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Methodology for seismic risk assessment for
tubular steel wind turbine towers: application to
Canadian seismic environment
Elena Nuta, Constantin Christopoulos, and Jeffrey A. Packer
Abstract: The seismic response of tubular steel wind turbine towers is of significant concern as they are increasingly
being installed in seismic areas and design codes do not clearly address this aspect of design. The seismic hazard is hence
assessed for the Canadian seismic environment using implicit finite element analysis and incremental dynamic analysis of
a 1.65 MW wind turbine tower. Its behaviour under seismic excitation is evaluated, damage states are defined, and a
framework is developed for determining the probability of damage of the tower at varying seismic hazard levels. Results
of the implementation of this framework in two Canadian locations are presented herein, where the risk was found to be
low for the seismic hazard level prescribed for buildings. However, the design of wind turbine towers is subject to change,
and the design spectrum is highly uncertain. Thus, a methodology is outlined to thoroughly investigate the probability of
reaching predetermined damage states under any seismic loading conditions for future considerations.
Key words: steel structure, wind turbine tower, tubes, finite element analysis, seismic analysis, incremental dynamic analy-
sis, fragility curve.
Re
´sume
´:La re
´ponse sismique des tours d’e
´oliennes en tubes d’acier est une question importante puisque ces dernie
`res
sont de plus en plus installe
´es dans zones sismiques et que les codes de calculs ne traitent pas clairement de cet aspect de
la conception. Les ale
´as sismiques sont ainsi e
´value
´s pour l’environnement sismique canadien en utilisant une analyse im-
plicite par e
´le
´ments finis et une analyse dynamique incre
´mentielle pour une tour d’e
´olienne de 1,65 MW. Son comporte-
ment sous une excitation sismique est e
´value
´, les dommages sont de
´finis et un cadre est e
´tabli pour de
´terminer la
probabilite
´de dommages a
`la tour a
`diffe
´rents niveaux d’ale
´as sismiques. Les re
´sultats de l’implantation de ce cadre en
deux endroits au Canada sont pre
´sente
´s, ou
`le risque e
´tait faible pour le niveau d’ale
´as sismiques prescrit pour les ba
ˆti-
ments. Toutefois, la conception des tours d’e
´oliennes est sujette a
`changement et la plage de conception est tre
`s incertaine.
Ainsi, une me
´thode est pre
´sente
´e afin d’examiner en de
´tail la probabilite
´d’atteindre des niveaux de dommages pre
´de
´termi-
ne
´s sous des conditions de charge sismique possibles dans l’avenir.
Mots-cle
´s:structure d’acier, tour d’e
´olienne, tuyaux, analyse par e
´le
´ments finis, analyse sismique, analyse dynamique in-
cre
´mentielle, courbe de fragilite
´.
[Traduit par la Re
´daction]
Introduction
Tubular steel monopole towers are the most common type
of supporting structure for wind turbines in the world today.
The increasing production of wind energy in North America
has led to installation of these structures in areas where ad-
ditional loading conditions, for which the tower was not ini-
tially designed, may exist. As some international design
codes are being adopted in Canada for the design of these
structures, several gaps are evident due to Canada’s unique
environment. One such gap is the assessment of seismic
risk pertaining to wind turbine towers, as the major develop-
ments of wind turbines have been in non-seismic areas.
Their very tall and slender geometry results in a structure
that cannot respond in a ductile manner, thus the capacity
of wind turbine towers when subjected to dynamic seismic
loads must be characterized, to ensure that they are not
overloaded in such loading conditions.
Existing code provisions are few (IEC 2005; CSA 2008),
and current research has thus far established that seismic
loads typically do not govern the design of the tower (Ba-
zeos et al. 2002; Lavassas et al. 2003). However, the seismic
risk of wind turbine towers is still of importance to owners
of wind turbine developments, especially wind turbine
farms, because all the towers are generally identical, and as
such, a seismic event would affect all the towers in the same
manner — if one tower fails, they would all fail. Such a
failure would result in severe financial losses as well as so-
cial implications if wind energy takes over more of the en-
ergy production in Canada. Thus, a methodology is
presented herein for determining the probability of damage
for a wind turbine tower at various levels of damage using
the finite element method (FEM).
Received 19 April 2010. Revision accepted 10 January 2011.
Published on the NRC Research Press Web site at cjce.nrc.ca on
8 February 2011.
E. Nuta, C. Christopoulos,1and J.A. Packer. Department of
Civil Engineering, University of Toronto, 35 St George Street,
Toronto, ON M5S 1A4, Canada.
Written discussion of this article is welcomed and will be
received by the Editor until 31 July 2011.
1Corresponding author (e-mail: c.christopoulos@utoronto.ca).
293
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Code provisions
The most significant international standards for design of
wind turbines are produced by the International Electrotech-
nical Commission (IEC), Germanischer Lloyd (GL), and Det
Norske Veritas (DNV). The standards from GL and DNV, as
well as other European standards, have been harmonized
with the IEC standards. The Canadian Standards Association
(CSA) has recently adopted the principal IEC standard for
wind turbines, IEC61400-1 (IEC 2005), while including
Canadian deviations that mostly concern external conditions
to which the wind turbine may be exposed (CSA 2008).
