frequency domain

+ KU = F(𝑡)

Figure 3

4 ωm
2σ ωm



 X −0.22 
16.04
a = 0.046  2 4; ωm =
U10
(XU10 )0.38
(2π) f

(11)

where X is fetch; U10 is wind speed at the height of 10 m above sea level; γ = 0.3; σ = 0.08.
For the purpose of primarily analyzing fatigue of offshore structures, P-M spectra is an appropriate
model in the study that deals with the state of sea with maximum wind speed (generating waves under
the infinite wind fetch). The most glaring difference between JONSWAP and P-M spectrum with the
same wind speed can be seen in Fig. 5.
3. Stochastic dynamics of wind turbine in frequency domain
3.1. The fundamental equation of the stochastic dynamic problem
Differential equation that describes stochastic oscillation of the offshore fix-structure system is as
following:
M U¨ + C U˙ + KU = F (t)
(12)

49


Vuong, N. V., Quan, M. H. / Journal of Science and Technology in Civil Engineering

where RFF (τ) is correlation function (self-correlation) of the steadily stochastic process (SSP) F(t),
performs Fourier integral transformation (complex form) to RFF (τ):

∞

RFF (τ) =

S FF (ω) eiωt dω

(13)

−∞

where S FF (ω) - Spectral density function of SSP F(t), is the Fourier map of the correlation function
RFF (τ):
∞

1
S FF (ω) = JRFF (τ) =
2π

RFF (τ) eiωt dω

(14)

−∞

Formula
pairs
Eqs.(τ)
(13)
(14) is called
formula(self-correlation)

Khinchin – Weinerr of
(only
SSP), which
where
RFF
isand
correlation
function
theapplicable
steadilytostochastic
play
a pivotal
role
in the
method of
solving
stochastic
dynamical problems.
Linking
to to
Eq.R(14),
allows
process
(SSP)
F(t),
performs
Furier
integral
transformation
(complex

form)
FF (τ):
∞ time-varied correlation function t, to one for frequencyto transform problem to be considered for
𝑖𝜔𝑡 forms of this transform.
varied density spectral function
ω.  Fig.
6 describes
typical
𝑅𝐹𝐹 (𝜏)
= ∫
𝑆𝐹𝐹 (𝜔) 𝑒
 𝑑𝜔
(13)
−∞

3.2. System response in frequency domain

where SFF(ω) - Spectral density function of
Khinchin
– Weiner
formula
SSPAlso
F(t),applying
is the Fourier
map
of the correlation
pairs
for
stochastic
process

u(t)
[11],
[noticing
that
function RFF (τ):
∞
1 output
the input
F(t) is SSP, also for
U(t) is SSP],
𝑆𝐹𝐹 (𝜔)   =  𝐽𝑅𝐹𝐹 (𝜏)   =   ∫−∞ 𝑅𝐹𝐹 (𝜏) 𝑒 𝑖𝜔𝑡  𝑑𝜔
2𝜋
we have:
(14)
∞

iωτ (14) is called
Formula
(τ) = Eqs.
(ω) eand
Ruupairs
dω
(15)
S uu(13)
formula Khinchin−∞– Weinerr (only applicable
to SSP), which play
∞ a pivotal role in the
1
method of solving
stochastic dynamical

S uu (ω) =
Ruu (ω) e−iωτ dω
(16)
problems. Linking
2π to Eq. (14), allows to
transform problem −∞
to be considered for timeApplying
correlation
theory
(or spectral
varied correlation function
t, totheory)
one –for
with
any
theories
of
SSP
into
the
Eq.
(16),
obtainfrequency-varied density spectral function ω.
ing important results:
Fig. 6 describes typical forms of this transform.

S uu (ω) = |H (iω)|2 S FF (ω)

(17)

In other words: The output spectral density
Figure 6. Description of spectral method
(system
is equal to
input onedomain
(load)
Figure 6. Description of spectral method
3.2 response)
System response
in the
frequency
multiplied by the square of the transfer function
Also applying Khinchin – Weiner formula pairs for stochastic process u(t) [9],
module (Fig. 8).
[noticing
that the input F(t) is SSP, also
for output U(t) is SSP], we have:
From Eq. (17) determine the average ∞
square (so-called variance) of the response:
∞ 𝑖𝜔𝜏  𝑑𝜔
𝑅𝑢𝑢 (𝜏)  ∞=   ∫ 𝑆𝑢𝑢 (𝜔) 𝑒

σ2u =

(ω)∞dω =
S uu −∞

|H (iω)|2 S FF (ω) dω

(15)

(18)

