Seismic response of wind turbine structures in the near ... · 1.1. Wind energy Wind energy has...

Faculty of Civil and Environmental EngineeringUniversity of Iceland

2015

Faculty of Civil and Environmental EngineeringUniversity of Iceland

2015

Seismic response of wind turbinestructures in the near-fault region

Guðmundur Örn Sigurðsson

SEISMIC RESPONSE OF WIND TURBINESTRUCTURES IN THE NEAR-FAULT REGION

Guðmundur Örn Sigurðsson

30 ECTS thesis submitted in partial fulfillment of aMagister Scientiarum degree in civil engineering

AdvisorsRajesh RupakhetySímon Ólafsson

Faculty RepresentativeEysteinn Einarsson

Faculty of Civil and Environmental EngineeringSchool of Engineering and Natural Sciences

University of IcelandReykjavik, December 2015

Seismic response of wind turbine structures in the near-fault region

30 ECTS thesis submitted in partial fulfillment of a M.Sc. degree in civil engineering

Copyright c© 2015 Guðmundur Örn SigurðssonAll rights reserved

Faculty of Civil and Environmental EngineeringSchool of Engineering and Natural SciencesUniversity of IcelandSæmundargötu 2101, Reykjavík, ReykjavikIceland

Telephone: 525 4000

Bibliographic information:Guðmundur Örn Sigurðsson, 2015, Seismic response of wind turbine structures in thenear-fault region, M.Sc. thesis, Faculty of Civil and Environmental Engineering, Univer-sity of Iceland.

Printing: Háskólaprent, Fálkagata 2, 107 ReykjavíkReykjavik, Iceland, December 2015

Fyrir Sögu Guðnýju

Abstract

This work focuses on seismic response of wind turbine structures in the near-fault re-gion. A computer program was prepared using the software MATLAB R© for dynamictime history analysis using the finite element method. Published results on 65-kWturbine model developed by the University of California at San Diego (UCSD) wasused to verify the finite element program. Numerical simulation of seismic responseof a 5-MW wind turbine tower, has been extensively used in the literature, wasconducted for a large set of recorded near-fault ground motion. Detailed analysis ofsimulated response show that: (1) seismic loads can be significant in the near-faultregion, and may even surpass design wind effects; (2) dominant period of near-faultground motion relative to the fundamental period of the tower is a very importantparameter; (3) response spectral analysis using modal combination is satisfactory forpreliminary design provided that a proper response spectral shape is used; (4) theEurocode 8 (EC8) response spectrum severely under-estimates the response of thestructure to near-fault ground motions. In light of the conclusions above, suitablemodels to account for near-fault effects were investigated. It was found that thespectral model proposed by Rupakhety et al. (2011) is more reliable than the EC8model. Seismic response predicted by this model was found to be much closer totime history analysis results than those predicted by the EC8 model.

v

Útdráttur

Í verkefni þessu er lögð megináhersla á svörun masturs vindmyllu í nærsviði jarðskjálfta.Skrifað hefur verið MATLAB R© forrit fyrir tímaháða greiningu með einingaraðfer-ðinni. Til að sannreyna niðurstöður greiningar með einingaraðferðinni hefur veriðstuðst við reiknilíkan þróað hjá University of California í San Diego (UCSD) fyrir 65-kW vindmyllumastur. Hermun á jarðskjálftasvörun 5-MW vindmyllumasturs, semhefur verið fjallað ítarlega um í fræðunum, var framkvæmd með því að nota safnyfirborðshröðunar tímaraða sem voru mældar í nærsviði jarðskjálfta.Nákvæm grein-ing á hermdri svörun sýnir: (1) áraun af völdum jarðskjálfta í nærsviði jarðskjálftagetur orðið veruleg og jafnvel orðið meiri en hönnunaráraun vegna áhrifa vinds;(2) ráðandi sveiflutími hröðunar yfirborðs í nærsviðs jarðskjálfta í samanburði viðgrunnsveiflutíma vindmyllumastursins er mjög mikilvæg grunnbreyta (3) greiningá svörunarrófi með sameiningu sveifluhátta er fullnægjandi fyrir forhönnun að þvítilskildu að beitt sé svörunarrófi að viðeigandi lögun; (4) Verulegt vanmat á nærsviðsjarðskjálftasvörun mannvirkja verður ef stuðst er við Eurocode 8 (EC8) svörunar-rófið. Með hliðsjón af niðurstöðum hér að ofan hafa viðeigandi reiknilíkön fyrirnærsviðs jarðskjálftasvörun verið rannsökuð. Niðurstan er að tíðnirúmslíkan Ru-pakhety o.fl. (2011) reyndist mun áreiðanlegra en EC8 líkanið. Jarðskjálftasvörunreiknuð með þessu líkani var mun nærri niðurstöðum úr tímaraðar hermunum en þvísem EC8 líkanið gerir ráð fyrir.

vi

Contents

List of Figures ix

List of Tables xiii

Abbreviations xv

Acknowledgments xvii

1. Introduction 11.1. Wind energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2. Wind turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3. Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3.1. Existing codes and standards . . . . . . . . . . . . . . . . . . 61.3.2. Wind Turbine Tower Modelling Methods . . . . . . . . . . . . 71.3.3. Modelling Software . . . . . . . . . . . . . . . . . . . . . . . . 8

1.4. Near-fault ground motions . . . . . . . . . . . . . . . . . . . . . . . . 81.5. Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.6. Organization of thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2. Near-fault ground motion 132.1. Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2. Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.1. Analytical near-fault pulse models . . . . . . . . . . . . . . . . 152.2.2. Near-fault response spectra . . . . . . . . . . . . . . . . . . . 16

2.3. Database . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3. Structural modeling and analysis 213.1. Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.2. SDOF type modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.3. Solution of SDOF response . . . . . . . . . . . . . . . . . . . . . . . . 273.4. Multiple Degree of Freedom (MDOF) modeling . . . . . . . . . . . . 28

3.4.1. Euler-Bernoulli beam-column elements . . . . . . . . . . . . . 283.4.2. Prior work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.4.3. Forcing frequencies . . . . . . . . . . . . . . . . . . . . . . . . 303.4.4. Structure used for computational verification . . . . . . . . . . 323.4.5. Details of 65-kW Turbine . . . . . . . . . . . . . . . . . . . . . 32

vii

Contents

4. Case Study: a 5-MW wind turbine structure 414.1. Modal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.2. Modal properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.2.1. Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.2.2. Mode shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5. Response Analysis and Results 475.1. Time history analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.1.1. Modal time history analysis . . . . . . . . . . . . . . . . . . . 475.1.2. Ground motion data . . . . . . . . . . . . . . . . . . . . . . . 52

5.2. Response spectral analysis . . . . . . . . . . . . . . . . . . . . . . . . 525.2.1. EC8 model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525.2.2. Response calculation . . . . . . . . . . . . . . . . . . . . . . . 53

5.3. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.3.1. Displacement . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.3.2. Drift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595.3.3. Shear demand . . . . . . . . . . . . . . . . . . . . . . . . . . . 625.3.4. Moment demand . . . . . . . . . . . . . . . . . . . . . . . . . 65

6. Conclusions 71

Bibliography 75

A. Near-fault records 81

viii

List of Figures

1.1. The maximum height of proposed wind turbines compared to an ex-perimental turbine and Hallgrímskirkja (Mannvit, 2014). . . . . . . . 2

1.2. Recent earthquake activity in the South Iceland Seizmic Zone. . . . . 5

1.3. An example of how multiple fracturing along a fault can amplify thewave amplitude. Here 3 waves propogating in the same direction,with similair phase and amplitude, combine to form a large pulsemotion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1. (a) Spreading of waves radiated from a point source. In the far-field,the source-site distance is large, time of wave propagation from thesource to site is much larger than time of rupture propagation on thesource, and therefore, the effect of extended source is negligible. (b)Spreading of waves radiated from different sections of an extendedsource. The dots indicate locations of radiation at different parts ofthe fault. The rupture is propagating towards right, causing simulta-neous arrival of waves at nearby stations to the right, which is termedas forward directivity effect. An opposite effect, known as backwarddirectivity, occurs at nearby stations lying in the direction oppositeto rupture propagation. At these locations, seismic energy is spreadover longer time resulting in lower amplitude and longer duration ofground motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2. The normalized pseudo-spectral velocity (PSVn) for each bin givenby Table 2.2 for 5% damping and rjb = 5 km. . . . . . . . . . . . . . 18

2.3. PSV of small to large earthquakes for 5% damping and rjb = 5 givenby equation 2.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.1. A mechanical model of a SDOF dynamic system with viscous damping. 23

ix

LIST OF FIGURES

3.2. Deformation response factor as a function of frequency ratio anddamping ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.3. A cantilever SDOF system with support rotation (AlHamaydeh andHussain, 2011). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.4. Schematic Power Spectral Density functions of wind and ocean wavesmodified from Sigbjörnsson and Rupakhety (2015). . . . . . . . . . . 31

3.5. Diagram of the 65-kW wind turbine structure (Prowell et al., 2009). . 32

3.6. The 65-kW wind turbine model geometry. . . . . . . . . . . . . . . . 34

3.7. Damping ratio as a function of frequency, two frequencies are used todetermine the shape as marked by dashed black lines. . . . . . . . . . 36

3.8. The first 3 front-aft mode shapes. . . . . . . . . . . . . . . . . . . . . 38

3.9. The first 3 side-to-side mode shapes. . . . . . . . . . . . . . . . . . . 38

3.10. Calculated acceleration response at the naccele of the 65-kW Turbine.Here lateral reffers to the SS motion and longitudinal to the FA motion. 39

3.11. Acceleration response at the naccele of the 65-kW Turbine for the ElCentro earthquake provided by (Prowell et al., 2009). Here lateralreffers to the SS motion and longitudinal to the FA motion. . . . . . . 40

4.1. The first four mode shapes in fore-aft motion. . . . . . . . . . . . . . 45

4.2. The first four mode shapes in side-to-side motion. . . . . . . . . . . . 46

5.1. Eurocode 8 normalized elastic response spectrum. . . . . . . . . . . . 53

5.2. Maximum horizontal nacelle displacement due to each ground motion;the results are divided into different magnitude bins as indicated inthe legend. The horizontal axis represents the predominant periodof velocity pulse (see, (Rupakhety et al., 2011)) normalized by thefundamental period of vibration of the structure. . . . . . . . . . . . 57

5.3. Average nacelle displacement in each bin computed from time historyanalysis and response spectral analysis. . . . . . . . . . . . . . . . . . 58

x

LIST OF FIGURES

5.4. The average spectral displacement of each bin plotted against theaverage RR2011 spectral displacement of each bin for 1% damping ofcritical. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.5. Average (for all the ground motions) drift ratio along the height ofthe tower. The red curve corresponds to the time history results, thegreen curve to GM SRSS, and the other curves represent contributionof the first three significant modes of vibration as indicated in thelegend. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5.6. Maximum drift ratios along the height of the tower: the dashed bluelines represent the result from time history analysis; the dashed redlines represent response spectrum analysis, and the other lines repre-sent contributions of the first three modes. . . . . . . . . . . . . . . 61

5.7. The total average drift ratio of all the motions using the time-historyand response spectra method (SRSS rule) by each bin. The driftcorreponding to each bin is as shown in legend. . . . . . . . . . . . . 62

5.8. Base shear demand due to each ground motion; the results are dividedinto different magnitude bins as indicated in the legend. . . . . . . . . 63

5.9. Average base shear demand in each bin computed from time historyanalysis and response spectral analysis. . . . . . . . . . . . . . . . . . 64

5.10. Overturning moment demand due to each ground motion; the resultsare divided into different Magnitude bins as indicated in the legend. . 65

5.11. Average overturning moment demand in each bin computed from timehistory analysis and response spectral analysis. . . . . . . . . . . . . . 66

5.12. The average rensponse spectra of each bin plotted against the equiv-alent EC8 and RR2011 spectras. . . . . . . . . . . . . . . . . . . . . . 68

5.13. Average response of all ground motions plotted against the averagecalculated spectras. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.14. The average spectral velocity of each bin plotted against the averageRR2011 and EC8 spectral velocity of each bin. . . . . . . . . . . . . . 70

xi

List of Tables

1.1. Properties of the wind turbines proposed in the Búrfell area (Mannvit,2014). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.1. Parameters of the PGV attenuation model given in Equation 2.2. . . 17

2.2. Parameters of spectral shape model given in Equation 2.3. . . . . . . 18

3.1. Properties of wind turbines, modified from Prowell (2011). . . . . . . 30

3.2. Properties of 65-kW wind turbine. . . . . . . . . . . . . . . . . . . . . 33

3.3. Modal properties of the 65-kW wind turbine tower. . . . . . . . . . . 37

3.4. Ground motion used for model verification (Prowell et al., 2009). . . . 39

4.1. Properties of 5-MW wind turbine, modified from Bir and Jonkman(2008). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.2. The modal properties of the 5MWwind turbine tower, the highlightedlines mark the modes contributing to seismic response in SS and FAmotion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

A.1. Near-fault ground motion records (highlighted records are not used). . 82

A.2. Near-fault ground motion records continued. . . . . . . . . . . . . . . 83




xiii

Abbreviations

ADAMS Automatic Dynamic Analysis of Mechanical SystemsCISN California Integrated Seismic NetworkCQC Complete Quadratic CombinationDFT Discrete Fourier TransformDOF Degree of FreedomDR Drift RatioEC8 Eurocode 8MDOF Multi-Degree of FreedomFA Fore-AftFAST Fatigue, Aerodynamics, Structures, and TurbulenceFE Finite ElementFEM Finite Element MethodFFT Fast Fourier TransformGL Germanischer LloydGMPE Ground Motion Prediction EquationHAWT Horizontal Axis Wind TurbineLHPOST Large High Performance Outdoor Shake TableMATLAB Matrix LaboratoryNGA Next Generation AttenuationNREL National Renewable Energy LaboratoryICEARRAY Icelandic Strong-motion ArrayISESD Internet Site for European Strong motion DataPGA Peak Ground AccelerationPGV Peak Ground VelocityPSA Pseudo-Spectral AccelerationPSV Pseudo-Spectral VelocitySD Spectral DisplacementSDOF Single Degree of FreedomRMS Root Mean SquareRPM Revolutions Per MinuteSRSS Square Root of Sum of SquaresSS Side-to-SideSSI Soil Structure InteractionVAWT Vertical Axis Wind TurbineUCSD University of California San Diego

xv

Acknowledgments

I would like to express my sincere gratitude to my teacher and mentor RajeshRupakhety for his teachings, motivation and guidance throughout my years inacademia, opening my mind to the wonders of mechanics and engineering as well ashelping me to reach my true potential.

I would also like to express my appreciation to Prof. Símon Ólafsson and late Prof.Ragnar Sigbjörnsson for advise and technical assistance during my thesis work.

Thanks to the staff of the Earthquake Engineering Research Centre for their kindhelp and co-operation during my summer internship; the experience gained withthem is invaluable.

I gratefully acknowledge a financial grant from Vísinda- og rannsóknarsjóður Suður-lands managed by Fræðslunet Símenntunar á Suðurlandi and Háskólafélag Suður-lands. This kind of acknowledgement is extremely meaningful for myself, giving meenthusiasm for this work as well as future projects in the field of engineering.

I also acknowledge the project grant (Verkefnastyrkur) from Félagstofnun stúdenta.It serves as an important ecouragement of the scientific work ahead, my ability tolearn and contribute to the academic society.

I would like to thank the faculty of Civil and Environmental Engineering at theUniversity of Iceland for excellent tutoring in various fields of engineering, mostnotably Bjarni Bessason for his teachings in structural analysis.

I would like to acknowledge with gratitude the help of my family and friends duringmy studies. To my significant other, Agnes B. Gunnarsdóttir, I owe the greatestthanks for supporting and encouraging me in my efforts.

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xvii

1. Introduction

1.1. Wind energy

Wind energy has been an exponentially growing industry in the past few years;the increase in installed total power has grown more than fivefold since 2000 andis now over 13% of the total installed power capacity in the European Union. In2013 alone roughly 11,159 MW of wind power capacity was installed, making thecurrent installed energy capacity more than 117.3 GW in the EU (EWEA, 2013)and 318.1 GW in the world (GWEC, 2015). Contributing factors that drive thisdevelopment, are for example, the economical benefits of wind turbines as well astheir sustainability, and positive influence on the environment due to reduction ingreen house gas emission. Wind farm projects generally have a shorter planning andconstruction time compared to conventional power projects.

Iceland has an abundance of renewable energy in production mostly in the hydroand geothermal energy field (Loftsdóttir et al., 2005). Most of the power consump-tion goes into manufacturing industries related to metal refining, such as aluminiumproduction which accounts for 71% of the 18,116 GWh used in 2013. Further devel-opment of power production is planned in the future in hopes of strengthening theeconomy, where future power projects would provide energy for further industriesor even be sold over a cable to Europe.