The seismic provisions in IEC61400-1 require that a seis-
mic analysis be carried out depending on site-specific condi-
tions, and earthquake assessment is not required in locations
that are excluded by the local codes due to weak seismic ac-
tion (IEC 2005). In locations where seismicity may be crit-
ical, the seismic loading must be combined with a
significant specified operational loading that occurs fre-
quently during the turbine’s lifetime (IEC 2005). The seis-
mic loading is based on the ground acceleration for a 475-
year recurrence period with design spectrum requirements
defined by the relevant local building codes (IEC 2005).
Evaluation of seismic loads may be carried out either in the
frequency-domain or in the time-domain. Furthermore, a
simplified conservative approach to calculate the seismic
loads is provided in Annex C of this standard, but this ap-
proach is only recommended if the tower is the only part of
the wind turbine that will experience significant loading due
to seismic action (IEC 2005).
The recently adopted CSA-C61400-1 (CSA 2008) only
adds one seismic provision to the IEC (2005) specifications.
It acknowledges that the NBCC (2005) does not address
earthquake forces acting vertically, and identifies this as a
problem because wind turbines may have vibration modes
with significant mass participation factors in the vertical di-
rection (CSA 2008). Additionally, a discrepancy arises in
the recurrence period of the seismic event to be used in de-
sign. The IEC61400-1 (IEC 2005), and thus the new CSA-
C61400-1 (CSA 2008), suggests a 475-year recurrence pe-
riod, whereas the NBCC (2005) defines seismic loading
based on a 2500-year return period.
Pertinent research
The majority of current relevant research has been con-
cerned with verifying that a given wind turbine can sustain
low or moderate seismic loadings safely, without assessing
the seismic capability limits of wind turbine towers. At
fairly low seismic loads, Bazeos et al. (2002) concluded
that seismic analysis does not produce the governing design
criterion for this type of structure, and Lavassas et al. (2003)
found that the seismic response was significantly less critical
than the response caused by wind loading.
Much focus has also been on comparisons of frequency-
domain and time-domain methods of seismic analysis, as it
has become feasible to incorporate time-domain analyses in
simulation packages for wind turbines, such as GH Bladed
(Witcher 2005) and Flex5 (Ritschel et al. 2003). Witcher
(2005) concluded that both methods were adequate, but dis-
crepancies arose when the system damping was not close to
that of the design spectra, which is typically 5%. For operat-
ing wind turbines, the total damping is close to 5% due to
significant aerodynamic damping and thus both methods
yield similar results (Witcher 2005). For turbines that are
not operating, the aerodynamic damping, and thus the total
damping, is much lower. Most building codes do not pro-
vide a method to correct for the level of damping when us-
ing the frequency-domain method, so the time-domain
method is advantageous because the correct level of damp-
ing can be applied (Witcher 2005). Therefore, Witcher
(2005) concluded that time-domain seismic analysis is ac-
ceptable, and in fact preferred, because the correct aeroelas-
tic interaction can be modelled. A similar investigation by
Ritschel et al. (2003) concluded that both methods are ad-
equate for obtaining tower forces, but that the time-domain
method was preferred for nacelle and rotor loads, which
were significantly influenced by the vertical earthquake
component.
Recent research has also addressed the effect of soil-struc-
ture interaction (SSI) when assessing the seismic resistance
of wind turbines. Although the wind turbine tower was iden-
tified as the most important structural component when ana-
lyzing dynamic response (Zhao and Maisser 2006), the
interaction between the structure, the foundation, and the
surrounding soil was also considered to be significant (Ba-
zeos et al. 2002; Zhao and Maisser 2006). For a weak earth-
quake load combined with design wind loading, Zhao and
Maisser (2006) found that the peak tower displacement was
dominated by wind forces. The inclusion of SSI resulted in
reduced fundamental frequencies of the wind turbine. Thus,
it was concluded that soil-structure interaction has a large
influence on the dynamic characteristics of the wind turbine
tower, particularly in areas with flexible soil, and this inter-
action should be included in dynamic analysis of wind tur-
bines (Bazeos et al. 2002; Zhao and Maisser 2006).
Numerical analysis: development and
validation
As the methodology established herein is based on numer-
ical modelling using ANSYS Multiphysics (2007), several
verification analyses were carried out to evaluate element
formulations, mesh size and material properties, and to ver-
ify local and global failure mechanisms. The finite element
(FE) model that facilitated the majority of the verifications
was that of a short tubular member in pure flexure.
Elements
The wall of the tower was represented with 8-noded shell
elements, and the ring flanges of the wind turbine tower
were modelled using 20-noded solid elements. Both ele-
ments are well suited to model curved boundaries, as they
have a mid-side node. A mesh sensitivity analysis of the
pure flexure model indicated that an element size up to ap-
proximately 12 times the thickness satisfactorily captured
the pure flexure response. Coarser mesh sizes captured the
pre-peak response, but not the post-peak response.
