Aalborg Universitet Soil-Structure Interaction For ...

Aalborg Universitet

Soil-Structure Interaction For Nonslender, Large-Diameter Offshore Monopiles

Sørensen, Søren Peder Hyldal

Publication date:2012

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Citation for published version (APA):Sørensen, S. P. H. (2012). Soil-Structure Interaction For Nonslender, Large-Diameter Offshore Monopiles.Department of Civil Engineering, Aalborg University. DCE Thesis No. 37

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ISSN 1901-7294 DCE Thesis No. 37

Soil-structure interaction for non-slender, large-diameter offshore

monopiles

VOL. 1

PhD Thesis

Defended in public at Aalborg University17th December 2012

Søren Peder Hyldal Sørensen

Department of Civil Engineering

DCE Thesis No. 37

Soil-structure interaction for non- slender, large-diameter offshore

monopiles

PhD Thesis defended in public at Aalborg University

17th December 2012

by


December 2012

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Published 2012 by

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ISSN 1901-7294

DCE Thesis No. 37

Preface

This thesis is submitted as one of the requirements for obtaining the degree of Ph.D.according to the regulations put forward by The Doctoral School of Engineering andScience at Aalborg University, Denmark.

The thesis concerns the interaction between soil and pile for monopile foundationsfor offshore wind turbines. The thesis is divided into two volumes. The first volumepresents the overall outcome of the Ph.D. fellowship. Further, the first volume isdivided into four parts which cover research areas that have been investigated duringthe Ph.D. fellowship:

• Part I – Review of laterally loaded piles in sand – This part presentsa review concerning the design of laterally loaded piles used as the foundationfor offshore wind turbines. The Winkler approach and the p–y curve formula-tion for piles in sand, currently adopted by design regulations of the AmericanPetroleum Institute, the International Organization for Standardization andDet Norske Veritas, are assessed thoroughly. The review highlights and as-sesses several limitations and uncertainties in the current design methodology.

• Part II – Physical modelling of laterally loaded, non-slender piles insand – This part deals with physical modelling of laterally loaded non-slenderpiles. A new test set-up for small-scale tests on laterally loaded piles hasbeen developed and validated. The test set-up facilitates the application of anoverburden pressure to the soil such that the soil properties for the small-scaletests are similar to the soil properties for sand around full-scale foundations.Tests have been conducted on both statically loaded and cyclically loaded piles.A scaling law is presented and validated against the small-scale tests.

• Part III – Numerical assessment of the initial part of p–y curves forpiles in sand – This part presents a parametric study on the initial part ofp–y curves for piles in sand. The parametric study is conducted through nu-merical modelling by means of the three-dimensional finite difference programFLAC3D. A new expression for the initial slope of p–y curves is determined so

Sørensen iii

Preface

as to accurately capture the behaviour of piles exposed to serviceability limitstate loads.

• Part IV – Design of offshore monopiles unprotected against scour– This part deals with the design of offshore monopiles that are unprotectedagainst the development of local scour. The time scale of the backfilling processas well as the relative density of the backfilled soil material is assessed throughlarge-scale physical modelling. The significance of the results from the physicalmodelling on the design of foundations for offshore wind turbines is elucidatedthrough a desk study.

The second volume of the thesis presents the test results from the physical modellingof laterally loaded non-slender piles in sand (Part II).

The Ph.D. thesis is based on the following collection of scientific papers and reportswritten by the author of the present thesis and in cooperation with other authors:

* Sørensen, S.P.H., Augustesen, A.H. & Ibsen, L.B. (2012). Revised expres-sion for the static initial part of p–y curves for piles in sand. Submitted forpublication.

* Sørensen, S.P.H., Ibsen, L.B. & Foglia, A. (2012). Testing of LaterallyLoaded Rigid Piles with Applied Overburden Pressure. Submitted for publica-tion.

* Sørensen, S.P.H. & Ibsen, L.B. (2012). Assessment of Scour Design forOffshore Monopiles Unprotected Against Scour. Submitted for publication.

Sørensen, S.P.H., Ibsen, L.B. & Frigaard, P. (2012). Relative Density of Back-filled Soil Material around Monopiles for Offshore Wind Turbines. Acceptedat the 22nd International Ocean and Polar Engineering Conference, XXIIISOPE, Rhodes, Greece.

* Sørensen, S.P.H. & Ibsen, L.B. (2012). Experimental Comparison of Non-Slender Piles under Static Loading and under Cyclic Loading in Sand. Ac-cepted at the 22nd International Ocean and Polar Engineering Conference,XXII ISOPE, Rhodes, Greece.

Leth, C.T., Sørensen, S.P.H., Klinkvort, R.T., Augustesen, A.H., Ibsen, L.B.& Hededal, O. (2012). A snapshot of present research at AAU and DTUon large-diameter piles in coarse-grained materials. Proceedings of the NordicGeotechnical Meeting, XVI NGM, Copenhagen, Denmark.

Sørensen, S.P.H. & Ibsen, L.B. (2012). Small-scale testing of laterally loadednon-slender piles in a pressure tank. Proceedings of the Nordic GeotechnicalMeeting, XVI NGM, Copenhagen, Denmark.

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Roesen, H.R., Thomassen, K., Sørensen, S.P.H. & Ibsen, L.B. (2011). Evalu-ation of Small-Scale Laterally Loaded Monopiles in Sand. Symposium Pro-ceedings: 64th Canadian Geotechnical Conference and 14th Pan-AmericanConference on Soil Mechanics and Engineering, 5th Pan-American Confer-ence on Teaching and Learning of Geotechnical Engineering, Toronto, Ontario,Canada: Pan-AM CGS Geotechnical Conference.

Thomassen, K., Roesen, H.R., Sørensen, S.P.H. & Ibsen, L.B. (2011). Small-scale testing of laterally loaded monopiles in sand. Symposium Proceedings:64th Canadian Geotechnical Conference and 14th Pan-American Conferenceon Soil Mechanics and Engineering, 5th Pan-American Conference on Teach-ing and Learning of Geotechnical Engineering, Toronto, Ontario, Canada:Pan-AM CGS Geotechnical Conference.

Brødbæk, K.T., Augustesen, A.H., Møller, M. & Sørensen, S.P.H. (2011).Physical modelling of large diameter piles in coarse-grained soil. Proceedings ofthe 21st European Young Geotechnical Engineers’ Conference, XXI EYGEC,4-7. September, Rotterdam, The Netherlands.

* Sørensen, S.P.H., Ibsen, L.B. & Frigaard, P. (2010). Experimental Evaluationof Backfill in Scour Holes around Offshore Monopiles. Proceedings of the 2ndInternational Symposium on Frontiers in Offshore Geotechnics, II ISFOG,Perth, Australia, 8-10 November 2010. Balkema Publishers, A.A. / Taylor &Francis, The Netherlands, 2010, pp. 617-622.

Frigaard, P. Lykke, T. Rodriguez, J.R.R., Sørensen, S.P.H., Martinelli, L.,Lamberti, A., Troch, P., de Vos, L., Kisacik, D., Stratigaki, V., Zou, Q., Monk,K., Vandamme, J., Damsgaard, M.L. & Graversen, H. (2010). Loads on En-trance Platforms for Offshore Wind Turbines. Proceedings of the HYDRALABIII Joiint Transnational Access User Meeting, Hannover, February 2010. Red./Joachim Grune, Mark Klein Breteier. Hannover: Forschungszentrum KusteFZK (Coastal Research Center), 2010, pp. 25-28.

Augustesen, A.H., Sørensen, S.P.H., Ibsen, L.B., Andersen, L., Møller, M. &Brødbæk K.T. (2010). Comparison of calculation approaches for monopilesfor offshore wind turbines. In Proceedings of the 7th European Conference onNumerical Methods in Geotechnical Engineering, VII NUMGE, (eds. Benzand Nordal), 2.-4. June, Trondheim, Norway, CRC Press, Taylor & FrancisGroup, 901-906.

Sørensen, S.P.H., Ibsen, L.B. & Augustesen, A.H. (2010). Effects of diameteron initial stiffness of p-y curves for large-diameter piles in sand. In Proceed-ings of the 7th European Conference on Numerical Methods in GeotechnicalEngineering, VII NUMGE, (eds. Benz and Nordal), 2.-4. June, Trondheim,Norway, CRC Press, Taylor & Francis Group, 907-912.

Sørensen v

Preface

Augustesen, A.H., Brødbæk, K.T., Møller, M., Sørensen, S.P.H., Ibsen, L.B.,Pedersen, T.S. & Andersen, L. (2009). Numerical Modelling of Large-DiameterSteel Piles at Horns Rev. In Proceedings of the 12th International Conferenceon Civil, Structural and Environmental Engineering Computing (eds. Topping,Costa Neves and Barros), 1.-4. September, Madeira, Portugal, Civil-CompPress, Dun Eaglais, Kippen, UK, Paper 239.

Sørensen, S.P.H., Brødbæk, K.T., Møller, M., Augustesen, A.H. & Ibsen,L.B. (2009). Evaluation of the Load-Displacement Relationships for Large-Diameter Piles in Sand. In Proceedings of the 12th International Conference onCivil, Structural and Environmental Engineering Computing, (eds. Topping,Costa Neves and Barros), 1.-4. September, Madeira, Portugal, Civil-CompPress, Dun Eaglais, Kippen, UK, Paper 244.

* Sørensen, S.P.H., Brødbæk, K.T., Møller, M. & Augustesen, A.H. (2012).Review of laterally loaded monopiles employed as the foundation for offshorewind turbines. DCE Technical Reports, No. 137, Department of Civil Engi-neering, Aalborg University, Aalborg, Denmark.

+ Sørensen, S.P.H. & Ibsen, L.B. (2011). Small-scale cyclic tests on non-slender piles situated in sand - Test results. DCE Technical Reports, No. 118,Department of Civil Engineering, Aalborg University, Aalborg, Denmark.

+ Sørensen, S.P.H. & Ibsen, L.B. (2011). Small-scale quasi-static tests onnon-slender piles situated in sand - Test results. DCE Technical Reports, No.112, Department of Civil Engineering, Aalborg University, Aalborg, Denmark.

Copies of the publications marked with ”*” are enclosed in the back of Vol. 1 of thethesis, while publications marked with ”+” are enclosed in Vol. 2 of the thesis.

The Ph.D. fellowship has been funded through the research project ”Seabed WindFarm Interaction”. The research project is funded by ”The Danish Agency for Tech-nology and Innovation” under the Program Committee for Energy and Environment,case no. 2104-07-0010. The funding is sincerely appreciated.

During the Ph.D. fellowship, supervision has been given by Professor Lars Bo Ibsen,Aalborg University, Denmark. I wish to thank Professor Lars Bo Ibsen for hisguidance and support during the course of my studies. His guidance is greatlyappreciated.

During the Ph.D. fellowship, I spent four months at the Centre for Offshore Foun-dation Systems (COFS), University of Western Australia, Perth, Western Australia,Australia, under the supervision of Professor Mark Randolph. At COFS, my workwas concentrated on numerical modelling of the behaviour of non-slender laterallyloaded piles. Further, Mark Randolph also provided me with great insight withinthe scope of physical modelling including practical use of dimensional analysis with

vi Sørensen

Preface

respect to laterally loaded piles. I would like to express gratitude to Professor MarkRandolph for his assistance and supervision during the time I spent at the Universityof Western Australia.

I would like to express gratitude to Kristian T. Brødbæk, Martin Møller and AndersH. Augustesen, COWI A/S, for their cooperation in connection with Part I of thethesis. Further, I wish to express my gratitude to Anders H. Augustesen for hiscooperation in connection with Part III of the thesis.

Kristian T. Brødbæk, Martin Møller, Kristina Thomassen, Hanne R. Roesen, LinasMikalauskas, Alejandro B. Moreno and Jose L. T. Diaz have assisted with the phys-ical modelling related to Part II of the project. Their assistance is sincerely ac-knowledged. I also wish to acknowledge the technical staff at the GeotechnicalEngineering Laboratory, Aalborg University for their assistance with the test set-upfor the experimental work.

I wish to acknowledge the technical staff at the Large Wave Channel (GWK) of theCoastal Research Centre (FZK) in Hannover, Germany. The large-scale testing onthe backfilling process presented in Part IV would not have been possible withouttheir assistance and support.

I wish to thank my colleague Aligi Foglia for many fruitful discussions regardingphysical modelling and for his cooperation in connection with Part III of the thesis.

Finally, I thank my colleagues, friends and family for moral support and helpfulnessduring the course of my studies.

Aalborg, May 2012


Sørensen vii

Preface

viii Sørensen

Summary in English

Strong political and industrial forces, especially in Northern Europe, support thedevelopment of new technologies as well as improvements of existing technologieswithin the field of renewable energy. Offshore wind power is a domestic, sustainableand largely untapped energy resource. Today, the modern offshore wind turbineoffers competitive production prices compared to other sources of renewable energy.Therefore, it is a key technology in breaking the dependence on fossil fuels and inachieving the energy and climate goals of the future.

For offshore wind turbines, the costs of foundation typically constitutes 20-30 % ofthe total costs. Hence, improved methods for the design of foundations for offshorewind turbines can increase the competitiveness of offshore wind energy significantly.The monopile foundation concept has been employed as the foundation for the ma-jority of the currently installed offshore wind turbines.

The overall aim of the present thesis is to enable low-cost and low-risk foundationsto be designed for future offshore wind farms. Therefore, the soil-pile interaction fornon-slender, large-diameter offshore piles has been investigated.

A review of current design methods for laterally loaded piles is presented. The re-view focuses on the Winkler approach in which the pile is considered as a beam on anelastic foundation. The elastic foundation consists of a series of uncoupled springswith stiffnesses governed by means of p–y curves. The p–y curve formulation forpiles in sand, which is currently adopted in design regulations of organisations suchas the American Petroleum Institute, the International Organization for Standard-ization and Det Norske Veritas, is presented in detail. Limitations to the Winklerapproach as well as limitations to the p–y curve formulation currently adopted bydesign regulations have been presented. The following uncertainties/limitations havebeen adressed in detail: shearing force between soil layers; ultimate soil resistance;influence of vertical loading on the lateral soil response; effect of pile flexibility; ini-tial stiffness of p–y curves; choice of horizontal earth pressure coefficient; shearingforce at the pile toe; shape of p–y curves; effect of soil layering; long-term cyclicloading; effect of scour/backfilling on the soil-pile interaction. Through the litter-ature study several limitations have been identified for the p–y curve formulation

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Summary in English

currently recommended in the design regulation. These limitations need to be ad-dressed in order to enable design of low-cost and low-risk monopile foundations foroffshore wind turbines.

The behaviour of laterally loaded piles can be investigated by means of small-scaletesting, large-scale testing, numerical modelling and by means of analytical meth-ods. A new test set-up for the small-scale testing of laterally loaded piles has beendeveloped. The test set-up enables the application of an overburden pressure to thesoil. Hereby, traditional uncertainties for the soil parameters for small-scale testshave been avoided. These traditional uncertainties include very high friction anglesand very low Young’s modulus of elasticity in comparison with soil properties forfull-scale foundations. Both a series of static tests and a series of cyclic tests havebeen conducted. A scaling law that includes an applied overburden pressure hasbeen proposed. The scaling law has been validated against the small-scale tests.The pile rotation at failure depends on the applied overburden pressure such thatthe rotation at failure increases with increasing overburden pressure. This finding issimilar to the increase of the strain at failure for increasing confining pressure whichcan be found for conventional drained triaxial tests on cohesionless materials. Cyclictests have illustrated another significant difference between tests with and withoutoverburden pressure applied: for the tests without overburden pressure, the cyclicloading caused a part of the soil volume to cave-in and a part of the soil volume togap; for the tests with overburden pressure applied, no soil cave-in was observed.

A parametric study on the initial part of p–y curves has been conducted. In theparametric study, the influence of a broad spectre of parameters have been adressed.These parameters include: the pile diameter, the Young’s modulus of elasticity forthe soil, the friction angle, the pile flexibility, the loading eccentricity, and the depthbelow seabed. The parametric study has been conducted by means of FLAC3D

which is a commercial, three-dimensional finite difference program. It has beenconcluded that the initial part of the p–y curves depends on the pile diameter,the Young’s modulus of elasticity for the soil and the depth below seabed, whilethe friction angle, the loading eccentricity and the pile flexibility do not have anysignificant effect on the initial part of the p–y curves. Based on the findings fromthe numerical study, a modified expression for the initial stiffness of p–y curves hasbeen proposed so the behaviour of piles exposed to serviceability limit state loadscan be captured accurately.

A large-scale test on backfill around piles in waves has been conducted at the largewave flume (GWK) at the Coastal Research Centre (FZK) in Hannover. The timescale of the backfilling process has been found to be significantly smaller than whatcan be expected on the basis of previously published small-scale tests on the back-filling process. This illustrates that more research is needed regarding the time scaleof backfilling in waves and that the scaling laws for the time scale of backfilling needfurther investigation. The relative density of the backfilled soil material has beenmeasured to vary from 65 % to 80 %. Hereby, the backfilled soil material can be

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Summary in English

categorised as medium dense to very dense and therefore the backfilled soil materialcan be expected to be rather stiff and to have a significant strength. Through a deskstudy, the significance of acounting for the time variation of scour/backfilling in thefatigue and ultimate limit state design has been elucidated.