The proposed location for a wind farm is in the Búrfell area along Þjórsá wheremost of Iceland’s power plants are located. This has been determined the mostfeasible location due to the wind field caused by a natural wind tunnel and pre-existing infrastructure at the site. Pairing wind power with hydro power in theproposed area has a few advantages. Hydroelectric production usually has seasonalfluctuations which are caused by the change in precipitation and temperature. Theopposite is true with regards to wind speed, with many low pressure depressionsheading over the area during the winter time. This effect can reduce flow regulationand improve efficiency of pre-existing power infrastructure.

1

1. Introduction

1.2. Wind turbines

The most common large scale wind turbine design in use today is the horizontal axiswind turbine (HAWT) which, as can be seen from Figure 1.1, is a tower structureusually with a 3-blade rotor spinning around the horizontal axis. A steel tower witha circular-hollow-section is the most common practice although truss and concretetower designs have been used for smaller turbines. This research project focuses onseismic response of large scale wind turbine structures, similar to the ones beingplanned by the National Power Company of Iceland (or Landsvirkjun), close toBúrfellsvirkjun, a pre-existing hydro-power plant in South Iceland. Some propertiesof the planned structures according to a preliminary study is shown in table 1.1.

Table 1.1: Properties of the wind turbines proposed in the Búrfell area (Mannvit,2014).

Property ValuePower of each turbine [MW] 2.5-3.5Mast height [m] 70-80Rotor diameter [MW] 90-110Number of turbines up to 80Set up power [MW] up to 200P50 capacity [GWh/year] 705

At the time of this study, there are two research wind turbines that have been inoperation at the site for a few years, estimating the wind-efficiency of the site andthe ability of the turbine to survive the harsh weather conditions of Iceland.

Figure 1.1: The maximum height of proposed wind turbines compared to experimentalturbine and Hallgrímskirkja(Mannvit, 2014).

2

1.2. Wind turbines

History

The use of wind power is not a new phenomena and in fact has a history dating backthousands of years. The first documented design of a wind-powered machine datesback to Heron of Alexandria who made a wind-powered organ in the 1st centuryAD. The first practical design of a windmill appeared in the 9th century in the areawhich now is the Middle East using a number of rectangular sails to drive a verticaldrive shaft. Windmills soon thereafter became popular in China, India and laterNorth-western Europe. Windmills were used to grind corn and flour, pump waterfor irrigation and salt making, drive ships and to power automated statues.

The first windmills used for electricity production were made in Scotland at Strath-clyde University in 1887. The designer, Professor James Blyth, used the turbine topower his home for 25 years. Later that same year, Charles F. Brush built a 12 kWturbine to power his mansion.

In 1920, the Darrieus turbine, which is often referred to as the eggbeater windmill,was invented. The Darrieus turbine is a vertical axis wind turbine(VAWT) mean-ing it’s drive shaft spins around the vertical axis in order to convey power to thegenerator. This design is still used in many countries around the world.

About 10 years later, a precursor to the modern horizontal wind turbine was designedin Yalta. The turbine generated 100kW and had a 30m tower. It had a remarkable32% load factor which, even by today’s standards, is considered fairly good.

The Gedser turbine in Denmark was made in 1956 by Johannes Jul and operateduntil 1967. It was 200kW, three bladed turbine with aerodynamic tip breaks whichare still used in contemporary designs.

In the 1970’s, NASA led a large commercial wind turbine research effort paving theway for today’s multi-megawatt technologies. In the 1980’s, the first wind-farm wasconstructed, and NASA continues to develop record-breaking wind turbines.

Design and development of wind turbines is still ongoing, striving to improve theefficiency of turbines and lowering the construction cost. The European Union has,since 1998, supported more than 40 projects in wind energy with funding, andcontinues to do so, in order to provide sustainable energy production to the worldin an economical way.

3

1. Introduction

Scope

The primary objective of this thesis is to study the seismic response of wind tur-bine structures in the near-fault region. The modelling procedure will involve theanalysis, using the finite element method, of a parked (not moving) wind turbinewhere the rotor, nacelle, and foundation are assumed to be stiff using the finite el-ement method. Only gravitational and seismic actions are considered in this study.By using multiple near-fault ground motions, the earthquake response of a largeland-based wind turbine structure is evaluated. Summary of literature and resultsregarding wind turbines and comparison with computed results will be presented.

Seismic risk

The area under investigation, Hafið, is essentially a large sand/tephra plain layingon top of basalt rock layer. The site lies close to the South Iceland Seismic Zone(SISZ) where strike-slip earthquakes common. A few major earthquakes have oc-curred recently in the area; on the 29th of May 2008 an earthquake of 6.3 momentmagnitude (Mw) occurred. Earthquakes of 6.5Mw and 6.6Mw occurred on the 17thand 21st of June 2000, respectively (Sigbjörnsson and Ólafsson, 2004).

Most notable for this project is the 1912 earthquake which was measured at 7.0Mw.The reason for this is not only the sheer scale of the earthquake but also it’s proximityto the wind turbine site. The orientation of the fault with respect to the site locationis considered as unfavourable since it strikes from north to south pointing towardsthe proposed site. As seen from Figure 1.2, the epicentre of the 1912 earthquake,marked by a red marker, is to the far east and the wind turbine site is approximately100 km towards north. In 1896 five earthquakes of size 6.6-6.9Mw took place in theSouth Iceland seismic zone. They occurred on the 26th and 27th of August andthen later on the 5th, 6th and 10th of September (Sigbjörnsson and Rupakhety,2014). The earliest well documented earthquake reported in the SISZ was the 7.1Mw

earthquake of 1784.

Considering the investment required for a wind farm project, and various disruptionon it due to potential earthquake-related failure, it is imperative that the windturbine structures are designed for seismic action. Compared to cities where thedesign of structures is very diverse, wind farms contain very few types of uniquestructures. This kind of similitude can be problematic in case of an earthquakewith unfavourable characteristics with respect to the turbine design. If such anevent would occur, it would mean, severe damage or destruction to the whole windfarm since their structural response would be more or less the same. Wind turbinesare designed as very slender, tall structures, and are flexible with relatively long

4

1.2. Wind turbines

vibration periods. This raises a concern for detailed seismic design of the turbinestructures in the near field, since ground motions in those areas have unfavourablecharacteristics for structures with long oscillation periods.

.

_ _ ^

#*Reykjavik

20°0'W20°30'W21°0'W21°30'W22°0'W22°30'W23°0'W

64°15

'N64

°0'N

63°45

'N 200 0 200100 kmReykjanes Peninsula

South Iceland Seismic Zone

__

14° W16° W18° W20° W22° W24° W

66° N

65° N

64° N

North American Plate

Eurasian Plate1 cm/yr

1 cm/yr

Legend^ 17 June 2000_ 21 June 2000_ 29 May 2008

Earthquake epicentresM

!( 3.5-4!( 4-5!( 5-6!( 6-7!( >7

Mid-Atlantic RidgeTransform faultsRingroadRoadsCalderasCentral VolcanoesGlaciersFissure swarmsFracture zones

Figure 1.2: Recent earthquake activity in the South Iceland Seizmic Zone.

Icelandic conditions

The design of structures in Iceland relies mostly on Eurocode standards (Standard,2005). These standards contain practical engineering methods used in design andanalyses of structures. They are, on one hand composed of theoretical methodsfounded by mathematical deduction and on the other on Empirical methods thatare based on statistics, experiments and experience. Most structures are designed onthe basis of response spectral analysis as specified in EC8. For some structures, thatdo not fulfill certain requirements set by the code, time history analysis is required.

To a certain degree the EC8 response spectra is adapted to Iceland by using aseismic acceleration map available in the Icelandic Annex. This means that theelastic design spectrum is obtained by scaling the EC8 spectral shapes by a peakground acceleration value that depends on the location of the structure and the

5

1. Introduction

level of acceptable risk. However the EC8 spectral shapes are not necessarily rep-resentative of ground motion characteristics in Iceland. In fact, average spectralshapes of ground motion recorded in Iceland show significant deviation from thatrecommended in EC8. The EC8 spectral shapes tend to under-estimate long-periodordinates and over-estimate short-peiod ordinates of response spectra obtained fromIcelandic ground motion data.

This discrepancy would not imply safety critical consequences for stiff and shortstructures, which are more common in Iceland. However, for tall and flexible struc-tures, which have vibration periods longer than about 0.5s, the EC8 spectral shapesmay result in significant under-estimation of seismic action. Wind mill towers beingstudied in this work are one of those structures. In addition, the EC8 spectral shapedoes not account for long-period nature of directivity affected ground motion in thenear-fault area. In this context, it is important to study suitability of code-specifiedseismic actions on such structures in the study area, and to quantify near-faulteffects on their seismic response.

1.3. Literature review

1.3.1. Existing codes and standards

Standards and regulations have been established providing details on design require-ments for wind turbines. The main codes and standards addressing seismic designare:

• Guidelines for Design of Wind Turbines (Veritas, 2002)

• Guideline for the Certification of Wind Turbines (Lloyd, 2003)

• Design of offshore wind turbine structures (Veritas, 2004)

• IEC 61400-3: Wind Turbines - Part 1: Design Requirements (IEC, 2005)

• Guideline for the Certification of Offshore Wind Turbines (Lloyd, 2005)

• IEC 61400-3: Wind Turbines – Part 3: Design Requirements for OffshoreWind Turbines (IEC, 2009)

Another useful document for wind turbine structural design is the ASCE/AWEARecommended Practice for Compliance of Large Land-based Wind Turbine Support

6


Structures (ASCE/AWEA, 2011).

The Veritas and Germanischer Lloyd (GL) guidelines provide little introduction tospecific details of earthquake engineering but rather suggest that local building codesbe applied. Within the standards above, the seismic actions incorporate:

• A 475 year design earthquake.

• Earthquake load is to be combined with all normal external conditions withsafety factor 1.0.

• At least 3 modes required for analysis in time and frequency domain.

• At least 6 simulations per load case for time domain.

• Tower is to behave elastically.

• Suggested damping is 1% of critical.

1.3.2. Wind Turbine Tower Modelling Methods

There are a few methods generally used for the modelling of wind turbine structureswhich vary significantly in complexity. The simple single degree of freedom (SDOF)systems can be used where the stiffness of a cantilever beam with the mass of therotor, nacelle and 1/4 of the tower mass is used to simulate the structure. A moreprecise model can be used where multi-degree of freedom (MDOF) finite element(FE) equations are built using beam-column, shell elements or as 3-dimensionalelements. The problem with modelling these kind of structures is that they arehinged to the rotor. This means that the model needs to be a multi-body system ifmodelled as operational. For simplification, turbine structures are often analysed asparked so that there are no moving parts during simulations. This kind of simulationhas been proven to be a conservative approach (Prowell, 2011). The loading scenarioscan vary as well, since the structure can be subject to forces due to gravity, wind,snow/ice, sea wave and earthquake loadings. A full system model is when a multi-body approach, along with the multi-physics of the combined loading cases, is usedin the modelling. The foundation which can effect the structural behaviour is alsoa popular subject of the literature, where many types and modelling methods havebeen proposed to account for it’s interaction with the structure.

7

1. Introduction

1.3.3. Modelling Software

The most notable wind turbine modelling tools which use full system modelling.

• GH Bladed uses a limited degree of freedom (DOF) modal model analysedin the time domain. Developed by Garrad Hassan (Bossanyi, 2009).

• FAST which is developed by the National Renewable Energies Laboratory(NREL) uses a combined modal and multibody formulation (Jonkman andBuhl Jr, 2005).

• FLEX5 developed by Stig Oye at the Technical University of Denmark usesmodal formulation in time-domain (Øye, 1999).

• HAWC2 developed at the Risø, National laboratory uses a multi-body timo-shenko beam model, where assembly of bodies is connected through constraintequations (Larsen and Hansen, 2007).

Both GH Bladed and FAST have been verified by Germanischer Lloyd (GL) forcalculating loads while operating. The first version of HAWC2 was verified and thelatter version verified against the first. Other general purpose structural analysisprograms that have been used for analysing turbine structures:

• OpenSees a open source finite element program for earthquake engineeringsimulation. (Mazzoni et al., 2006)

• SAP2000 a structural analysis program developed by Computers and Struc-tures (CSI).

• ADAMS a multi-body dynamic analysis program.

1.4. Near-fault ground motions

Forward directivity is one of the most important effect that influences amplitude andfrequency content of ground motion in the vicinity of extended earthquake faults.This effect is a result of constructive interference of seismic waves radiated fromdifferent sections of causative fault. As shear wave velocity and rupture velocity on afault are usually very close, at stations near the fault, waves radiated from differentsections arrive almost simultaneously, causing impulsive motion. The impulsivenature is more evident in ground velocity, which is often a strong pulse with most of

8

1.5. Objectives

the energy concentrated in a narrow band of frequency. This frequency is stronglydependent on the size of the earthquake. Such ground motion usually are of higheramplitude and narrower frequency content than ground-motion in the far field. Near-field ground motion with strong narrowband pulses affect structures whose vibrationfrequencies are close to the pulse frequency more than other structures.

Figure 1.3: An example of how multiple fracturing along a fault can amplify thewave amplitude. Here three waves propogating in the same direction, with similairphase and amplitude, combine to form a large pulse motion.

1.5. Objectives

The objectives of this research are to model common large scale wind turbines usingfinite elements, and to simulate their structural response to earthquake excitations.Specifically ground-motion in the near-fault area will be considered, due to theirpotential adverse effects on tall tower structures.

1. Data collection and processing: This invloves collection of ground-motion aswell as structural data. Ground motion data recorded in the near-fault regionin south Iceland have been compiled and uniformly processed. This includesthe recordings of May 29 2008 Ölfus Earthquake. During this earthquake, in-tense velocity pulses were recorded in Hveragerði by the strong-motion arrayICEARRAY (Halldorsson and Sigbjörnsson, 2009). These recordings are inthe extreme near-fault area (only about 3km) from the source, and provide aunique opportunity to study effects of near-fault ground motion on civil engi-neering structures. A representative ground-motion from Hveragerði is used instructural response calculation presented in later chapters. Furthermore, datafrom the 17 June 2000, and 21 June 2000 earthquakes (Halldórsson et al., 2007)are used. To supplement the database, near-fault ground motion records com-piled and processed by (Rupakhety et al., 2011) is utilized. Data regardingthe structural properties of commonly constructed wind towers were also col-

9

1. Introduction

lected. This includes wind tower studies available in the scientific literature,as well as the towers installed by Landsvirkjun.

2. Structural modelling: Mathematical models of wind towers were created forcomputer simulation. Stiffness and inertial properties of towers modelled us-ing standard structural analysis methods. In addition, structural dynamicsprinciples were applied for simulation of seismic response.

3. Response simulation and analysis: Comprehensive dynamic and pseudo-dynamicanalysis of different wind turbine towers were performed. Time history anal-ysis of the tower structures was performed for a large set of ground motionrecorded during past earthquakes. Pseudo-dynamic analysis, in the form ofresponse spectral method, was also performed. In this method, three differ-ent types of response spectra were considered, namely, response spectra basedon EC8 and scaled with peak ground acceleration of ground motion used intime history analysis, actual response spectra of the ground motion records,and near-fault ground-motion spectra presented by Rupakhety et al (2011).Detailed analysis and comparison of the results obtained from these analysismethods were performed to understand the salient features of response, toidentify critical ground-motion parameters, and to investigate suitable meth-ods for practical analysis and design.

4. Reporting and publication: Considerable work was accomplished in reportingand publication of research results in the scientific domain. A paper (Sigurðs-son et al., 2015) outlining the preliminary results was published and presentedin the IZIIS-50 International Conference on Earthquake Engineering and En-gineering Seismology. An abstract for another paper outlining the suitabilityof various response spectral models in the analysis of wind tower turbines hasbeen submitted to the 16th World Conference in Earthquake Engineering, anda full paper for this publication is being prepared. A more detailed presenta-tion based on the results presented in this thesis is being prepared as a journalpaper to be submitted to the Bulletin of Earthquake Engineering.

1.6. Organization of thesis

The thesis is split into six chapters each covering an important aspect of the researchproject. The first chapter presents a broad overview of the research project, statesits objectives, and research methods, and the scope and importance of the work thatis carried out in this project.

The second chapter presents an overview of the nature of ground-motion in the near-

10

1.6. Organization of thesis

field area. A concise survey of literature covering amplitude and frequency contentof near-fault ground motions is presented, and various models used in the literatureare discussed.

The third chapter deals with finite element and structural dynamics theory relevantto computer simulation of seismic response of wind tower structures. In additionto basic theory, some discussion on simple and more complex modelling options arediscussed.

The fourth chapter describes the properties of the case study structure, which is a5-MW structure. Its geometry, elastic and inertial properties, and other relevantdetails and assumptions utilized in finite element modelling are discussed in detail.

The fifth chapter presents the results of dynamic (time history) and pseudo-dynamic(response spectral) analysis of seismic response. Various response parameters suchas base shear, overturning moment, displacement demand, and drift demand areinvestigated. Effects of earthquake size and frequency content of ground motionare analysed and discussed in detail. Comparison between results of dynamic andresponse spectral analysis with a critical discussion on the suitability of differentresponse spectral models are presented.