Tubular members in bending
Flexural member cross-sections are classified by many co-
des based on their slenderness, which governs a section’s
ability to carry moment (AISC 2005; CEN 2005; CSA
294 Can. J. Civ. Eng. Vol. 38, 2011
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2009). If elements of the cross-section that are in compres-
sion are too slender, the flexural member may buckle locally
instead of reaching its global flexural capacity. Sections of
wind turbine towers fall within the realms of class 3 and
class 4 in bending, where class 4 is defined as slender. This
definition varies considerably between various codes. The
bottom part of the specific wind turbine tower considered
later in this paper is class 3 in flexure according to CSA
S16, while most of the tower’s height is well past the class
3 limit and is hence class 4 (Fig. 1).
Material properties
Typical steel wind turbine towers are made from flat steel
plates that are rolled into cylindrical or conical pieces, and
then welded longitudinally (Danish Wind Industry Associa-
tion 2003). Due to this fabrication process, the material
properties of the tower are similar to cold-formed tubular
members. The stress–strain curve of the material shows a
low proportional limit, followed by gradual yielding, no
clear yield plateau, and significant strain hardening.
No material data in the form of stress–strain behaviour
from an actual wind turbine tower was available. For the
verification analyses, three sets of material properties were
used (Fig. 2): gradual yielding, taken from the average of
several coupon tests of cold-formed circular HSS sections
performed by Voth (2010); stress–strain curve with yield
plateau, adapted from Voth (2010); and bilinear stress–
strain, obtained from Elchalakani et al. (2002).
Finite element comparison with experimental specimen
An FE model of geometrically-comparable ratios to an
experimental specimen from Elchalakani et al. (2002) was
carried out. The response curve shape was similar, but the
agreement was not ideal as the peak was over-estimated by
9% (Fig. 3). This is believed to be due to imperfections in
the experimental specimen. In addition, the FE model used
Fig. 1. Properties of 1.65 MW wind turbine tower.
Fig. 2. True stress–strain curves used in verification analyses.
Nuta et al. 295
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an assumed bilinear stress–strain curve, since the true stress–
strain curve was not reported by Elchalakani et al. (2002).
Despite these differences, the buckling failure mode was
captured well (Fig. 3).
Effect of material properties
Two pure flexure models, class 3 and class 4, were used
to assess the effect of material properties on flexural re-
sponse (Fig. 4). For the class 3 member, the presence of a
yield plateau in the stress–strain curve influences how early
the member buckles, whereas the behaviour of the class 4
member is almost unaffected by the material properties. For
the subsequent analyses, the gradual yielding stress–strain
curve was employed. The material properties were kept con-
stant for all subsequent analyses and thus the uncertainty re-
lated to these properties was not considered in this study. It
was deemed that material uncertainty would be insignificant
when compared to the uncertainty related to the input
ground motions.
Analysis of small wind turbine tested at
UCSD
A full-scale shake table test of a small wind turbine was
carried out at the University of California, San Diego (Pro-
well et al. 2008 and 2009). The turbine was 22.6 m tall and
consisted of three sections of constant cross-section con-
nected by conical joints (Fig. 5). A simple FE model was
created using shell elements and additional mass elements,
uniformly distributed throughout the tower, to reach the
mass specified by Prowell et al. (2008). Modal analysis esti-
mated the first modal period to be 0.58 s, which was in good
agreement with the experimentally observed first mode of
0.59 s (Prowell et al. 2008).
The model was subjected to the same ground motions as
the shake table test corresponding to the results presented in
Prowell et al. (2008), 143% of the east–west component of
the 1992 strike-slip Landers Earthquake. More recently, Pro-
well et al. (2009) presented results for the 100% and 200%
level of the Landers earthquake, but the FE analyses dis-
cussed herein were compared to the 2008 publication. The
ground motion record, obtained from the US Geological
Survey database, was 80 s long, and the analyses had an ad-
ditional 15 s of free vibration.
Comparison of effect of damping
Based on experimental results, Prowell et al. (2008) cal-
culated the amount of viscous damping to be between 0.4%
and 0.6% of critical for the small wind turbine described
Fig. 3. Response of FE model VF-el compared with experimental results from Elchalakani et al. (2002).
Fig. 4. Effect of material properties on pure flexure response. Fig. 5. Details of small wind turbine tested at UCSD.
296 Can. J. Civ. Eng. Vol. 38, 2011
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above. This is similar to the estimated value of 0.5% used
by Bazeos et al. (2002) in their dynamic analysis of a wind
turbine. However, industry guidelines suggest the use of 1%
of critical damping for a parked wind turbine (blades locked
against motion) (IEC 2005).
Rayleigh damping was specified in the FE analyses to ob-
tain 0.5%, 1%, and 1.5% of critical damping for the first and
second modes. The FE results and the experimental results
are plotted for the acceleration at the top of the nacelle and
at the upper joint, respectively, for the first 20 s of the earth-
quake (Fig. 6 and Fig. 7). This duration was chosen to allow
for a comparison with the results presented in Prowell et al.
(2008).
The agreement between the FE results and the experimen-
tal results is reasonable, considering all the simplifying
modelling assumptions — uniform distribution of additional
mass, no modelling of the blades, and rigid fixity at the
base. Prowell et al. (2008) presented better agreement in
their publication from a numerical model wherein the parked
blades were included using beam elements. This suggests
that modelling the blades changed the higher mode effects
and thus affected the response of the upper joint, which is
dominated by the higher modes. However, no details of the
blades were available, thus the influence of the blades can-
not be assessed.