The Ph.D. research project has lead to an improved understanding of the interactionbetween soil and pile for offshore pile foundations. Hereby, the research contributesto the design of low-cost and low-risk foundations for offshore wind turbines.

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Summary in English

xii Sørensen

Resume (Summary in Danish)

Udviklingen af nye teknologier samt forbedringer af eksisterende teknologier inden-for vedvarende energi bliver støttet af indflydelsesrige politikere, økonomisk stærkevirksomheder og fonde. Denne politiske og industrielle støtte er især udbredt iNordeuropa. Offshore vindenergi er en bæredygtig energiform og en i høj grad uud-nyttet energiressource. Produktionspriserne for nye havvindmøller har efterhandennaet et niveau, hvor offshore vindenergi er konkurrencedygtig i forhold til andre for-mer for vedvarende energi. Optimering af teknologien inden for offshore vindenergier derfor særdeles vigtig, for at bryde afhængigheden af fossile brændstoffer samt forat møde fremtidens energi- og klimamal.

Omkostningerne forbundet med funderingen af havvindmøller udgør typisk 20-30% af de samlede omkostninger for havvindmøller. Dermed kan forbedringer af denuværende designmetoder for funderingen af havvindmøller være med til at øgekonkurrenceevnen for offshore vindenergi væsentligt. Den mest anvendte funder-ingstype for offshore vindmøller er monopæle.

Det overordnede mal med denne afhandling er at optimere de nuværende design-metoder for monopæle fundamenter, saledes at konkurenceevnen for offshore vindmøllerkan forbedres. Derfor er interaktionen mellem jord og pæl blevet undersøgt for stiveoffshore pæle.

Et litteraturstudie af de nuværende designmetoder for horisontalt belastede pælepræsenteres. Litteraturstudiet fokuserer pa Winkler metoden, hvori pælen mod-elleres som en bjælke pa et elastisk fundament. Det elastiske fundament bestar afen række ukoblede elastiske fjedre, hvoraf fjederstivhederne bestemmes ved brug afp–y kurver. p–y kurve formuleringen for sand, der i dag er inkorporeret i standarderfra the American Petroleum Institute, the International Organization for Standard-ization og Det Norske Veritas, præsenteres og analyseres. Begrænsninger bade iforbindelse med Winkler metoden og i forbindelse med den nuværende p–y kurve for-mulering præsenteres. De følgende usikkerheder/begrænsninger analyseres og vur-deres: forskydning mellem jordlag; ultimativ jordtryk; indflydelse af vertikal belast-ning pa det horisontale jordtryk; betydningen af en pæls fleksibilitet; initialstivhedenaf p–y kurver; valg af horisontal jordtrykskoefficient; forskydning ved pælespidsen;

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p–y kurvernes form; betydningen af lagdelt jord; betydningen af cyklisk belastning;betydningen af scour/backfill pa interaktionen mellem jord og pæl. For at optimeredesignet af offshore pæle og hermed øge konkurrenceevnen for offshore vindenergi erdet nødvendigt at undersøge de ovennævnte usikkerheder/begrænsninger.

Interaktionen mellem jord og pæl for horisontalt belastede pæle kan undersøges vedsmaskala forsøg, storskala forsøg, numerisk modellering og ved analytiske bereg-ninger. En ny forsøgsopstilling for smaskala forsøg af horisontalt belastede pæleer blevet udviklet. Forsøgsopstillingen muliggør paførslen af et overlejringstryk.Idet et overlejringstryk paføres, kan de traditionelle usikkerheder i forbindelse medbestemmelsen af jordens egenskaber ved smaskala forsøg undgas/formindskes. Fortraditionelle smaskala forsøg udført ved normalt spændingsniveau vil jorden haveen meget stor friktionsvinkel samt en meget lille stivhed sammenlignet med egen-skaberne for jorden omkring fuldskala pæle. Der er bade udført en forsøgsseriemed statisk og cyklisk belastning. En skaleringslov, der inkluderer det paførteoverlejringstryk, er blevet udledt. Skaleringsloven er blevet valideret i forhold tilforsøgsserien pa stive pæle udsat for statisk belastning. Ud fra forsøgsserien hvoren statisk belastning er pasat er det erfaret, at pælens rotation ved brud stigerved stigende overlejringstryk. Denne sammenhæng mellem pælens rotation og over-lejringstrykket tilsvarer sammenhængen mellem brudtøjning og den mindste hoved-spænding ved drænede triaksialforsøg. Ved de cykliske forsøg kunne det observeres,at der dannes et ’hul’ (gap) bag pælen idet denne belastes. Udviklingen af dette’hul’ afhænger dog af om der er paført et overlejringstryk eller ej: for forsøgeneuden overlejringstryk blev ’hullet’ delvist tilbagefyldt (cave-in); for forsøgene medoverlejringstryk blev tilbagefyldning af sandmateriale (cave-in) ikke observeret.

Et parametrisk studie vedrørende den initiale del af p–y kurver er udført. Betydnin-gen af følgende parametre er undersøgt i det parametriske studie: pælens diameter;jordens elasticitetsmodul; jordens friktionsvinkel; pælens fleksibilitet; lastens excen-tricitet; samt dybden under havbunden. Det parametriske studie er udført ved brugaf det kommercielle finite difference program FLAC3D. Gennem det parametriskestudie erfares det, at den initiale del af p–y kurverne afhænger af pælens diameter,jordens elasticitetsmodul samt dybden under havbunden, hvorimod friktionsvinklen,lastens excentricitet samt pælens fleksibilitet ikke har nogen signifikant betydningfor den initiale del af p–y kurverne. Et modificeret udtryk for initialstivheden af p–ykurver for pæle i sand er blevet præsenteret baseret pa det numeriske studie. Detmodificerede udtryk er fremkommet saledes, at den initiale del af p–y kurverne forpæle i sand tilnærmes med god nøjagtighed.

I den store bølgerende (GWK) ved Coastal Research Centre (FZK) i Hannoverer der udført et storskala forsøg pa backfill omkring pæle i bølger. Tidsskalaenfor backfill-processen var betydeligt mindre end hvad der kan forventes baseret papublicerede smaskala forsøg omhandlende backfill. Dette tydeliggør nødvendighedenaf udvidet forskning indenfor backfilling i bølger samt at de nuværende skaleringslovefor tidsskalaen af backfill kræver yderligere validering. I storskala forsøget blev den

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relative lejringstæthed fundet til 65-80 %, hvormed det kan konkluderes, at dettilbagefyldte sand-materiale har en høj stivhed og styrke. Betydningen af at tagehøjde for den tidslige variation i scour-dybde ved undersøgelse af udmattelses- ogbrudgrænsetilstanden er blevet belyst.

Ph.D.-projektet har ført til en øget forstaelse af interaktionen mellem jord og pælfor offshore pælefundamenter. Ph.D.-projektet bidrager dermed til en øget konkur-renceevne for offshore vindenergi.

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Contents

1 Foundations for offshore wind turbines 1

1.1 Loads acting on foundations for offshore wind turbines . . . . . . . . 2

1.2 Types of foundation for offshore wind turbines . . . . . . . . . . . . 3

1.2.1 The monopile foundation concept . . . . . . . . . . . . . . . . 3

1.2.2 The gravity based foundation concept . . . . . . . . . . . . . 4

1.2.3 The bucket foundation concept . . . . . . . . . . . . . . . . . 5

1.2.4 The tripod and jacket foundation concept . . . . . . . . . . . 6

1.2.5 Floating foundations . . . . . . . . . . . . . . . . . . . . . . . 8

2 Aims of thesis and specific objectives 9

2.1 Overall aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Specific objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 The research project 11

3.1 Part I – Review of laterally loaded piles in sand . . . . . . . . . . . . 11

3.2 Part II – Physical modelling of laterally loaded, non-slender piles . . 12

3.3 Part III – Numerical assessment of the initial part of p–y curves forpiles in sand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.4 Part IV – Design of offshore monopiles unprotected against scour . . 16

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CONTENTS

4 Conclusions 19

4.1 Part I – Review of laterally loaded piles in sand . . . . . . . . . . . . 19

4.2 Part II – Physical modelling of laterally loaded, non-slender piles . . 21

4.3 Part III – Numerical assessment of the initial part of p–y curves forpiles in sand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.4 Part IV – Design of offshore monopiles unprotected against scour . . 23

4.5 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5 References 27

6 Enclosed scientific papers 31

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CHAPTER 1

Foundations for offshore wind turbines

Wind energy is a competitive and promising source of renewable energy, and herebywind energy plays an important role when trying to break the dependence on fossilfuels and when trying to reduce carbon emissions. Wind energy is a sustainablesource of energy. Today, the majority of the installed wind turbines are positionedonshore. However, in countries with dense populations and vast coastlines, offshorewind energy is an alternative to onshore wind energy. Placing wind turbines offshoreoffers advantages such as: higher wind speeds; less turbulent wind; less or no visualimpact; and no human neighbours. However, both construction costs and main-tenance costs are significantly higher for offshore wind turbines than for onshorewind turbines. To minimise the construction and maintainance costs, offshore windturbines should preferably be placed near shore and at low water depths.

The first offshore wind farm was erected in Vindeby, Denmark, and consisted of 11wind turbines with capacities of 450 kW. The first large-scale offshore wind farm waserected in 2003 at Horns Rev, Denmark. Horns Rev Offshore Wind Farm consistsof 80 wind turbines, and it has a total capacity of 160 MW. In 2009, the capacityof offshore wind energy in Europe was approximately 2 GW. The European WindEnergy Association (EWEA) has set targets for the offshore wind energy capacitiesin Europe. By 2020 and 2030, the European offshore wind energy capacity shouldreach 40 GW and 150 GW, respectively. The installation of offshore wind energy isexpected primarily to take place in Northern Europe. (www.ewea.org)

For offshore wind turbines, the costs of foundation typically constitutes of 20-30 %of the total costs. Therefore, it is of high interest to optimise the foundation design.This can be accomplished either by improving existing technologies or by developingnew technologies.

Today, the majority of the installed offshore wind turbines have capacities up to

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3.6 MW, are positioned within a distance of 10 km from shore and are located atpositions with water depths less than 20 m. However, the installation of severaloffshore wind turbines with capacities of up to 7 MW, distances to shore of up to100 km and water depths of up to 60 m have been consented/planned.

1.1 Loads acting on foundations for offshore wind tur-bines

Offshore wind turbines are exposed to environmental loads from waves, wind andcurrents. The foundations for offshore wind turbines are therefore exposed to largelateral loads as well as large overturning moments. The vertical loading originatesfrom the selfweight of the wind turbine and of the foundation. Therefore, the ver-tical loading is rather small. The loading from wind and waves are cyclic. So,resonance between the loading frequency and the natural frequencies of the offshorewind turbine structure should be avoided. Further, the deformation/rotation of thefoundation, due to long-term cyclic loading as well as the fatigue-life of the steelmaterial of both the foundation and the wind turbine, should be investigated.

The frequency range of extreme waves is typically in the range of 0.07-0.14 Hz whilethe energy rich wind turbulency typically is below 0.1 Hz. The rotor of modern off-shore wind turbines typically undergoes 10-20 revolutions per minute correspondingto a frequency of 0.17-0.33 Hz. This frequency is denoted the rotor frequency, 1P.Due to aerodynamic imbalances or imbalances in the mass distribution, minor exci-tations can take place with a frequency of 1P. The rotor blades pass the tower witha frequency of 3P, 0.5-1 Hz. Large excitations take place with this frequency due tothe impulse-like excitation from blades passing the tower. Today, most foundationsfor offshore wind turbines are designed such that the first natural frequency of thewind turbine including foundation lies within 1P and 3P. The natural frequenciesof offshore wind turbines depends on both the stiffness of the foundation and towerstructure as well as on the stiffness of the interaction between soil and foundation.The stiffness of the material used for the tower and foundation can be predicted withhigh accuracy. However, determination of the stiffness of the interaction betweenthe soil and the foundation is complicated. Furthermore, the cyclic loading mightchange this stiffness since cyclic loading can lead to possible softening/hardening ofthe soil. Furthermore, erosion of seabed material causes the stiffness og the interac-tion between soil and foundation to vary with time and sea conditions.

For offshore wind turbines, the permanent rotation of the foundation arising frominstallation as well as from long-term loading is typically required to be less than0.5◦. Therefore, an accurate prediction of the long-term variation of the stiffnessof the interaction between soil and foundation is needed. An accurate prediction ofthis stiffness is also important when designing the steel material in the foundation

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and tower against fatigue damage.

Besides loading from wind and waves, offshore wind turbine foundations are alsoloaded from currents. In comparison with wave loading, the loading from currentsis rather small. Both currents and waves induce shear stresses on the seabed, andtherefore they can cause erosion of seabed material near to the foundations. Toavoid erosion of the seabed around offshore foundations, scour protection consistingof rock infill can be positioned.

For offshore wind turbines located in cold waters, drifting ice can induce majorloads on the foundation. In order to minimise the loading arising from drifting ice,foundations for offshore wind turbines located in cold waters are typically designedwith either an upward breaking cone or a downward breaking cone in the height ofthe mean water level.

1.2 Types of foundation for offshore wind turbines

Several types of foundation concepts can be employed as the foundation for offshorewind turbines, for instance the monopile foundation concept, the gravity based foun-dation concept, the bucket foundation concept, the jacket foundation concept andthe tripod foundation concept. The majority of these concepts have originally beendeveloped for the foundation of offshore structures for the oil and gas sector. Off-shore structures used for the oil and gas sector, typically, have significant masses.Therefore, both the vertical and the lateral loading on the foundation are significantfor foundations used in the offshore oil and gas sector. In contrast, the lateral loadsand overturning moments are dominant for foundations used for offshore wind tur-bines. The choice of foundation depends on several factors: the water depth, thesea conditions, the soil conditions, the wind turbine size, etc.

1.2.1 The monopile foundation concept

The monopile foundation concept is presently the most used type of foundation foroffshore wind turbines. Monopiles are typically hollow steel piles driven or drilledinto the seabed. The pile diameter is typically 4-6 m, and the embedded pile lengthranges from approximately 15 to 35 m. Until today, monopiles have been used forwater depths up to approximately 25 m.

For monopiles, the loading is primarily transferred to the ground by means of lateralbedding as the vertical loading is small in comparison with the lateral loads andoverturning moments. The upper soil layers of the bedding are therefore importantfor the load transfer.

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To connect the monopile with the wind turbine tower, so-called transition piecesare used. The space between the transition pieces and the monopiles is typicallygrouted. In fig. 1, a monopile as well as a transition piece are shown.

Figure 1: Monopile foundation being loaded on board a vessel. The yellow pillar at the rear is a

transition piece. www.dongenergy.com

After the lifetime of an offshore wind turbine, the monopile foundation is typicallycut-off several meters below the seabed. This is a costly process and one of thedownsides of the monopile foundation concept. Another disadvantage is the envi-ronmental concerns regarding the installation when pile driving is employed.

1.2.2 The gravity based foundation concept

Gravity based foundations employed in the offshore sector typically consist of cais-sons made of reinforced concrete, steel or composite material (see fig. 2). Caissonswith a cellular design, so they can be floated to the site, are often used. As ballast-ing, sand, gravel, concrete, etc. can be employed. For gravity based foundations,the loads are transferred to the seabed by means of normal shear stresses at thebase of the foundation. Hence, a large base as well as a large ballast are necessaryto withstand the overturning moments. The hydrodynamic loads are generally largeon gravity based foundations. For gravity based foundations, the subsoil close tothe seabed surface needs to have a sufficient bearing capacity. Any soft top layersneed to be removed prior to installation. Further, the seabed needs to be levelledand a course base layer should be placed prior to installation. The gravity based

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foundations erected up till now are primarily erected at locations with water depthsof up to 10 m. For larger water depths, the hydrodynamic loads will be very large,and subsequently the costs of foundation would be very large.

Figure 2: Gravity based foundation to be used as foundation at the Nysted Offshore Wind Farm.

The gravity based foundation has been designed with a downward breaking ice cone. www.no-tiree-

array.org.uk.

1.2.3 The bucket foundation concept

The bucket foundation concept is a rather new foundation concept for offshore windturbines. The foundation type originates from the oil and gas sector in which suctionanchors have been used for the anchoring of floating structures. A bucket foundationcomprises of a steel cylinder closed at the top. The bearing behaviour of bucketfoundations are similar to the classical foundation concept. Bucket foundations areinstalled into the seabed by creating a vacuum inside the pile. Initially, when abucket foundation is to be installed, the selfweight of the structure will cause thebucket to sink a certain depth into the soil. Afterwards, the installation is continuedby pumping out water from inside the bucket. This creates suction inside the bucket.Further, for cohesionless soils, the applied suction causes a flow of water from outsidethe bucket. This loosens the soil and therefore reduces the shaft resistance inside the

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bucket and the base resistance. After the lifetime of the offshore wind turbine, thebucket foundation can be uninstalled by means of pumping water into the bucket.Hereby, a pressure will build up inside the bucket causing uplift.