Chapter six presents the main conclusions of the research work, including modellingand analysis constraints and limitations, and discusses the scope for future researchin this subject.

11

2. Near-fault ground motion

2.1. Characteristics

Structures that are in close vicinity to the epicentre of an earthquake will most likelybe subjected to near-fault effects. These may be described as pulse like groundmotions that have a tendency to increase the displacement response and ductil-ity demand of relatively flexible structures. Near-fault ground motions also have atendency to increase spectral acceleration at long periods, meaning that structuralsystems with long oscillation periods will tend to resonate with the ground excita-tion. For tall structures where the dominant period of ground motion is less thanthe fundamental mode period of the structure, Tp < Tf , resonance may occur athigher modes causing wave travelling up the length of the structure, resulting inincreased displacement and shear forces. The amplitude and frequency content ofthese impulsive motions are controlled by source, path, and site parameters. Themost significant effect in the near-field is the so-called forward directivity effect,which is a result of the focusing of seismic waves radiated from different sections ofan extended fault. The impulsive nature of near-fault ground motions, where theenergy is concentrated in a short duration, can cause severe damage to structuresdesigned for non-impulsive motion. Figure 2.1 illustrates earthquake waves radi-ated from a single point versus those radiated from different sections of an extendedfault, causing focusing effect at a site located in the direction of rupture propa-gation. Apart from directivity effect, pulse-like ground motion can also occur dueto static displacement, also known as the fling effect. This is a result of coseismicpermanent displacement and is observed only in the extreme vicinity of the fault.These effects can be important, for example, when a structure such as a pipeline ora tunnel crosses a seismogenic fault. These effects attenuate rapidly with distance,and are not significant unless the site of interest lies very close to a fault. In thisstudy, only forward directivity effects are considered. The conditions required forforward directivity are that the rupture should propagate towards the site, and thatthe slip vector on the fault plane should point towards the site. These conditions aresatisfied at many locations close to a strike-slip fault. Since earthquakes in SouthIceland exclusively occur on strike-slip faults, and the site of interest lies to thenorth of north-south trending almost vertical strike-slip faults of the South IcelandSeismic Zone, forward directivity effects are expected to occur in the study area.

13


Figure 2.1: (a) Spreading of waves radiated from a point source. In the far-field,the source-site distance is large, time of wave propagation from the source to siteis much larger than time of rupture propagation on the source, and therefore,the effect of extended source is negligible. (b) Spreading of waves radiated fromdifferent sections of an extended source. The dots indicate locations of radiationat different parts of the fault. The rupture is propagating towards right, causingsimultaneous arrival of waves at nearby stations to the right, which is termed asforward directivity effect. An opposite effect, known as backward directivity, occursat nearby stations lying in the direction opposite to rupture propagation. At theselocations, seismic energy is spread over longer time resulting in lower amplitudeand longer duration of ground motion.


A study conducted by Bertero et al. (1978) on the Olive View Hospital MedicalTreatment and Care Facility during the 1971 San Fernando, California earthquakewas the first to display how near-fault ground motions can cause large displacementductility demands in structures compared to the code provisions of the time. Near-fault ground motions which are generally associated with few large amplitude cycleswere also shown to affect the structural integrity of structures significantly morethan far-fault motions which have numerous small amplitude cycles. Anderson andBertero (1987) discovered that the nonlinear response of structures is controlled bythe period of the pulse motion relative to the fundamental period of a structure. Hallet al. (1995) demonstrated that near-fault ground motions can cause severe displace-ment demands in high rise and base isolated structures. Iwan (1997) observed howwaves caused by near-fault pulses can travel along the height of structures.Andersonet al. (1999) discovered that increasing the stiffness of flexible structures is not ben-eficial with respect to near-fault pulses. Alavi and Krawinkler (2004) evaluatedthe response of generic frames to near-fault motions and their equivalent pulses. Itwas found that the design codes greatly underestimated the excitation of near-fault

14


ground motion and that shear demand was highest at the top of tall building whenTf > Tp and that yielding migrates from there to the bottom of the structure. Inthe case of Tf < Tp yielding would migrate from the base to the top.

2.2.1. Analytical near-fault pulse models

To simulate the pulse like behaviour of the near-fault motion many researchershave used simple waveforms. These include square and triangular pulses as well assinusoidal and wavelet pulse types;

Hall et al. (1995)A simple triangular velocity pulse.

Makris (1997)Cycloidal front velocity pulse, using cosine functions.

Makris and Chang (2000)Type C pulse added with n displacement cycles called a Cn pulse.

Alavi and Krawinkler (2004)Three types of triangular velocity pulses

Menun and Fu (2002)A pulse model using the product of sine and exponential functions.

Mavroeidis and Papageorgiou (2003)Modified Gabor wavelet.

He and Agrawal (2008)Amplitude-modulated sinusoidal waveforms.

The accuracy of pulse models in adequately representing near-fault ground motionsof multiple degree of freedom structures was studied by Rupakhety and Sigbjörnsson(2011) where steel moment resisting frames of different heights were subjected to aset of recorded near-fault ground motion and equivalent pulses fitted to them ac-cording to the model of Mavroeidis and Papageorgiou (2003). It was shown that, onaverage equivalent pulses underestimate the response due to actual ground motion,especially when the fundamental period of vibration of the structure was close to thepulse period. This is explained in part by higher mode excitation which was foundto be important in the upper portion of the taller frames, and the narrow-bandednature of equivalent pulses which results in their inability to model seismic action at

15


dynamically significant modes of vibration of a structure. This observation indicatesthat while use of simple equivalent pulses is useful for an overall understanding ofnear-fault phenomenon, frequencies other than that of the dominant pulse play animportant role in seismic response of tall structures. This implies that responsespectral models which are accurate only near the pulse period of ground motion,but fail to model amplitudes at other frequencies, are not suitable for quantifyingseismic action in the near-fault area. Therefore, near-fault response spectral shapes,which model a wide range of frequencies including the dominant pulse frequenciesare more suitable for seismic design of tall structures in the near-fault area.

2.2.2. Near-fault response spectra

A common approach of quantifying seismic action on structures is through theso-called earthquake response spectrum. In EC8, such a spectrum is constructedby a pre-specified spectral shape (pseudo-spectral acceleration normalized by peakground acceleration) with the design peak ground acceleration at a given site. Suchpeak ground accelerations are often referred to different mean return periods, de-pending on the level of acceptable risk, and are obtained by probabilistic seismichazard assessment (PSHA). PSHA makes uses of empirical ground motion predictionequations (GMPEs), also known as attenuation equations, to model amplitude atten-uation of seismic waves as a function of source, path, and site parameters. There areno specific provisions in EC8 for PSHA modeling the near-fault effects. In addition,the spectral shapes specified in EC8 are based mostly on far-fault data, and there-fore fail to capture the spectral characteristics of near-fault ground motion. Somemodels for elastic response spectra applicable to near-fault ground motions havebeen presented in the literature, for example; The broadband directivity models bySomerville et al. (1997) and Abrahamson (2000), and narrowband directivity modelsproposed by Tothong et al. (2007). The model used in this study was presented byRupakhety et al. (2011) which is applicable to near-fault earthquake events wherethe Joyner-Boore distance from the site is less than 30 km (rjb ≤ 30km) and the av-erage shear wave velocity in the first 30m of subsoil is not very low (vs,30 ≥ 240m/s).This model presents empirical equations for the predominant pulse period, atten-uation equation for peak ground velocity (PGV), the predominant period (Td) isdefined as the period at which the 5% damped linear-elastic PSV reaches its peakvalue. The predominant period scales with moment magnitude (Mw) as:

log(Td) = αMw + β + ε (2.1)

where the regression parameters where found to be α = 0.47 and β = −2.87 and ep-silon is a normally distributed random variable with 0 mean and standard deviation

16


σ = 0.18.

The peak ground velocity (PGV ) is related to the magnitude and source-to-sitedistance (R). The Joyner & Boore (rjb) distance should be used (Joyner and Boore,1981), that is the least distance from an earthquake fault to the site, if not availablethen the epicentral distance (repi) can be applied as well. The PGV is given as:

log(PGV ) =

{a+ bMw + cM2

w + d log(R2 + e2) + η + ε if Mw ≤Msat

a+ bMsat + cM2sat + d log(R2 + e2) + η + ε otherwise

(2.2)

Here the terms η and ε refer to error terms due to inter- and intra-event variationand are assumed to be normally distributed random variables each with 0 meanand standard deviation σ1 and σ2 respectively. Assuming that these variables arestatistically independent, the standard deviation of log PGV is σt =

√σ21 + σ2

2. Themodel parameters and standard deviation of the residuals are given in Table 2.1.The values of the regression coefficients are as found in Table 2.1.

Table 2.1: Parameters of the PGV attenuation model given in Equation 2.2.a b c d e Msat σ1 σ2 σt

-5.17 1.98 -0.14 -0.10 0.75 7.0 0.081 0.135 0.16

To model response spectra, approximate equations for spectral shape (pseudo-spectralvelocity, PSV normalized by PGV) is given as:

PSVn =I1 exp{−0.5(ln(Tn) + 1.4)2}+ (4.92− 0.58Mw)

(

1−(TnTd

)2)2

+ 4Dm2

(TnTd

)2

−0.5Tn

(2.3)

where Tn is the undamped natural period of vibration of a SDOF system, and theother model parameters are given in Table 2.2.

17


Table 2.2: Parameters of spectral shape model given in Equation 2.3.Mw I1 Dm

5.5 < Mw ≤ 6.0 0.320ξ−0.5 1.54ξ + 0.396.0 < Mw ≤ 6.3 0.239ξ−0.5 1.73ξ + 0.446.3 < Mw ≤ 6.6 0.211ξ−0.5 2.41ξ + 0.476.6 < Mw ≤ 6.8 0.204ξ−0.5 2.82ξ + 0.506.8 < Mw ≤ 7.3 0.283ξ−0.5 4.18ξ + 0.587.3 < Mw ≤ 7.6 0.242ξ−0.5 3.38ξ + 0.59

Figure 2.2 shows the 5% damped spectral shapes given by Equation 2.3. The figureshows how the change in shape is controlled by the parameters provided in Table2.2.

Undamped Natural Period, Tn (s) 0.1 0.25 0.5 1 2 3 4 5 7 10

Norm

alizedpseudos-spectralvelocity

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8Mw = 5.6Mw = 6.2Mw = 6.6Mw = 6.8Mw = 7.3Mw = 7.6

Figure 2.2: The normalized pseudo-spectral velocity (PSVn) for each bin given byTable 2.2 for 5% damping and rjb = 5 km.

18


Once the PGV and PSVn have been determined we can determine the pseudo-spectral velocity as:

PSV = PGV · PSVn (2.4)

The pseudo-spectral acceleration and spectral-displacement are then given as:

PSA = PSV ω = PSV2π

T(2.5)

SD = PSV ω−1 = PSVT

2π(2.6)

An example of the modelled response spectra can be seen in Figure 2.3 for differentvalues of earthquake magnitude for a distance of 5 km and 5% damping. The Figureshows that that as the earthquake magnitude increases the velocity is amplified, andfurthermore the PSV peak shifts to a longer period of oscillation.

Undamped Natural Period, Tn (s) 0.1 0.25 0.5 1 2 3 4 5 7 10

Pseudos-spectral

velocity

(m/s)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8 Mw = 5.6Mw = 6.2Mw = 6.6Mw = 6.8Mw = 7.3Mw = 7.6

Figure 2.3: PSV of small to large earthquakes for 5% damping and rjb = 5 given byEquation 2.4.

19


2.3. Database

The database used contains 93 near-field ground motions from around the world.In total 29 different earthquakes are used, some recorded from multiple sites. Themajority of the records come from the NGA database (Power et al., 2006) alongwith the accompanying metadata.

The Internet site for European Strong-Motion Data (ISESD) provided strong-motionrecords of the Icelandic earthquakes of 17 and 21 June 2000 as well as 29th May2008 Ölfus Earthquake. (Ambraseys et al., 2004).

A single record corresponding to WID 90 (EERC basement) was obtained from thedatabase of Earthquake Engineering Research Center, University of Iceland. Meta-data regarding Icelandic earthquakes is calculated based on several publications,including Halldórsson et al. (2007).

California Integrated Seismic Network (CISN) provided accelerograms for the 2004Parkfield Earthquake. Metadata is based in various publications. Records of the2009 L’Aquila Earthquake were provided by the Italian accelerometric network (Luziet al., 2008). Permanent displacements if any within the ground motions has beenremoved by subtracting a half-sine pulse from the acceleration records as describedin Rupakhety et al. (2010).

20

3. Structural modeling andanalysis


In a detailed study of a 450-kW turbine, by Bazeos et al. (2002) studied the minimumload combination that would produce local buckling in the tower structure; they usedshell elements to model the tower. They studied the effects of geometric and materialproperties of load bearing elements as well as load distribution. The influence ofa door opening and array of stiffeners on the structural behaviour of the towerwas further investigated. The prototype was found to have adequate strength withrespect to natural loading scenarios containing pseudo-static wind and earthquakeactions. Their study revealed that highest stresses would be developed near themid-height of the tower, and not at its base as might be generally expected.

Lavassas et al. (2003) performed a non-linear structural analysis of a 1-MW (72mtall) wind turbine using 4-node shell elements. A buckling analysis of the shell basedon Eurocode 3 was performed under the action of self-weight, wind and earthquakeground motion. They found that a simplified linear static model was sufficient toestimate the basic response and eigenvalues of the tower. Extreme wind action wasfound to control the dominant load combination. At seismically hazardous, soft soilsites located far from coastal zone, seismic action was found to be critical for design.

Ritschel et al. (2003) studied the dynamic response of a 60m high wind turbinetower. They used beam elements to model the tower and performed time historyanalysis using ground-motion time series simulated to be compatible to the EC8design seismic action. Their results showed that earthquake action correspondingto 0.3g PGA would generate about 70% of the response corresponding to a 50-yearwind action specified in IEC 61400-1 (IEC, 2005).

Haenler et al. (2006) did further analysis of the same tower under seismic actions.Their results showed that higher modes of vibration participate in structural re-sponse more during ground motion than during normal operational actions.

21

3. Structural modeling and analysis

Witcher (2005) modelled a 2-MW wind turbine using the GH-bladed software, andshowed that overturning moment demand due obtained from time- and frequency-domain solution are comparable. He found that operational wind turbines can ex-perience a total damping close to 5% of critical, which is what is often prescribedin seismic design codes for buildings.

Zhao and Maisser (2006) used a multi-body dynamics model considering soil-structureinteraction (SSI) to investigate the seismic response of wind turbine towers in thetime domain. It was shown that SSI reduces the vibration frequencies of the struc-ture and has significant influence on seismic response.

Comparing the response of a 400-kW turbine to a 2-MW turbine, Ishihara andSarwar (2008) observed that higher vibration modes are important for large wind-turbines, and that the building standard law of Japan (BSL standard) are not suit-able for large structures with relatively low damping values.

AlHamaydeh and Hussain (2011) also concluded that SSI affects the natural fre-quencies considerably, and that ignoring it leads to under-design of the system.

Harte et al. (2012) studied the 1.5-MWNREL baseline turbine using Euler-Lagrangianapproach in the frequency domain. They concluded that, on stiff soil sites, SSI doesnot affect peak bending moments and shear forces but increases fatigue on rotorblades.

In a subsequent study of the 1.5-MW NREL Baseline HAWT, Valamanesh andMyers (2014) presented analytical equations to describe the aero-dynamic dampingfrom the rotor in the fore-aft and side-to-side motion. Simulations showed howdamping increased when the cut-in wind speed of the turbine was reached.

3.2. SDOF type modelling

Single degree of freedom (SDOF) modelling can be used, as a first approximation, forsimple structures or systems. It models one dimensional motion of a mass attachedto a spring, and a viscous dash-post can be added to model energy dissipation. Suchmodels are commonly used in practical seismic design; for example, seismic loadsspecified in design codes are based on equivalent SDOF models of structures.

22


Figure 3.1: A mechanical model of a SDOF dynamic system with viscous damping.