Comparison of the FE results and the experimental results
shows that the nacelle response is better captured using
lower damping, while the upper joint response is better rep-
resented by higher damping. A damping value of 1% of crit-
ical was chosen for seismic analysis of further wind turbine
towers, as a compromise between achieving the best match
for the nacelle response and for the upper joint response.
Properties of typical wind turbine tower
model
A typical 1.65 MW wind turbine tower is analyzed in this
paper, with a diameter and thickness that ranges from
3650 mm and 35 mm at the base to 2282 mm and 10 mm
at the top, respectively (Fig. 1). The finite element model
has a fine mesh (element size to thickness ratio of 12) with
a good aspect ratio in the bottom section of the tower, where
buckling failure typically occurs. The model also includes
two openings at the base: a door and a cable hole. Holes
are left in the tower FE shell where the actual door and ca-
ble holes are located. The door section covers 1/6 of the
tower’s circumference and is approximately twice as thick
as the rest of the wall at that height in the tower. The bot-
tom section, where the cable hole is located, is already quite
thick (35 mm) and there is a lip around the hole. It is impor-
tant to include these details, as they may affect the response
of the tower.
Modal analysis of the tower calculated the fundamental
frequency to be 3.17 s. The first three modes in the horizon-
tal direction are shown in Fig. 1.
Pushover analysis
Pushover analysis is a simplified inelastic analytical pro-
cedure developed to estimate the seismic response of struc-
tures. Many pushover procedures have been developed and
Fig. 6. Finite element and experimental values: acceleration at top of nacelle.
Nuta et al. 297
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validated for particular types of buildings and bridges, but
none have been tailored for a structure similar to a wind tur-
bine tower. As such, a simple multimode load pattern
(Barros and Almeida 2005) was used to determine the ca-
pacity of the tower and to assess its behaviour. The load pat-
tern consisted of a linear combination of the first three
modes in the horizontal direction, as follows:
½1LP ¼Xaifi
where LP = load pattern; ai= modal participation factor of
mode i;fi= mode shape of mode i, normalized to mass ma-
trix.
The resultant force of the load pattern (Fig. 8) acts at
45.9 m above the ground. The pushover analysis was carried
out at 22.58increments around the circumference of the
tower (Fig. 9) to determine the weakest angle of incidence.
The capacity curve of the pushover analysis at an angle of
08(Fig. 8) was similar to that of the pure flexure specimens:
nearly-linear response until yield, followed by slightly curvi-
linear response until the peak, where a buckle formed and
the tower quickly shed the load. The response at various an-
gles of incidence was very similar (Fig. 9), but the peak load
varied slightly, with the lowest peak load being achieved
when the angle of incidence was 22.58, followed by 458.
This is believed to be the case because the compression
Fig. 7. Finite element and experimental values: acceleration at upper joint.
Fig. 8. Pushover analysis load pattern, buckled failure, and capacity curve at 08angle.
298 Can. J. Civ. Eng. Vol. 38, 2011
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side is very close to the corner of the thickened tower door
section, so stress concentrations for those analyses are al-
most exactly at the location where the buckle forms, thereby
causing failure earlier than when the tower is pushed in any
other direction. In addition, one pushover analysis was car-
ried out without modelling the door and cable hole at the
bottom of the tower and, as expected, these details are in-
deed necessary in the model of the wind turbine tower. The
most significant result of the pushover analyses is the
buckled failure of the tower (Fig. 8). As expected, the fail-
ure occurs close to the base, but above the thickened door
section.
Time-history analysis
The described model was subjected to time-history analy-
sis by applying orthogonal earthquake components at the
base of the tower as displacement ground motion records.
At the end of the record, the analyses were continued for an
additional 60–65 s of free vibration until the tower’s oscilla-
tions diminished to near zero. The buckling failure of the
wind turbine tower during seismic excitation typically oc-
curred at either 10 m above the base or around 43 m above
the base. This is a different location from that obtained in
the pushover analyses, where the failure occurred much
closer to the base, just above the stiffened door section.
This difference is due to the effect of higher modes in the
dynamic seismic response of the structure.
Effect of damping
The wind turbine tower’s sensitivity to damping was as-
sessed by running one seismic event with varied damping
values: 0.5%, 1%, and 1.5% of critical, at magnification fac-
tors 1, 2, and 4. The peak and pre-peak response was not
heavily influenced, especially as the magnification factor
was increased. However, the post-peak time-history response
of the wind turbine tower was significantly influenced by
the amount of damping. Nonetheless, the resulting residual
displacement was almost identical between the various
damping values, although the analyses with lower damping
oscillated for much longer in free vibration before the tower
came to rest.
Effect of vertical acceleration
The vertical earthquake component of one seismic event
was included to determine the extent to which it affects the
response of the wind turbine tower at magnification factors
1, 2, and 4. The peak vertical ground acceleration was
0.723g, almost as high as one of the horizontal components.
Thus, the vertical component for this particular earthquake
record is quite significant.
Despite including such a significant vertical earthquake
component, the response of the tower was barely affected.
This is because the normal stress created in the tower’s bot-
tom section under gravity loads is small (less than 10%)
compared to the normal stress in the same section due to
bending for the reference earthquake (magnification factor
= 1).