In 2002, a bucket foundation was installed as foundation for a 3 MW wind turbinein an embanked area at Frederikshavn harbour, Frederikshavn, Denmark (see fig.3). The bucket foundation concept has, furthermore, been employed for a met mastat Horns Rev 2. The bucket foundation concept is a promising foundation concept.However, it still needs to be proven that the concept can be used for a range of soilconditions and that the foundation can be handled during transport and installationin rough sea conditions.

Figure 3: Bucket foundation for a 3 MW wind turbine in Frederikshavn, Denmark.

www.hornsrev.dk.

1.2.4 The tripod and jacket foundation concept

For water depths larger than approximately 30 m, the costs of foundation for themonopile foundation concept and the gravity based foundation concept are verylarge. For such water depths, use of the tripod or the jacket foundation conceptswill typically be optimal. These two concepts can both be considered as steel framestructures. They are typically prefabricated and piles are typically used for theanchoring of the steel frames. Moreover, suction buckets can also be employed forthe anchoring. The tripod foundation concept consists of a main pipe with threelegs, while jacket foundations typically consists of a steel frame with four legs. For

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the Alpha Ventus offshore wind farm, both the tripod and the jacket foundationconcept have been used. The wind farm is located in the North Sea, approximately45 km north of the German coastline. Both types of foundation support six 5 MWwind turbines. The tripod and the jacket foundations installed at Alpha Ventus areillustrated in fig. 4 and fig. 5, respectively.

Figure 4: Tripod foundation for a 5 MW wind turbine at the Alpha Ventus offshore wind farm,

Germany. www.owt.de.

For steel frame structures such as the tripod or the jacket foundation concepts, thevertical loading as well as the overturning moments give rise to alternating tensileand compressive forces in the piles or suction buckets used to anchor the steel frameinto the seabed. In order to minimise the tensile loading, which often is critical,additional balasting can be employed. The lateral loading is carried by either lateralbedding or by the use of piles that are inclined.

If piles are used for the anchoring of the steel frames, these should be cut-off severalmeters below the seabed at removal.

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Figure 5: Jacket foundations for the 5 MW wind turbines at the Alpha Ventus offshore wind farm,

Germany. www.panoramio.com.

1.2.5 Floating foundations

For very large water depths, floating foundation concepts might be optimal. Floatingtype foundations have been used succesfully in the offshore oil and gas industry. Un-till today, floating foundations have, however, only been employed for one full-scaleoffshore wind turbine, the so-called Hywind, which has been installed approximately10 km southwest of Karmøy, Norway. This floating foundation supports a 2.3 MWturbine and the water depth at the location is approximately 220 m. A ballaststabilised floating foundation has been employed at Hywind. A ballast stabilisedfloating foundation consists of a hollow steel cylinder filled with ballast consistingof water and rocks. The foundation is attached to the seabed by means of mooringlines.

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CHAPTER 2

Aims of thesis and specific objectives

Offshore wind energy is a sustainable and largely untapped energy resource. Foroffshore wind turbines, the costs related to the foundation typically comprises of 20-30 % of the total costs. Hence, reduction in the costs of the foundation for offshorewind turbines can increase the competitiveness of offshore wind energy significantly.Reductions can be obtained by for instance:

• optimisation of existing types of foundations for offshore wind turbines.

• improvement of the design guidelines for existing types of foundations for off-shore wind turbines such that the foundation behaviour can be predicted moreaccurately.

• development of new foundation concepts for offshore wind turbines.

The overall aims and specific objectives of the present Ph.D. research programmeconcern the monopile foundation concept, and they are within the field of geotech-nical engineering. One of the specific objectives concerns coastal engineering as wellas geotechnical engineering.

2.1 Overall aim

The overall aim was to improve the knowledge regarding the behaviour for laterallyloaded, non-slender piles situated in the offshore environment and hereby to enablethe construction of low-risk and low-cost monopile foundations for offshore windturbines.

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Aims of thesis and specific objectives

2.2 Specific objectives

The specific objectives were:

• to review the current knowledge regarding the behaviour of laterally loaded,non-slender piles in sand and further to identify, analyse and assess limitationsin the current design guidelines for laterally loaded offshore piles.

• to develop a new test set-up for the small-scale testing of laterally loaded,non-slender piles. The new test set-up should enable the application of anoverburden pressure to the soil such that the traditional uncertainties for small-scale testing related to small effective stresses in the soil can be avoided. Thenew test set-up should be proven through a test series on statically loaded andcyclically loaded piles.

• to investigate the stiffness of the interaction between pile and soil throughnumerical modelling and to establish a new formulation for the initial slope ofp–y curves for piles in sand such that the pile behaviour for piles exposed toserviceability limit state loads can be captured accurately.

• to investigate the time scale of backfill in waves and further to investigate therelative density of backfilled soil material. Further, the effect of scour/backfillingon the design of offshore monopile foundations should be assessed.

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CHAPTER 3

The research project

The research conducted in connection with the Ph.D. fellowship has, as previouslymentioned, been divided into four parts. Part I presents a review of the currentdesign methodology for offshore monopile foundations. Further, in Part I, uncer-tainties and limitations related to the current design methodology is presented andassessed. Two of these uncertainties and limitations have been investigated furtherin Part III and Part IV. In Part II, a new and innovative test set-up for laterallyloaded piles is presented and validated against a large test series on laterally loadedpiles.

In this chapter, the contents of the four research parts are presented. Further, anoverview of the contents of the six publications, attached at the back of the presentPh.D. thesis, is presented. The overview includes background information, rationale,objectives and methods.

3.1 Part I – Review of laterally loaded piles in sand

Various design approaches exist for laterally loaded offshore monopiles. Organisa-tions such as the American Petroleum Institute, the International Organization forStandardization and Det Norske Veritas (API, 2000; ISO, 2007; and DNV, 2010)recommend the use of the Winkler approach (Winkler, 1867) for the design of off-shore monopiles exposed to lateral loading. This part of the research project consistsof the scientific publication ”Review of laterally loaded monopiles employed as thefoundation for offshore wind turbines”. The paper presents a review of the designapproaches for offshore monopiles. The review focuses on the Winkler approach inwhich the interaction between soil and pile is addressed by means of p–y curves.

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The p–y curve formulation for piles in sand currently adopted in API (2000), ISO(2007) and DNV (2010) is primarily based on the research presented in Cox et al.(1974), Reese et al. (1974), O’Neill and Murchison (1983), and Murchison andO’Neill (1984). The outline of the paper is as follows:

• Introduction – The monopile foundation concept for offshore wind turbinesis presented. Furthermore, various design approaches for offshore monopilesare briefly described.

• p–y curves and Winkler approach – The Winkler approach is presentedin detail. The presentation includes a historic timeline of the development ofthe Winkler approach as well as the development of p–y curve formulationsfor piles in sand.

• Formulations of p–y curves for piles in sand – The p–y curve formulationoriginally suggested by O’Neill and Murchison (1983) and currently adopted indesign regulations such as API (2000), ISO (2007) and DNV (2010) is presentedin detail. Both the analytical derivations/assumptions and the field tests thatform the basis of the p–y curve formulation are presented.

• Limitations of p–y curves – Based on a review of published litterature con-cerning the behaviour of laterally loaded offshore monopiles, the uncertaintiesand limitations of the currently adopted p–y curve formulation for piles in sandis addressed in detail. Alternative p–y curve formulations as well as alterna-tive design approaches for the design of offshore monopiles are assessed. Thefollowing uncertainties/limitations have been addressed: the shearing forcebetween soil layers; the ultimate soil resistance; the influence of vertical pileload on the lateral soil response; the effect of soil-pile interaction; the effect ofdiameter on the initial stiffness of p–y curves; the choice of horizontal earthpressure coefficient; the shearing force at the pile-toe; the shape of p–y curves;the effect of layered soil; the effect of long-term cyclic loading; and the effectof scour on the soil-pile interaction.

This part of the thesis highlights uncertainties and limitations in the Winkler ap-proach as well as in the currently used p–y curve formulation for piles in sand.Hereby, Part I of the thesis constitutes a basis for Parts II-IV.

3.2 Part II – Physical modelling of laterally loaded,non-slender piles

The behaviour of laterally loaded piles can be examined by means of, for instance,small-scale testing, large-scale testing, numerical modelling and analytical methods.

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Since large-scale testing is expensive and time-consuming, small-scale testing is auseful tool for analysis of the behaviour of laterally loaded piles. Further, small-scaletests can be used for validation of numerical models. When conducting traditionalsmall-scale tests on laterally loaded piles, the low effective stresses in the soil causesignificant uncertainties regarding the soil properties. This part of the Ph.D. researchproject has concerned the development of a new and innovative test set-up for thesmall-scale testing of laterally loaded piles. The new test set-up has been developedand validated at the Geotechnical Laboratory at Aalborg University, Denmark.

Many researchers have published results from physical modelling on the behaviourof laterally loaded piles. For example, Mansur et al. (1964), Cox et al. (1974)and Bhushan et al. (1981) have investigated the behaviour of flexible piles in sandthrough physical modelling. The behaviour of non-slender piles has been investigatedby, for instance, LeBlanc et al. (2010a) and Peralta and Achmus (2010). Theirinvestigations were based on small-scale tests conducted at 1-g.

The new test set-up enables the application of an overburden pressure to the soil. Byapplication of an overburden pressure to the soil, the traditional uncertainties relatedto the determination of the friction angle and the Young’s modulus of elasticity forthe soil can be overcome. Further, these parameters will be almost constant withdepth when an overburden pressure is applied to the soil. However, the applicationof overburden pressure also causes the effective stresses to vary trapezoidally alongthe pile length instead of triangularly. For laterally loaded piles several researchershave proposed scaling laws, for instance, Gudehus and Hettler (1983), Peralta andAchmus (2010), and LeBlanc et al. (2010a). However, these scaling laws do notaccount for the overburden pressure applied to the soil. A new scaling law hastherefore been developed so that small-scale tests on laterally loaded, non-slenderpiles with overburden pressure applied to the soil can be compared to small- and full-scale tests on laterally loaded, non-slender piles with no overburden pressure applied.This scaling law is presented in the paper ”Testing of laterally loaded rigid piles withapplied overburden pressure”. The scaling law is validated against a series of statictests on laterally loaded, non-slender piles with and without overburden pressureapplied to the soil. The outline of the paper is as follows:

• Introduction – The background for the test series on laterally loaded non-slender piles is presented. Further, the purpose of applying an overburdenpressure to the soil during tests on laterally loaded piles is detailed.

• Test set-up – The test set-up is presented in detail. The description of thetest set-up includes a description of the soil preparation, the soil properties, thepile properties, the measuring system and the method in which an overburdenpressure has been applied to the soil.

• Dimensional analysis – A scaling law that enables the scaling of tests onlaterally loaded piles with applied overburden pressure is presented.

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• Load-displacement relationships – The test results are presented and theproposed scaling law is validated against the small-scale tests. Furthermore,a discussion on the advantages/disadvantages of applying an overburden pres-sure to the soil, when conducting small-scale tests on laterally loaded piles, ispresented.

• Potential implication for design – The scaling law is used for the scalingof the small-scale tests to full-scale foundations.

In ”Experimental Comparison of Non-Slender Piles under Static Loading and underCyclic Loading in Sand”, the pile behaviour of laterally loaded, non-slender pilesexposed to static and cyclic loading are evaluated. The evaluation is based on a testseries on small-scale piles in which an overburden pressure has been applied to thesoil. In the paper, the advantages/disadvantages of applying an overburden pressureto the soil when conducting small-scale tests on laterally loaded piles exposed tostatic loading and cyclic loading are discussed. The paper outline is as follows:

• Introduction – The background for the test series on laterally loaded piles ispresented.

• p–y curve formulation – The p–y curve formulation suggested by O’Neilland Murchison (1983) is briefly presented.

• Delimitations concerning the current p–y curve formulation – Delimi-tations concerning the p–y curve formulation proposed by O’Neill and Murchi-son (1983) is addressed. Especially the effect of flexible/rigid pile behaviouron the soil-pile interaction is discussed.

• Test set-up – The test set-up and the test programme is presented.

• Results – The test results are presented. The effect of overburden pressureon the static and cyclic pile behaviour is addressed in detail. The advan-tages/disadvangages of applying an overburden pressure to the soil when con-ducting small-scale tests on laterally loaded piles are evaluated based on thetest results.

3.3 Part III – Numerical assessment of the initial part

of p–y curves for piles in sand

For offshore monopiles employed as the foundation for offshore wind turbines, thesum of the rotation due to installation and of the rotation due to long-term loadingis typically required to be less than 0.5◦. Further, the first natural frequency ofthe wind turbine including foundation is designed to be within a narrow range so

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fatigue damage to the steel material used for the foundation and for the wind turbinetower is minimised. Therefore, accurate prediction of the foundation stiffness andhereby also of the inital slope of the p–y curves is of high importance. In the p–y curve formulation suggested by O’Neill and Murchison (1983), the inital slopeof the p–y curves depends only on the depth below seabed and the friction angle.Various researchers have investigated the initial slope of p–y curves for piles in sand,however, with contradictory conclusions: Terzaghi (1955), Vesic (1961), Ashfordand Juirnarongrit (2005), and Fan and Long (2005) indicated that the initial slopeof p–y curves for piles in sand should be independent of the pile diameter; Carter(1984) and Ling (1988) proposed a p–y curve formulation in which the initial slope ofthe p–y curves is linearly proportional with the pile diameter; Lesny and Wiemann(2006) suggested that the initial slope of p–y curves for piles in sand increases non-linearly with the depth below seabed. In this part of the thesis, the initial slope ofp–y curves for piles in sand has been investigated by means of numerical modelling.A parametric study has been conducted with use of the commercial finite differenceprogram FLAC3D. The numerical study is presented in the scientific paper ”Revisedexpression for the static initial part of p–y curves for piles in sand”. The outline ofthe paper is as follows:

• p–y curve formulation – Briefly, the p-y curve formulation proposed byO’Neill and Murchison (1983) is presented. The validity of the formulationwith respect to non-slender, large-diameter piles is discussed. Especially, thevalidity/accurateness of the initial slope of the p–y curves for non-slender large-diameter piles is addressed.

• Numerical modelling – A numerical model established in the commercialfinite difference program FLAC3D is presented in detail. The numerical modelis validated against the small-scale tests on laterally loaded, non-slender pilespresented in Part II of the thesis.

• Results – A parametric study on the initial slope of p–y curves for piles in sandis presented. The parametric study is conducted by means of the numericalmodel. Based on the parametric study, a modified expression for the initialslope of p–y curves for piles in sand is presented. The modified expressionaims at improving the prediction of the behaviour of monopiles exposed toserviceability limit state (SLS) loads. Although the modified expression hasbeen determined so the pile behaviour can be predicted accurately for SLS-loads, the procedure used for the determination of the modified expression canwith minor changes be used for the determination of a modified expressionsuitable for other limit states.

• Example – Horns Rev 1 – The predicted pile behaviour when employingthe modified expression for the initial slope of p–y curves and the initial slopeof p–y curves as suggested by O’Neill and Murchison (1983), respectively, are

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compared. Further, these predictions are compared with the results from three-dimensional analysis in FLAC3D. The comparison is made for a monopileemployed as the foundation for an offshore wind turbine at the Horns Rev 1Offshore Wind Farm.

3.4 Part IV – Design of offshore monopiles unprotectedagainst scour

Local erosion can take place around monopile foundations in the offshore environ-ment. Hence, local scour holes can be formed causing decreased stiffness and capac-ity of the foundation. Scouring is especially an issue when the upper layers of theseabed consists of sandy or silty soils. The scour phenomena has been investigatedby several researchers, for instance, Breuser et al. (1977), Sumer et al. (1992a),Sumer et al. (1992b) and Sumer et al. (1993). Local scouring can lead to scourdepths of up to approximately 2.0D. Hence, local scouring significantly decreasesthe stiffness and capacity of the foundation. Offshore monopiles can therefore bedesigned either with or without scour protection. If an offshore monopile is designedwithout scour protection, the monopile needs extra embedded length to account forthe decrease in stiffness and capacity caused by the local scouring.

The local scour depth around monopiles unprotected against the development ofscour depends on factors such as the pile diameter, the water depth, the sea condi-tions and the soil properties. Further, the scour depth does not change momentarily.Therefore, the scour depth depends on the variation with time of the current veloc-ity, the water depth and the wave height. An equilibrium scour depth exists for agiven sea condition. Generally, the equilibrium scour depth is large when currentsare dominating and small when waves are dominating. The process in which thescour hole decreases is denoted backfilling. The knowledge regarding the backfillingprocess is currently rather limited. Hartvig et al. (2010) studied the time scale ofbackfilling and the shape of the scour hole during the backfilling process throughsmall-scale testing. This part of the Ph.D. thesis consists of two scientific publica-tions: the paper ”Experimental Evaluation of Backfill in Scour Holes around OffshoreMonopiles” and the paper ”Assessment of scour design for offshore monopiles un-protected against scour”. The paper, ”Experimental Evaluation of Backfill in ScourHoles around Offshore Monopiles”, presents a large-scale tests on the backfillingprocess around a vertical pile in waves. Both the time scale of backfilling as wellas the properties of the backfilled soil material is evaluated through the large-scaletest. An overview of the paper is given below:

• Introduction – The background for the paper is briefly stated.