Modelling wind turbine tower as a SDOF system, motion of the nacelle can beconsidered as the relevant degree of freedom. The tower can then be modeled as acantilever beam, and its flexural stiffness provides the spring constant, k. The massof the rotor and the nacelle along with some fraction of the mass of the tower can beassumed to be lumped at the tip of the tower. The angular frequency of vibrationof the simplified model is given by:

ω =

√k

m(3.1)

and the period of vibration is given by:

T =2π

ω(3.2)

which can be expressed as a function of geometric, inertial, and elastic properties ofthe structure as:

T = 2π

√m

k= 2π

√mh3

3EI(3.3)

where m represents lumped at the tip of the tower, h is the height of center ofmass from the base of the tower, E is the elastic modulus of the tower and I is thesecond moment of area of the tower cross-section. With energy dissipation modelledby viscous damping ratio, ξ (expressed as a percentage of critical damping), the

23


damped angular frequency is given by:

ωD = ω√

1− ξ2 (3.4)

with the damping ratio given by:

ζ =c

2mω(3.5)

with c as the damping coefficient that relates damping force to velocity of motionlinearly. The damped and undamped frequencies are often taken as equal value forlow values of damping (under 20% of critical). The effect of damping is noticeablewhen excitation with a given frequency ω on the system is in the vicinity of thenatural frequency ω. Figure 3.2 shows the ratio between displacement of a dynamicsystem and that of a static system with same stiffness as a function of frequencyratio (loading frequency per unit natural frequency of the system) and dampingratio. This ratio is also known as the displacement response factor (or dynamicamplification factor). It can be observed that, when the frequency ratio approachesunity, dynamic response is greatly amplified, a phenomenon commonly known asresonance. Damping significantly reduces dynamic response near resonance, but isnot as influential when the loading frequency and system frequency are very different.

24


β =ω

ω

0 0.5 1 1.5 2 2.5 3

Rd

0

1

2

3

4

5

6

ζ = 0.05ζ = 0.10ζ = 0.20ζ = 0.50ζ = 0.70

Figure 3.2: Deformation response factor as a function of frequency ratio and damp-ing ratio.

Foundation flexibility can be incorporated into the SDOF model by introducing arotational spring at the base of the tower. If horizontal sliding at the foundationinterface is also to be modelled, additional springs can be introduced. A simplesystem with rotational spring at the base is shown in Figure 3.3. This model canbe replaced by an equivalent SDOF model whose stiffness is given by:

k =kksk + ks

(3.6)

25


st

sks

F(t)uus

ut

m m m

Figure 3.3: A cantilever SDOF system with support rotation (AlHamaydeh and Hus-sain, 2011).

In this model, the horizontal motion of the mass is due to flexural bending of thetower (u) and a rigid body rotation due to the foundation spring (us). The totaldisplacement is the sum of the two displacements due to the two effects and a differ-ential equation of motion can be formulated for this equivalent SDOF system. It isnoteworthy that the displacement of the mass due to foundation rotation increaseswith the height of the tower. Various models are available to determine the springstiffness at the base which depend on the shape of the foundation and the underly-ing soil. For example using the Borowicka (1943) model the rocking stiffness for acircular foundation is given by:

ks =8GR3

3(1− ν)(3.7)

where G and ν represent the shear modulus and Poisson’s ratio of the soil. R isthe foundation radius. This is only one of the many models that are available,and models to account for horizontal and vertical stiffness of the soil, as well as itsinertial and damping properties are available in the literature.

26

3.3. Solution of SDOF response

3.3. Solution of SDOF response

The dynamic response of a damped system is computed by solving the followingdifferential equation of motion (Clough and Penzien, 1975)

mu(t) + cu(t) + ku(t) = f(t) (3.8)

Seismic action can be modelled as an equivalent force related to ground acceleration(ug(t)) as:

mu(t) + cu(t) + ku(t) = −mug(t) (3.9)

This equation can be solved in the time for the frequency domain. A simple ap-proach is to use the Duhamel’s integral, which is a convolution integral as shown inEquation 3.8. Alternatively, the equation can be solved in the frequency domain. Inthis method, Fourier Transform is used. In the frequency domain, the convolutionoperation reduces to a multiplication operation. Solution in frequency domain isstraightforward and computationally efficient, thanks to the fast Fourier transformalgorithm. Both the Duhamel’s integral and the frequency domain solution as basedon the superposition principle, and are valid only for linearly elastic systems.

u(t) =1

mωd

∫ t

0

e−ξω(t−τ)(f(τ) sin(ωd(t− τ)))dτ (3.10)

For inelastic systems, principle of superposition is not valid, and the differentialequation of motion needs to be solved numerically by using time-stepping integrationalgorithms. One of the most commonly used time-stepping methods is the so-calledNewmark-beta method (Newmark, 1959). It is an initial value time stepping schemewhere integration is proceeded forward by solving the response quantities of the endof each time step. Further details of the method along with its accuracy and stabilityconditions are provided in Chopra (Chopra, 1995).

27


3.4. Multiple Degree of Freedom (MDOF)modeling

SDOF models are simple and not able to account for potentially significant phe-nomenon in the response of the structures being studied. For example, the effect ofdistributed mass of the tower can not be accurately captured by a SDOF model. Inaddition, due to the eccentric mass of the rotor blades, response of the system inorthogonal directions is coupled. Apart from this, torsional effects due to the headmass are not effectively captured by SDOF models. A better representation of thestructure can be obtained by using multiple degrees of freedom finite elements. Var-ious degrees of complexity can be introduced in such modeling. For example, fullythree-dimensional solid elements can be used to model the tower. An alternativeis to used shell elements. For this study, use of beam-column elements is deemedsufficient, as the objective of the study is not to study the detailed stress distribu-tion in the tower, but rather to understand its general characteristics in terms ofseismic response. For the structures being studied, past studies have shown thatbeam and shell elements give remarkably similar results in seismic analysis (Bazeoset al., 2002). Beam-column elements are more convenient alternative as they resultin fewer degrees of freedom and reduce computational time, allowing for a largenumber of time history analysis. To account for variation in diameter and thicknessof tower along its height, it is divided into multiple beam elements, each modeledas a 3-dimensional beam-column element based on Euler-Bernoulli hypothesis.

3.4.1. Euler-Bernoulli beam-column elements

The stiffness matrix of a beam-column element used is given by:

[ke] =

AEL

0 0 0 0 0 −AEL

0 0 0 0 0

012EI

z′L3 0 0 0

6EIz′

L2 0−12EI

z′L3 0 0 0

6EIz′

L2

0 012EI

y′L3 0

−6EIy′

L2 0 0 0−12EI

y′L3 0

−6EIy′

L2 0

0 0 0 JGL

0 0 0 0 0 −JGL

0 0

0 0−6EI

y′L2 0

4EIy′

L0 0 0

6EIy′

L2 02EI

y′L

0

06EI

z′L2 0 0 0

4EIz′

L0

−6EIz′

L2 0 0 02EI

z′L

−AEL

0 0 0 0 0 AEL

0 0 0 0 0

0−12EI

z′L3 0 0 0

−6EIz′

L2 012EI

z′L3 0 0 0

−6EIz′

L2

0 0−12EI

y′L3 0

6EIy′

L2 0 0 012EI

y′L3 0

−6EIy′

L2 0

0 0 0 −JGL

0 0 0 0 0 JGL

0 0

0 0−6EI

y′L2 0

2EIy′

L0 0 0

6EIy′

L2 04EI

y′L

0

06EI

z′L2 0 0 0

2EIz′

L0

−6EIz′

L2 0 0 04EI

z′L

(3.11)

where A is the area of cross-section at the middle of a tapering element, I ′z and I ′y

28

3.4. Multiple Degree of Freedom (MDOF) modeling

are the second moment of area about the minor and major axes of cross section (alsotaken at the middle of the beam), E is the elastic modulus of the material, L is thelength of the element, G is the shear modulus of the material, and J is the torsionalconstant of the cross section at the middle of the beam.

The consistent mass matrix of each element is given by:

[me] =m

420

140 0 0 0 0 0 70 0 0 0 0 00 156 0 0 0 22L 0 54 0 0 0 −13L0 0 156 0 −22L 0 0 0 54 0 13L 0

0 0 0 140JA

0 0 0 0 0 70JA

0 00 0 −22L 0 4L2 0 0 0 −13L 0 −3L2 00 22L 0 0 0 4L2 0 13L 0 0 0 −3L2

70 0 0 0 0 0 140 0 0 0 0 00 54 0 0 0 13L 0 156 0 0 0 −22L0 0 54 0 −13L 0 0 0 156 0 22L 0

0 0 0 70JA

0 0 0 0 0 140JA

0 00 0 13L 0 −3L2 0 0 0 22L 0 4L2 00 −13L 0 0 0 −3L2 0 −22L 0 0 0 4L2

(3.12)

where m is the total mass of the element considering its self-weight and any otherloads imposed on it.

3.4.2. Prior work

Wind turbines have been the research subject of a number of scientific articles inrecent years. Following are the most commonly studied wind turbine structures.Their salient features are given in Table 3.1.

65-kw TurbineThe 65-kW wind turbine has been the subject of a full-scale shake table ex-periment at the Network for Earthquake Engineering Simulation(NEES) onthe Large High Performance Outdoor Shake Table (LHPOST). The study in-volved the system identification of the structure using dense instrumentation,for parked and operating states at different levels of ground shaking. Theturbine design has been used for comparing the FAST code with OpenSees(Prowell et al., 2010).

900-kW TurbineThe 900-kW NEG Micon turbine was tested at Oak Creek Energy Systems(OCES) as a part of a structural system identification study (Prowell, 2011).The study showed that, while operating, the modal damping is higher than

29


recommended by IEC (3% to 4%) but are in line with parked values (1%),most likely due to aerodynamic damping.

1.5-MW TurbineThe WindPACT Turbine Rotor Design Study (Malcolm and Hansen, 2002)was an extensive work on many of the aspects regarding the design and costsof mid-range sized wind turbines. A test model was installed and studied atOCES. The study provided many modification, that help improve the design,such as using carbon fibers in the blades and a fluid container installed at 2/3of the heights, tuned for energy dissipation at specific frequency.

5-MW TurbineThe NREL Baseline turbine is obtained from broad design information basedon published documents of turbine manufacturers (Jonkman et al., 2009). Thisis currently the only publicly available large-scale wind turbine design avail-able.

Table 3.1: Properties of wind turbines, modified from Prowell (2011).Power Rating 65-kW 900-kW 1.5-MW 5-MWManufacturer Nordtank NEG Micon WindPACT NRELHub height (m) 22.6 55 84 90Mass of rotor (t) 1.6 18.3 32 111Mass of nacelle (t) 2.7 23 51 240Mass of tower (t) 6.1 68.7 122 350

Fundamental Period (s) 0.59 1.75 2.48 3.22

3.4.3. Forcing frequencies

The operational frequencies of the rotor can have a resonance effect on the structuralsystem. The frequency at which the turbine operates changes with wind velocityover a certain range, from parked to emergency brake. There are two frequencyranges which have to be accounted for:

• The 1P frequency which represents the rotational frequency caused by masseccentricity of the spinning rotor

• The 3P frequency represents the blade passing frequency for a 3 bladed turbine.The blade passing frequency is caused by a shadowing effect from the bladeon the tower resulting from a drop in the wind velocity as each blade passesin front of it (Bhattacharya et al., 2012).

30


It is desirable to not have the natural frequency of the structure within the operatingfrequency range. In order to avoid these frequency ranges 3 approaches can beadopted:

• Soft-soft design - First natural frequency below 1P lower limit, representingvery flexible structures.

• Soft-stiff design - First natural frequency between 1P upper and 3P lower limit,the most common approach in offshore turbines.

• Stiff-stiff design - First natural frequency above 3P upper limit, representingvery stiff structure.

1P 3P

Soft-soft Soft-stiff Stiff-stiff

Figure 3.4: Schematic Power Spectral Density functions of wind and ocean wavesmodified from Sigbjörnsson and Rupakhety (2015).

Figure 3.4 shows an example of the 1P and 3P operating ranges of a 5-MW windturbine designed by NREL. It also shows normalised wind-, sea- and earthquakespectral amplitude models which are considered appropriate for North Sea locations.The chosen design approach affects many aspects such as cost, fatigue tolerance andthe structural characteristics of the turbine, it would appear that the most commonpractice in the literature is the soft-stiff design. The operational frequency range ofthe turbine is often represented with a Campbell diagram as well.

31


3.4.4. Structure used for computational verification

A 65-kW turbine model developed by the University of California, San Diego (UCSD)isused for verification of modeling techniques, analysis procedure, and computer codesprepared for further analysis of the case study structure. The case study structure isa 5-MW turbine, which is described in detail in Chapter 4. The 65-kW structure andthe 5-MW structure are subsequently called as calibration structure and case studystructure, respetively. It is a small and simple design, since this particular turbinehas been subject to a full scale shake test at the LHPOST we have very detailedand reliable information about the design. Information on the structures stiffness,damping and mass is provided as well as modal analysis and time-history analy-sis results from a publicly available earthquake record. Therefore if one is capableof replicating the analysis output parameters of this design, making other similarstructural models based on the experience can accomplished with good confidence.

3.4.5. Details of 65-kW Turbine

The structure was made by Nordtank in Denmark. A schematic diagram of thestructure is shown in Figure 3.5, and its salient properties are listed in Table 3.2.

LOWER JOINT

UPPER JOINT

TOWER BASE

LATERAL BASE EXCITATION

NACELLE

MIDDLE SECTION

UPPERSECTION

MIDDLESECTION

LOWERSECTION

HUB

ROTOR

leader

X

Y

Z

Figure 3.5: Diagram of the 65-kW wind turbine structure (Prowell et al., 2009).

32


Table 3.2: Properties of 65-kW wind turbine.Property ValueRated Power 65-kWRated wind speed 12 m/sRotor diameter 16 mTower height 21.9 mLower section length 8.0 mLower section diameter 2.0 mMiddle section length 7.9 mMiddle section diameter 1.6 mTop section length 6.0 mTop section diameter 1.2 mLength of nacelle 2.2 mTower wall thickness 6.0 mmRotor hub height 22.6 mTower mass 6400 kgNacelle mass 2400 kgRotor mass (with hub) 1860 kg

Geometry

The wind turbine is composed of four main parts that are relevant to structuralmodelling. The tower itself, which spans 21.9 m, is divided into three sections bytwo tapering portions along the height of the tower as seen in Figure 3.5. Nodesare placed at the base, the end and centre of the tapering portions as well as thenacelle. The nacelle is modelled as rigid with its total weight lumped at the it’scentre. The rotor is made of three blades, each containing 12 beam elements, theyare modelled as rigid with a varying mass density along the length of the blades.There is a hinge located at the centre of the rotor allowing for the rotation of theblades around the x-axis, the initial positions of the rotor is as seen in Figure 3.6.The base of the structure is modelled as fixed meaning that all DOFS at the basenode are constrained.

33


Figure 3.6: The 65-kW wind turbine model geometry.

Stiffness

The stiffness of the tower is computed using the geometry described by Prowell(2011). The mean cross-sectional area of each element is calculated using the pro-vided thickness. The elastic modulus is given as E = 200GPa and Poisson ratio asυ = 0.3. For the tower structure the modelling is a straight forward procedure sincethe circular-hollow-section is simple and well defined mechanically. The blades onthe other hand have a non-symmetric and complex air-foil cross section, with littledetails regarding material stiffness. Therefore the blades are modelled as rigid andonly the tower is modelled as elastic. The cross-sectional area of a circular-hollow-section is determined as:

A =π(d2out − d2in)

4(3.13)

The second moment of area can be calculated as:

Ir =π(d4out − d4in)

64(3.14)

34


The perpendicular axis theorem then yields the polar moment of area:

J = 2Ir (3.15)

The shear modulus is found from the relation:

G =E

2(1− υ)(3.16)

Inertia/Mass

The total weight of each section of the tower is provided in the tower description.Mass density corresponding to the given weight was estimated, and a distributedmass system was used to estimate consistent mass matrices of the beam elementsas described previously. The mass of the nacelle is lumped at the center of massand the rotor blade mass distribution is found iteratively by examining the bladestructure and by matching the pre-existing modal results. The mass along the towercross section, is lumped at the nodes, this is expectable in this study since there islittle or no rotational excitation induced to the tower in the simulations. Consistentmass takes into account the rotation of the nodes which are minimal this study,making the use of consistent mass unnecessary.

Damping

When modelling the damping ratio of a wind turbine there are three types of damp-ing that can be considered: structural damping, aerodynamic damping and foun-dation damping. The aerodynamic damping has been shown to be a function ofthe wind speed acting on the structure as well as the rotational speed of the rotor.The structural and foundation damping is caused by the internal energy dissipationwithin the structural elements. The results from the full scale testing indicate that1% of critical damping is a good estimate, given that the turbine is in a parkedstate. The damping model used in the analysis is the Rayleigh damping model,which is a stiffness and mass proportional damping model (see Figure 3.7). TheRayleigh damping model is a classical damping model, meaning it is best applied tostructures of homogeneous material and components. The damping matrix is given

35


by:

[C] = α0[M ] + α1[K] (3.17)

The constants α0 and α1 are then determined by selecting two frequencies and as-signing them a certain damping ratio. These frequencies are often chosen from thestructures natural frequencies. Other classical damping models such as constantdamping or Caughey damping (Caughey and O’kelly, 1965), which is a generaliza-tion of Rayleigh’s model, could also be used considering the aerodynamic and SSIeffects, is likely to be non-proportional, and therefore ill-represented by the Rayleighmodel. Despite these limitations, Rayleigh model is selected in this study for sim-plicity. The selection is justified because the main objective of this study is tounderstand the overall nature of seismic response of wind turbine structures, andpeculiarities due to the variation from proportional damping can be ignored in thefirst approximation. In addition, modelling aerodynamic and SSI effects involvesanother set of uncertainties and effects which may compete with the main effectbeing studied– the effect of near-fault pulses in seismic response.