1
−𝑖𝜔𝜏
0
(16)
 ∫ 𝑅 (𝜔) 𝑒
 𝑑𝜔
2𝜋 −∞ 𝑢𝑢
where H(iω) - transfer function (complex form) also known as “frequency characteristics” of the
Applying correlation theory (or spectral theory) – with any theories of SSP into the
system, receiving this equation:
Eq. (16), obtaining important results:
1
2
(17)
(19)
=
𝑆𝑢𝑢 (𝜔)  H=(iω)
  |𝐻(𝑖𝜔)|
 𝑆𝐹𝐹2(𝜔)
K − Mω
+ iCω
In other words: The output spectral density (system response) is equal to the input
50
one (load) multiplied by the square of the transfer
function module (Fig. 8)
From Eq. (17) determine the average square (so-called variance) of the response:
𝑆𝑢𝑢 (𝜔)   =0  

∞

𝜎𝑢2

=

∫ 𝑆𝑢𝑢 (𝜔) 𝑑𝜔

∞

=

∫ |𝐻(𝑖𝜔)|2  𝑆𝐹𝐹 (𝜔) 𝑑𝜔

(18)


A spectrum can be used to recreate a time signal. By assuming that the phase
is distributed randomly, harmonic waves can be recreated based on the power spec
density at each separate frequency, combined with a randomly picked phase angle
time series created in this way is never the exact copy of the time series but the spe
are theandsame,
provided
that Engineering
the signal is long enough. Fig. 7 show
Vuong, N. V., Quan, M. H. / parameters
Journal of Science
Technology
in Civil
inverse conversion from frequency to time domain as well as the normal transform

4. Fatigue analysis
from time to frequency domain. For both transformations standard algorithm
available, the most commonly used is the Fast Fourier Transform (FFT) and its In
4.1. Fourier transformation
one (IFFT) [10].

A spectrum can be used to recreate a time
signal. By assuming that the phase angle is distributed randomly, harmonic waves can be recreated based on the power spectrum density at each
separate frequency, combined with a randomly
picked phase angle. The time series created in this
way is never the exact copy of the time series but
the spectral parameters are the same, provided that
Figure 7. Transformation from time series to frequency domain and vice versa
the signal is long enough. Fig. 7 shows the inTransformation
time series
to spectrum de
A time signal canFigure
be also7. used
to recreate afrom
spectrum,
the power
verse conversion from frequency to time domain
frequency domain and vice versa
per frequency defined as:
as well as the normal transformation from time to
1 2
1
(𝑆𝑛 /Δf)
= {(𝐴2𝑞 +B
frequency domain. For both transformations standard algorithms

are available,
the𝑞2 )𝑇}
most commonly
2
2
used is the Fast Fourier Transform (FFT)
its Inverse
one (IFFT)
as aand
function
of frequency,
where[12].
the Fourier coefficients Aq and Bq defined by:
A time signal can be also used to recreate a spectrum,
the power spectrum density
2 𝑇
2 𝑇 per frequency
𝐴𝑞 = ∫ 𝑧(𝑡)cos(2πf𝑞 𝑡)dt and 𝐵𝑞 = ∫ 𝑧(𝑡)sin(2πf𝑞 𝑡)dt
defined as:
𝑇
𝑇 0
1 2 When the
1 0 2 spectral
of frequency, we
S n /∆ f = power
Aq + B2q T density is plotted as a function (20)
2 obtain a power
2 density spectrum.
as a function of frequency, where the Fourier
coefficients

Aq in
and
Bqseries
defined by:
4.2 Fatigue
analysis
time

Fatigue is the process of gradual damage done to materials (mainly is steel mat
T
when these are subjected to continually
changing stresses. Due to these stress cha
2
2
the
material
slowly
deteriorates,
initiating
Aq =
z (t) cos 2π fq t dt and Bq =
z (t) sin 2πcracks
fq t dtwhich will eventually
(21) lead to brea
T
of the material. OffshoreTwind turbines are by default subjected to loads varying in
0
0
from wind as well as waves. This means that the stress response will also
offshore

wind turbine’s
to fatigue.
When the power spectral density iscontinuously,
plotted as making
a function
of frequency,
weresponse
will obtain
a power
The fatigue calculation method for variable stress ranges in the time domain c
density spectrum.
summarized by the flowchart in Fig. 8. Calculation of the stresses experienced b
4.2. Fatigue analysis in time series detail being considered under all possible load cases during the lifetime will resul
T

Fatigue is the process of gradual damage done to materials (mainly is steel material) when these
are subjected to continually changing stresses. Due to these stress changes, the material slowly deteriorates, initiating cracks which will eventually lead to breaking of the material. Offshore wind turbines
number
of stress
Byinfiltering
thewind
number
of stress
variations
for every
arelarge
by default
subjected
to time
loadsseries.

varying
time from
as well
as waves.
This means
that the
stress
range
class,
the
Miner
sum
can
be
calculated
to
check
whether
D
<
1.0.
fat
stress response will also vary continuously, making offshore wind turbine’s response
to fatigue.