• Scour phenomenon – A short review of the present knowledge regardingscour/backfilling around vertical offshore piles is presented.

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• Test set-up – The test set-up employed for the backfill test at the large waveflume (GWK) at the coastal research centre (FZK) in Hannover, Germany ispresented. The presentation includes the preparation of the initial scour hole,the water led-in, the wave generation as well as information concerning thetaken soil samples and the conducted cone penetration tests.

• Results – The test results regarding the time-scale of backfilling for piles inwaves and the relative density of the backfilled soil material are presented.Further, the impact of the test results on the design of offshore monopilesunprotected against the development of scour is shortly discussed.

The paper, ”Assessment of scour design for offshore monopiles unprotected againstscour”, presents an adaptive scour design approach in which the variation of scourdepth with time and sea conditions is considered. It should be emphasised thatfurther research concerning the backfill process is needed before the adaptive scourdesign approach can be put into practice. The purpose of the adaptive scour de-sign approach is merely to illustrate the potential savings that can be obtained byaccounting for the variation in scour depth with time when designing monopile foun-dations that are unprotected against scour development. The outline of the paperis as follows:

• Introduction – The design of monopiles for offshore wind turbines and thescour/backfilling phenomena around vertical piles in waves is described.

• Review of the scour/bacfkilling phenomena – A review of the scourand backfilling phenomena for vertical piles in the offshore environment ispresented. The review considers the equilibrium scour depth, the predictionof the variation of scour depth with time, and the properties of the backfilledsoil material.

• Adaptive scour design – An adaptive scour design approach is presented.The design approach takes the variation of scour depth with time and theproperties of the backfilled soil material into account.

• Example – Design of monopile foundations for offshore wind tur-bines based on revised scour adaptive approach – The fatigue limitstate design and the ultimate limit state design of a monopile foundation foran offshore wind turbine is assessed for varying assumptions regarding thescour/backfilling conditions. The Horns Rev 1 Offshore Wind Farm has beenemployed as example.

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CHAPTER 4

Conclusions

Offshore wind energy is a competitive and a largely untapped source of renewableenergy. Hence, offshore wind energy plays a major role in the attempt to breakthe dependence on fossil fuels and in trying to reduce the human-induced carbonemission. The present Ph.D. thesis aims at improving the knowledge regarding thebehaviour of laterally loaded, non-slender piles situated in the offshore environment.This can enable the construction of low-risk and low-cost monopile foundationsfor offshore wind turbines and hereby contribute to improved competitiveness foroffshore wind energy. The Ph.D. thesis has been divided into four parts. Three ofthese parts deal with topics within the field of geotechnical engineering. The fourthresearch topic concerns both geotechnical engineering and coastal engineering.

In this chapter, the major contributions and main conclusions from the Ph.D. re-search project are summarised.

4.1 Part I – Review of laterally loaded piles in sand

In this part of the Ph.D. thesis, a litterature review of the present knowledge regard-ing the behaviour of laterally loaded piles has been presented. In the review, theWinkler approach and the p–y curve formulation originally proposed by O’Neill andMurchison (1983) have been used as reference points. The p–y curve formulationproposed by O’Neill and Murchison (1983) are based primarily on physical modellingon flexible piles. The monopiles used for the foundation of todays offshore wind tur-bines are non-slender, and therefore the applicability of the p–y curve formulation byO’Neill and Murchison (1983) can be questioned. Several limitations/uncertaintiesconcerning the p–y curve formulation proposed by O’Neill and Murchison (1983)

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Conclusions

were found and addressed: the shearing force between soil layers; the ultimate soilresistance; the influence of vertical pile load on the lateral soil response; the effect ofsoil-pile interaction; the effect of diameter on the initial stiffness of p–y curves; thechoice of horizontal earth pressure coefficient; the shearing force at the pile-toe; theshape of p–y curves; the effect of layered soil; the effect of long-term cyclic loading;and the effect of scour on the soil-pile interaction. Of these uncertainties and limita-tions, especially the effect of diameter on the initial stiffness of p–y curves, the effectof long-term cyclic loading on the accumulated pile rotation and on the foundationstiffness, and the effect of scour on the soil-pile interaction are important for thedesign of monopile foundations for offshore wind turbines.

For offshore wind turbines, it is of great interest to enable accurate predictions of thefoundation stiffness, so the rotation of the foundation and the natural frequenciesof the wind turbine can be predicted accurately. Therefore, it is also importantto be able to determine the initial stiffness of p–y curves for laterally loaded pilesin sand with high accuracy. The initial stiffness of p–y curves for laterally loadedpiles in sand has been investigated by several researchers. Terzaghi (1955), Vesic(1961), Reese et al. (1974), Ashford and Juirnarongrit (2005) concluded that theinitial stiffness is independent of the pile diameter. In contrast, Carter (1984) andLing (1988) found that the the initial stiffness is linearly proportional to the pilediameter. Further, both a linear and a non-linear effect of the depth below seabedon the initial stiffness has been suggested. Hence, more research is needed to enableaccurate predictions of the stiffness of monopile foundations in sand.

Offshore wind turbines are exposed to long-term cyclic loading due to primarily windand waves. It is therefore important to include the effect of long-term cyclic loadingon the soil-pile interaction. This has been investigated by several researchers bymeans of either small-scale testing or by implementing results from cyclic triaxialtests in three-dimensional numerical models.

For monopile foundations for offshore wind turbines, the pile behaviour for long-termcyclic loading is of great interest when determining the accumulated tilt of the foun-dation and when predicting the time variation of the first natural frequency of thestructure. Cyclic loading is only in a very simplified manner incorporated in the p–ycurve formulations proposed by O’Neill and Murchison (1983). The accumulationof pile deflection due to long-term cyclic loading have been investigated by meansof both numerical modelling and small-scale tests. Most researchers conclude thatthe pile deflection accumulates exponentially with the number of cycles. Further,factors such as the relative density, the ratio between the cyclic load amplitude andthe static capacity as well as the ratio between the maximum and minimum loadduring a load cycle affect the accumulated rotation.

For random cyclic loading, contradicting conclusions have been presented. For in-stance, LeBlanc et al. (2010b) found that the accumulated pile rotation is indepen-dent of the loading sequency, while Peralta and Achmus (2010) concluded that the

20 Sørensen

Conclusions

loading sequence influences the accumulated pile rotation.

Only a limited number of researchers have investigated the variation of the stiffnessof the soil-pile interaction with cyclic loading. LeBlanc et al. (2010a) suggestedthat the stiffness increases logarithmically with the number of cycles independentlyof the relative density of the soil. However, they only considered piles in loose tomedium dense sand. Hence, further research is needed to enable a better predictionof the pile behaviour for long-term cyclic loading. Especially full-scale tests couldlead to a better understanding of this topic.

Both global and local scour will take place for offshore piles installed without scourprotection. The scour depth will depend on the sea conditions and therefore thescour depth will vary with time. The presence of global and local scouring aroundoffshore monopiles lead to decreased stiffnesses and capacities of monopile founda-tions. Design regulations such as ISO (2007) and API (2010) suggest a simplifiedmethod for modification of p–y curves due to scouring. However, the method relieson empirical consideration and needs to be validated. Lin et al. (2010) pointedout that the soil becomes overconsolidated when scouring takes place. Hence, thecoefficient of horizontal earth pressure and the friction angle of the soil increases.Lin et al. (2010) present a method in which the p–y curves can be modified so thatthe overconsolidation of the soil is taken into account.

Due to changing sea conditions, the depth of the scour holes around unprotectedoffshore piles will vary with time. Knowledge is needed regarding the properties ofbackfilled soil material. Such knowledge can be essential for optimising the fatiguedesign of monopiles that are designed unprotected against scour development.

4.2 Part II – Physical modelling of laterally loaded,

non-slender piles

A new and innovative test set-up for the small-scale testing of laterally loaded pileshas been developed. The new test set-up for laterally loaded piles enables the appli-cation of an overburden pressure to the soil. Traditionally, when conducting small-scale tests at normal stress level, the friction angle will be high and the Young’smodulus of elasticity for the soil will be low due to low effective stresses. Further-more, accurate determination of these parameters is very difficult for small-scaletests, since triaxial tests at confining pressures less than 5-10 kPa are subject tolarge uncertainties. When an overburden pressure is applied to the soil, the uncer-tainties mentioned above can be avoided. The new test set-up has been validatedbased on a large test series on laterally loaded piles. Small-scale tests with and with-out overburden pressure applied to the soil have been conducted for both staticallyloaded and cyclically loaded, non-slender piles. The main findings of the physicalmodelling were as follows:

Sørensen 21

Conclusions

• The test set-up worked as planned. Generally, the uncertainties related to thetest set-up was found to decrease when overburden pressure was applied to thesoil.

• Rather similar load-displacement relationships was found for tests on open-ended and closed-ended piles, respectively. Therefore, the shear and normalstresses acting on the pile toe only slighly affected the behaviour of the testpiles.

• The pile stiffness and the pile capacity increases significantly when applyingan overburden pressure to the soil.

• A scaling law has been proposed for the behaviour of non-slender, laterallyloaded piles. The scaling law captures the behaviour of piles with overburdenpressure applied to the soil. The scaling law was validated against the small-scale tests for loading eccentricities of 0.74 Lp to 1.54 Lp and slenderness ratiosof 3 to 6.

• In a normalised plot of the moment-rotation relationship, the tests with over-burden pressure generally has a lower stiffness than the tests without overbur-den pressure applied to the soil. Further, the pile rotation at failure was foundto increase for increasing value of the overburden pressure. These findings isanalogue to the relationship between the strain at failure and the confiningstress in triaxial tests.

• For the tests on cyclically loaded piles, the formation of a gap behind the pilewas found to depend on whether overburden pressure has been applied to thesoil. The gap was significantly more pronounced for the tests with overburdenpressure applied to the soil than for the tests without overburden pressureapplied to the soil. The reason for this observation needs further examination.Further, the presence of a gap behind large-scale piles installed in cohesionlesssoils needs to be investigated.

• During unloading for the cyclic tests, friction along the sides of the pile wasobserved. The friction, however, only had a moderate value. This indicatesthat the pile capacity is governed primarily by frontal resistance.

• Comparison of the load-displacement relationships for static and cyclic loadingindicated that the accumulated pile displacement is primarily governed by thelargest applied loading. Similarly, LeBlanc et al. (2010b) also concluded thatthe accumulated pile displacement depends primarily on the largest appliedloading.

22 Sørensen

Conclusions

4.3 Part III – Numerical assessment of the initial partof p–y curves for piles in sand

In the litterature review presented in Part I of the thesis, it was pointed out thatseveral researchers have investigated the initial stiffness of p–y curves for piles insand, however, with contradictory conclusions. For offshore wind turbines, it is amajor concern to enable accurate estimations of the foundation stiffness. There-fore, accurate predictions of the initial stiffness of p–y curves for piles in sand issimilarly a major concern. In the present part of the thesis, a numerical study onthe initial slope of p–y curves for piles in sand has been presented. The aim of thenumerical study has been to investigate which paramers affect the initial slope ofthe p–y curves for piles in sand. The commercial three-dimensional finite differenceprogram FLAC3D was employed for the numerical study. The numerical model wassuccesfully calibrated/validated against the experimental tests on laterally loadedpiles presented in Part II of the thesis.

The initial slope of p–y curves for piles in sand was found to depend on the depthbelow seabed, the pile diameter and the Young’s modulus of elasticity for the soil.The friction angle, the loading eccentricity and the pile flexibility were found not toaffect the initial slope of the p–y curves. A modified expression for the initial slope ofp–y curves for piles in sand was fitted to the numerical simulations so that accuratepredictions of the pile behaviour for piles exposed to serviceability limit state loadshas been enabled. The modified expression is not expected to be well-suited wheninvestigating the first natural frequency of an offshore wind turbine. However, byimplementation of an associative model capturing the small strain behaviour of soil,a similar method can be used to determine values for the initial slope of p–y curveswhich should be employed for accurate determination of the first natural frequency.

4.4 Part IV – Design of offshore monopiles unprotectedagainst scour

Around offshore piles situated in cohesionless soils, currents and waves can lead tothe development of scour holes. The size of these scour holes will vary with timegiven that the sea conditions affect the equilibrium scour depth. Much research hasbeen conducted so far on the equilibrium scour depth for varying sea conditions.Furthermore, the time scale of the process in which the scour depth increases hassimilarly been studied intensively. However, little knowledge exists regarding thetime scale of the process in which the scour depth decreases (backfilling). Further-more, no knowledge exists regarding the relative density of backfilled soil material.The variation of scour depth with time as well as the relative density of the back-filled soil material have a significant influence on the stiffness and capacity of offshore

Sørensen 23

Conclusions

pile foundations. A large-scale test on backfilling around piles in waves has beenconducted at the large wave flume (GWK) at the coastal research centre (FZK) inHannover, Germany. Both the time scale and the relative density of the backfilledsoil material has been investigated. Due to limited time available at the large waveflume, it has only been possible to conduct one test on the backfill around piles inwaves. Therefore, the conclusions of the study on the backfilling process for pilesin waves are only indicative and further research is needed to validate the findings.The following results were observed:

• The normalised time scale of backfilling determined in the large-scale test wassignificantly smaller than the normalised time scale of backfilling for the small-scale tests reported by Hartvig et al. (2010). The Shields parameter and theKeulegan-Carpenter number for the small- and large-scale tests were of similarvalues. Therefore, the dependency of the time scale on these parameters cannotexplain the significant difference in the normalised time scale. The large-scaletest hereby demonstrates that more research is needed regarding the time-scaleof backfilling around piles in waves. Further, the scaling of the time scale ofbackfilling needs further investigation.

• The relative density of the backfilled soil material was found to be approxi-mately 80 % at the new soil surface and decreasing with depth to 65 % atthe bottom of the original scour hole. The relative density was determinedafter the waves were stopped. Therefore, the variation of the relative densitywith time has not been investigated. Further, it is not known whether thebackfilled soil material underwent liquefaction during the backfilling process.Further research is needed regarding the influence of the Shields parameter,the Keulegan-Carpenter number and time on the backfilling process.

• The backfilling process around piles in combined waves and current needs tobe investigated.

• Since, the findings of Hartvig et al. (2010) contradicts the results of the large-scale test, the backfilling process around piles needs to be investigated througha combination of small- and large-scale tests.

A desk study has been conducted concerning the influence of the time variationof scour depth and the relative density of backfilled soil material on the design ofmonopiles for offshore wind turbines. The soil profile, foundation geometry and windturbine geometry of the Horns Rev 1 Offshore Wind Farm has been employed in thedesk study. From the desk study, the variation of the scour depth with time as wellas the properties of the backfilled soil material were shown to have a major impacton especially the fatigue life of an offshore wind turbine. Several assmuptions havebeen employed in the desk study. Therefore, the desk study should only be seen asindicative. However, based on the desk study, it can be concluded that accounting

24 Sørensen

Conclusions

for the time variation of scour depth in the design can reduce the foundation costssignificantly. It is emphasised that further research is needed regarding the timescale of backfill around piles and regarding the properties of backfilled soil in orderto enable a more optimised foundation design.

4.5 Concluding remarks

The research project in the present Ph.D. thesis was aimed at improving the designof offshore monopiles used as the foundation for offshore wind turbines. The be-haviour of offshore non-slender, large-diameter offshore piles were studied through acombination of physical and numerical modelling. The outcome of the research haslead to an improved understanding of the behaviour of offshore piles and hence theresearch contributes to an improved economic feasibility of offshore wind energy.

Sørensen 25

Conclusions

26 Sørensen

CHAPTER 5

References

API, 2000. Recommended practice for planning, designing, and constructing fixedoffshore platforms - Working stress design, API RP2A-WSD, American PetroliumInstitute, Washington, D.C., 21. edition.

Ashford S. A., and Juirnarongrit T., March 2003. Evaluation of Pile Diameter Effecton Initial Modulus of Subgrade Reaction. Journal of Geotechnical and Geoenviron-mental Engineering, 129(3), pp. 234-242.

Bhushan, K., Lee, L.J., and Grime, D. B., 1981. Lateral Load Tests on Drilled Piersin Sand. Drilled Piers and Caissons, ASCE, pp. 114.131.

Breuser, H., Nicolett, G., and Shen, H., 1977. Local scour at cylindrical piers.Journal of Hydraulic Research, 15, pp. 211-252.

Carter D. P., 1984. A Non-Linear Soil Model for Predicting Lateral Pile Response.Rep. No. 359, Civil Engineering Dept,. Univ. of Auckland, New Zealand.

Cox W. R., Reese L. C., and Grubbs B. R., 1974. Field Testing of Laterally LoadedPiles in Sand. Proceedings of the Sixth Annual Offshore Technology Conference,Houston, Texas, paper no. OTC 2079.

DNV, 2010. Design of Offshore Wind Turbine Structures, DNV-OS-J101. DetNorske Veritas, Det Norske Veritas Classification A/S.

Fan C. C., and Long J. H., 2005. Assessment of existing methods for predictingsoil response of laterally loaded piles in sand. Computers and Geotechnics 32, pp.274-289.

Sørensen 27

References

Gudehus G., and Hettler A., 1983. Model Studies of Foundations in Granular Soil,In Development in Soil Mehcanics and Foundation Engineering 1, pp. 29-63.