Incremental dynamic analysis
The typical 80 m tower supporting a 1.65 MW turbine
was subjected to incremental dynamic analysis (IDA) to as-
sess its response to seismic loading. Intensity measures and
damage measures are required to extract information from
the IDA, and damage states of interest must be character-
ized.
Intensity measures
The intensity measures are commonly the peak ground ac-
celeration or the peak ground velocity (Vamvatsikos and
Cornell 2002). The intensity measure is chosen such that
the dispersion of all the incremental time-history analysis
curves is minimized. For the IDA of the wind turbine tower,
the intensity measure employed was the magnification fac-
tor. Since all the earthquakes were chosen to represent the
design response spectrum, the magnification factor repre-
sents the intensity of the ground motion with respect to the
intensity of the design earthquake. Other intensity measures
investigated were the peak ground displacement, the peak
ground velocity, and the peak ground acceleration, but the
dispersion of the IDA curves was smallest when the magni-
fication factor was used as the intensity measure, followed
closely by the peak ground velocity.
Damage measures
The damage measure is typically the peak roof drift of a
structure (Vamvatsikos and Cornell 2002). Several damage
measures were considered: the peak displacement, the peak
rotation, and the residual displacement. The peak stress was
also investigated.
Peak displacement
For each analysis, the displacement at hub height in three
orthogonal directions (x,y, and z) was obtained for each
time increment throughout the analysis. The resultant dis-
placement was computed based on the two lateral displace-
ments, and the maximum displacement was thus obtained
for each analysis. The peak lateral displacement (Dmax)is
described as a percentage of the hub height.
Fig. 9. Directions of pushover analyses in top view of tower, and peak load for pushover analyses acting at various angles.
Nuta et al. 299
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Peak rotation
The peak rotation of the tower, qmax, was computed at a
specific time through the analysis, typically at the time the
peak displacement occurred.
The rotation was calculated as the relative angle of 32
segments that correspond to the pieces of the tower (Fig. 1).
These segments were employed in defining the peak rotation
to simplify the post-processing analysis, but the tower may
be evenly divided into segments that are approximately
70% of the tower’s diameter at the base. Furthermore, the
displacement of the tower at each location along the height
was taken as the average of 12 evenly spaced points around
the circumference at that elevation, ensuring that the de-
formed shape represented the centreline of the tower and
was not influenced by any ovalisation that may have oc-
curred.
For analyses where buckling occurred, the rotation of the
segments very close to the buckle was not considered accu-
rate due to local crumpling of the shell on one side and flat-
tening of the tower wall on the side opposite the buckle.
Two or three segments were thus ignored in calculating the
rotation for analyses that buckled. The centrelines of the two
segments without severe deformation that bracketed the
buckled area were extrapolated and the relative rotation be-
tween these two extrapolated lines was taken as the peak ro-
tation.
Peak stress
The peak stress considered was the peak von Mises stress
(smises). Prior to buckling, the peak stress typically occurred
at the side of the door hole opening on the inside of the
tower. In the incremental analyses where the tower buckled,
the peak stress was typically at the location of the buckle.
Residual deformation
The residual lateral deformation (Dres) at hub height is
stated as a percentage of the hub height. In most cases, there
was a small residual displacement even after analyses where
the peak stress did not exceed the yield stress of the material
(Fy= 389 MPa). This occurred because the stress–strain
curve is slightly curvilinear until nominal yield, due to the
material properties being assumed to be similar to those of
a cold-formed tubular member.
Damage states
Limit states are typically defined using prescribed values
to ensure safety of occupants and stability of buildings.
However, wind turbine towers do not fall in the same cate-
gory as buildings, as they are generally not occupied. In the
absence of clearly defined limit states for seismic perform-
ance assessment of wind turbine structures, several damage
measures were defined for this study. It was deemed that
these damage states would be related to the functionality
and the cost of repair of wind turbines following a major
earthquake.
0.2% residual out-of-straightness
The acceptable out-of-straightness for wind turbine towers
is not well defined, but this value for other structures varies
in Canadian standards between 0.1% (CSA 2004, 2009) and
0.2% (CSA 2001). This out-of-straightness is typically de-
fined for erection purposes. As there is some residual defor-
mation before the yield stress is reached due to the
curvilinear material properties, an out-of-straightness limit
of 0.1% was considered to be too severe. For this study, a
residual out-of-straightness of 0.2% was taken as the first
damage state. Linear interpolation between the two analyses
that enveloped a residual displacement of 0.2% of hub
height was carried out to determine the damage and inten-
sity measures at this damage state.
First yield
Linear interpolation between the two analyses that envel-
oped a peak yield stress, Fy= 389 MPa, was carried out to
define the values of the second damage state.
1.0% residual out-of-straightness
Yielding of the tower typically falls within 0.2% residual
out-of-straightness (the first damage state) and 1.0% residual
out-of-straightness. Due to the uncertainty of the material
properties of the wind turbine tower, this damage state was
investigated as well. Similar to the previous two damage
states, linear interpolation was employed to obtain the val-
ues that define 1% residual out-of-straightness.