Figure
fatiguecalculation
calculation
[13]
Figure8.8.Flowchart

Flowchart of
of fatigue
[11]

Fatigue curve linked between the number of stresses S and the number of stress
The fatigue
calculation
method for variable stress ranges in the time domain can be summarized
cycles
N is revealed
as following:
by the flowchart in Fig. 8. Calculation of the stresses experienced by the detail being considered
−m will result in a large number of stress time series.
under all possible load cases during
lifetime
(22) By
N the
= KS
, S>0
51

where K and m are random variables due to inherent physical and statistical
uncertainty. The value of K can depend on the mean stress Sa in the stress cycles. Where
K0 is the value of K from tests with zero mean stress and where Su is the ultimate tensile
strength.


Vuong, N. V., Quan, M. H. / Journal of Science and Technology in Civil Engineering
Figure 8. Flowchart of fatigue calculation [11]

filtering the number
of curve
stress variations
for every
range
the SMiner
can be calculated
Fatigue
linked between
thestress
number
of class,
stresses
and sum
the number
of stress
to check whether
D fisat revealed
< 1.0. as following:
cycles N
Fatigue curve linked between the number of stresses S and the number of stress cycles N is
(22)
revealed as following:
N = KS −m , S > 0
N = KS −m , S > 0
(22)
where K and m are random variables due to inherent physical and statistical
where K and
m are random
due

todepend
inherentonphysical
andstress
statistical
The value
of
uncertainty.
The variables
value of K
can
the mean
Sa in uncertainty.
the stress cycles.
Where
K can depend
on
the
mean
stress
S
in
the
stress
cycles.
Where
K
is
the
value
of

K
from
tests
with
0 where Su is the ultimate tensile
K0 is the value of K froma tests with zero mean stress and
zero mean strength.
stress and where S u is the ultimate tensile strength.
On the above
diagram,
index the
i is index
the number
stress of
ithstress
of structure,
the ratiothe
of ratio
fatigue
On the
above the
diagram,
i is the of
number
ith of structure,
of
damage D ffatigue
theissum
of the fatigue
damage

duefatigue
to the number
stresses
at is calculated
damage as
Dfat
calculated
as the sum
of the
damage of
due
to the caused
numberinofa
short sea state.
stresses caused in a short sea state.
The magnitude
and number
of stresses
are
The magnitude
and number
of stresses
calculated
from fatigue
data by
calculated are
from
fatigue stress
data bystress
counting

To take
all peaks
method. Tocounting
take allmethod.
peaks into
account
withoutinto
without
doubling,
the rain-flow
doubling, account
the rain-flow
method
resembles
rain
method
resembles
rain
flowing
flowing off a pagoda roof as shown in Fig.off
9. a
pagoda
roof
as
shown
in
Fig.
9.
When
When the stress time series is rotated 90 degrees,

thealgorithm
stress time
the counting
starts. series is rotated 90
degrees, the counting algorithm starts.
Figure 9. Description of rainflow method [12]
When the method has been performed, the sigFigure 9. Description of rainflow method [14]
nal is taken apart in a number of half stress range
When the method has been performed, the signal is taken apart in a number of half
variations, that is, the rain-flow cycle runs only in
stress range variations, that is, the rain-flow cycle runs only in one direction each time.
one direction each time. The mean value of cumulative fatigue damage during 1 year and the maxiThe mean value of cumulative fatigue damage during 1 year and the maximum mean
mum meanfatigue
fatiguelifetime
lifetimeTT maxofofthe
thehot
hotspot
spotare
areobtained
obtainedas
asfollows:
follows:
max

[D]
365 × 24 × 3600
ni
D1year = 365x24x3600
𝑛𝑖 ; T max = [D]
T0

D1year =
∑i Ni ; Tmax = D1year
T0
𝑁𝑖
D1year

(23)
(23)

i

where i is investigated stress domain; ni is the number of stress cycles at the ith load; Ni is the numwherethei iscrashes
investigated
of of
stress
cycles
at the
ith load;
thenumber
duration
stress
in time
series;
[D]
ber of cycles until
occur stress
at the domain;
ith load; nTi 0isisthe
N
is

the
number
of
cycles
until
the
crashes
occur
at
the
ith
load;
T
is
the
duration
of
i
0
is permissible fatigue, given in used design standard (for offshore structure [D] = 0.5, from API
stress
in
time
series;
[D]
is
permissible
fatigue,
given
in