Hartvig P. A., Thomsen J. M., and Andersen T. L., 2010. Experimental study of thedevelopment of scour & backfilling. Coastal Engineering Journal, 52, pp. 157-194.

ISO, 2007. Petroleum and natural gas industries - Fixed steel offshore structures.International Organization for Standardization, ISO 19902:2007 (E).

LeBlanc C., Houlsby G. T., and Byrne B. W., 2010a. Response of Stiff Piles toLong-term Cyclic Loading, Geotechnique, 60(2), pp. 79-90.

LeBlanc C., Houlsby G. T., and Byrne B. W., 2010b. Response of stiff piles torandom two-way lateral loading. Geotechnique, 60(9), pp. 715-721.

Lesny K., and Wiemann J., 2006. Finite-Element-Modelling of Large DiameterMonopiles for Offshore Wind Energy Converters. Geo Congress 2006, February 26to March 1, Atlanta, GA, USA.

Lin C., Bennett C., Han J., and Parsons R. L., 2010. Scour effects on the response oflaterally loaded piles considering stress history of sand. Computers and Geotechnics,37, pp. 1008-1014.

Ling L. F., 1988. Back Analysis of Lateral Load Test on Piles. Rep. No. 460, CivilEngineering Dept., Univ. of Auckland, New Zealand.

Mansur, C. I., Hunter, A. H., and Davisson, M. T., 1964. Pile Driving and LoadingTests - Lock and Dam No 4, Arkansas River and Tributaries, Fruco and Associates,St. Louis, Missouri.

Murchison J. M., and O’Neill M. W, 1984. Evaluation of p–y relationships in cohe-sionless soils. Analysis and Design of Pile Foundations. Proceedings of a Symposiumin conjunction with the ASCE National Convention, pp. 174-191.

O’Neill M. W., Murchison J. M., 1983. An Evaluation of p-y Relationships in Sands.Research Report No. GT-DF02-83, Department of Civil Engineering, University ofHouston, Houston, Texas, USA.

Peralta P., and Achmus M., 2010. An experimental investigation of piles in sandsubjected to lateral cyclic loads, Physical Modelling in Geotechnics, Taylor & FrancisGroup, London.

Reese L. C., Cox W. R., and Koop, F. D., 1974. Analysis of Laterally Loaded Pilesin Sand. Proceedings of the Sixth Annual Offshore Technology Conference, Houston,Texas, 2, paper no. OTC 2080.

Sumer, B. M., Christiansen, N., and Fredsøe, J., 1992a. Time scale of scour arounda vertical pile. Third International Offshore and Polar Engineering Conference,

28 Sørensen

References

ISOPE, San Francisco, USA, pp. 308-315.

Sumer, B. N., Fredsøe, J., and Christiansen, N., 1992b. Scour around Vertical Pilein Waves. Journal of Waterway, ort, Coastal and Ocean Engineering, 118(1), pp.15-31.

Sumer, B. M., Christiansen, N., Fredsøe, J., 1993. Influence of cross section on wavescour around piles. Journal of Waterway, Port, Coastal and Ocean Engineering,119(5), pp. 477-495.

Terzaghi K., 1955. Evaluation of coefficients of subgrade reaction. Geotechnique,5(4), pp. 297-326.

Vesic A. S., 1961. Beam on Elastic Subgrade and the Winkler’s Hypothesis. Pro-ceedings of the 5th International Conference on Soil Mechanics and Foundation En-gineering, Paris, 1, pp. 845-850.

Winkler E., 1867. Die lehre von elasticzitat and festigkeit (on elasticity and fixity),Prague, 182 p.

Sørensen 29

References

30 Sørensen

CHAPTER 6

Enclosed scientific papers

Sørensen, S.P.H., Brødbæk, K.T., Møller, M. & Augustesen, A.H. (2012). Reviewof laterally loaded monopiles employed as the foundation for offshore wind turbines.DCE Technical Reports, No. 137, Department of Civil Engineering, Aalborg Uni-versity, Aalborg, Denmark.

Sørensen, S.P.H., Ibsen, L.B. & Foglia, A. (2012). Testing of Laterally Loaded RigidPiles with Applied Overburden Pressure. Submitted for publication.

Sørensen, S.P.H. & Ibsen, L.B. (2012). Experimental Comparison of Non-SlenderPiles under Static Loading and under Cyclic Loading in Sand. Proceedings of the22nd International Ocean and Polar Engineering Conference, XXII ISOPE, Rhodes,Greece.

Sørensen, S.P.H., Augustesen, A.H. & Ibsen, L.B. (2012). Revised expression forthe static initial part of p–y curves for piles in sand. Submitted for publication.

Sørensen, S.P.H., Ibsen, L.B. & Frigaard, P. (2010). Experimental Evaluation ofBackfill in Scour Holes around Offshore Monopiles. Proceedings of the 2nd Interna-tional Symposium on Frontiers in Offshore Geotechnics, II ISFOG, Perth, Australia,8-10 November 2010. Balkema Publishers, A.A. / Taylor & Francis, The Nether-lands, 2010, pp. 617-622.

Sørensen, S.P.H. & Ibsen, L.B. (2012). Assessment of Scour Design for OffshoreMonopiles Unprotected Against Scour. Submitted for publication.

Sørensen 31

Title:

Review of laterally loaded monopiles employed as the foundation for offshore windturbines.

Authors:

Sørensen, S. P. H., Brødbæk, K. T., Møller, M., and Augustesen, A. H.

Year of publication:

2012

Published in:

DCE Technical Reports, Department of Civil Engineering, Aalborg University, Aal-borg, Denmark, No. 137.

Number of pages:

48

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K0x tanϕtr sin β

tan(β − ϕtr) cosα. /0

+ γ′xtan β

tan(β − ϕtr)(D − x tan β tanα)

+ γ′x(K0x tanϕtr(tanϕtr sinβ − tanα)

−KaD)

pcd = KaDγ′x(tan8 β − 1) . 10+K0Dγ′x tanϕtr tan

4 β

pcs +3 4#$+( #& 35#$$)6 ('7&53 #,( pcd #&(''7 ('7&538 γ′ +3 &5' '9' &+4' %,+& 6'+-5&8#,( ϕtr +3 &5' #,-$' ): +,&'*,#$ :*+ &+),;#3'( ), &*+#<+#$ &'3&3= >5' :# &)*3 α #,(β ?'#3%*'( +, ('-*''3 #, ;' '3&+?#&'( ;@&5' :)$$)6+,- *'$#&+),32

α =ϕtr

2. !0

β =45◦ +ϕtr

2. A0B', '8 &5' #,-$' β +3 '3&+?#&'( # )*(+,-&) C#,D+,'E3 &5')*@ 65+ 5 +3 4#$+( +: &5'

7+$' 3%*:# ' +3 #33%?'( 3?))&5= >5' :# &)*α ('7',(3 ), &5' :*+ &+), #,-$' #,( $)#(&@7'= B)6'4'*8 &5' '9' & ): $)#( &@7' +3,'-$' &'( +, . !0= Ka #,( K0 #*' &5' )':FG +',&3 ): # &+4' 5)*+H),&#$ '#*&5 7*'33%*'#,( 5)*+H),&#$ '#*&5 7*'33%*' #& *'3&8 *'F37' &+4'$@2

Ka = tan2(45 −ϕtr

2) . I0

K0 = 0.4 . J0>5' 4#$%' ): K0 ('7',(3 ), 3'4'*#$ :# F&)*38 '=-= &5' :*+ &+), #,-$'8 ;%& . J0 ()'3,)& *'K' & &5#&=>5' &5')*'&+ #$ %$&+?#&' *'3+3&#, '8 pc8 #3:%, &+), ): ('7&5 +3 35)6, +, G-= =L3 35)6,8 &5' &*#,3+&+), ('7&5 +, *'#3'36+&5 (+#?'&'* #,( #,-$' ): +,&'*,#$ :*+ F&+),= B', '8 :)* 7+$'3 6+&5 # $)6 3$',('*F,'33 *#&+) &5' &*#,3+&+), ('7&5 ?+-5& #7F7'#* :#* ;','#&5 &5' 7+$'F&)'=M@ )?7#*+,- &5' &5')*'&+ #$ %$&+?#&' *'F3+3&#, '8 pc8 6+&5 &5' :%$$F3 #$' &'3&3 #&N%3&#,- O3$#,(8 P)< '& #$= . QJ!0 :)%,(# 7))* #-*''?',&= >5'*':)*'8 # )'R +',&A +3 +,&*)(% '( 65', #$ %$#&+,- &5' # F&%#$ %$&+?#&' 3)+$ *'3+3&#, '8 pu8 '?7$)@'(+, &5' pSy %*4' :)*?%$#&+),32

pu = Apc . T0>5' 4#*+#&+), ): &5' )'R +',& A 6+&5,),F(+?',3+),#$ ('7&58 x/D8 ('7',(3 ),65'&5'* 3&#&+ )* @ $+ $)#(+,- +3 #77$+'(=>5' 4#*+#&+), ): A +3 35)6, +, G-= /#=>5' (':)*?#&+), #%3+,- &5' %$&+?#&' 3)+$*'3+3&#, '8 yu8 := G-= T8 +3 ('G,'( #33D/80=p y "#$% &'#(")*+,'->5' 3)+$ *'3+3&#, ' 7'* %,+& $',-&58 pm8 #&ym = D/608 := G-= T8 #, ;' #$ %$#&'(#32

pm = Bpc . Q0B +3 # )'R +',& ('7',(+,- ), &5' ,),F(+?',3+),#$ ('7&5 x/D8 #,( 65'&5'* 3&#F&+ )- @ $+ $)#(+,- +3 ),3+('*'(= >5' 4#F*+#&+), ): B 6+&5 ,),F(+?',3+),#$ ('7&5 +3

!

0 1 2 3 4 5 6

x 104

0

5

10

15

20

25

30

pc [kN/m]

x [

m]

φtr=30

°

φtr=40

°

!" D = 1.0 0 1 2 3 4 5 6

x 105

0

20

40

60

80

100

120

pc [kN/m]

x [

m]

φtr=30

°

φtr=40

°

#" D = 4.0 $%&'() **+ !"#$%#&' )* +*&' )&# %#,',&)- #. pc.), /+- &'$- $/ &"# 0#1&"2 γ′= 10 345 3 "), 6##-+,#0 &$ 1*$& &"# 78+%#2 !"# &%)-,'&'$- 0#1&", )%# )%3#0 9'&" '% *#,2"##$%&'(&)* "+ ,-. /0. 1)+ )3 4 #" #5(*6"+- "% &(7)+ "+&5 ( 5$+& 04 ( ')*$ &"5+ 58&9) +5+6*":)+%"5+(# 5+%&(+&% A (+* B.;4 #" #5(*"+- 5+#4 (<) &% &9) p=y $'>)%%"-+", (+&#4 (& *)?&9% 8'5: &9) %5"# %$'8( )&5 x@D = 3.5.A9) %#5?) 58 &9) "+"&"(# %&'("-9& #"+)3 p1(% %95B+ "+ ,-. C3 *)?)+*% 5+ &9) "+"&"(#:5*$#$% 58 %$0-'(*) ')( &"5+3 k3 (+* &9)*)?&9 x. A9"% "% *$) &5 &9) 8( & &9(& &9) "+6%"&$ D5$+-E% :5*$#$% 58 )#(%&" "&4 (#%5 "+6 ')(%)% B"&9 *)?&9. F$'&9)'3 "& "% (%%$:)*&9(& &9) %#5?) 58 &9) "+"&"(# %&'("-9& #"+)"+ ')(%)% #"+)('#4 B"&9 *)?&9 %"+ ) #(05'(6&5'4 &)%& %95B%3 &9(& &9) "+"&"(# %#5?) 58 &9)%&')%%6%&'("+ $'>) 85' %(+* "% ( #"+)(' 8$+ 6&"5+ 58 &9) 5+,+"+- ?')%%$')3 8. A)'G(-9"H I!!J. A9) "+"&"(# &(+-)+& %&"<+)%% 58 &9)

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py01)$ &'&(&2, %("2&.)( ,&'$ &% .&#$' 345p1(y) = E∗

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!"#$%&! '!()%$* +,-

.!"/0 $1!

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43/&! $1!

0#$!2 $#3"!

56 7//)!

89

: 8: ;: <: 9: =::

9::::

>::::

<::::

?::::

;::::

@::::

8::::

=::::

:

8A @: @< ;: ;?

7//)! B!'%CD '!()! E!()! 56 '!()!

F2%G$%/( #(H"!I +'!H2!!)-

J

+JK#LD-

!"#$% &'( !"#!$#%& %' #&#$#!( )%*+(+, %' ,+-./"!*0 "0! $#%& k !, '+& $#%& %' "0(!$#20 *0&,#$34!'$0" 567 89:::;<D-% %J+#*)'( ?'0 *-% F#0#"'2#3 p23 ?. B,.H3 )$ &%$ 0)"%& "EKp2(y) = Cy1/n 78 :A-%0% C #(& n #0% '($*#(*$. D-% '($*#(*$ #(& *-% F#0#"'2#L$ $*#0* F')(*7yk3pk: #0% &%*%0>)(%& "E *-% ?'22'A)(, 0)*%0)#Kp1(yk) = p2(yk) 788:p2(ym) = p3(ym) 78C:

∂p2(ym)

∂y=

∂p3(ym)

∂y78M:D-% '($*#(*$ #( *-%( "% #2 +2#*%& "EK

n =pmmym

78N:C =

pm

y1/nm

78!:yk = (

C

kx)n/(n−1) 78O:A-%0% m )$ *-% $2'F% '? *-% 2)(%3 p3.

! "#$%&' (PL;%)22 #(& Q+0 -)$'( $+,,%$*%& # >'&1)B%& ?'0>+2#*)'( '? *-% pRy +0@%$. D-%>'&)B%& %GF0%$$)'( )$ +00%(*2E 0% '>1>%(&%& )( *-% &%$),( 0%,+2#*)'($3 %.,. 45678999: #(& /;< 789 9:. 6( *-%)0 >'&)B%&pRy +0@% ?'0>+2#*)'(3 *-% #(#2E*) #2 %G1F0%$$)'($ ?'0 *-% +2*)>#*% $')2 0%$)$*#( %37 8: #(& 7 C:3 #0% #FF0'G)>#*%& +$)(, *-%&)>%($)'(2%$$ F#0#>%*%0$ C13 C2 #(& C3K

pu = min

(

pus = (C1x+C2D)σ′

v

pud = C3Dσ′

v

)78H:D-% '($*#(*$ C13 C2 #(& C3 #( "% &%1*%0>)(%& ?0'> B,. M.25 30 35 40 450

1

2

3

4

5

6

friction angle, φ [degrees]

C1 a

nd

C2 [

−]

2C

1C

)*+ C1 !&* C2<25 30 35 40 450

20

40

60

80

100

120

friction angle, φ [degrees]

C3 [

−]

3C

),+ C3< !"#$% &-( !"#!$#%& %' $=0 >!"!)0$0", C14 C2!&* C3 !, '+& $#%& %' !&/(0 %' #&$0"&!( '"# $#%&4!'$0" 567 89:::;<4 -EF%0"'2) ?'0>+2# )$ +$%& *' &%$ 0)"%*-% 0%2#*)'($-)F "%*A%%( $')2 0%$)$*#( %#(& F)2% &%S% *)'( )($*%#& '? # F)% %A)$%?'0>+2#*)'( #$ F0'F'$%& "E >%*-'& 4Kp(y) = Apu tanh

(

kx

Apuy

) 78T:

!"#$ &$' ($)* + &,-. $(*#$/ 0$ .$*$/12()$. 3/&2 456 78 &/ 09:A =

(

3.0− 0.8HD ≥ 0.9 ; <*8*( -&8.()5

0.9 ; 9 -( -&8.()5 )=>?@A() $:dp

dy|y=0= Apu

kxApu &<#2( kxyApu

)|y=0= kx => @*#$ pBy ,/C$D< ()(*(8- <-&E$ (< *#$) <(2(-8/,<()5 *#$ *F& 2$*#&.<; 36 =7?@6 +-<& *#$,EE$/ 0&,). &3 <&(- /$<(<*8) $ F(-- 8EE/&G1(28*$-9 0$ *#$ <82$6 H&F$C$/; *#$/$ (<8 &)<(.$/80-$ .(I$/$) $ () <&(- /$<(<*8) $E/$.( *$. 09 *#$ *F& 2$*#&.< F#$) &)1<(.$/()5 *#$ E(-$ .$J$ *(&) 0$*F$$) yk 8).

yu 8< <#&F) () 456 K6 "#$ <&(- E8/82$*$/<3/&2 *806 #8< 0$$) ,<$. *& &)<*/, * *#$pBy ,/C$< <#&F) () 456 K6

0 0.05 0.1 0.15 0.2 0.25 0.3 0.350

500

1000

1500

2000

2500

3000

y [m]

p [

kN

/m]

Method A

Method B

k

m

u

x = 10 m

x = 5 m

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@ MMTD ,% '33%(&$ )*% 4$% '2 @QID7@!AD 2',Pmax0 τmax0 η #(& ξ;

Pmax = K2

pγx @QIDτmax = Kγx tan(δ) @QBD

η = 0.8 @!MDξ = 1.0 @!ADS*#(. %) #+; @ MMTD /,'/'$% )*% $-&% 2,- 7)-'( #(& 2,'()#+ ,%$-$)#( % )' =#,1 5-)*&%/)* $-3-+#, )' )*% =#,-#)-'( /,'/'$%& >1E,#$#& #(& J*#,- @ABBBD; <*%1 '3/#,%&)*%-, 3%)*'& 5-)* $3#++7 #(& +#,.%7$ #+%)%$)$ #(& 2'4(& )*%-, 3%)*'& )' >% $+-.*)+1 '($%,=#)-=% #$ )*% /-+% #/# -)-%$ #+ 47+#)%& >1 )*%-, /,'/'$%& 3%)*'& -( #=%,7#.% 5#$ I U $3#++%, )*#( )*% 3%#$$4,%&/-+% #/# -)-%$; R4,)*%,0 /#,#3%)%,$ $4 *#$ )*% %3>%&&%& /-+% +%(.)*0 )*% $+%(&%,7(%$$ ,#)-'0 )*% % %(),- -)1 ,#)-'0 eVL0 #(&)*% 2,- )-'( #(.+% &-& (') #W% ) )*% # 47,# 1 '2 )*%-, 3%)*'&0 2; L.; ;<*% -3/',)#( % '2 -( +4&-(. $-&% 2,- )-'(-( )*% 2',34+#)-'( '2 pXy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

!