Angular frequency, ω (rad/s)10 20 30 40 50 60 70 80 90

Dam

pingratio,

ξ

0

0.02

0.04

0.06

0.08

0.1RayleighMass proportionalStiffness proportional

Figure 3.7: Damping ratio as a function of frequency,two frequencies are used todetermine the shape as marked by dashed black lines.

36


Results

The natural frequencies of the 65-kW wind turbine were computed and comparedto existing results. As seen from Table 3.3 the first frequencies are quite close tothe original study (Prowell, 2011). Although the higher modes are not as accurate,this has insignificant influence on simulated response, as higher modes participateless during seismic excitation. The error is larger for the fore-aft motion indicatingthat blade flexibility is a likely cause of the error. The forcing frequencies for theoperating range of 45-55 RPM are:

1P ={45, 55}

60s= {0.750, 0.917}Hz

3P = 3{45, 55}

60s= {2.25, 2.75}Hz

None of the natural frequencies lie within the operational frequency ranges as ex-pected. Schematic diagrams of the oscillation shapes, better know as mode shapes,of the structure are shown in Figure 3.8 where the fore-aft (FA) modes are shownand Figure 3.9 where the side-to-side (SS) modes are illustrated.

Table 3.3: Modal properties of the 65-kW wind turbine tower.Frequency (Hz)Mode number Mode type This study OpenSees

1 1st FA 1.69 1.702 1st SS 1.70 1.703 1st Torsional 9.22 9.24 2nd FA 9.98 9.75 2nd SS 11.23 12.16 3rd FA 24.67 21.52

37


Figure 3.8: The first 3 fore-aft mode shapes.

Figure 3.9: The first 3 side-to-side mode shapes.

38


Verification

Verification of the structural response can be done by comparing simulation resultswith published data. The modal frequencies and mode shapes simulated in thisstudy are very close to those reported in Prowell et al. (2009). Results of timehistory analysis using the ground acceleration recorded at Array station 9 duringthe El Centro Earthquake are reported by Prowell et al. (2009). The computationalmodel developed in this study was used to simulate the response for this groundmotion, and the simulated response is compared with that of (Prowell et al., 2009)in Figure 3.10 and 3.11.

Table 3.4: Ground motion used for model verification (Prowell et al., 2009).Earthquake Moment Magnitude Station PGA Epicentral distance1940 El Centro 6.9 Array Station 9 0.35 g 12.2 km

The results show very good consistency for the lateral direction (see Figure 3.10).The longitudinal response and is most likely explained by the lack of details providedon the blade structure, which is modelled as rigid in this study but as elastic byProwell et al. (2009). The mass distribution and Rayleigh damping parameters forthe simulation were defined by using 1% damping of critical for 1.7 Hz mode and3.5% of critical for 12 Hz.

Time (s)0 5 10 15 20 25 30 35

Acceleration(g)

-1

0

1

Nacelle Acceleration - Lateral

Time (s)0 5 10 15 20 25 30 35

Acceleration(g)

-1

0

1

Nacelle Acceleration - Longitudinal

Figure 3.10: Calculated acceleration response at the naccele of the 65-kW Turbine.Here lateral reffers to the SS motion and longitudinal to the FA motion.

39


0 5 10 15 20 25 30 35

-1

0

1

Time (s)

Acc

el (g

)Nacelle Acceleration - Lateral

FAST

OpenSees

0 5 10 15 20 25 30 35

-1

0

1

Time (s)

Acc

el (g

)


0 5 10 15 20 25 30 35

-1

0

1

Time (s)

Acc

el (g

)Nacelle Acceleration - Lateral

FAST

OpenSees

0 5 10 15 20 25 30 35

-1

0

1

Time (s)

Acc

el (g

)


Figure 3.11: Acceleration response at the naccele of the 65-kW turbine reported inProwell et al. (2009). Here lateral reffers to the SS motion and longitudinal tothe FA motion.

40

4. Case Study: a 5-MW windturbine structure

The 5-MW NREL baseline wind turbine is thoroughly described by Jonkman et al.(2009). This turbine is intended to be used publicly as a reference for researchand development of large scale, on-shore and off-shore wind turbines. The tower isdesigned to be made of steel with elastic modulus 210 GPa and shear modulus 80.8GPa. Considering density of steel as 7850 kg/m3, the effective density of tower istaken as 8500 kg/m3 to account for paint, bolts, welds, and flanges. The tower hasa circular hollow-section with diameter and wall thickness decreasing linearly alongits height. The thickness of wall is scaled up by 30% to ensure that the first FAand SS tower frequencies are placed between 1P and 3P frequencies throughout theoperational range of the wind turbine. The structural damping was assumed to be1% as recommended. Some important properties of the structure are summarizedin Table 4.1.

Table 4.1: Properties of 5-MW wind turbine, modified from Bir and Jonkman (2008).Property ValueRated Power 5-MWRated wind speed 11.4 m/sRotor diameter 126 mTower height 87.6 mLower section diameter 6.0 mLower section wall thickness 27 mmTop section diameter 3.87 mTop wall thickness 19 mmLength of nacelle 2.2 mRotor hub height 90 mTower mass 347 460 kgNacelle mass 240 000 kgRotor mass (with hub) 111 000 kgHead moment of inertia about rotor-parallel axis (x direction) 4.37×107 kgm2

Head moment of inertia about lateral axis (perpendicular to rotor) 2.35×107 kgm2

Head moment of inertia about vertical axis 2.54×107 kgm2

41

4. Case Study: a 5-MW wind turbine structure

Since the blades possess an air-foil profile they have a varying cross-section; the prop-erties of a blade is therefore defined in many sections along the length. A completeFE model of the structure was made in MATLAB using the information reported inTable 4.1 and Jonkman et al. (2009). The tower was modelled with 100 linear elasticbeam-column elements. The base or the foundation of the structure is consideredas fixed and the rotor and nacelle are modelled as rigid mass. Translational androtational masses corresponding to the nacelle, rotor, and hub were lumped at thetip of the tower. The values of the lumped masses are given in Table 4.1, and areas reported in (Bir and Jonkman, 2008).

4.1. Modal analysis

Natural vibration frequencies and mode shapes of an undamped system are givenby the following eigen-value problem.

[[K]− ω2[M ]

]{φ} = {0} (4.1)

where [K] and [M ] are the stiffness and mass matrices defined in chapter 3, theω represents natural frequencies and φ stands for the mode shape vector. Thecharacteristic equation of this eigenvalue problem (see Eq. 4.2) gives the eigen-valueswhich are the squares of natural frequencies. The mode shapes are representedby the eigen-vectors, which are obtained from Equation 4.1 for each eigen-valueobtained from Equation 4.2. If N is the rank of the [K] and [M] matrices, N vibrationfrequencies and corresponding mode shapes are possible.

det([K]− ω2[M ]

)= 0 (4.2)

The mode shape matrix is formed by arranging the eigenvectors {φ} along thecolumns of a matrix.

[Φ] =[{φ1} {φ2} {φ3} · · · {φN}

]=

φ11 φ12 φ13 · · · φ1N

φ21 φ22 φ23 · · · φ2N

φ31 φ32 φ33 · · · φ3N...

...... . . . ...

φN1 φN2 φN3 · · · φNN

(4.3)

where the element φij corresponds to DOF i and mode j.

42

4.2. Modal properties

A reduction to a standard eigenvalue problem can be performed in order to producea more stable solution. Equation 4.1 can be reduced by pre-multiplying Equation4.2 by [M ]−1 yielding:

([M ]−1[K]− ω2[I]) {φ} = {0} (4.4)

where I is the identity matrix. The form of Equation 4.4 is that of a standardeigenvalue problem for which excellent numerical solution algorithms are available.


4.2.1. Frequencies

The undamped natural frequencies obtained from eigenvalue analysis of the finiteelement model are presented in Table 4.2. The frequencies of the tower calculatedshow good correlation with the baseline values from published literature. The fun-damental mode is found to be side-to-side (SS) motion while the second mode isfore-aft motion (FA). For comparison, frequencies computed from other software asreported by J. Jonkman and Scott (2009) are also presented in Table 4.2. In thisstudy, only unidirectional ground motion is considered, and the effective modal massof the various modes for ground motion in fore-aft and side-to-side direction are asshown in Table 4.2.

Table 4.2: The modal properties of the 5MW wind turbine tower, the highlightedlines mark the modes contributing to seismic response in SS and FA motion.

Frequency (Hz)Mode number Mode type This study BModes ADAMSEffective modal mass

1 1st SS 0.328 0.329 0.319 67.6%2 1st FA 0.332 0.332 0.322 69.4%3 1st Torsional 1.478 1.470 1.476 0.0%4 2nd SS 1.801 1.880 1.882 10.6%5 2nd FA 2.278 2.243 2.239 10.7%6 3rd SS 4.583 4.652 4.724 8.1%7 3rd FA 5.056 4.986 5.183 6.3%8 1st Axial 7.927 8.131 7.937 0.0%9 4th SS 11.27 11.31 11.268 4.2%10 4 FA 11.43 11.45 11.472 4.1%

43


The modes participating in the fore-aft motion are highlighted light gray in Table4.2, these modes will subsequently be referred to as the first, second, third, andfourth mode. The same is then done for the side-to-side direction, it should benoted that the effective mass is calculated separately for each direction i.e., in eachdirection, modal mass sums up to the total structural mass. It can be observed fromTable 4.2 that these four modes account for above 90% of the effective modal massin fore-aft motion.

The operating range of the turbine rotor is between 6.9-12.1 RPM or in frequencyterms:

1P ={6.9, 12.1}

60s= {0.115, 0.2017}Hz

3P = 3{6.9, 12.1}

60s= {0.345, 0.605}Hz

As mentioned before the fundamental period of the structure is located between theoperating frequencies making it a stiff-soft design. All other natural frequencies alsolie outside of the operational frequencies which is indicative of a good design.

4.2.2. Mode shapes

The mode shape are consistent with what is traditionally observed from cantileverbeam models. The fundamental mode accounts for nearly 70% of the effective mass.Figures 4.1 and 4.2 show schematic diagrams of the significant mode shapes in FAand SS motion. The mode shapes are normalized with the tip displacement andscaled with effective modal mass.

44


Modal displacement

Height

1st FA2nd FA3rd FA4th FA

Figure 4.1: The first four mode shapes in fore-aft motion.

Comparing the modes in Figures 4.1 and 4.2 we see that thay are more or less thesame. This leads to the conclusion that it is reasonable to study seismic responseindependently in two orthogonal horizontal directions, at least at parked state. Insubsequent analysis, unidirectional ground motion parallel to the rotor axis willbe considered. To model torsional effects, bi-directional excitation should be used.Since this study focuses on the effect of near-fault pulses, which are often polar-ized in one of the horizontal components (often the fault-normal direction), onlyunidirectional excitation is considered.

45


Modal displacement

Height

1st SS2nd SS3rd SS4th SS

Figure 4.2: The first four mode shapes in side-to-side motion.

46

5. Response Analysis and Results

Two types of analysis are performed, namely, time history analysis and responsespectrum analysis. The former makes use of a set of recorded near-fault groundmotion time series. The latter is based on response spectral models specified inEC8, and a near-fault specific model proposed by Rupakhety et al. (2011). Thischapter describes the analysis procedure and the main results.

5.1. Time history analysis

5.1.1. Modal time history analysis

Modal response history analysis is based on the decoupling of dynamic system ofequations. This becomes feasible due to the orthogonality property of the modeshapes with respect to both the mass and the stiffness matrices. Furthermore, fora proportional damping model, the damping matrix is also orthogonal with respectto the mode shapes. By virtue of this [Φ]T [K][Φ], [Φ]T [M ][Φ], and [Φ]T [C][Φ] are alldiagonal matrices. By applying a transformation of the form {u} = [Φ]{y}, with {y}being modal coordinates, and pre-multiplying the system equation by [Φ]T , a set of Nuncoupled second order differential equations are obtained. Such equations resemblethose of SDOF systems, and can be solved by methods described in Chapter 3. Thesolutions obtained in this way are modal coordinates which can be transformed tothe structural coordinates by using mode shape matrix.

The equation of motion for a MDOF system with external excitation is of the form:

[M ]{u}+ [C]{u}+ [K]{u} = {p} (5.1)

For any mode i, the generalized mass is defined as

Mi = {φi}T [M ] {φj} (5.2)

47


and the generalized stiffness is defined as

Ki = {φi}T [K] {φj} (5.3)

Then the frequency of mode i can also be obtained as

ωi =

√Ki

Mi

(5.4)

The generalized mass matrix is defined as:

[M]

= [Φ]T [M ] [Φ] (5.5)

in a similar manner, the generalized stiffness matrix is defined as:

[K]

= [Φ]T [K] [Φ] (5.6)

and the generalized damping matrix as:

[C]

= [Φ]T [C] [Φ] (5.7)

the generalized damping of each mode can be determined by assigning each mode adamping value using the following relation:

Ci = 2ξiMiωi (5.8)

where the damping ratio ξi can be determined for each mode as a constant. Thedynamic part of the response, described by Equation 5.1, can be uncoupled by usingthe modal expansion of displacements in the following way:

[Φ]T [M ][Φ]{y}+ [Φ]T [C][Φ]{y}+ [Φ]T [K][Φ]{y} = [Φ]T{p} (5.9)

48


where p is the dynamic load vector represented as:

{p} = −[M ]{r}ug (5.10)

where ug is the ground acceleration and {r} is the influence vector. Containing 1at the DOFS affected by support motion and 0 at all other DOFS. In other words,this vector represents the displacement of the structural DOFs when the support ismoved slowly (not generating inertia effects) by an unit amount. Equation 5.9 canthen be written in terms of generalized mass, stiffness and damping as:

[M ]{y}+ [C]{y}+ [K]{y} = −[Φ]T [M ]{r}ug (5.11)

which can be simplified to:

[M ]{y}+ [C]{y}+ [K]{y} = −{L}ug (5.12)

where {L} represents a vector of earthquake excitation factors defined for each modei as:

Li = {φi}T [M ]{r} (5.13)

Equation 5.12 is now decoupled, and can be written for each mode i as:

Miyi + Ciyi + Kiyi = −Liug (5.14)

Displacements

The solution of the equation of motion can be obtained by dividing Equation 5.14with mass by:

yi + 2ξiωiyi + ω2i yi = −Γiug (5.15)

49


where Γi is the modal participation factor defined as:

Γi =Li

Mi

={φi}T [M ]{r}{φi}T [M ]{φ}

(5.16)

The displacements can then be solved, for example, by using Duhamel’s integral:

yi =−LiMiωDi

∫ t

0

exp [−ξiωi(t− τ)] sin [ωDi(t− τ)] ugdτ (5.17)

or the Newmark-beta method.

Displacements due to mode i in the geometric coordinate system is given by:

{ui} = {φi}yi (5.18)

and the total displacement can be obtained as:

{u} = [Φ]{y} (5.19)

Drift ratio

The drift ratio (expressed as a percentage) is the deflection slope of the structure.For any mode i, the drift ratio at level j is given by:

DRi(j, t) =Γih

[φi(j)− φi(j − 1)] yi(t) · 100 (5.20)

where h is the length of each element (implying, for example, storey height, in abuilding). Using modal superposition, the total drift at node j can be obtained as:

DR(j, t) =nm∑i=1

= DRi(j, t) (5.21)

50


where nm is the number of modes considered.The maximum drift ratio is then givenby:

DRmax(j) = max |DR(j, t)| (5.22)

At each DOF the time when the interstory drift demand reaches maximum is denotedas tj. The contribution of mode i to DRmax(j) at DOF j is then given as:

δi,j =

{|DRi(j, tj)| if i = 1

sgn [DRi(j, tj)]DRi(j, tj) if i > 1(5.23)

The sgn[•] operator represents signum function. The first mode contribution isalways taken as positive.

Base shear forces

The nodal forces acting at each degree of freedom at each time is then given as:

{f} = [K]{u} = [K][Φ]{y} (5.24)

It is worth noting that the vectors and matrices in Equation 5.24 contain onlyunconstrained degrees of freedom. In other words, the support degrees of freedomhave been eliminated before solving the eigenvalue problem. The base shear forcecan be described as the total reaction force at the supports of the structure. For thedirection in which ground motion is applied, the maximum base shear force can bedetermined as:

V maxb = max |{r}T{f}| (5.25)

Overturning moment

The base overturning moment is given by:

Mmaxb = max |{h}T{f}| (5.26)

51


where {h} is vector of heights of various nodes from the base of the structure.