First buckle – loss of tower
The last damage state corresponds to the first incremental
analysis that causes the tower to buckle. The wind turbine
tower is considered as a complete loss after this damage
state is reached, given the fact that the sections comprising
the tower are class 3 or class 4. However, the tower is likely
still standing after the first buckle is formed. For this dam-
age state, there is no linear interpolation, and the lowest
magnification factor that produces buckling of the tower de-
fines the intensity and damage measures of this damage
state.
Some of the incremental analyses were continued past the
last damage state and a few buckled very severely. The FE
model was able to capture buckling failure for all of the
earthquakes, indicating a robust model.
Sites considered
Incremental dynamic analysis of the wind turbine tower
was carried out for three locations: Los Angeles (LA), East-
ern Canada, and Western Canada.
The LA earthquake suite is made up of 10 recorded earth-
quakes (20 records for the orthogonal components of the
earthquake), compiled and scaled by Somerville et al.
(1997). This suite of earthquakes is representative of earth-
quakes having a 475-year return period or a probability of
exceedance of 10% in 50 years, and is defined as the
design-based earthquake (ASCE 2005). The average spec-
trum of the 20 records is well matched to the design spec-
trum (Fig. 10).
For the Canadian sites, the uniform hazard spectrum was
used to represent the design earthquake, as dictated by
NBCC (2005), which corresponds to a 2500-year return pe-
riod or a probability of exceedance of 2% in 50 years. The
earthquake suites for these locations were based on data-
bases of simulated earthquake time histories over a range of
magnitudes, distances, and site conditions created by Atkin-
son (2009), who also outlines a method of selecting and
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scaling records to create an appropriate suite. Each database
was made up of several record sets of similar magnitudes
and distances from which records can be selected.
The Eastern Canada location chosen was on the north
shore of Lake Erie, south-west of Dunnville, Ontario. It is
one of the locations close to Toronto, Ontario, currently
being investigated for wind turbine farm developments. Due
to the lower variability of simulated records, the Eastern
Canada earthquake suite only comprised 7 earthquake re-
cords (14 orthogonal component records). The average spec-
trum of the 14 records is very closely matched to the
uniform hazard spectrum of the area (Fig. 11).
The Western Canada location chosen was offshore just
south of Victoria, BC. While that area is not under consider-
ation for wind turbine developments to the authors’ knowl-
edge, it represents one of the most severe seismic hazards
in Canada and was thus investigated in this paper. The
earthquake suite for this site has six records from the data-
base for Western Canada that had good agreement, on aver-
age, with the target spectrum (Fig. 12). In addition, a
seventh earthquake, representing an event occurring on the
Cascadia subduction zone, was also included in the study to
assess the impact of such a large magnitude, large distance
event on the seismic response of this wind turbine structure.
As can be seen in Fig. 12, this event has lower spectral ac-
celerations in the short period range but is in good agree-
ment with the spectral accelerations of the target design
spectrum for periods greater than 2 s.
Method of scaling records
For each earthquake record, the initial analysis was the
reference record that was matched to the target spectrum.
The subsequent analyses aimed to reach the defined damage
states. However, the predictability of the magnification fac-
tor required to reach any given damage state was found to
be very low.
Fragility curves
Statistics of incremental dynamic analyses can be used to
generate fragility curves, which serve the purpose of esti-
mating the probability of reaching a defined damage state
for a range of intensity values (Nasserasadi et al. 2008).
The fragility curve is characterized by a lognormal distribu-
tion and thus employs the mean (m) of the intensity meas-
ures and the standard deviation (s) of the natural logarithms
of the intensity measures (Deierlein et al. 2008). Using these
statistics, the following lognormal distribution function de-
fines the probability that the damage will exceed the damage
state (DS) at a given intensity measure:
½2pðdamage DSjIMÞ
¼Z
IM
0
1
IMsffiffiffiffiffiffi
2p
pexp 1
2
lnðIMÞlnðmÞ
s
dðIMÞ
Incremental dynamic analysis results
The IDA curves for the Los Angeles location and the
Western Canada location are shown in Fig. 13 and Fig. 14,
respectively. It is clear that the recorded earthquakes of the
LA earthquake suite have much more variability. The simu-
lated earthquakes of the Western Canada earthquake suite
also have high dispersion, but earthquake records from the
same record set have very low dispersion, as can be seen
from the IDA curves for WCan02, WCan03, WCan04, and
WCan05 (Fig. 14).
For the Eastern Canada location, it was found that the
seismic response was very slight for the reference earth-
quakes. Analyses at a magnification factor of 10 produced a
response that was well below the first damage state, and the
predicted magnification factors to reach the first damage
state ranged from 25 to 62. It was thus deemed that further
analyses were unnecessary for this wind turbine tower at the
Fig. 10. Acceleration response spectrum for Los Angeles earth-
quake suite.
Fig. 11. Acceleration response spectrum for Eastern Canada earth-
quake suite.
Fig. 12. Acceleration response spectrum for Western Canada earth-
quake suite.
Nuta et al. 301
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Eastern Canada location. However, given the high degree of
uncertainty associated with this design spectrum and the ex-
tremely low spectral accelerations in the long-period range
that is relevant to the response of turbine towers, the seismic
assessment of such structures should be carefully re-assessed
as the seismicity of Eastern Canada is refined in the future.
Fig. 14. Incremental dynamic analysis curves for the Western Canada location.