!"#$% &'( !"# % &' #%" "()*"++,&-+ &' ./#,01#" *"+,+#1- " )*&)&+"2 34 51-+"- "# 1/6 789:8;< =*&0+789:>;< ?"#*1+&@,#+ 1-2 AB1*2 789CD;< E"4"*%&' "# 1/6 789F8; 1-2 ?*1+12 1-2 G%1*, 78999;< H%1-I "#1/6 7DJJK;60 1 2 3 4 5 6

−40

−20

0

20

40

60

Pile length, L [m]

Err

or

[%]

4 6 8 10 12 14 16−40

−20

0

20

40

60

Slenderness ratio, L/D [−]

Err

or

[%]

0 1 2 3 4−40

−20

0

20

40

60

Eccentricity ratio, e/L [−]

Err

or

[%]

30 35 40 45 50−40

−20

0

20

40

60

Friction angle, φ [°]

Err

or

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35'3'1$* ?% 8((52+) :.KKO=E ,#- # -1?+1$* ') "5-+C-+/ "$1"-)B '& '#$1-')/$111'-/E ,+1 +33/-$* "' $C35$11 "#$ 1"-N)$11*$B5+*+"-')6 G #2(1 $" +/6 :;!!K?= 35$>1$)"$* + 3+5+2$"5- +/ 1"(*% ') "#$ + (>2(/+"-') '& 3-/$ *$4$ "-') *($ "' % /- /'+*-)B -) ,#- # "#$ 3-/$ *-+2$"$5E "#$3-/$ /$)B"#E "#$ /'+*-)B $ $)"5- -"%E "#$5$/+"-@$ *$)1-"% +)* ζb ,+1 @+5-$* ,-"#-)D = 2.5 − 7.5 2E L = 20 − 40 2E e =0 − 40 2E 2$*-(2 *$)1$ "' *$)1$ 1+)*+)* ζb = 0 − 0.66 H'5 +// "#$ 1-2(/+"-')1')$>,+% /'+*-)B ,-"# ζc = 0 ,$5$ +33/-$*6P+1$* ') "#$ 3+5+2$"5- 1"(*% "#$% 35$>1$)"$* *$1-B) #+5"1 5$/+"-)B "#$ 5+"-' ?$>",$$) "#$ 1"+"- +)* % /- 3-/$ *$4$ "-'):+ (2(/+"-') 5+"$ '& *$&'52+"-')= ,-"# ζb&'5 @+5%-)B )(2?$51 '& /'+* % /$16 D#$%&'()* "#+" "#$ 3-/$ *-+2$"$5E "#$ $2?$*>*$* 3-/$ /$)B"#E +)* "#$ 5$/+"-@$ 1'-/ *$)>1-"% +N$ " "#$ + (2(/+"-') 5+"$ '& *$&'5>2+"-') "#5'(B# "#$-5 $N$ " ') "#$ 1"+"- 3-/$ +3+ -"% +)* #$) $ +/1' "#$-5 $N$ " ')"#$ )'52+/-9$* /'+*6Q$5+/"+ +)* G #2(1 :;!.!= ')*( "$* +1$5-$1 '& .>B "$1"1 ') ?'"# 4$C-?/$ +)*5-B-* 3-/$1 -) '5*$5 "' -)@$1"-B+"$ "#$ ?$>#+@-'(5 '& % /- /'+*$* 3-/$16 D#$ 3-/$*-2$)1-')1 ,+1 D = 60 − 63mm +)*L = 200 − 500mm6 D#$ 3-/$ 2+"$5-+/ $2>3/'%$* &'5 "#$ "$1"1 @+5-$* &5'2 1"$$/ "'#-B# *$)1-"% 3'/%>$"#%/$)$ :8RQS=6 D#$3-/$1 2+*$ '& 8RQS ?$#+@$* +1 1/$)*$53-/$1 *($ "' "#$ 1-B)-A +)"/% /',$5 T'()BJ12'*(/(1 '& $/+1"- -"% &'5 8RQS6 U)$>,+% % /- /'+*-)B ,-"# ζc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θs= Tb(ζb,ID)Tc(ζc)N

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1/0.31

+ (θsTbTc)1/0.31i Ni)

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Title:

Testing of Laterally Loaded Rigid Piles with Applied Overburden Pressure.

Authors:

Sørensen, S. P. H., Ibsen, L. B., and Foglia, A.


2012

Published in:

Submitted for publication.

Number of pages:

7

1

Testing of Laterally Loaded Rigid Piles with Applied Overburden Pressure Søren P. H. Sørensen, Lars B. Ibsen and Aligi Foglia

Department of Civil Engineering, Aalborg University

Aalborg, Denmark

ABSTRACT

Small-scale tests have been conducted for the purpose of investigating the quasi-static behaviour of laterally loaded, non-slender piles

installed in cohesionless soil. For that purpose, a new and innovative test setup has been developed. The tests have been conducted in a

pressure tank such that it was possible to apply an overburden pressure to the soil. Hereby, the traditional uncertainties related to low

effective stresses for small-scale tests has been avoided. A scaling law for laterally loaded piles has been proposed based on dimensional

analysis. The novel testing method has been validated against the test results by means of the scaling law.

KEY WORDS: Pile foundations; Model tests; Overburden pressure;

Earth pressure; Dimensional analysis; Sand.

INTRODUCTION

For offshore wind turbines, the monopile foundation concept is often

employed. Typically, the monopile foundation concept consists of an

open-ended steel tube, which is either drilled or driven into the seabed.

The pile diameter, D, and the embedded pile length, Lp, are usually in

the range of 4-6 m and 15-30 m, respectively. Hence, the slenderness

ratio, Lp/D, is in the order of four to seven, and therefore the piles

exhibit a rather rigid body motion.

The Winkler model approach is traditionally employed in the design

of offshore monopiles. In this approach, the interaction between the

soil and the pile is modelled by means of uncoupled non-linear

springs. The stiffness of the nonlinear springs is described by means of

p-y curves. These curves describe the soil resistance acting on the pile

wall as a function of the pile deflection. Design regulations of the

American Petroleum Institute, API (2000), and Det Norske Veritas,

DNV (2010), recommend the use of the p-y curve formulation

proposed by O'Neill and Murchison (1983) for piles situated in

cohesionless soils. The formulation has been validated by Murchison

and O'Neill (1984) through tests on piles with diameters up to

approximately 2 m and length to diameter ratios larger than 10. The

formulation has, however, not been validated for piles with Lp/D � 5

and D = 4-6 m. Therefore, further research is needed regarding the

behaviour and design of large-diameter, non-slender piles.

An extensive test programme has been conducted at Aalborg

University in order to investigate the behaviour of non-slender piles in

sand exposed to quasi-static lateral loading. Piles with diameters of 60

to 100 mm, embedded pile lengths of 240 to 500 mm and slenderness

ratios of 3 to 6 have been tested. Hence, the scale in comparison with

real monopiles is between 1:40 and 1:100. Traditionally, when small-

scale tests are conducted, the low effective stresses in the soil cause

significant scale-effects. The internal friction angle, �, and the

Young's modulus of elasticity for the soil, Es, depend heavily on the

effective stresses in the soil. Therefore, the average values of these

parameters for traditional 1-g small-scale tests deviate from the

average values of these parameters in the soil around full-scale

foundations. To avoid this, it is necessary to increase the effective

stresses in the soil. This can be accomplished by either testing in a

centrifuge or by testing in a pressure tank. The tests presented in this

paper have been conducted in a pressure tank in which an overburden

pressure of P0 = 0-100 kPa has been applied to the soil. For P0 = 100

kPa, the average vertical stress in the small-scale tests is slightly

higher than 100 kPa and similar to the average vertical effective stress

in the soil around a foundation with Lp � 20-25 m.

When applying an overburden pressure to the soil, the effective stress

distribution with depth becomes trapezoidal instead of triangular.

Hereby, the stress distribution for the small-scale tests with applied

overburden pressure is significantly different from the stress

distribution around full-scale piles. However, this difference can be

overcome by means of scaling.

In the present paper, the pile behaviour of non-slender piles is assessed

on the basis of small-scale tests in a pressure tank. The test setup is

thoroughly described. A scaling law relating the pile rotation to the

applied overturning moment is presented. The new and innovative test

method is validated against test results by means of the scaling law.

TEST SETUP

23 quasi-static tests were conducted on laterally loaded piles. The tests

were conducted in a pressure tank such that it was possible to apply an

overburden pressure to the soil.

Aluminium piles with diameters of 60 to 100 mm were tested. The

behaviour of both closed-ended and open-ended piles was

investigated. A wall thickness, wt, of 5 mm was used for all the test

piles. The ratio between the wall thickness and the pile diameter is

approximately three times higher for the test piles than for real

monopiles. However, since aluminium is approximately three times

softer than steel, the ratio between the pile bending stiffness, EpIp, and

the pile diameter, D, is similar for the test piles and for typical

monopiles used as foundation for offshore wind turbines.

2

Pressure Tank

The small-scale tests were conducted in a pressure tank at Aalborg

University. The pressure tank had an inner diameter of approximately

2.1 m and a height of approximately 2.5 m. It contained trap doors

enabling access into the tank. Further, wiring from measurement

devices could be led out of the tank through openings.

A cross-sectional view of the test setup is shown in Fig. 1. It was

possible to let water into and out of the tank through a pipe located at

the bottom of the tank. At the bottom of the tank, a saturated gravel

layer was positioned which ensured an even distribution of the water

coming from the inlet. A layer of saturated sand was placed on top of

the gravel layer.

Fig. 1. Cross-sectional view of the test setup.

In order to increase the effective stresses in the soil, an elastic

membrane was placed on top of it. The membrane hermetically sealed

off the air on top of the membrane from the water in the voids of the

soil material. To ensure a hermetic seal, rubber mouldings were

attached to the sides of the membrane. Further, an inflated fire hose

was employed to press the membrane out against the walls of the

pressure tank. A retainer clamp was used to seal the gap between the

pile and the membrane. It was not possible to make a perfect seal

between the membrane and the tank wall as well as between the

membrane and the pile wall. Approximately 15 cm of water was

therefore placed on top of the membrane. This ensured that the soil

remained saturated in spite of a minor leakage through the membrane.

Moreover, the minor leakage was minimised, because, at a

temperature of 20 °C, the dynamic viscosity of water is approximately

50 times larger than the dynamic viscosity of air. Therefore, when

water was placed on top of the membrane instead of air, the

volumetric leakage through gaps in the membrane was approximately

50 times slower. The water flow through the membrane varied

between 20 and 50 l/hour. The test results are not expected to be

influenced by this minor water flow through the membrane. The drain

pipe located at the bottom of the pressure tank was connected to an

ascension pipe so that, a hydrostatic pore pressure could be maintained

throughout the tests.

The test piles were loaded by means of a hydraulic piston which was

connected to the test piles with use of a thin steel wire.

Measuring System

The lateral load and the lateral pile displacement were measured as

shown in Fig. 2. The pile displacement was measured by means of

wire transducers of the type WS10-1000-R1K-L10 from ASM GmbH

at three levels along the piles: respectively 200 mm, 370 mm and 480

mm above the soil surface. A force transducer was connected in series

between the hydraulic piston and the steel wire. A force transducer of

the type HBM U2B 20 kN was employed. An absolute pressure

transducer of the type HBM P6A 10 bar was employed to measure the

air pressure in the pressure tank.

In order to ensure drained soil conditions, the loading of the test piles

was displacement-controlled with a loading velocity of 0.01 mm/s. In

Pedersen and Ibsen (2009) a detailed description of the data

acquisition is presented.

Fig. 2. Positioning of displacement and force transducers.

Soil Properties and Preparation of Soil

All the tests were conducted on Aalborg University Sand No. 1

(Baskarp Sand No. 15) which is a graded sand type. The largest grains

are round while the smallest grains have sharp edges. The sand has

been tested thoroughly by Larsen (2008) and Ibsen et al. (2009). The

soil properties are summarised in Table 1. Ibsen et al. (2009) proposed

an expression, valid for Aalborg University Sand No. 1, relating the

secant internal friction angle, �, with the relative density, ID, and the

minor effective stress, �’3:

� � �� (1)

In Eq. 1, the relative density should be inserted in per cent and the

confining pressure should be inserted in kPa.

Prior to each test, the soil was prepared by means of a two-step

procedure. At first an upward gradient of 0.91 was applied to the soil,

and afterwards the soil was vibrated mechanically in a standardised

pattern. For a detailed description of the soil preparation see Sørensen

and Ibsen (2011).

Table 1. Properties of Aalborg University Sand No. 1, after Larsen

(2008).

Specific grain density, ds 2.64

Maximum void ratio, emax 0.858

Minimum void ratio, emin 0.549

50 % - quantile, d50 0.14 mm

U = d60/d10 1.78

Cone penetration tests (CPT) were conducted prior to each test. The

relative density, determined based on the CPT's, varied from 0.75 to

0.91 throughout the test programme. Hence, the soil was classified as

dense to very dense sand which is similar to typical compactions of

offshore sand.

3

DIMENSIONAL ANALYSIS

Scope of the Dimensional Analysis

Dimensional analysis is essential to geotechnical physical modelling.

Only by means of that, the small-scale effects can be understood and

the test results used for prototype design. Generally, the friction angle,

�, and the Young's modulus of elasticity for the soil, Es, are effective

stress dependent such that the friction angle is high and the Young's

modulus of elasticity is low for low effective stresses. Hence, the

average values of the soil parameters for traditional small-scale tests

conducted at normal stress level differ from the average values of the

soil parameters in the soil around full-scale foundations. In order to

overcome this, an overburden pressure was applied in the small-scale

tests presented in this paper.

Several researchers have proposed scaling laws for laterally loaded

piles (e.g. Gudehus and Hettler, 1983; Peralta and Achmus, 2010; and

Bhattacharya et al., 2011). However, these scaling laws do not account

for an applied overburden pressure. A scaling law accounting for an

applied overburden pressure has therefore been developed. The

purpose of such scaling law is to enable comparison between tests

conducted at different overburden pressures and to scale up the results

to full-scale foundations. For the design of monopile foundations for

offshore wind turbines accurate determination of the pile rotation, �, is

essential. The pile rotation is expected to be a function of the relative

density of the sand, ID, the loading eccentricity, e, the embedded pile

length, Lp, the pile diameter, D, the overburden pressure, P0, and the

friction angle of the soil, �. These properties are in the following

derivation shown to be included within the moment pile capacity, RM,

and the applied overturning moment, MR.

Derivation of the Scaling Law

According to Rankine, the total passive earth pressure per unit length,

EpRankine, acting on a retaining wall is given as follows:

�� !� "#�$%

&#$ '#$( (2)

h is the height of the retaining wall, p is the overburden pressure, c is

the cohesion of the soil and Kp�, K

pp and Kp

c are passive earth pressure

coefficients. The expression in Eq. 2 is based on a deformation pattern

consisting of rigid body lateral translation. Further, the retaining wall

is assumed to have an infinite length and the interaction between wall

and soil is assumed to be smooth. In contrast, offshore monopiles are

loaded eccentrically, causing the pile deformation pattern to primarily

consist of rotation, and furthermore, the piles are circular, resulting in

a three-dimensional deformation pattern in the soil surrounding them.