5.1.2. Ground motion data

The near-fault ground motion data used in this study is a subset of data describedin (Rupakhety et al., 2011). The strong ground motion data are collected from 29different earthquake events, mostly from the Next Generation Attenuation (NGA)database. Strong-motion records from the June 2000 Earthquakes and May 2008Earthquake in South-Iceland were obtained from the Internet Site for Strong MotionData (ISESD). Accelerograms from the Parkfield Earthquake are obtained from theCalifornia Integrated Seismic Network (CISN). Permanent displacements if any areremoved by subtracting half a sine pulse from the acceleration records.

Records from soft sites (average shear wave velocity in the upper 30 m less than 260)are excluded. Furthermore, only records within 30 km distance from the causativefaults are considered. Low quality records, such as the 1991 Sierra Madre Earth-quake, the 1981 Westmorland Earthquake recorded at the Parachute test site andthe 1992 Cape Mendocino Earthquake, are excluded. In total 70 ground motionswhich range from 5.7 Mw to 7.6 Mw are used for further analysis. A full list ofnear-fault ground motion records is presented in Appendix A, in which the ones notused in this study are highlighted.

5.2. Response spectral analysis

5.2.1. EC8 model

The design spectra used in Iceland, the Eurocode 8 response spectra, is defined bythe following equations and is schematically shown in Figure 5.1.

Se =

ag · S · (1 + T/TB · (η · 2.5− 1) if 0 ≤ T ≤ TB

ag · S · η · 2.5 if TB ≤ T ≤ TC

ag · S · η · 2.5 · (Tc/T ) if TC ≤ T ≤ TD

ag · S · η · 2.5 · (Tc · TD/T 2) if TD ≤ T ≤ 4s

52

5.2. Response spectral analysis

Se Elastic response spectrumag Design ground acceleration on type A ground

TB, TC , TD Corner periods of the spectrumS Soil factorη Damping correction factor

Period (s)

TB TC TD

Se/a

g

S

2.5Sη

Figure 5.1: Eurocode 8 normalized elastic response spectrum.

5.2.2. Response calculation

For most earthquake analyses, and particularly for design, time-history analysisprocedures are not practical since they are computationally expensive. The choiceof the appropriate earthquake record, if available in the first place, is also a dilemmaan engineer is faced with. It is, for these reasons, practical as well as permitted bymost design codes,to use response spectra for seismic design of structures. Theresponse spectra are either created from a set of ground-motion records availablefrom a similar tectonic environment, or are adopted from design codes. Responsespectra provide maximum response of a SDOF system subjected to a certain levelof ground shaking. The response spectra of each ground motion can be created by

53


simulating SDOF response of a dynamic system using the Newmark method andfinding the maximum amplitude of the response quantity. A brief description of theprocedure used in computing seismic response using the response spectrum analysismethod is given below.

Displacements

The maximum value of the generalized coordinate yi is simply the ordinate of thespectral displacement (SD) for a ground motion scaled by Γi. Using this argument,and denoting the spectral displacement of ug by D, and the PSA by A we have

ymaxi = ΓiD(Ti, ξi) (5.27)

where Ti, and ξi are the period of vibration, and damping ratio of mode i. Then themaximum displacement of the structure in the ith mode is given by

{u}maxi = {φi}ymaxi = {φi}ΓiA(Ti, ξi)

ω2i

(5.28)

Base shear forces

The base shear force can be described as the total reaction force at the supportsof the structure. The maximum base shear can be found for any direction for eachmode i as:

V maxbi = {r}T{f}maxi = {r}T [M ]{φi}ΓiA(Ti, ξi) (5.29)

Overturning moment

The moment is obtained in the same way but now with the height of each nodeacting as an arm:

Mmaxbi = {h}T{f}maxi = {h}T [M ]{φi}ΓiA(Ti, ξi) (5.30)

54

5.3. Results

where the factors multiplying the PSA value has the units of mass and is called asthe effective modal mass of mode i defined as:

M∗i = {r}T [M ]{φi}Γi =

{r}T [M ]{φi}{φi}T [M ]{r}{φi}T [M ]{φi}

(5.31)

These quantities provide a measure of how much each mode is participating inthe vibration of the structure. For regular structures, only the first few modeshave significant effective mass, and it is sufficient to consider only those modes inevaluating the total response of the structure.

Modal combination

Combination rules are needed to combine the contribution of each mode to the totalresponse of the structure. The Square-Root of Sum of Squares (SRRS) combinationrule, which was commonly used in design codes when dynamic analysis was limitedto 2-dimensional frames, is used in the analysis. The method is best suited forstructures where modal frequencies are well separated and therefore don’t correlatewith each other. The turbine structures in this study satisfy this separation criteriaof the SRSS rule and is henceforth used in the analysis.

The SRSS rule is defined as:

Rmax ≤

√√√√ N∑i=1

(Rmaxi )2 (5.32)

Where R is any response quantity, N is the number of modes considered and Rmaxi

is the maximum response due to mode i.

5.3. Results

Different types of analysis were performed using the finite element model and ground-motion data described above. Damping is considered to be 1% of critical value inall the modes of vibration. Time history analysis is performed in the modal coor-dinates using Newmark’s integration algorithm. Peak response parameters such asmaximum top displacement, maximum base shear, maximum overturning moment,

55


and maximum drift ratios are computed for each ground motion using time historyanalysis. The response parameters are also computed by using SRSS combinationrule and elastic response spectra. For each ground motion, three response spec-tra are used: one corresponding to the recorded time series, one which is based onEC8-1 spectra scaled by the peak ground acceleration (PGA) of the recorded timeseries and the last one uses the spectral shape described by Rupakhety et al. (2011).The results obtained from these analysis procedures will henceforth be referred toas ’Time History’, ’GM SRSS’, ’EC8 SRSS’, and ’RR2011 SRSS’, respectively.

5.3.1. Displacement

The maximum horizontal nacelle displacement obtained from time history analysisusing the 70 ground-motion records is shown in Figure 5.2 as a function of normalizedperiod (pulse period normalized by the fundamental period of the structure). Theaverage maximum displacement is about half a meter and the range of values isbetween a few centimetres to just under 1.5 m. The figure shows that values thatare close to 1 in the normalized period have the largest displacement response due tothe resonant behaviour of the structure to the pulse of the near-fault ground motion.

56

5.3. Results

TP /Tf

0 0.5 1 1.5 2 2.5 3 3.5

Displacement(m

)

0

0.5

1

1.5

6.5 > Mw

6.5 ≤ Mw

≤ 6.9

6.9 < Mw

Figure 5.2: Maximum horizontal nacelle displacement due to each ground motion;the results are divided into different magnitude bins as indicated in the legend. Thehorizontal axis represents the predominant period of velocity pulse (see, Rupakhetyet al. (2011)) normalized by the fundamental period of vibration of the structure.

It is also noteworthy that some earthquakes in the smaller magnitude bin producelarger response than those in the larger magnitude bin. This is due to two reasons. Insome cases, it is due to the proximity of an earthquake to the structure which resultsin nearby small earthquake causing higher response than far away large earthquake.In most cases, however, it is due to the scaling effect of pulse period with earthquakemagnitude. For the structure being studied, pulse periods of ground motion in thesecond magnitude bin are the closest to the fundamental period of the structure.This is the reason why earthquakes in this magnitude bin seem to produce, on theaverage, larger response than earthquakes with larger size. Average displacementdemands at the top of the tower for each magnitude bin are shown in Figure 5.3 forthe 4 analysis procedures described previously. It is noteworthy that the two largerbins produce significantly larger displacement demands than the bin with smallestsize earthquakes. Time history and GM SRSS results are very close to each other,implying that response spectral analysis is appropriate as long as the spectrum used

57


in analysis is accurate. RR2011 SRSS results, for average displacement in each binseem to adequately simulate the response of the structure.

Time history GM SRSS RR2011 SRSS EC8 SRSS

Displacement(m

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8 6.5 > Mw

6.5 ≤ Mw

≤ 6.9

6.9 < Mw

Figure 5.3: Average nacelle displacement in each bin computed from time historyanalysis and response spectral analysis.

On the contrary, the EC8 spectral shapes, even when scaled with the PGA of in-dividual ground motion, seem to over-estimate the response for small earthquakes,and significantly under-estimate it for larger earthquakes. It is noteworthy thatin practice, EC8 spectral shapes are generally scaled with design PGA conformingto acceptable risk. This leads to the conclusion that, even if PGA was accuratelyestimated, using EC8 shapes for seismic analysis of wind tower structures in thenear-fault region is not suitable. This is not surprising because EC8 spectral shapeis based mostly on far-fault ground motion records. Furthermore the spectral shapeis magnitude independent, except for the specification of type 1 and 2 spectra, whichseem inadequate to account for frequency content of near-fault ground motions andits dependence on earthquake size. In this context, rather than using a fixed spectralshape scaled by PGA, using a magnitude dependent spectral shape, as is done inRupakhety et al. (2011) seems to provide more reliable results. To shed further lightinto this discussion, average spectral displacement of each bin are compared withthat obtained from Rupakhety et al. (2011) model in Figure 5.4. The vertical linesin the figure represent the periods of vibration of significant modes of the structure.

58

5.3. Results

It is evident from the figure that, on the average, the model predicts the spectraldisplacement of the three magnitude bins accurately, and hence the results obtainedfrom this model are very close to those obtained from time history analysis.

0.25 0.5 1 2 3 4

0.1

0.2

0.3

6.5 > Mw

0.25 0.5 1 2 3 4

Spectral

displacement(m

)

0.2

0.4

0.6

6.5 ≤ Mw ≤ 6.9

Period [s]0.25 0.5 1 2 3 4

0.2

0.4

0.6

0.8

6.9 < Mw

GMEC8RR2011

Figure 5.4: The average spectral displacement of each bin plotted against the averageRR2011 spectral displacement of each bin for 1% damping of critical.

5.3.2. Drift

The drift ratio, which may be considered the slope of the deformed tower alongits height, is shown in Figure 5.5 (average across all ground motions) and Figure5.6 (average across ground motions in the three bins). Average drift demands ineach bin obtained from time history analysis and response spectral analysis (usingresponse spectrum of each ground motion and SRSS combination) are shown in thefigure. The contributions of the first three modes of vibration are also shown. It canbe seen that the drift demands are considerably smaller for the bin with smallestmagnitude earthquakes. The drift demand is the largest for the second bin. This

59


is due to the proximity of pulse period to the fundamental structural period (seeFigure 5.2). As earthquake magnitude increases, the pulse period also increases, andfor the second bin, pulse period lies very close to the fundamental structural period.

δ (%)-0.2 0 0.2 0.4 0.6 0.8 1 1.2

Height(m

)

0

10

20

30

40

50

60

70

80

90

δmax

δSRSS

δ1

δ2

δ3

Figure 5.5: Average (for all the ground motions) drift ratio along the height of thetower. The red curve corresponds to the time history results, the green curve toGM SRSS, and the other curves represent contribution of the first three significantmodes of vibration as indicated in the legend.

As earthquake size is increased further (bin 3), the pulse period increases, while thespectral displacement at the fundamental period of the structural is reduced. Theseeffects are clearly visible in the spectral displacement plot shown in Figure 5.2. Itcan also be noticed that the contribution of higher modes in the drift demand is notsignificant. This is due to the fact that the higher modes of vibration correspondto the periods where spectral displacement is relatively small. This implies thatresults obtained from time history analysis and response spectrum analyses arealmost equal. The difference between the two is the largest in the first bin becausein this bin, spectral displacement at the fundamental period is relatively small (withrespect to higher modes) than in the other two bins. It should be noted that the

60

5.3. Results

results presented here are based on response spectra of recorded ground motion,and if a smooth response spectra like those prescribed in design codes are used, thedifferences are expected to be higher.

δ (%)0 0.5 1

Heigh

t(m

)

0

10

20

30

40

50

60

70

80

906.5 > Mw (n = 29)

δ (%)0 0.5 1 1.5 2

Heigh

t(m

)

0

10

20

30

40

50

60

70

80

906.5 ≤ Mw ≤ 6.9 (n = 17)

δ (%)-0.5 0 0.5 1 1.5

Heigh

t(m

)0

10

20

30

40

50

60

70

80

906.9 < Mw (n = 24)

δmax

δSRSS

δ1

δ2

δ3

Figure 5.6: Maximum drift ratios along the height of the tower: the dashed bluelines represent the result from time history analysis; the dashed red lines representresponse spectrum analysis, and the other lines represent contributions of the firstthree modes.

From Figure 5.7 we see better how well the SRSS combination rule works for thedrift estimation. For bin 1 the combination rule is not as effective as for bins 2 and3. It is also evident that most of the drift underestimation takes place near the topof the tower. This indicates that more than one mode is contributing to the drift attop section since the underestimation is caused by the sum of multiple modes.

61


δ (%)0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Heigh

t[m

]

0

10

20

30

40

50

60

70

80

90

6.5 > Mw

6.5 ≤ Mw

≤ 6.9

6.9 < Mw

Figure 5.7: The total average drift ratio of all the motions using the time-historyand response spectra method (SRSS rule) by each bin. The drift correponding toeach bin is as shown in legend.

5.3.3. Shear demand

The base shear demand of the structure due to all the ground motions is shown inFigure 5.8. There is a clear amplification of shear forces when the pulse period isclose to the natural period of the structure. The results indicate that the base sheardemand is the largest when the pulse period to structural period ratio is in the range0.5-1.5. This is the range where resonance of the structure with ground-motion ismost likely.

62

5.3. Results

TP /Tf

0 0.5 1 1.5 2 2.5 3 3.5

Basesheardem

and(M

N)

0

1

2

3

4

5

6

6.5 > Mw

6.5 ≤ Mw

≤ 6.9

6.9 < Mw

Figure 5.8: Base shear demand due to each ground motion; the results are dividedinto different magnitude bins as indicated in the legend.

The sharp amplification of response near resonance is also due to the fact thatthe damping ratio is rather small at 5%. Provision of additional damping cansignificantly reduce this resonance effect. It is also noteworthy how larger magnitudeearthquakes seem to produce, on the average, lower base shear demands than smallerones. This is due to the fact that as earthquake size increases, the dominant periodof ground motion increases, with more energy being radiated at longer periods, andless energy at high frequencies. Since base shear is related to peak accelerationresponse and therefore sensitive to high frequency content of ground motion, largerearthquakes seem to produce relatively lower PSA (but higher PSV and SD) andtherefore lower base shear demand.

When examining the efficiency of different methods to evaluate the shear demand wesee can see from Figure 5.9 that all the all the response spectra methods show similarresults for mid-sized earthquakes. Eurocode however underestimates the base shearof large earthquakes and overestimates that small earthquakes. The model proposedby Rupakhety et al. (2011) is very close to the actual ground motion spectra forall bins. The results also indicate that response spectral analysis is not accuratein predicting base shear as it is in predicting peak displacement demands. This

63


implies that higher mode effects are more dominant in base shear calculation thanin displacement calculation. This is expected because base shear is more closelyrelated to drift demands than displacements. As was shown in Figure 5.7, responsespectral analysis has largest error in drift estimation at the top of the tower. This isalso the location where most of the mass of the structure is location. This explainsrelatively larger error in base shear estimation by response spectral analysis. Itis noteworthy that the RR2011 model and response spectra of individual groundmotions yield similar base shear results.


Basesheardem

and(M

N)

0

0.5

1

1.5

2

2.5 6.5 > Mw

6.5 ≤ Mw

≤ 6.9

6.9 < Mw

Figure 5.9: Average base shear demand in each bin computed from time historyanalysis and response spectral analysis.

This is an indication that the differences in time history results and RR2011 SRSSresults is due to the limitations of the combination rule used here. Nevertheless, itappears that response spectral analysis tends to slightly under-estimate base sheardemands for this structure as compared to time history analysis. The relatively (ascompared to displacement response) good performance of the EC8 spectral shape isdue to the fact they have been scaled with PGA of individual ground motion, im-plying proper modelling of PGA which controls base shear. Therefore it can be saidthat inability of EC8 shape in modelling long-period spectral content seems to haveserious consequence in displacement estimation, but relatively milder consequencein estimating base shear. Despite this, the use of EC8 spectral shapes, even when

64

5.3. Results

scaled by correct PGA, seems inappropriate for very large earthquakes.

5.3.4. Moment demand

Overturning moment demand obtained from time history analysis using the 70ground-motion records is shown in Figure 5.10 as a function of normalized pe-riod (pulse period normalized by the fundamental period of the structure). Theresults indicate a strong dependence of overturning moment on the normalized pe-riod. Maximum overturning moment is around 325 MNm which is close to what isreported in other studies (Prowell, 2011). The values exceed moment demands ofextreme wind loads previously reported as 98 MNm based on extensive simulations(Fogle et al., 2008). Another study from NREL (Jonkman, 2007), where an extremeload factor of 1.35 is used, reported a maximum overturning moment demand of 153MNm which is also considerably smaller than that due to near-fault seismic loadsconsidered here.

TP /Tf

0 0.5 1 1.5 2 2.5 3 3.5

Momentdem

and(M

Nm)

0

50

100

150

200

250

300

350

6.5 > Mw

6.5 ≤ Mw

≤ 6.9

6.9 < Mw

Figure 5.10: Overturning moment demand due to each ground motion; the resultsare divided into different magnitude bins as indicated in the legend.