Fig. 13. Incremental dynamic analysis curves for the Los Angeles location.
302 Can. J. Civ. Eng. Vol. 38, 2011
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Assessment of damage measures
The peak rotation is a good damage measure because it
indicates very clearly when buckling occurs. Although the
response is not entirely linear up to that point, the increase
in the peak rotation once buckling occurs is very drastic in
every case.
The residual displacement is also important because it de-
fines two of the damage states. Of the three damage meas-
ures, the residual displacement has the least dispersion,
which is an important factor for IDA analyses.
The peak displacement appears to be the least indicative
damage measure. There are a few analyses where the tower
buckled yet the peak displacement IDA curves did not give
any indication of this, depending on the height where the
buckle formed.
Probability of exceeding the damage states
The resulting fragility curves for Los Angeles and West-
ern Canada are shown in Fig. 15. A magnification factor of
1 represents the design earthquake for each location, which
is 1 in 475 years for Los Angeles and 1 in 2500 years for
Western Canada. Each curve can then be interpreted by
choosing a magnification factor, i.e., the intensity of an
event with respect to the design earthquake, and then using
the curve to determine the probability of exceeding a partic-
ular damage state during an earthquake of that intensity.
The fragility curves (Fig. 15) show that the probability of
damage of the 1.65 MW wind turbine tower during a seis-
mic event is fairly low at both locations. Considering an
event twice as intense as the design earthquake (i.e., magni-
fication factor of 2), the fragility curves for LA indicate that
there is 26% probability of exceeding the first damage state
and 12% probability of exceeding the second damage state,
while the fragility curves for the Western Canada location
indicate that only the first damage state may be exceeded
with a low probability of 3%. It is apparent that the seismic
risk of wind turbine towers in Los Angeles is much greater
than in Western Canada.
Conclusions
The behaviour of the tubular steel tower of a typical
1.65 MW parked wind turbine has been numerically investi-
gated under seismic loading, and its seismic risk was eval-
uated at three locations, two of which were in Canada. For
this analysis, a finite element model of the steel tower was
developed and thoroughly validated and the expected failure
mode, buckling in flexure, was adequately captured. Earth-
quake suites were assembled and used to carry out nonlinear
incremental dynamic analysis. Fragility curves were defined
for four potential damage states of the wind turbine tower:
0.2% residual out-of-straightness, first yield at a stress con-
centration, 1% residual out-of-straightness, and first buckle.
The results obtained represent the seismic hazard of the in-
vestigated wind turbine tower at the investigated locations.
In the process of analyzing this typical wind turbine tower,
a methodology for the seismic risk assessment resulting in
fragility curves has been outlined, and may be applied to
any tubular steel wind turbine tower subject to any level of
seismic hazard.
The incremental analyses for either location in Canada
(Victoria, BC and Southern Ontario) suggest that the seismic
risk for the wind turbine tower that was investigated is very
small. The seismic risk of this wind turbine tower in the Los
Angeles area is much higher, although still not significant at
the intensity level of the design earthquake. This is due to
the long fundamental period of the tower and the short pre-
dominant period of most earthquakes.
However, the analyses presented herein demonstrated that
these structures must be designed for large safety factors
against any overloading, as they are prone to collapse when
the tower is excited beyond its elastic limit. As the design of
wind turbine towers is quickly evolving, with a tendency for
taller structures, the seismic response may become more
critical.
Acknowledgements
Financial support has been provided to the first author by
Ontario Graduate Scholarships (OGS), the Natural Sciences
and Engineering Research Council of Canada (NSERC),
and the Steel Structures Education Foundation (SSEF). Also
gratefully acknowledged are the Ontario Centres of Excel-
lence (OCE) and the Fraunhofer Centre Windenergie und
Meerestechnik, Bremerhaven, Germany, where the first au-
thor interned. Experimental shake-table data of the small
wind turbine was provided by UC San Diego from a pilot
Fig. 15. Fragility curves.
Nuta et al. 303
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test series conducted under the direction of Profs. Ahmed
Elgamal and Jose Restrepo.
References
AISC. 2005. Specification for Structural Steel Buildings. Standard
ANSI/AISC 360-05, American Institute of Steel Construction,
Chicago, Ill., USA.
ANSYS Multiphysics. 2007. ANSYS Element Reference. Release
11.0, Documentation for ANSYS. ANSYS Inc.
ASCE. 2005. Minimum design loads for building and other struc-
tures. Standard ASCE/SEI 7-05. American Society of Civil En-
gineers, Reston, Va., USA.
Atkinson, G.M. 2009. Earthquake time histories compatible with
the 2005 National Building code of Canada uniform hazard
spectrum. Canadian Journal of Civil Engineering, 36(6): 991–
1000. doi:10.1139/L09-044.
Barros, R.C., and Almeida, R. 2005. Pushover analysis of asym-
metric three-dimensional building frames. Journal of Civil Engi-
neering and Management, 11(1): 3–12.
Bazeos, N., Hatzigeorgiou, G.D., Hondros, I.D., Karamaneas, H.,
Karabalis, D.L., and Beskos, D.E. 2002. Static, seismic and sta-
bility analyses of a prototype wind turbine steel tower. Engi-
neering Structures, 24(8): 1015–1025. doi:10.1016/S0141-
0296(02)00021-4.