For piles it should be noted that side friction also contributes to the

pile capacity and pile stiffness. Although the behaviour of retaining

walls and laterally loaded piles are significantly different, the capacity

of both types of structures arises primarily from lateral soil pressures

acting against the structures. It is assumed that the lateral pile

capacity, RH, can be calculated as:

)* � +!+�� , � +!+� -!� ". �$% /�. $ '. $( 0, (3)

where the factor k1 adjusts for the rotation of the pile, and the factor k2

adjusts for the change from two- to three-dimensional soil-structure

interaction. The factor k1 is expected to depend on the ratio between

the loading eccentricity and the embedded pile length, e/Lp, since this

ratio affects the depth to the point of rotation. k1 is also expected to

depend on the slenderness ratio, Lp/D, since this ratio governs the pile

flexibility and, therefore, also governs the depth to the point of

rotation. Reese et al. (1974) suggested that the lateral extent of the

wedge forming in front of a laterally loaded pile depends on the

friction angle and the relative density of the soil. Therefore, the factor

k2 is expected to depend on these parameters. The last term in Eq. 3,

cLpKpc, can be disregarded, since a cohesionless soil material was

employed in the experimental tests. The passive earth pressure

coefficients, Kp� and Kp

p, can be calculated as:

$% � $ � 123� -4�� 5�0 (4)

The loading eccentricity was 0.37 m for all the tests, which

corresponds to between 0.74Lp and 1.54Lp. For offshore wind turbines,

the design load from wind and waves often has an eccentricity

between 0.5Lp and 2.0Lp. Therefore, the applied overturning moment

around the point of rotation, MR, has a large influence on the pile

behaviour of both the test piles and full-scale piles. MR is calculated

as:

6� � 789 +�. : (5)

where H is the applied lateral load and k3Lp is the depth of the point of

rotation. The depth to the point of rotation depends on e/Lp and Lp/D.

Hereby, k3 depends on both e/Lp and Lp/D. Because both the test piles

and full-scale piles behave rigidly and are eccentrically loaded, the

value of k3 has been chosen to 0.8. This value agrees well with the

point of zero deflection determined from the centrifuge tests of non-

slender laterally loaded piles reported by Klinkvort and Hededal

(2010), and the small-scale tests on rigid piles reported by Christensen

(1961).

The overturning moment capacity around the point of zero deflection,

RM, can be estimated as a dimensionless factor, k4, multiplied by the

embedded pile length and the lateral pile capacity:

); � +<. )* � +!+�+<. �� , (6)

The factor k4 primarily depends on the depth to the point of rotation. k4

is therefore dependent on e/Lp and Lp/D.

The pile rotation, �, depends on the ratio between the applied

overturning moment around the point of rotation and the moment

capacity:

= � > -;?�@0 � > A *8�B�CDE:

�F�G�HDEI?JKLMKNE O (7)

where f is, as yet, an unknown function. All the experiments

conducted were designed such that the test piles had a slenderness

ratio comparable to the slenderness ratio used for full-scale

foundations for offshore wind turbines. Further, the ratio between the

loading eccentricity and the embedded pile length was also

comparable to the ratio for full-scale foundations. The test piles were

installed in dense to very dense sand, similar to typical sand deposits

in the offshore environment. Therefore, the values of the factors k1, k2,

k3 and k4 are expected to deviate only slightly between different scales.

Thus, for small- and full-scale tests of typical monopiles used as the

foundation of offshore wind turbines, Eq. 7 can be reduced to:

= � > A*8�B��DE:DEI?JKLMKNE O, for Lp/D � 5 and e/Lp � 0.5-2.0 (8)

The normalised overturning moment, Mnorm, is defined as:

4

6�PQR � *8�B��DE:DEI?JKLMKNE (9)

RESULTS

The load-displacement relationship for a test with D = 100 mm, Lp =

500 mm and P0 = 0 kPa and a test with D = 100 mm, Lp = 500 mm and

P0 = 100 kPa are shown in Fig. 3 and Fig. 4, respectively. Significant

fluctuations can be observed in the measured lateral load for the test

with P0 = 0 kPa while the fluctuations of the measured lateral load are

small for the test with P0 = 100 kPa. The reason for this is that the

capacity of the hydraulic piston is large compared to the applied load

for the test with P0 = 0 kPa. These fluctuations were observed for all

the tests conducted at normal stress level. The fluctuations are only

considered to exhibit a minor influence on the load-displacement

relationships. In the following figures, the lateral load shown for the

tests at normal stress level is smoothed as a running average calculated

over 10 s. Since a loading velocity of 0.01 mm/s was used, the lateral

displacement increased 0.1 mm within 10 s. When comparing the

load-displacement relationships shown in Fig. 3 and Fig. 4, it can be

observed that the application of an overburden pressure dramatically

increases the pile stiffness and pile capacity. The observed increase is

as expected.

Fig. 3. Load-displacement relationship for a test with D = 100 mm, Lp

= 500 and P0 = 0 kPa.

Fig. 4. Load-displacement relationship for a test with D = 100 mm, Lp

= 500 mm and P0 = 100 kPa.

For a pile diameter of 80 mm both open- and closed-ended piles were

tested. In Fig. 5, the load-displacement relationships obtained for

open- and closed-ended piles are compared. No significant difference

in the load-displacement relationship can be observed. This

corroborates the fact that the pile stiffness and pile capacity originate

primarily from lateral bedding and that the shear and normal stress

acting at the pile toe merely has a secondary influence on the pile

behaviour for lateral loading.

Fig. 5. Comparison of load-displacement relationships for open-

/closed-ended piles, P0 = 0 kPa.

The normalised overturning moment, Mnorm, is in Fig. 6 plotted against

the pile rotation, �. The pile rotation was determined as an average

rotation:

123S=T � USVW��T�B��DE (10)

where y is the pile deflection and x is the depth below soil surface.

Fig. 6 show some scatter in the normalised plot. The scatter is

however minimised heavily when only the tests with overburden

pressure applied are considered. The figure illustrates that the

relationship between the pile rotation and the normalised overturning

moment are comparable for varying P0, Lp/D and e/Lp. Hence, the test

results validate the scaling law.

Fig. 6. Mnorm versus � for all the conducted tests.

In Fig. 7, the normalised overturning moment is plotted against the

pile rotation for the tests with pile diameters of 80 mm slenderness

ratios of 5 and with applied overburden pressures varying from 0 to

0 5 10 15 20 25 30 35 400

100

200

300

400

500

600

700

Displacement at hydraulic piston [mm]

Hori

zonta

l lo

ad [

N]

0 5 10 15 20 25 30 350

2000

4000

6000

8000

10000

12000

14000

16000

Displacement at hydraulic piston [mm]

Hori

zonta

l lo

ad [

N]

0 5 10 15 20 25 30 35 40 450

100

200

300

400

500

600

700

800

H [mm]y

[N

]

L/D = 4, open

L/D = 4, closed

L/D = 6, open

L/D = 6, closed

0 0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

1.2

Θ [°]

Mn

orm

[−

]

P0 = 0 kPa

P0 > 0 kPa

5

100 kPa. The curves for the tests with overburden pressure applied to

the soil are almost identical in the normalised plot, although, the

normalised pile stiffness, Mnorm/�, seems to decrease slightly for

increasing P0. The two tests without overburden pressure seem to

reach the pile capacity at a smaller value of pile rotation than the tests

with overburden pressure. From consolidated drained triaxial tests on

Aalborg University Sand No. 1, Hokkesund Sand, Santa Monica

Beach Sand and Sacramento River Sand, Ibsen and Lade (1999) found

that the vertical strain at failure increases for increasing values of

confining pressure. Kolymbas and Wu (1990) found a similar result

from consolidated drained triaxial tests on Karlsruhe medium dense

sand. A correlation exists between the pile rotation and the strain in

the soil. Hence, the effect of the applied overburden pressure on the

pile rotation at failure is analogue to the effect of the confining stress

on the vertical strain at failure. The mean values of the effective

stresses in the soil are comparable for the small-scale tests with an

overburden pressure of 100 kPa applied to the soil and full-scale

foundations. Test with overburden pressure applied might therefore

capture the relationship between the pile rotation and the normalised

overturning moment for full-scale foundations. Although, in order to

validate this statement, validation against full-scale tests is needed.

Fig. 7. Mnorm versus � for varying P0, D = 80 mm, Lp = 400 mm.

Fig. 8. Mnorm versus � for the tests with Lp/D = 5, P0 = 100 kPa.

Fig. 8 and Fig. 9 indicate that the scaling law proposed in Eq. 8 is

robust in such a way that it captures a variation of e/Lp and Lp/D

within 0.74-1.54 and 4-6, respectively. Hence, the small-scale tests

corroborate the proposed scaling law.

Fig. 9. Mnorm versus � for the tests with D = 80 mm, P0 = 100 kPa.

POTENTIAL IMPLICATION FOR DESIGN

Gudehus and Hettler (1983) suggested the following expression for

the displacement of a rigid pier:

X � YXZ� - *

%C0[

(11)

where Au depends on e/Lp and Lp/D, Ce depends on the void ratio, e,

and µ is a dimensionless constant. Similar to the proportionality

between the pile displacement and the horizontal loading raised to the

power of µ as suggested by Gudehus and Hettler (1983), it is assumed

that the pile rotation is proportional to the normalised overturning

moment raised to the power of µ:

= � Z6�PQR[

(12)

C is a dimensionless constant. The parameters C and µ should be fitted

to test results. It should be emphasised that Eq. 11 and 12 show no

maximum for H/Mnorm. These, equations are therefore not able to

predict H/Mnorm for very large displacements/rotations.

In Fig. 10, Eq. 12 is fitted to the test results for the small-scale tests

with overburden pressure applied. The least squares fitting method has

been used for the fitting. It can be observed that the fitted function

provides a reasonable fit with the test results for pile rotations up to

1.5-2.0°. For pile rotations larger than 1.5-2.0°, the fitted function

starts to overestimate the normalised overturning moment. Since, Eq.

12 is not bounded by an upper limit for Mnorm, the poor fit for large

values of the pile rotation is as expected.

A typical monopile foundation for offshore wind turbines has a pile

diameter of 4 m, an embedded pile length of 20 m and a loading

eccentricity of 30 m corresponding to 1.5 times the pile length. Hence,

the slenderness ratio and the ratio between the eccentricity and the pile

length are in the same order as for the small-scale tests. Typically, the

soil is medium dense to dense. Therefore, a friction angle of 40° has

been assumed. When scaling up the results from the small-scale tests

to a full-scale foundation with the above mentioned parameters, the

load-rotation relationship shown in Fig. 11 is found. It should be

emphasised that the scaling law needs validation against large- or full-

scale tests before small-scale testing with overburden pressure applied

0 1 2 3 40

0.2

0.4

0.6

0.8

1

1.2

Θ [°]

Mnorm

[−

]

P0 = 0 kPa

P0 = 25 kPa

P0 = 50 kPa

P0 = 75 kPa

P0 = 100 kPa

0 0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

1.2

Θ [°]

Mnorm

[-]

e/Lp

= 1.23

e/Lp

= 0.93

e/Lp

= 0.74

0 0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

1.2

Θ [°]

Mnorm

[-]

Lp/D = 3

Lp/D = 4

Lp/D = 5

Lp/D = 6

6

to the soil can be applied in the design of monopile foundations for

offshore wind turbines.

Fig. 10. Eq. 12 fitted to the test results for the tests with overburden

pressure, Lp/D = 3-6, e/Lp = 0.74-1.54, P0 = 25-100 kPa.

Fig. 11. Load-rotation relationship for a full-scale monopile with D =

4 m, Lp = 20 m, e = 30 m situated in a cohesionless soil with � = 40°.

CONCLUSIONS

The behaviour of non-slender laterally loaded piles was investigated

by means of small-scale tests conducted with varying ratios between

the loading eccentricity and the embedded pile length, varying

slenderness ratios and varying overburden pressures. A scaling law

relating the pile rotation with the normalised overturning moment was

proposed. The major conclusions of the experimental work are:

• A new and innovative test setup for small scale testing was

developed in which the effective stresses in the soil can be

increased. The test setup worked as planned.

• The pile capacity and pile stiffness for open- and closed-

ended piles were found to be rather similar. Therefore, the

shear and normal stresses acting at the pile toe only slightly

affects the pile behaviour for non-slender laterally loaded

piles.

• A scaling law of the relationship between the overturning

bending moment and the pile rotation was proposed. The

scaling law was found to be very accurate for the conducted

tests and it hereby proved to be valid for eccentricities

between 0.74Lp and 1.54Lp and for slenderness ratios of 3 to

6.

• The pile rotation at failure was found to depend on the mean

value of the effective soil stresses. This finding is analogue

to the relationship between the strain at failure and the

confining stress in triaxial tests.

• The small-scale tests results were scaled up to a typical full-

scale foundation. Regarding the scaling from small-scale to

full-scale it should be noted that the scaling law needs

validation against large- or full-scale tests.

ACKNOWLEDGEMENTS

The experimental work has only been possible with the financial

support from the Energy Research Programme administered by the

Danish Energy Authority. The experimental work is associated with

the ERP programme "Physical and numerical modelling of monopile

for offshore wind turbines", journal no. 033001/33033-0039. The

funding is sincerely acknowledged. Appreciation is extended to

Kristian T. Brødbæk, Martin Møller, Hanne R. Roesen, Kristina

Thomassen, Alejandro B. Moreno, Linas Mikalauskas and Jose L. T.

Diaz for helping with the experimental work. Furthermore, the authors

would like to thank the staff at the laboratory at the Department of

Civil Engineering, Aalborg University, for their immeasurable help

with the test setup.

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constructing fixed offshore platforms - Working stress design'', API

RP2A-WSD. American Petroleum Institute, Washington, D.C., USA,

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relationships for physical modelling of monopile-supported offshore

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Christensen, N. H. (1961). ''Model tests with transversally loaded rigid

piles in sand''. Danish Geotechnical Institute, Copenhagen, Denmark,

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DNV (2010). ''Design of Offshore Wind Turbine Structures'', DNV-

OS-J101. Det Norske Veritas, Det Norske Veritas Classification A/S.

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Granular Soil''. In Development in Soil Mechanics and Foundation

Engineering, Vol. 1, pp. 29-63.

Ibsen, L. B., Hanson, M., Hjort, T. H. & Thaarup, M. 2009. ''MC

parameter calibration for Aalborg University Sand No. 1''. DCE

Technical Report no. 62, Department of Civil Engineering, Aalborg

University, Denmark.

Ibsen, L. B. & Lade, P. V. 1999. ''Effects of nonuniform stresses and

strains on measured characteristic state''. Proceedings of the second

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Klinkvort, R. T. & Hededal, O. 2010. ''Centrifuge modelling of

offshore monopile foundations''. Proceedings of International

Symposium Frontiers in Offshore Geotechnics 2, Perth, Western

Australia, November 8 to 10 2010.

Kolymbas, D. & Wu, W (1990). ''Recent results of triaxial tests with

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

Θ [°]

Mn

orm

[−

]

Mnorm

= 0.484θ0.732

0 0.5 1 1.5 20

2

4

6

8

10

12

14

Θ [°]

H [

MN

]

7

granular materials''. Powder Technology, Vol. 60, pp. 99-119.

Larsen, K. A. (2008). ''Static behaviour of bucket foundations''. DCE

Thesis no. 7, Department of Civil Engineering, Aalborg University,

Denmark.

Murchison, J. M. & O'Neill, M. W. (1984). ''Evaluation of p-y

relationships in cohesionless soils. Analysis and design of pile

foundations''. Proceedings of a Symposium in conjunction with the

ASCE National Convention, New York, New York, USA, pp. 174-

191.

O'Neill, M.W. & Murchison, J. M. (1983). ''An Evaluation of p-y

Relationships in Sands''. Research Report No. GT-DF02-83,

Department of Civil Engineering, University of Houston, Houston,

Texas.

Pedersen, T. S. & Ibsen, L. B. 2009. ''Manual for dynamic triaxial

cell''. DCE Technical Report no. 75, Department of Civil Engineering,

Aalborg University, Denmark.

Peralta, P. & Achmus, M. (2010). ''An experimental investigation of

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Reese, L. C., Cox., W. R. & Koop, F. D. (1974). ''Analysis of

Laterally Loaded Piles in Sand''. Proceedings of the Sixth Annual

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473-483.

Sørensen, S. P. H. & Ibsen, L. B. (2011). ''Small-scale quasi-static

tests on non-slender piles situated in sand - Test results''. DCE

Technical Report no. 112, Department of Civil Engineering, Aalborg


Title:

Experimental Comparison of Non-Slender Piles under Static Loading and underCyclic Loading in Sand.

Authors:

Sørensen, S. P. H., and Ibsen, L. B.


2012

Published in:

Accepted at the 22nd International Ocean and Polar Engineering Conference, XXIIISOPE, Rhodes, Greece.

Number of pages:

7

Due to copyright, the paper is not included

Title:

Revised expression for the static initial part of p–y curves for piles in sand.

Authors:

Sørensen, S. P. H., Augustesen, A. H., and Ibsen, L. B.


2012

Published in:


Number of pages:

40

1

Date of submission: 26th

of April 2012

Title: Revised expression for the static initial part of p-y curves for piles in sand

Authors: Søren Peder Hyldal Sørensen1

Anders Hust Augustesen

2

Lars Bo Ibsen3

Affiliations: 1 Ph.D. fellow, Master of Science in Civil Engineering, Department of Civil

Engineering, Aalborg University, Denmark.

2 Chief specialist in Geotechnical Engineering, Ph.D., Master of Science in Civil

Engineering, COWI A/S.