used
design
standard
(for
standard).
offshore structure [D] = 0.5, from API standard).
5. Results and discussions
In this paper, the Offshore Jacket Wind Turbine (OJWT) in water depth of 70 m is modeled for
analysis showed in Fig. 10. As shown in Fig. 10, a full-scale offshore wind turbine model includes7
turbine support, transitions, blades and Jacket support. At the top of the support is a 5 MW turbine,
the main specifications are listed in Table 1.
a. Structural dimensions
The size of the wind turbine support structure is selected as Fig. 11 for the analysis of fatigue
damages under the action of sea environment loads such as waves and wind.
The main dimensions of the entire Jacket support structure with the tower and the wind directions
to OJWT are shown in Figs. 12 and 13, respectively. From top to bottom, the Jacket size is 32 m2 on
the seafloor.
52


with the tower and the wind
directions to OJWT are shown in
Figs. 12 and 13 respectively.
From top to bottom, the Jacket
N. V., Quan, M. H. / Journal of Science and Technology in Civil Engineering
size is 32m2 on Vuong,
the seafloor.
Table 1. Characteristics of offshore wind turbines

Power

5
MW
Cut-out wind speed
25 support-structure wind m/s
Figure 10. 3D model of Jacket
turbine
Cut-in
wind
speed
3
m/s
With regard to the input data of waves and winds, the probability of occurrence of
ussions both in theBlade
scopenumber
of this research is taken in 08 directions 3as shown in Tables 2 -and 3.
Null
diameter
3 OJWT. Meanwhile,
m the
EachWind
direction
is 45 indegrees
apart
before
acting on the
ffshore Jacket
Turbine (OJWT)
water depth
of 70m
is

Blade
diameter
126
howed in Fig.
10. As shown
the Figure, are
a full-scale
offshore
prevailing
windindirections
the South
West, East and North East and the wind mspeeds
mass
top-turbine
120000
kg
ludes turbine
support,
blades
andatJacket
support. At
vary
from transitions,
0Concentrated
m/s to 20
m/s.

a 5MW turbine,
main parameters
specifications are listed in Tab. 1.

b)the
Wave
sions
Table 1. Characteristics of offshore wind turbines
nd turbine
5
MW
elected as Power
of fatigue
25
m/s
ion of sea Cut-out wind speed
h as waves

ons of the
structure
the wind
e shown in
spectively.
the Jacket
loor.

Cut-in wind speed

3

m/s

Blade number

3

-

Null diameter

3

m

Blade diameter

126

m

120000

kg

Concentrated mass at
top-turbine

Figure 10. 3D model of Jacket support-structure wind turbine

Figure
10.winds,
3D model
of Jacket support-structure
input data of waves

and
the probability
of occurrence of
wind
turbine in Tables 2 and 3.
s research is taken in 08 directions
as shown
degrees apart before acting on the OJWT. Meanwhile, the
ons are the South West, East and North East and the wind speeds
m/s.

Figure 11. Main dimensions of OJWT

Figure 11. Main dimensions of OJWT

8

of offshore wind turbines

5

MW

25

m/s

3

m/s

3

-

3

m

126

m

120000

kg

Figure 12. Wave directions to OJWT

Figure 12. Wave directions to OJWT

Figure 13. Tower, Brace and diagonal diameters

Table 2. Probability
wave directions
to OJWT
Figure 12. Wave directions
to OJWT of occurrence of Figure
13. Tower,
Brace and diagonal diameters

0⁰
45⁰
90⁰
135⁰
180⁰
225⁰
270⁰
315⁰
Wave
Figure 11. Main dimensions of OJWT
Total
Figure
13.
Tower,
Brace
and
diagonal
diameters
directions
SW
S
SE
E
NE
N
NW
SW

Probability
of occurrence

of wavethe
directions
to OJWT
With regard to theTable
input2. data
of waves
and winds,
probability
of occurrence of both in the
0⁰
135⁰ as 180⁰
315⁰ direction is 45
scope
of this research
is45⁰
taken in90⁰
08 directions
shown in225⁰
Tables 2270⁰
and 3. Each
Probability
Wave
0.3012 0.0353 0.046
0.2964 0.0039 0.002 0.0524 Total
1.000
8
(P)
0.2629
degrees
apart

before
acting
on
the
OJWT.
Meanwhile,
the
prevailing
wind
directions
directions
SW
S
SE
E
NE
N
NW
SW are the South