These results support that earthquake loads may indeed be design-driving for largewind turbines and especially in areas that are in the near-fault region. The results

65


also indicate that the most critical ground motions for the wind turbines of this typeare near-fault earthquakes with moment magnitude in the range 6.5 to 6.9. This ismainly due to the fact that in this magnitude range, the pulse period is close to thefundamental period of the structure. It seems that seismic loads due to near-faultground motions are the largest when the pulse period is between about 0.5 to 1.5times the fundamental period of the structure.

It can be observed from Figure 5.10 that the pulse period is, on the average, closeto the fundamental period of the structure in the second magnitude bin, which alsoexplains the higher demand due to earthquakes in this bin as is evident in Figure5.10. The average overturning moment demands in each bin are shown in Figure5.11. Results from time history analysis, response spectrum analysis using responsespectra of individual ground motion, that using EC8 spectra scaled with PGA ofindividual ground motion, and the RR2011 spectra are compared in the figure.


Momentdem

and(M

Nm)

0

50

100

150 6.5 > Mw

6.5 ≤ Mw

≤ 6.9

6.9 < Mw

Figure 5.11: Average overturning moment demand in each bin computed from timehistory analysis and response spectral analysis.

As is also evident from Figure 5.10, the second bin corresponds to the largest momentdemands, while the first bin corresponds to smallest demands. It is also notedthat the difference in time history analysis and response spectral analysis is notgreat when response spectrum of each ground motion is used. If, however, responsespectral shapes from EC8 scaled with PGA of each ground motion is used, the resultsdo vary significantly from those obtained by time history analysis. The greatest

66

5.3. Results

difference lies in bin 2, which also represents the most critical loading condition.In terms of accuracy of the different analysis methods, similar conclusions as thosearrived at concerning base shear demands may be made.

To explain these differences, reference is made to Figure 5.12. The EC8 spectrumsignificantly under-estimates the average spectral acceleration of the second bin atthe fundamental structural period. This results in under-estimation of momentdemand. It is noted that although the EC8 spectrum over-estimates spectral accel-eration at higher modes, and yet, results in under-estimation of moment demand.This is due to smaller mass participation in higher modes of vibration. The sameconclusions apply to bin 3. For bin 1, the EC8 spectral acceleration is slightly aboveaverage of the bin at fundamental period, but significantly larger at higher modes,which results in over-estimation of total overturning moment demand.

From Figure 5.12 we see how the model proposed by Rupakhety et al. (2011) fitsthe average near-fault response spectra of each bin. The first mode is for all bins fitsthe model very well compared to the EC8 model. In the long period range we seethat the RR2011 curve is generally above the ground mean ground motion spectra.Since the difference is very slight the RR2011 model can be considered to be on thesafe side in terms of structural capacity.

67


0.1 0.25 0.5 1 2 3 4

0.5

1

1.5

6.5 > Mw

0.1 0.25 0.5 1 2 3 4

Pseudo-spectral

acceleration

(g)

0.5

1

1.5

2

6.5 ≤ Mw ≤ 6.9

Period [s]0.1 0.25 0.5 1 2 3 4

0.2

0.6

1

1.4

6.9 < Mw

GMEC8RR2011

Figure 5.12: The average rensponse spectra of each bin plotted against the equivalentEC8 spectra.

The overall mean spectra are presented in Figure 5.13. The figure clearly shows theproblem stated in Chapter 1 where the EC8 spectra even when scaled by a PGAlarger than 0.5 g underestimates the earthquakes forces acting on structures with anatural period higher than 0.75 s. The RR2011 spectra on the other hand followsthe data better providing a safer alternative for seismic loading assessment in the

68

5.3. Results

long period range for near-field sites.

Period (s)0.1 0.25 0.5 1 2 3 4

Spectralpseudo-acceleration

(m/s

2)

0

2

4

6

8

10

12

14

16GMEC8RR2011

Figure 5.13: Average response of all ground motions plotted against the averagecalculated spectras.

Figure 5.14 shows the mean PSV computed from the time-series in each bin plottedagainst the mean PSV corresponding to the RR2011 model for each bin. The ac-curacy of the RR2011 model is very good for the towers natural frequencies for allthe bins. This observation suggests that the model captures the resonate behaviourof the structure very well with respect to PSV. The EC8 model on the other handshows severe underestimation of the PSV for the fundamental structural period.

69


0.1 0.25 0.5 1 2 3 4

0.2

0.4

0.6

0.8

1

1.2

6.5 > Mw

0.1 0.25 0.5 1 2 3 4

Pseudo-spectral

velocity

(m/s)

0.5

1

1.5

2

6.5 ≤ Mw ≤ 6.9

Period [s]0.1 0.25 0.5 1 2 3 4

0.5

1

1.56.9 < Mw

GMEC8RR2011

Figure 5.14: The average spectral velocity of each bin plotted against the averageRR2011 and EC8 spectral velocity of each bin.

70

6. Conclusions

This study presents the seismic response of a large land-based wind turbine in thenear-fault region. The focus of the study lies in understanding the salient featuresof structural response of wind turbine towers subjected to pulse-like ground motionscommonly experienced in the forward directivity region of active seismic faults. Inmost of the existing large wind energy farms, safety critical loads are often imposedby wind actions. However, the present study shows that seismic action on large-scalewind turbine towers in the vicinity of earthquake faults capable of generating mod-erate to large size earthquakes may surpass design wind action. With the potentialinstallation of large-scale wind farms in seismically active regions, for example, theSouth Iceland lowland, proper consideration on seismic action is crucial for bothsafety and reliability of wind farms. To study the salient features of seismic re-sponse of large-scale wind turbine towers in the near-fault area, dynamic analysisof a typical 5-MW wind turbine tower is conducted using a large set of pulse-likeground motions.

It is observed that the dominant period of near-fault ground motion is the mostcritical parameter controlling seismic response. As expected, the response is thelargest when the fundamental vibration period of the tower is close to the dominantperiod of ground motion. For the structure being studied, the fundamental vibrationperiod is around 3 s; and the corresponding critical near-fault earthquakes are ofsize Mw 6.6-6.9. Contrary to popular belief, earthquakes larger than these result,on the average, in lower response. This is due to the fact that the dominant periodof ground motion increases with earthquake magnitude, thus moving the excitationperiod away from the fundamental structural period. In this context, the traditionalseismic design concept, which relies more on amplitude of ground motion than itsfrequency content, can be misleading.

71

6. Conclusions

In order to assess the suitability of simplified analysis procedures recommended indesign codes, namely the response spectrum analysis, results obtained from timehistory analysis were compared with those from three different response spectra:

• The response spectrum of the recorded ground motion.

• The EC8 spectral shape scaled with PGA of recorded ground motion.

• A near-fault specific spectral model (Rupakhety et al. (2011), denoted asRR2011) scaled with PGV of recorded ground motion.

The results indicate that the EC8 model is not suitable to evaluate seismic actionon tall wind turbine towers. This is due to the inability of the model to account forlong-period energy content in near-fault ground motions. The RR2011 model wasfound, on the average, to represent the results obtained from time history analysisvery well.

It is observed that response spectral analysis using the SRSS combination rule givessatisfactory results as long as a proper response spectrum is used. Higher modeeffects are found to be significant at the top of the tower. As almost the half ofthe total mass is located at the top of the tower, higher mode effects are seen to besignificant in base shear and overturning moment. Displacement demand, however,is seen to be less sensitive to higher modes.

The analysis is based on a linearly elastic model of the structure with some simpli-fication in numerical modelling. In particular, the foundation flexibility has beenignored. With this effect included, the periods of the structure are expected to belonger, which might result in larger displacement demands for the largest magni-tude earthquakes considered in this study. Furthermore, the flexibility of nacelleand rotor is also ignored. These simplifications might introduce some limitations inthe computed results, but the main observations of the study are not likely to beinfluenced.

Future research scope

Certain simplifications have been introduced in the present study in order to explorethe general characteristics of seismic response of tall wind turbine towers in the near-fault region. Some physical effects, which might be important and warrant furtherresearch are mentioned below.

• Soil-Structure Interaction has been shown to affect the damping of struc-tures as well as their natural frequencies. This can make the structural more

72

flexible, and thus more susceptible to larger earthquakes. At the same time,additional damping provided by foundation flexibility can reduce seismic re-sponse. If the tower foundation is properly anchored to the bedrock, SSI effectsmay not be as important as when a surface foundation on a relatively soft soilis used. In such situations, a detailed soil structural interaction analysis usingappropriate ground motion time history is recommended.

• The P-delta effect is a second order non-linear effect that may change thenatural frequencies as well as result in increased gravity loads. Due to the largeheight of the structure, and relatively large mass at the top, theses secondaryeffects may introduce additional action, and need proper consideration.

• Multi-body system modelling may be conducted in order to estimate thestructural response of a wind turbine in an operational state. This kind ofanalysis however needs to incorporate additional methods to include the windloading effects on the turbine and the spin of the rotor. The use of pre-existing analysis codes specifically used for wind turbine design as mentionedin Chapter 1 is recommended for such tasks.

• Damping is a very critical parameter in seismic response of structures nearresonance. When the towers like the one studied here are excited by near-faultpulses with dominant period close to the fundamental period of the tower,response is very sensitive to damping. Damping models suitable for thesestructures are not yet well understood. Aerodynamic and SSI effects are likelyto result in a non-proportional damping mechanism in the structure. Thisresults in non-classical modes of vibration, which require advanced analysismethods compared to proportionally damped systems. In particular, classicalvibration modes are not able to uncouple the modes of vibration, and complexmodal transformations become necessary. As an alternative, direct integrationon matrix equation of motion can be used. This, however, requires a properspecification of structural damping matrix. In order to understand the natureof damping in these structures, experimental studies on full-scale models can beuseful. In particular, structural vibration monitoring and experimental modelanalysis may be employed. By recording vibration on existing towers due towind loads, system identification methods can be used to understand boththe modal and damping characteristics of the structure. In the South Icelandlowland, some experimental wind turbine towers have been installed. Sincethe wind action in the area of these installations is often severe, vibrationmonitoring of these installation can be very useful, from practical as wellas scientific point of view, in understanding dynamic characteristics of thesestructures. In addition, instrumentation of vibration monitoring systems infuture installations of large-scale wind turbine towers in the region is highlyrecommended.

73

Bibliography

Abrahamson, N. A. (2000). Effects of rupture directivity on probabilistic seismichazard analysis. In Proceedings of the 6th International Conference on SeismicZonation, volume 1, pages 151–156. Palm Springs CA.

Alavi, B. and Krawinkler, H. (2004). Behavior of moment-resisting frame structuressubjected to near-fault ground motions. Earthquake engineering & structural dy-namics, 33(6):687–706.

AlHamaydeh, M. and Hussain, S. (2011). Optimized frequency-based foundationdesign for wind turbine towers utilizing soil–structure interaction. Journal of theFranklin Institute, 348(7):1470–1487.

Ambraseys, N., Smit, P., Douglas, J., Margaris, B., Sigbjörnsson, R., Olafsson, S.,Suhadolc, P., and Costa, G. (2004). Internet site for european strong-motion data.Bollettino di Geofisica Teorica ed Applicata, 45(3):113–129.

Anderson, J. C. and Bertero, V. V. (1987). Uncertainties in establishing designearthquakes. Journal of Structural Engineering, 113(8):1709–1724.

Anderson, J. C., Bertero, V. V., and Bertero, R. D. (1999). Performance improve-ment of long period building structures subjected to severe pulse-type ground mo-tions. Number 9. Pacific Earthquake Engineering Research Center, College ofEngineering, University of California.

ASCE/AWEA (2011). Recommended practice for compliance of large land-basedwind turbine support structures. Technical report, American Wind Energy Asso-ciation/American Society of Civil Engineers.

Bazeos, N., Hatzigeorgiou, G., Hondros, I., Karamaneas, H., Karabalis, D., andBeskos, D. (2002). Static, seismic and stability analyses of a prototype windturbine steel tower. Engineering structures, 24(8):1015–1025.

Bertero, V. V., Mahin, S. A., and Herrera, R. A. (1978). Aseismic design impli-cations of near-fault san fernando earthquake records. Earthquake engineering &structural dynamics, 6(1):31–42.

75

BIBLIOGRAPHY

Bhattacharya, S., Cox, J. A., Lombardi, D., and Wood, D. M. (2012). Dynamicsof offshore wind turbines supported on two foundations. Proceedings of the ICE-Geotechnical Engineering, 166(2):159–169.

Bir, G. and Jonkman, J. (2008). Modal dynamics of large wind turbines withdifferent support structures. In ASME 2008 27th International Conference onOffshore Mechanics and Arctic Engineering, pages 669–679. American Society ofMechanical Engineers.

Borowicka, H. (1943). Über ausmittig belastete, starre platten auf elastisch-isotropem untergrund. Archive of Applied Mechanics, 14(1):1–8.

Bossanyi, E. (2009). Gh bladed user manual. Garrad Hassan Bladed.

Caughey, T. and O’kelly, M. (1965). Classical normal modes in damped lineardynamic systems. Journal of Applied Mechanics, 32(3):583–588.

Chopra, A. K. (1995). Dynamics of structures, volume 3. Prentice Hall New Jersey.

Clough, R. W. and Penzien, J. (1975). Dynamics of structures. Technical report.

EWEA (2013). Ewea annual report 2013. Technical report, European Wind EnergyAssociation and others.

Fogle, J., Agarwal, P., and Manuel, L. (2008). Towards an improved understanding ofstatistical extrapolation for wind turbine extreme loads. Wind Energy, 11(6):613–635.

GWEC (2015). Global wind report: annual market update 2014.

Haenler, M., Ritschel, U., and Warnke, I. (2006). Systematic modelling of windturbine dynamics and earthquake loads on wind turbines. In European WindEnergy Conference and Exhibition, pages 1–6. European Wind Energy AssociationAthens, Greece.

Hall, J. F., Heaton, T. H., Halling, M. W., and Wald, D. J. (1995). Near-sourceground motion and its effects on flexible buildings. Earthquake spectra, 11(4):569–605.

Halldórsson, B., Ólafsson, S., and Sigbjörnsson, R. (2007). A fast and efficientsimulation of the far-fault and near-fault earthquake ground motions associatedwith the june 17 and 21, 2000, earthquakes in south iceland. Journal of EarthquakeEngineering, 11(3):343–370.

Halldorsson, B. and Sigbjörnsson, R. (2009). The mw6. 3 ölfus earthquake at 15:45 utc on 29 may 2008 in south iceland: Icearray strong-motion recordings. SoilDynamics and Earthquake Engineering, 29(6):1073–1083.

76

BIBLIOGRAPHY

Harte, M., Basu, B., and Nielsen, S. R. (2012). Dynamic analysis of wind turbinesincluding soil-structure interaction. Engineering Structures, 45:509–518.

He, W.-L. and Agrawal, A. K. (2008). Analytical model of ground motion pulsesfor the design and assessment of seismic protective systems. Journal of StructuralEngineering, 134(7):1177–1188.

IEC (2005). Iec 61400-3: Wind turbines–part 1: Design requirements. InternationalElectrotechnical Commission, Geneva.

IEC (2009). Wind turbines: Part 3: Design requirements for offshore wind turbines.IEC.

Ishihara, T. and Sarwar, M. (2008). Numerical and theoretical study on seismicresponse of wind turbines. In European Wind Energy Conference and Exhibition,pages 1–5.

Iwan, W. (1997). Drift spectrum: measure of demand for earthquake ground mo-tions. Journal of structural engineering, 123(4):397–404.

J. Jonkman, S. Butterfield, W. M. and Scott, G. (2009). Definition of a 5-mwreference wind turbine for offshore system development. Technical report, NationalRenewable Energy Laboratory.

Jonkman, J. M. (2007). Dynamics modeling and loads analysis of an offshore floatingwind turbine. ProQuest.

Jonkman, J. M. and Buhl Jr, M. L. (2005). Fast user’s guide. National RenewableEnergy Laboratory, Golden, CO, Technical Report No. NREL/EL-500-38230.

Jonkman, J. M., Butterfield, S., Musial, W., and Scott, G. (2009). Definition of a 5-MW reference wind turbine for offshore system development. National RenewableEnergy Laboratory Golden, CO.

Joyner, W. B. and Boore, D. M. (1981). Peak horizontal acceleration and velocityfrom strong-motion records including records from the 1979 imperial valley, cali-fornia, earthquake. Bulletin of the Seismological Society of America, 71(6):2011–2038.

Larsen, T. J. and Hansen, A. M. (2007). How 2 HAWC2, the user’s manual. RisøNational Laboratory.

Lavassas, I., Nikolaidis, G., Zervas, P., Efthimiou, E., Doudoumis, I., and Ban-iotopoulos, C. (2003). Analysis and design of the prototype of a steel 1-mw windturbine tower. Engineering structures, 25(8):1097–1106.

Lloyd, G. (2003). Guidelines for the certification of wind turbines. Technical report,Germanischer Lloyd.