CEN. 2005. Eurocode 3: Design of steel structures, Part 1.1: Gen-
eral rules and rules for buildings. Standard EN 1993-1-1:2005,
European Committee for Standardisation, British Standards In-
stitution, London, UK.
CSA. 2001. Antennas, Towers, and Antenna-Supporting Structures.
Standard CAN/CSA S37-01, Canadian Standards Association,
Toronto, Ont.
CSA. 2004. Steel (Fixed Offshore) Structures. Standard CAN/CSA
S473-04. Canadian Standards Association, Toronto, Ont.
CSA. 2008. Wind turbines – Part 1: Design requirements. Standard
CAN/CSA C61400-1:08. Canadian Standards Association, Tor-
onto, Ont.
CSA. 2009. Design of steel structures. Standard CSA-S16-09. Ca-
nadian Standards Association, Toronto, Ont.
Danish Wind Industry Association. 2003. Manufacturing wind tur-
bine towers. [Online.] Available from http://www.talentfactory.
dk/en/tour/manu/towerm.htm [accessed 8 April 2009].
Deierlein, G.G., Liel, A.B., Haselton, C.B., and Kircher, C.A. 2008.
ATC-63 methodology for evaluating seismic collapse safety of
archetype buildings. ASCE-SEI Structures Congress, Vancouver,
B.C., 24–26 April 2008.
Elchalakani, M., Zhao, X.L., and Grzebieta, R. 2002. Bending tests
to determine slenderness limits for cold-formed circular hollow
sections. Journal of Constructional Steel Research, 58(11):
1407–1430. doi:10.1016/S0143-974X(01)00106-7 .
IEC. 2005. Wind turbines – Part 1: Design requirements. 3rd ed.
Standard IEC 61400-1:2005-08. International Electrotechnical
Commission, Geneva, Switzerland.
Lavassas, I., Nikolaidis, G., Zervas, P., Efthimiou, E., Doudoumis,
I.N., and Baniotopoulos, C.C. 2003. Analysis and design of the
prototype of a steel 1-MW wind turbine tower. Engineering
Structures, 25(8): 1097–1106. doi:10.1016/S0141-0296(03)
00059-2.
Nasserasadi, K., Ghafory-Ashtiany, M., Eshghi, S., and Zolfaghari,
M.R. 2008. Developing seismic fragility function of structures
by stochastic approach. Journal of Applied Sciences, 8(6): 975–
983. doi:10.3923/jas.2008.975.983.
NBCC. 2005. National Building Code of Canada. National Re-
search Council of Canada, Ottawa, Ont.
Prowell, I., Veletzos, M., Elgamal, A., and Restrepo, J. 2008.
Shake table test of a 65 kW wind turbine and computational si-
mulation. In 14th World Conference on Earthquake Engineering,
Beijing, China, 12–17 October 2008, Paper ID 12-01-0178.
Prowell, I., Veletzos, M., Elgamal, A., and Restrepo, J. 2009. Ex-
perimental and Numerical Seismic Response of a 65 kW Wind
Turbine. Journal of Earthquake Engineering, 13(8): 1172–1190.
Ritschel, U., Warnke, I., Kirchner, J., and Meussen, B. 2003. Wind
turbines and earthquakes. In Proceedings of the 2nd World Wind
Energy Conference (WWEC), Cape Town, South Africa, 24–26
November 2003.
Somerville, P., Punyamurthula, S., and Sun, J. 1997. Development
of ground motion time histories for Phase 2 of the FEMA/SAC
Steel Project. Report No. SAC/BD-97/04, SAC Joint Venture,
Sacramento, Calif., USA.
Vamvatsikos, D., and Cornell, C.A. 2002. Incremental dynamic
analysis. Earthquake Engineering & Structural Dynamics, 31(3):
491–514. doi:10.1002/eqe.141.
Voth, A.P. 2010. Branch plate-to-circular hollow structural section
connections. Ph.D. thesis, Department of Civil Engineering,
University of Toronto, Toronto, Ont.
Witcher, D. 2005. Seismic analysis of wind turbines in the time do-
main. Wind Energy (Chichester, England), 8(1): 81–91.
Zhao, X., and Maisser, P. 2006. Seismic response analysis of wind
turbine towers including soil-structure interaction. Proceedings
of the Institution of Mechanical Engineers, Part K: Journal of
Multi-body Dynamics, 220(1): 53–61. doi:10.1243/
146441905X73691.
List of Symbols
Doutside diameter of a CHS
DS damage state
EYoung’s modulus of elasticity
Fuultimate tensile stress
Fyyield tensile stress
Hhub height of wind turbine tower
Imoment of inertia
IM intensity measure
LP load pattern
Mbending moment
Mpplastic moment of a cross-section
Myyield moment of a cross-section
PGA peak ground acceleration
tthickness
Tiperiod of mode i
aimodal participation factor of mode i
Dlateral deflection
Dmax peak lateral displacement
Dres residual lateral displacement
3uultimate strain at fracture
qmax maximum rotation of tower as defined in this paper
kcurvature
kpcurvature at plastic moment: Mp/EI
maverage or mean, used in defining fragility curves
smises von Mises stress
fimode shape of mode i, normalized to mass matrix
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