(SW – South West; S – South; SE – South East; E – East; NE – North East; N –

53
Probability
North; NW
– North
West; SW
– South West).0.2964 0.0039
0.3012
0.0353

0.046
(P)
0.2629

0.002

0.0524

1.000

c) Wind parameters:
3. Probability of occurrence of wind directions to OJWT
(SW – South West; Table
S – South;
SE – South East; E – East; NE – North East; N –
Directions


Vuong, N. V., Quan, M. H. / Journal of Science and Technology in Civil Engineering

West, East and North East and the wind speeds vary from 0 m/s to 20 m/s.
b. Wave parameters
Table 2. Probability of occurrence of wave directions to OJWT

0◦

45◦

90◦

135◦

180◦

225◦

270◦

315◦

SW

S

SE

E

NE

N

NW

SW

0.3012

0.0353

0.046

0.2629

0.2964

0.0039

0.002

0.0524

Wave directions
Probability (P)

Total
1.000

(SW – South West; S – South; SE – South East; E – East; NE – North East; N – North; NW – North
West; SW – South West).
c. Wind parameters
Table 3. Probability of occurrence of wind directions to OJWT

Wind Speed Middle
(m/s)
Value

Directions
45

90

0-5
2.50 0.0146 0.0329
5 - 10
7.50 0.1653 0.0938
10 - 15
12.50 0.1531 0.0036
15 - 20
17.50 0.0098 0.0000
Total
0.3428 0.1303

135

180

225

270

315

360

0.0337
0.0162
0.0000
0.0000
0.0498

0.0375
0.0299
0.0002
0.0000
0.0676

0.0321
0.1603
0.0515
0.0000
0.2439

0.0148
0.0751
0.0361
0.0000
0.1260

0.0054
0.0056
0.0004
0.0000
0.0114

0.0065
0.0116
0.0084
0.0016
0.0282

Total
0.1774
0.5579
0.2533
0.0115
1.0000

After taking the estimation of Weibull Parameters for long term distribution of wind speeds in
each direction, the fitted parameters U0 and K are obtained as illustrating in Table 4. The wind data
measured in the field is fitted rather precisely with the Weibull distribution function as shown in Fig.
14.
Table 4. The fitted Weibull parameters for wind distribution

Wind Directions

Fitted Weibull
Parameter

0

45

90

135

180

225

270

315

U0
K

6.050
2.200

2.750
2.250

2.350
2.150

4.250
2.250

8.250
2.875

6.975
1.475

3.350
1.500

6.725

2.225

d. Results
After obtaining the results of wind turbine analysis from SACS software under hot-spot stress
spectrum as showing in Figs. 15 and 16, then utilizes the Fourier transform to convert the hot-spot
stress into a time domain for two cases caused by waves and winds as showing in Figs. 17 and 18.
In the case of wind turbine systems subjected to both waves and winds is going to take a linear
combination of two results due to wave and wind in time series, and obtain the combining results as
Fig. 19 shown.
54


Vuong, N. V., Quan, M. H. / Journal of Science and Technology in Civil Engineering

o o
Figure
Long term
term distribution
distributionofofwind
windspeeds
speeds– –curve
curvefitting
fitting– direction
– direction
Figure 14.
14. Long
4545

d)
d)Results

Results
Figure 14. Long term distribution of wind speeds – curve fitting – direction 45
Figure
14.
Long term distribution of wind speeds – curve fitting – direction 45◦
d) Results
After
the results of
of wind
windturbine
turbineanalysis
analysisfrom
fromSACS
SACSsoftware
softwareunder
under
hotAfter obtaining
obtaining
hoto

After obtaining the results of wind turbine analysis from SACS software under hot-

Figure 16. Hot-spot stress spectrum (wind induced)

Figure 15. Hot-spot stress spectrum (wave induced)

spot stress spectrum as showing in Figs. 15 and 16, then utilizes the Fourier transform to
convert the hotspot stress into a time domain for two cases caused by waves and winds
as showing in Figs. 17 and 18. In the case of wind turbine systems subjected to both
Figureof