77

BIBLIOGRAPHY

Lloyd, G. (2005). Guideline for the certification of offshore wind turbines.

Loftsdóttir, Á., Guðmundsson, B., Ketilsson, J., Georgsdóttir, L., et al. (2005).Orkutölur.

Luzi, L., Hailemikael, S., Bindi, D., Pacor, F., Mele, F., and Sabetta, F. (2008).Itaca (italian accelerometric archive): a web portal for the dissemination of italianstrong-motion data. Seismological Research Letters, 79(5):716–722.

Makris, N. (1997). Rigidity–plasticity–viscosity: Can electrorheological dampersprotect base-isolated structures from near-source ground motions? Earthquakeengineering & structural dynamics, 26(5):571–591.

Makris, N. and Chang, S.-P. (2000). Effect of viscous, viscoplastic and frictiondamping on the response of seismic isolated structures. Earthquake Engineering& Structural Dynamics, 29(1):85–107.

Malcolm, D. and Hansen, A. (2002). Windpact turbine rotor design study. NationalRenewable Energy Laboratory, Golden, CO, 5.

Mannvit (2014). Búrfellslundur vindmyllur á rangárþingi ytra og skeiða- og gnúpver-jahreppi. Technical report, Mannvit verkfræðistofa.

Mavroeidis, G. P. and Papageorgiou, A. S. (2003). A mathematical representationof near-fault ground motions. Bulletin of the Seismological Society of America,93(3):1099–1131.

Mazzoni, S., McKenna, F., Scott, M. H., Fenves, G. L., et al. (2006). Openseescommand language manual. Pacific Earthquake Engineering Research (PEER)Center.

Menun, C. and Fu, Q. (2002). An analytical model for near-fault ground motionsand the response of sdof systems. Earthquake Spectra, pages 249–58.

Newmark, N. M. (1959). A method of computation for structural dynamics. Journalof the Engineering Mechanics Division, 85(3):67–94.

Øye, S. (1999). Flex5 user manual. Danske Techniske Hogskole.

Power, M., Chiou, B., Abrahamson, N., and Roblee, C. (2006). The next generationof ground motion attenuation models (nga) project: An overview. In Proceedings,Eighth National Conference on Earthquake Engineering.

Prowell, I. (2011). An experimental and numerical study of wind turbine seismicbehavior. PhD thesis, University of California.

Prowell, I., Elgamal, A., and Jonkman, J. (2009). Fast simulation of wind turbineseismic response.

78

BIBLIOGRAPHY

Prowell, I., Elgamal, A.-W. M., and Jonkman, J. M. (2010). FAST simulation ofwind turbine seismic response. National Renewable Energy Laboratory.

Ritschel, U., Warnke, I., Kirchner, J., and Meussen, B. (2003). Wind turbines andearthquakes. In 2nd World Wind Energy Conference, pages 1–8. Citeseer.

Rupakhety, R., Halldorsson, B., and Sigbjörnsson, R. (2010). Estimating coseismicdeformations from near source strong motion records: methods and case studies.Bulletin of Earthquake Engineering, 8(4):787–811.

Rupakhety, R. and Sigbjörnsson, R. (2011). Can simple pulses adequately representnear-fault ground motions? Journal of Earthquake Engineering, 15(8):1260–1272.

Rupakhety, R., Sigurdsson, S., Papageorgiou, A., and Sigbjörnsson, R. (2011).Quantification of ground-motion parameters and response spectra in the near-fault region. Bulletin of Earthquake Engineering, 9(4):893–930.

Sigbjörnsson, R. and Ólafsson, S. (2004). On the south iceland earthquakes injune 2000: Strong-motion effects and damage. Bollettino di Geofisica teorica edapplicata, 45(3):131–152.

Sigbjörnsson, R. and Rupakhety, R. (2014). A saga of the 1896 south iceland earth-quake sequence: magnitudes, macroseismic effects and damage. Bulletin of earth-quake engineering, 12(1):171–184.

Sigbjörnsson, R. and Rupakhety, R. (2015). On offshore earthquake engineering:Modelling and dynamic analysis. In Proceedings of IZIIS-50 International Con-ference on Earthquake Engineering and Seismology.

Sigurðsson, G., Rupakhety, R., and Sigbjörnsson, R. (2015). Dynamic analysis of5-mw wind turbine subjected to near-fault ground motions. In Proceedings ofIZIIS-50 International Conference on Earthquake Engineering and Seismology.

Somerville, P. G., Smith, N. F., Graves, R. W., and Abrahamson, N. A. (1997).Modification of empirical strong ground motion attenuation relations to includethe amplitude and duration effects of rupture directivity. Seismological ResearchLetters, 68(1):199–222.

Standard, B. (2005). Eurocode 8: Design of structures for earthquake resistance—.

Tothong, P., Cornell, C. A., and Baker, J. (2007). Explicit directivity-pulse inclusionin probabilistic seismic hazard analysis. Earthquake Spectra, 23(4):867–891.

Valamanesh, V. and Myers, A. (2014). Aerodynamic damping and seismic responseof horizontal axis wind turbine towers. Journal of Structural Engineering.

Veritas, D. N. (2004). Design of offshore wind turbine structures. Det Norske Veritas.

79

BIBLIOGRAPHY

Veritas, N. (2002). Guidelines for design of wind turbines. Det Norske Veritas Windenergy department, Risø National Laboratory.

Witcher, D. (2005). Seismic analysis of wind turbines in the time domain. WindEnergy, 8(1):81–91.

Zhao, X. and Maisser, P. (2006). Seismic response analysis of wind turbine towersincluding soil-structure interaction. Proceedings of the Institution of MechanicalEngineers, Part K: Journal of Multi-body Dynamics, 220(1):53–61.

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A. Near-fault records

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A.

Near-fault

records

Table A.1: Near-fault ground motion records (highlighted records are not used).

EQID WID Location Date Mw Station PGV(cm/s2)

EpiD(km)

Joyner-BooreDist.(km)

vs,30

1 1 Parkfield, CA, USA 27.06.1966 6.19 CO2 75.10 31.04 6.27 1852 2 San Fernando, CA, USA 09.02.1971 6.61 PCD 116.50 11.86 0.00 20163 3 Tabas, Iran 16.09.1978 7.11 TAB 121.87 55.24 1.79 7674 4 Coyote lake, CA, USA 08.06.1979 5.74 GA6 51.50 4.37 0.42 663

5 5 Imperial Valley, CA, USA 15.10.1979 6.53 AeroportoMexicalli 44.30 2.47 0.00 275

5 6 Imperial Valley, CA, USA 15.10.1979 6.53 Agrarias 54.40 2.62 0.00 275

5 7 Imperial Valley, CA, USA 15.10.1979 6.53 Brawleyairport 36.12 43.15 8.54 209

5 8 Imperial Valley, CA, USA 15.10.1979 6.53 EC countycenter FF 54.50 29.07 7.31 192

5 9 Imperial Valley, CA, USA 15.10.1979 6.53 EC MelolandOverpass FF 115.04 19.44 0.07 186

5 10 Imperial Valley, CA, USA 15.10.1979 6.53 E10 46.92 26.31 6.17 2035 11 Imperial Valley, CA, USA 15.10.1979 6.53 E0 3 41.10 28.65 10.79 1635 12 Imperial Valley, CA, USA 15.10.1979 6.53 E04 77.93 27.13 4.90 2095 13 Imperial Valley, CA, USA 15.10.1979 6.53 E05 91.48 27.80 1.76 2065 14 Imperial Valley, CA, USA 15.10.1979 6.53 E06 111.87 27.47 0.00 2035 15 Imperial Valley, CA, USA 15.10.1979 6.53 E07 108.82 27.64 0.56 2115 16 Imperial Valley, CA, USA 15.10.1979 6.53 E08 48.55 28.09 3.86 206

5 17 Imperial Valley, CA, USA 15.10.1979 6.53 El CentroDifferential Array 59.61 27.23 5.09 202

5 18 Imperial Valley, CA, USA 15.10.1979 6.53 HoltvillePost Office 55.15 19.81 5.51 203

6 19 Mexicalli Valley, Mexico 09.06.1980 6.33 VCT 76.71 11.79 6.07 2757 20 Irpinia, Italy-01 23.11.1980 6.9 Sturno 41.50 30.35 6.78 1000

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Table A.2: Near-fault ground motion records continued.


EpiD(km)


vs,30

8 21 Westmorland 26.04.1981 5.9 Parachutetest site 35.85 20.47 16.54 349

9 22 Morgan Hill, CA, USA 24.04.1984 6.19 GilroyArray # 6 35.39 36.34 9.85 663

9 23 Morgan Hill, CA, USA 24.04.1984 6.19 HAL 39.55 3.94 3.45 28210 24 Palm Springs, CA, USA 08.07.1986 6.06 NPS 73.63 10.57 0.00 34510 25 Palm Springs, CA, USA 08.07.1986 6.06 DSP 29.69 10.38 0.99 345

11 26 San Salvador 10.10.1986 5.8Geotech

Investigationcenter

62.26 7.93 2.14 545

12 27 Whittier Narrows, CA, USA 10.10.1987 5.99 DOW 30.40 16.04 14.95 272

12 28 Whittier Narrows, CA, USA 10.10.1987 5.99 LB OrangeEve 32.88 20.68 19.80 270

13 29 Superstition Hills, CA, USA 24.11.1987 6.54 PTS 106.76 15.99 0.95 34913 30 Superstition Hills, CA, USA 24.11.1987 6.54 ELC 52.05 35.83 18.20 192

14 31 Loma Prieta, CA, USA 17.10.1989 6.93 Alameda NavalAir Stn Hanger 32.16 90.77 70.90 190

14 32 Loma Prieta, CA, USA 17.10.1989 6.93 Gilroy Array #2 45.67 29.77 10.38 271

14 33 Loma Prieta, CA, USA 17.10.1989 6.93 Oakland OuterHarbor Wharf 49.21 94.00 74.16 249

14 34 Loma Prieta, CA, USA 17.10.1989 6.93 LGP 101.68 18.46 0.00 47814 35 Loma Prieta, CA, USA 17.10.1989 6.93 STG 57.23 27.23 7.58 37115 36 Sierra Madre, CA, USA 28.06.1991 5.56 COG 14.99 NA NA NA16 37 Erzincan, Turkey 13.03.1992 6.69 ERZ 95.42 8.97 0.00 27517 38 Cape Mendocino 25.04.1992 7 Petrolia 82.10 4.51 0.00 71318 39 Landers, CA, USA 28.06.1992 7.28 LUC 123.11 44.02 2.19 685

18 40 Landers, CA, USA 28.06.1992 7.28 Yermo FireStation 53.22 85.99 23.62 354

83

A.

Near-fault

records



EpiD(km)


vs,30

19 41 Northridge, CA, USA 17.01.1994 6.7 JFA 67.43 12.97 0.00 373

19 42 Northridge, CA, USA 17.01.1994 6.7 JFAgenerator 67.38 13.00 0.00 526

19 43 Northridge, CA, USA 17.01.1994 6.7 LA WadsworthVA hospital North 32.38 19.55 14.55 392

19 44 Northridge, CA, USA 17.01.1994 6.7 LA Dam (LDW) 77.11 11.79 0.00 62919 45 Northridge, CA, USA 17.01.1994 6.7 NWS 87.75 21.55 2.11 286

19 46 Northridge, CA, USA 17.01.1994 6.7 Pacoima dam(upper left) 107.08 20.36 4.92 2016

19 47 Northridge, CA, USA 17.01.1994 6.7 RRS 167.20 10.91 0.00 28219 48 Northridge, CA, USA 17.01.1994 6.7 SCG 130.27 13.11 0.00 25119 49 Northridge, CA, USA 17.01.1994 6.7 SCH 116.56 13.60 0.00 371

19 50 Northridge, CA, USA 17.01.1994 6.7 Sylmar OliveView Medical FF 122.73 16.77 1.74 441

20 51 Kobe, Japan 19.01.1995 6.9 Takarazuka 72.65 38.60 0.00 31221 52 Izmit, Tukey 17.08.1999 7.51 ARC 29.38 53.68 10.56 52321 53 Izmit, Tukey 17.08.1999 7.51 GBZ 45.68 47.03 7.57 79222 54 Chi-Chi, Taiwan 20.09.1999 7.6 CHY006 64.72 40.47 9.77 43822 55 Chi-Chi, Taiwan 20.09.1999 7.6 TCU031 59.86 80.09 30.18 48922 56 Chi-Chi, Taiwan 20.09.1999 7.6 TCU036 62.43 67.81 19.84 27322 57 Chi-Chi, Taiwan 20.09.1999 7.6 TCU038 50.86 73.11 25.44 27322 58 Chi-Chi, Taiwan 20.09.1999 7.6 TCU040 53.00 69.04 22.08 36222 59 Chi-Chi, Taiwan 20.09.1999 7.6 TCU042 47.34 78.37 26.32 27322 60 Chi-Chi, Taiwan 20.09.1999 7.6 TCU046 43.96 68.89 16.74 466

84



EpiD(km)


vs,30

22 61 Chi-Chi, Taiwan 20.09.1999 7.6 TCU049 44.82 38.91 3.78 48722 62 Chi-Chi, Taiwan 20.09.1999 7.6 TCU053 41.90 41.20 5.97 45522 63 Chi-Chi, Taiwan 20.09.1999 7.6 TCU054 60.92 37.64 5.30 46122 64 Chi-Chi, Taiwan 20.09.1999 7.6 TCU065 127.68 26.67 0.59 30622 65 Chi-Chi, Taiwan 20.09.1999 7.6 TCU075 88.44 20.67 0.91 57322 66 Chi-Chi, Taiwan 20.09.1999 7.6 TCU076 63.73 16.03 2.76 61522 67 Chi-Chi, Taiwan 20.09.1999 7.6 TCU082 56.12 36.20 5.18 47322 68 Chi-Chi, Taiwan 20.09.1999 7.6 TCU103 62.18 52.43 6.10 49422 69 Chi-Chi, Taiwan 20.09.1999 7.6 TCU128 78.66 63.29 13.15 60022 70 Chi-Chi, Taiwan 20.09.1999 7.6 TCU129 70.08 14.16 1.84 66423 73 Chi-Chi, Taiwan aftershock 20.09.1999 6.2 TCU076 33.10 20.80 13.04 61523 71 Chi-Chi, Taiwan aftershock 20.09.1999 6.2 CHY024 69.93 25.52 18.47 42823 72 Chi-Chi, Taiwan aftershock 20.09.1999 6.2 CHY080 59.35 29.48 21.34 55324 74 Chi-Chi, Taiwan aftershock 25.09.1999 6.3 CHY101 36.26 49.98 34.55 25925 75 South Iceland 17.06.2000 6.57 Flagbjarnarholt 73.84 5.29 4.20 80026 76 South Iceland 21.06.2000 6.49 Thorsarbru 82.02 5.32 2.80 80026 77 South Iceland 21.06.2000 6.49 Thorsartun 67.14 5.59 3.60 80026 78 South Iceland 21.06.2000 6.49 Solheimar 109.99 11.02 4.10 56027 79 Parkfield, CA, USA 28.09.2004 6 Parkfield fault zone 12 57.50 11.08 0.94 33927 80 Parkfield, CA, USA 28.09.2004 6 Parkfield Cholame 2 west 49.98 11.53 1.88 185

85

A.

Near-fault

records



EpiD(km)


vs,30

27 81 Parkfield, CA, USA 28.09.2004 6 Parkfield Cholame 2 east 23.67 11.63 2.50 37627 82 Parkfield, CA, USA 28.09.2004 6 Parkfield fault zone 1 64.15 8.39 0.00 33927 83 Parkfield, CA, USA 28.09.2004 6 Parkfield Cholame 3 west 45.00 11.88 2.50 33927 84 Parkfield, CA, USA 28.09.2004 6 Parkfield Cholame 4 west 38.37 12.37 3.44 43827 85 Parkfield, CA, USA 28.09.2004 6 Parkfield Cholame 4A west 22.16 13.01 4.69 33927 86 Parkfield, CA, USA 28.09.2004 6 Parkfield Stone Corral 1 east 44.95 7.17 2.81 33927 87 Parkfield, CA, USA 28.09.2004 6 Parkfield fault zone 9 26.10 9.98 1.25 43827 88 Parkfield, CA, USA 28.09.2004 6 Parkfield Cholame 3 east 34.54 11.86 5.63 37627 89 Parkfield, CA, USA 28.09.2004 6 Parkfield Cholame 1 east 53.10 11.56 1.88 33928 90 Ölfus, South Iceland 25.05.2008 6.3 EERC, Basement 41.13 8.00 3.33 80028 91 Ölfus, South Iceland 25.05.2008 6.3 Selfoss City Hall 33.03 8.00 3.33 80028 92 Ölfus, South Iceland 25.05.2008 6.3 Hveragerdi Retirement House 54.31 3.00 1.40 80029 93 L’Aquila, Italy 06.04.2009 6.3 AQK 46.57 4.00 0.00 580

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