16.
Hot-spot
stress
spectrum
(wind
induced)
Figure
16.
Hot-spot
spectrum
(wind
induced)
Figure
Hot-spot
spectrum
(wave
induced)
andstress
windsspectrum
is going(wave
to take
a linear combination
two
resultsstress
due
to
wave and
Figure15.
15.waves
Hot-spot

induced)
Figure 15. Hot-spot
stressseries,
spectrum
(wavethe
induced)
Figureas16.
Hot-spot
stress spectrum (wind induced)
wind
in
time
and
obtain
combining
results
Fig.
19
shown.
spot
as showing
showing in
in Figs.
Figs.15
15and
and16,
16,then
thenutilizes
utilizesthetheFourier
Fouriertransform

transform
spotstress
stress spectrum
spectrum
to to
Fatigue damage at high-concentrated stress points (hotspots) is calculated by
convert the
the
hotspotthestress
aa range
time
domain
two
bybywaves
winds
convert
hotspot
into
time(HSSR)
domain
for
two
cases
and
winds
evaluating
hot-spotinto
stress
andfor
make

usecases
of
this caused
ascaused
input date
forwaves
S-N and
fatigue curve. The stress concentration factors (SCF) is defined as following:
showing in
in Figs. 17 and 18.
In
to toboth
asas showing
18.SCF
In the
the case
caseofofwind
windturbine
turbinesystems
systemssubjected
subjected
both
(24)
= HSSR/ Nominal Stress Range
waves and
and winds
winds
to take
aa linear
combination

ofof
two
due
andand
For all is
concentric
of the
structure
system, the SCF
coefficient
will be
taken
waves
goingmasses
take
linear
combination
tworesults
results
duetotowave
wave
as 2.0 in this paper.
windinin time
timeCorresponding
series, and toobtain
the
results
as Fig.
shown.
wind

series,
obtain
the combining
combining
Fig.1919method
shown.
each hotspot
stress in time results
series, theasrain-flow
is applied
here
under
aiding
of
MATLAB
software
so
that
the
rain-flow
matrices
at
Fatigue
damage
at
high-concentrated
stress
points
(hotspots)
is iscalculated

Fatigue damage
high-concentrated stress points (hotspots)different
calculatedbyby
hotspot points due to wave and wind are obtained without any trouble as shown in Figs.
evaluating20the
the
hot-spot stress range
and
make
use
of this
date for S-N
evaluating
range (HSSR)
(HSSR)due
and
makeand
use
thisasasinput
input
and 21. Finally, the rain-flow
matrices
to wave
windofinteraction
can be date for S-N
easilyThe
obtained
in theconcentration
same manner andfactors
the result(SCF)

can be seen
in the Fig.
fatiguecurve.
curve.
The
isisdefined
as22.
fatigue
stress
concentration
factors
(SCF)
defined
asfollowing:
following:

== HSSR/
Nominal
Stress
Range
SCF
HSSR/
Nominal
Stress
Range
FigureFigure
17.SCF
Hot-spot
(wave
induced)

17. Hot-spot stress
stress in in
timetime
seriesseries
(wave induced)
Figure 17. Hot-spot stress in time series (wave induced)

(24)
(24)

For all
all concentric
concentric masses of
taken
For
of the
the structure
structuresystem,
system,the
theSCF
SCFcoefficient
coefficientwill
willbebe
taken
2.0inin this
this paper.
paper.
asas2.0
Corresponding to each hotspot
is isapplied

Corresponding
hotspot stress
stressinintime
timeseries,
series,the
therain-flow
rain-flowmethod
method
applied
10
here
under
aiding
of
MATLAB
software
so
that
the
rain-flow
matrices
at
different
here under aiding
MATLAB software so that the rain-flow matrices at different
hotspot
points
due
to
wave

in in
Figs.
hotspot points due to wave and
and wind
wind are
areobtained
obtainedwithout
withoutany
anytrouble
troubleasasshown
shown
Figs.
20
and
21.
Finally,
the
rain-flow
matrices
due
to
wave
and
wind
interaction
can
20 and 21. Finally, the rain-flow matrices due to wave and wind interaction canbebe
easilyobtained
obtained in
in the

the same
same Figure
manner
and
the
can
18. Hot-spot
time series
(windbe
induced)
easily
manner
andstress
theinresult
result
can
beseen
seenininthe
theFig.
Fig.22.22.
Figure 18. Hot-spot stress in time series (wind induced)
Figure 18. Hot-spot stress in time series (wind induced)

55

10 10


Hot-spot stress
in time series

(wind induced) in Civil Engineering
Vuong, N. V., Quan,Figure
M. H.18./ Journal
of Science
and Technology

Figure 19. Hot-spot stress in time series (wave and wind induced)

Figure 19. Hot-spot stress in time series (wave and wind induced)

Fatigue damage at high-concentrated stress points (hot-spots) is calculated by evaluating the hotspot stress range (HSSR) and make use of this as input date for S-N fatigue curve. The stress concentration factors (SCF) is defined as following:
SCF = HSSR/Nominal Stress Range

(24)

For all concentric masses of the structure system, the SCF coefficient will be taken as 2.0 in
this paper.
11

Figure 20. Rain-flow matrix at hot-spot point due to wave

Figure 20. Rain-flow matrix at hot-spot point due to wave

Figure
20. cycles
Rain-flow
matrix
hot-spot point
Some
that

areatcounted
with the
due
to
wave
amplitude and average stress value at the

Some cycles that are counted with the

Figure 21. Rain-flow matrix at hot-spot point due to wind

Figure 21. Rain-flow matrix at hot-spot point
Figure 21. Rain-flow matrix at hot-spot point due to wind
due to wind

hot-spot point can be extracted from the
amplitude
and average
stress stress
valueinattime
the
Corresponding
to each
rain-flow
matrix.
Thishot-spot
type of matrix
hasseries, the rain-flow method is applied here under
hot-spot
point

can
be
extracted
from
the
aiding
MATLAB
software
that the rain-flow
beenofwidely
applied
forsofatigue
analysis matrices at different hot-spot points due to wave
rain-flow
matrix.
This
type
of
matrix
has in Figs. 20 and 21. Finally, the rain-flow matrices
and
wind areof
obtained
without form,
any trouble
as shown
because
its simple
time-saved
been

widely
applied
for
fatigue
analysis
due
to wave and and
wind interaction
can be easily
obtained in the same manner and the result can be seen
computing,
its expression
provides
because
its simple
form,
time-saved
ingeneral
Fig. 22.of
information
on the
nature
of loads
computing,
and
expression
provides
[13].
mentioned
earlier,

PalmgrenSomeAs
cycles
that its
are counted
with the
amplitude and average stress value at the hot-spot point can
general
information
on
thematrix.
nature
oftype
loads
hypothesis
assumes
thatThis
the
total
beMiner’s
extracted
from the rain-flow
of matrix has been widely applied for fatigue analysis
of fatigue
damage
is calculated
taking aand its expression provides general information on
[13].
As
earlier, by
Palmgrenbecause

of itsmentioned
simple form,
time-saved
computing,
linear
combination
any
individual
Miner’s
thatearlier,
the total
the
naturehypothesis
of
loads [15].assumes
As of
mentioned
Palmgren-Miner’s hypothesis assumes that the total of
cycles.
The
fatigue
of
at each
damage
is calculated
by structure
takingby
a linear
combination
of any individual cycles. The fatigue life

offatigue
fatigue
damage
is life
calculated
taking
a
hot-spot
is
listed
in
Tab.
5,
6
and
7
below
Figure
22.
Rain-flow
matrix
at hot-spot17.5
pointm/s)
due to both wave
of structure
at each hot-spot
Tables 5, 6 and 7 (the mean
wind
velocity:
linear

combination
ofis listed
any in individual
and wind

cycles.
Thewind
fatigue
life of
structure at each
(the mean
velocity:
17.5m/s):
56
hot-spot is listed in Tab.
5, 65.and
7 below
Table
Fatigue
life of OWT support
structure
(wave induced)
Figure
22. Rain-flow
matrix at hot-spot point due to both wave
and wind
Fatigue
life
Chord (cm)
(year)

OD
WT
Table 5. Fatigue life of OWT support structure (wave induced)
3600
Y
70
2
829.25

[D] velocity:
T (sec)17.5m/s):
Node type
(theNo.
mean wind
1

0.5

Status
Ok


w matrix at hot-spot point due to wave

Vuong, N. V., Quan, M. H. / Journal of Science and Technology in Civil Engineering
Figure 21. Rain-flow matrix at hot-spot point due to wind

es that are counted with the
average stress value at the
can be extracted from the

ix. This type of matrix has
applied for fatigue analysis
s simple form, time-saved
nd its expression provides
ation on the nature of loads
ntioned earlier, Palmgrenhesis assumes that the total
age is calculated by taking a
nation of any individual
igue life of structure at each

d in Tab. 5, 6 and 7 below

Figure 22. Rain-flow matrix at hot-spot point due to both wave

Figure 22. Rain-flow matrix at hot-spot
and wind point due to both wave and wind

velocity: 17.5m/s):
Table 5.structure
Fatigue (wave
life of induced)
OWT support structure (wave induced)
Table 5. Fatigue life of OWT support

T (sec)

Node type
No.

3600

3600
3600
3600
3600
3600

1
2
3
4
5
6

[D]

Y
Y
Y
X
X
X

0.5
0.5
0.5
0.5
0.5
0.5

Fatigue life

Chord (cm)
Chord (cm)
OD
WT
T
(sec)
Node type (year)
OD
WT
70
2
829.25
70
2 Y
561.36
3600
70
2
3600
70
2
70
2 Y
996.15
3600
70
2
80
2 Y
937.57

3600
X
80
2
120
4.5
1005.21
3600
X
120
4.5
120
4.5
1258.02
3600

X

120

4.5

StatusFatigue life
Ok (year)
Ok 829.25
Ok 561.36
Ok 996.15
Ok 937.57
Ok 1005.21
1258.02

Status
Ok
Ok
Ok
Ok
Ok
Ok

Figure 6. Fatigue life of OWT support structure (wind induced)
Table 6.(cm)
Fatigue life of OWT
support
Chord
Fatigue
lifestructure (wind induced)

T (sec)

Node type
Y
1Y

Status
OD
WT
(year)
Chord (cm)
Ok Fatigue life
[D] 70 T (sec) 2 Node type 197.81

(year)
OD
WT Ok
70
2
151.26
2
196.2170
0.5 70 3600
Y
2 Ok
197.81

3600
3600
3600

Y
No.
2
3
4
5
6
7

0.5
0.5
0.5
0.5

0.5
0.5

3600
3600
3600
3600
3600
3600

Y
Y
X
X
X
Y

70
70
80
120
120
70

2
2
2
4.5
4.5
2

151.26
196.21
12
271.26
306.12
465.32
182.13

Status
Ok
Ok
Ok
Ok
Ok
Ok
Ok

Apart from the result of mean wind velocity 17.5 m/s, Fig. 23 shows the fatigue life curve of OWT
due to different velocities, whereas there are mean wind velocities that are greater than the cut-out
mean wind velocity.
57


4
0.5
3600
X
80
2

271.26
5
0.5
3600
X
120
4.5
306.12
6 Vuong,
0.5 N. V.,
3600
120 and Technology
4.5
465.32
Quan, M. H. /XJournal of Science
in Civil
Engineering
7
0.5
3600
Y
70
2
182.13
Table 7. Fatigue life of OWT support structure (wave and wind induced)

Ok
Ok
Ok
Ok

Figure 7. Fatigue life of OWT support structure (wave and wind induced)

No.
1
2
3
4
5
6
7

life life
Chord
(cm)
Chord
(cm) Fatigue
Fatigue
Status
Status
(year)
ODOD WTWT
(year)
1
0.5
3600
Y
70
2
176.38

Ok
20.5 0.5 3600
3600
YY
70 70
2 2
132.58
Ok Ok
176.38
30.5 0.5 3600
3600
YY
80 70
2 2
273.32
Ok Ok
132.58
40.5 0.5 3600
3600
XY
80 80
2 2
278.51
Ok Ok
273.32
5
0.5
3600
X
120

4.5
291.46
Ok
0.5
3600
X
80
2
278.51
Ok
6
0.5
3600
X
120
4.5
452.96
Ok
291.46
70.5 0.5 3600
3600
YX
70120
2 4.5
172.34
Ok Ok
0.5Apart from
3600
X
120

4.5
452.96
Ok
the result of mean wind velocity 17.5m/s, the Fig. 23 shows the fatigue
0.5
3600
Y
70
2
172.34
Ok
life curve of OWT due to different velocities, whereas there are mean wind velocities
that are greater than the cut-out mean wind velocity.
No.

(sec)
[D] [D] T T
(sec)

Node type

Node type

Figure
23. Thelife
fatigue
life of
curve
of OWT
corresponding toto

each
mean
wind velocity
Figure 23. The
fatigue
curve
OWT
corresponding
each
mean
wind velocity

6. Conclusion
To calculate the fatigue life of OJWT, in the scope of the paper, a wind turbine
6. Conclusions
model with jacket support structure in the water depth of 70m is utilized. All blades,

turbine
support
towermodel
that mass
To calculate
themachine
fatigueand
lifemachine-support
of OJWT, in thetower
scopeare
ofsimplified
the paper,into
a wind

turbine
with jacket
is
concentrated
on
top,
and
is
supported
by
jacket
structure.
In
terms
of
wind
data,
support structure in the water depth of 70 m is utilized. All blades, turbine machine and machineWeibull distribution is used to generate input data for fatigue analysis of OJWT. Wind
support tower are simplified into support tower that mass is concentrated on top and is supported
by jacket structure. In terms of wind data, Weibull distribution is used to generate input data for
13
fatigue analysis of OJWT. Wind and wind-induced wave loads act on structure in stochastic directions,
however, only 08 directions are considered with evenly spaced 45-degree angle to compute fatigue
life of each components’ jacket support structure. The Airy wave theory is applied for computing the
static and dynamic transfer function of wave to support the fatigue analysis, and further study should
be utilized different wave theories. The results are rather reasonable since the simultaneous interaction
between wind and wind-induced wave is considered.

58

Vuong, N. V., Quan, M. H. / Journal of Science and Technology in Civil Engineering

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