3 Professor in Civil Engineering, Department of Civil Engineering, Aalborg


Contact address: Søren Peder Hyldal Sørensen, Sohngaardsholmsvej 57, 9000 Aalborg, Denmark

Telephone: +45 60755884

E-mail: [email protected]

Number of words: 4945

Number of tables: 2

Number of illustrations: 18

2

Abstract: Monopile foundations with diameters of 4 to 6 m are often employed for offshore wind turbines.

The Winkler model approach, where the soil pressure acting against the pile wall is provided by uncoupled

springs with stiffnesses provided by p-y curves, is traditionally used in the design of monopiles. However,

the method is developed for slender piles with diameters up to approximately 2 m when considering piles

in sand. Hence, the method is not validated for piles employed for wind turbines used nowadays.

The aim of the paper is to modify the p-y curve formulation proposed by the American Petroleum Institute

to large-diameter non-slender piles in sand. A modified expression for the static part of the p-y curves for

piles in sand is proposed in which the initial slope of the p-y curves depends on the depth below the soil

surface, the pile diameter and Young’s modulus of elasticity of the soil. The reassessment of the p-y curves

recommended by the American Petroleum Institute is based on three-dimensional numerical analyses

conducted by means of the commercial program FLAC3D

incorporating a Mohr-Coulomb failure criterion.

List of notations:

a, b, c and d: Dimensionless factors

A: Dimensionless correction factor for

the ultimate soil resistance

Ap: Shear area of the pile

C1, C2 and C3: Dimensionless factors

D: Pile diameter

Dref: Reference pile diameter

e: Loading eccentricity

E0.1: Young’s modulus of elasticity for

the soil at a strain level of 0.1 %

Ep: Young’s modulus of elasticity of

the pile

Epy: Secant stiffness of p-y curves

E*

py: Initial stiffness of p-y curves,

0

*

py

y

dpE

dy=

=

Es: Young’s modulus of elasticity of

the soil

Es,ref: Reference value of Young’s

modulus of elasticity for the soil

Gp: Shear modulus of the pile

H: Horizontal force

Ip: Second moment of area of the pile

Lp: Embedded pile length

k: Initial modulus of subgrade

reaction

M: Overturning bending moment

p: Lateral soil resistance

pu: Ultimate soil resistance

P0: Overburden pressure

V: Vertical force

wt: Pile wall thickness

x: Depth below soil surface

xref: Reference depth below soil surface

y: Pile deflection

γ/γ’: Unit weight/effective unit weight

δ: Wall friction angle

ν: Poisson’s ratio

φ: Internal friction angle

ψ: Dilatancy angle

Keywords: Piles, soil/structure interaction, stiffness

3

Revised expression for the static initial

part of p-y curves for piles in sand

1. Introduction

The monopile foundation concept is often employed in the design of offshore wind turbines. Monopiles are

welded steel pipe piles driven open-ended into the soil. In order to be able to sustain the large forces and

moments, the outer pile diameter, D, is typically four to six meters with an embedded pile length, Lp, in the

range of 15 to 30 m. Hence, the slenderness ratio, Lp/D, is around five.

The American Petroleum Institute (API, 2000) and Det Norske Veritas (DNV, 2010), recommend to employ

the Winkler model approach in the design of monopiles, i.e. the pile is considered as a beam on an elastic

foundation. The elastic foundation consists of a discrete number of springs with stiffness’s determined by

means of p-y curves (Figure 1). p-y curves describe the variation of soil resistance, p, acting against the pile

wall as a function of the lateral pile displacement, y.

For piles in sand, API (2000) and DNV (2010) recommend a p-y curve formulation, which is based on full-

scale tests at Mustang Island (Cox et al. 1974). Two identical circular piles with diameters of 0.61 m and

embedded pile lengths of 21 m were tested. This corresponds to a slenderness ratio of 34.4. A total of

seven load cases were conducted; 2 static and 5 cyclic. The p-y curve formulation has in addition to these

tests been validated for slender piles with diameters up to approximately 2 m (Murchison and O’Neill

1984). The formulation has, however, not been validated for piles with diameters of 4 to 6 m and Lp/D ≈ 5.

Hereby, the influence of pile properties such as the pile diameter, the pile bending stiffness and the pile

slenderness ratio on the soil response still needs to be investigated.

In the serviceability state, only small rotations of the monopiles are allowed. Further, strict demands are set

to the total stiffness of the foundation in order to avoid resonance with the wind and wave loading.

4

Hereby, the initial stiffness, e.g. the initial slope of the p-y curves, is of high importance in the design of

monopile foundations for offshore wind turbines.

In the present paper, the p-y curve formulation recommended by API (2000) and DNV (2010) is re-

evaluated for static loading conditions. The main focus is on the initial part of the p-y curves. In the design

of offshore wind turbine foundations, the cyclic behaviour is of high interest due to the cyclic behaviour of

wind and wave loads. However, the trend of the initial part of the p-y curves is expected to be similar for

static and cyclic loading. According to Kramer (1996) the backbone curve of a soil can be described by two

parameters: the initial (low-strain) stiffness and the (high-strain) shear strength. It is assumed that the soil-

structure interaction similarly can be described by an initial slope, dp/dy, and an ultimate resistance. An

expression of the initial slope of the p-y curves is proposed aiming at accurate predictions of the pile

behaviour when the pile is exposed to serviceability limit state (SLS) loads. The expression is determined

based on a numerical study. The effect on the pile behaviour by incorporating the modified expression for

the initial slope of the p-y curves in a Winkler model is illustrated for a monopile foundation situated at

Horns Rev, Denmark.

2. p-y curve formulation

API (2000) and DNV (2010) recommend the p-y curve formulation given in Equation 1 for piles located in

sand.

( ) tanhu

u

kxp y Ap y

Ap

=

(1)

pu is the ultimate soil resistance, k is the initial modulus of subgrade reaction and x is the depth below the

soil surface. A is a dimensionless factor depending on the loading scenario, i.e. static or cyclic:

5

3 0 0 8 0 9

0 9

. . . , Static loading

. , Cyclic loading

x

A D

− ≥

=

(2)

Based on lateral pile translation the ultimate soil resistance can in accordance with Bogard and Matlock

(1980) be estimated as:

( )γ

γ

+ =

1 2

3

'min

'u

C x C D xp

C D x (3)

C1, C2 and C3 are dimensionless factors varying with the internal friction angle, φ. k depends on the relative

density/internal friction angle of the soil. The initial slope of the p-y curves denoted E*

py is thereby:

20

0

=

=

= = =

*

cosh

u

py u

y

u y

kx

ApdpE Ap kx

dy kxy

Ap

(4)

Hence, E*

py is considered to be independent of the pile properties, e.g. the pile diameter, D, the slenderness

ratio, Lp/D, and the pile bending stiffness, EpIp. E*

py varies linearly with depth below the soil surface.

Several authors have investigated the influence of the pile diameter on E*

py with contradictory conclusions.

Terzaghi (1955), Ashford and Juirnarongrit (2003) and Fan and Long (2005) conclude that the pile diameter

has no significant effect on the initial slope of the p-y curves. In contrast, Carter (1984) and Ling (1988)

propose a linear dependency between pile diameter and initial stiffness.

Based on numerical investigations and a linear variation of Epy* with depth as given in Equation 4, Lesny and

Wiemann (2006) conclude that the stiffness is overestimated for large depths. Instead, they propose a

nonlinear variation of E*

py with depth, i.e. Epy* is proportional with x

0.6.

The pile-soil interaction and pile response are affected by the flexibility of the pile. The slenderness ratio for

monopiles for modern offshore wind turbines is significantly lower than the slenderness ratio for the piles

6

tested at Mustang Island. Therefore, monopiles used for offshore wind turbine foundations exhibit a rather

stiff behaviour in contrast to the rather flexible piles tested at Mustang Island. Several authors have

proposed criteria for flexible/stiff pile behaviour, i.e. Poulus and Hull (1989), Dobry et al. (1982) and Budhu

and Davies (1987). According to Poulus and Hull (1989), a pile behaves as stiff or flexible when the

embedded pile length, Lp, fulfils the criteria given in Equation 5 and Equation 6, respectively.

0 25

1 48

.

. stiff pile behaviourp p

p

s

E IL

E

<

(5)

0 25

4 44

.

. flexible pile behaviourp p

p

s

E IL

E

>

(6)

The Young’s modulus of elasticity for the pile and the soil are denoted Ep and Es, respectively. Ip denotes the

second moment of area for a cross-section of the pile. Hence, a monopile typically employed for offshore

wind turbine foundations (pile diameter, D = 4 m, wall thickness, wt = 0.05 m, and embedded pile length, Lp

= 20 m) behaves rigidly when Es < 7.6 MPa and flexible when Es > 617 MPa. The Young’s modulus of

elasticity is even for dense sands normally less than 100 - 130 MPa implying more rigid pile behaviour than

flexible. In contrast, the piles tested at Mustang Island behave flexible when Es > 0.34 MPa. The sand at

Mustang Island was, according to Cox et al. (1974), medium dense to dense. Hence, the two test piles

clearly satisfy the criteria for flexible pile behaviour.

In conclusion, the p-y curve formulation currently recommended by API (2000) and DNV (2010) is at first

sight not well-suited for the design of monopile foundations for offshore wind turbines due to scale effects.

Knowledge is especially needed regarding the initial part of the p-y curves. A concise state-of-the-art review

of p-y curves for piles in sand is presented by Sørensen et al. (2012).

3. Numerical modelling

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3.1 Establishing the numerical model

A numerical model has been constructed in the commercial program FLAC3D

(FLAC3D

3.1 manual, 2006),

with the objective of determining the behaviour of monopiles exposed to static lateral loading.

Due to symmetry, only half of the soil and pile is modelled (Figure 2). The pile and the soil are divided into

zones each consisting of five 4-noded constant strain-rate sub-elements of tetrahedral shape. An outer

diameter of 40D, as proposed by Abbas et al. (2008), is used whereas the bottom boundary is placed 15 m

below the pile toe. This ensures that the model boundaries do not influence the results.

For practical reasons the pile is modelled as a solid pile. Therefore, the Young’s modulus of elasticity and

the density of the solid pile are scaled to ensure that the bending stiffness and the weight including soil are

identical to the properties of a tubular pile. The plug ratio is assumed equal to unity. The shear stiffness,

ApGp, is not scaled correctly, which is of minor importance since bending is governing in the design of

monopiles. Analyses, not presented here, show that the difference in the maximum deflections at the

seabed is for a pile with Lp/D = 5 less than 2 % when comparing the results based on the solid pile model

with the results obtained by means of a shell pile model reflecting the tubular pile.

The Mohr-Coulomb material model is employed for the sand. The reason for using such a simple model is

that the soil parameters employed in the model can be determined from few experimental tests. Further, it

is convenient to have few model parameters in a parametric study. Hence, it seems naturally to incorporate

a material model with only one stiffness parameter. Achmus et al. (2009), Chik et al. (2009) and Kim and

Jeong (2011) have successfully modelled horizontally loaded piles in clay and sand, respectively, by

employing the Mohr-Coulomb material model for the soil. The interface between the pile and the soil is

modelled by means of a linear Coulomb shear strength criterion allowing gapping and slipping between the

pile and the soil.

8

A displacement-controlled horizontal loading is applied as a velocity to the centre nodes of the pile head.

Hereby, a number of steps are prescribed in order to reach the desired pile deflection. To ensure a quasi-

static behaviour of the pile-soil system, the velocity of the pile is set to 10-6

m/s. For piles with slenderness

ratios larger than 10, numerical instability arises if displacement controlled loading is employed. Instead,

the load for these piles has been applied as a load distributed evenly to all nodes at the pile head.

Damping is introduced since FLAC3D

is a dynamic, explicit finite difference solver. Combined damping is

employed since it, according to FLAC3D

3.1 manual (2006), is preferable for uniform motions. When using

combined damping both the velocity and the derivative of the unbalanced force contribute to the damping

force. Due to the small velocities applied, it has not been necessary to introduce absorbing model

boundaries.

The numerical simulations are executed in stages. First, the initial stresses in the soil are generated using a

K0-procedure. Secondly, an equilibrium state is established for the pile and the soil in which the soil

properties are employed for the pile material. At this stage, the interface between the soil and the pile is

assumed smooth. Thirdly, a new equilibrium state is calculated in which the pile and the interface are given

the correct properties. After reaching equilibrium, the horizontal load is applied as described.

In order to investigate the convergence of the numerical model, a pile with D = 4 m, Lp = 20 m, t = 0.05 m

situated in a soil with φ = 40° and Es = 53 MPa has been simulated. The simulation has been carried out

with respectively 2660, 8022, 18828 and 67480 zones in the model. The load-displacement relationships

are shown in Figure 3. It can be observed that with 18828 and 67480 elements similar results are obtained.

Approximately 20000 elements are therefore used in the numerical simulations.

3.2 Validation

The numerical model has been validated against 23 laboratory tests conducted in a so-called pressure tank,

cf. Sørensen et al. (2009) and Sørensen and Ibsen (2011). The cross-sectional view of the test setup is

9

shown in Figure 4. Aluminium piles with diameters of 40-100 mm and embedded pile lengths of 200-500

mm were exposed to lateral loading. The piles were embedded in saturated sand. Aalborg University Sand

No. 1 (Baskarp Sand No. 15) was used for the testing and it has been rigorously tested (Ibsen et al. 2009).

Prior to each test the sand was prepared by mechanical vibration. Cone penetration tests were conducted

prior to each test by means of a laboratory CPT-cone. The relative density was for all the tests found to be

approximately 80 %. Hence, the soil was classified as dense to very dense sand which is similar to typical

compactions of offshore sand.

A rubber membrane was placed on top of the soil material sealing off the air on top of the membrane

hermetically from the water in the voids of the soil material. Hereby, it was possible to increase the

effective soil stresses homogeneously. The increase in effective vertical soil stresses corresponds to the

application of an overburden pressure. Traditionally, significant scale-effects are present for small-scale

tests at normal stress level, for instance, the friction angle of the soil is very large and the Young’s modulus

of elasticity for the soil is low. Further, the soil parameters will vary strongly with depth. These

uncertainties are avoided when applying an overburden pressure. Application of an overburden pressure to

the soil causes an unrealistic stress distribution with depth as the effective vertical stress is nonzero at the

soil surface. The small-scale tests are therefore not directly scalable. When calibrating the numerical model

against the small-scale tests, the actual model dimensions are employed as input to the numerical model.

Further, the applied overburden pressure is also applied to the soil in the numerical model. Soil parameters

determined from cone penetrations tests and triaxial tests have directly been employed in the numerical

model.

Results from two tests (Lp/D = 5 and P0 = 100 kPa in both cases but D equalling 40 mm and 100 mm,

respectively) as well as load-settlement curves established by means of the FLAC3D

model are shown in

Figure 5. A reasonable concordance between the numerical simulations and the test results has been

10

found, especially for y/D less than 0.25. The same tendency has been observed when comparing numerical

simulations with 21 other laboratory tests (Lp/D = 5, D = 40-100 mm and P0 = 0-100 kPa).

3.3 Pile and soil properties

Steel piles with pile diameters of D = 1-7 m and length of Lp = 20 m have been studied. Hence, the

slenderness ratio, Lp/D, varies between 3 and 20. For practical purposes the pile wall thickness, wt, is

assumed constant and equal to 0.05 m. This leads to bending stiffnesses, EpIp, varying between 3.5 GNm2

and 1384 GNm2. According to the criteria by Poulus and Hull (1989) the pile with D = 1 m behaves flexibly

for Es > 8.6 MPa and rigidly for Es < 0.1 MPa and the pile with D = 7 m behaves flexibly for Es > 3362 MPa

and rigidly for Es < 41.5 MPa. Hence, for D = 1 m flexible pile behaviour is expected while a rather rigid pile

behaviour is expected for D = 7 m.

According to Klinkvort et al. (2010) the location of the force resultant, e with respect to the embedment

length, Lp, influences the shape of the p-y curves. Normally, e/Lp is in the interval of 0.5 to 2.0 for the design

load of monopiles for offshore wind turbines. In this study, e/Lp = [0.50; 0.75; 1.00; 1.50; 2.00] have been

applied.

A Young’s modulus of elasticity, Ep, a Poisson’s ratio, ν, and a unit weight, γ, of 210 GPa, 0.3 and 77 kN/m3,

respectively, have been assumed for the steel material. A homogeneous soil is employed. The internal

friction angle of the sand has been varied between φ = 30-43°. The wall friction angle, δ, between the soil

and the pile is as proposed by Brinkgreve and Swolfs (2007) set to:

2

3

tan( )arctan

ϕδ

=

(7)

Hereby, the wall friction angle takes values from 21° to 32°. The dilatancy angle, ψ, of the soil material is

given in Equation 8 (Brinkgreve and Swolfs, 2007):

30 [ ]ψ ϕ= − ° (8)

11

Hence, the dilatancy angle assumes values varying from zero to thirteen degrees. Young’s modulus of

elasticity for the soil has been varied in the range 21 to 93 MPa. For sand, Young’s modulus of elasticity for

the soil is typically within this range.

Generally the stiffness of sand is effective stress dependent. However, in order to decouple the influence of

soil stiffness and depth below soil surface on E*

py, the Young’s modulus of elasticity for the soil, Es, has been

assumed constant with depth in the parametric study of parameters influencing the initial slope of the p-y

curves.

4. Results

4.1 Effects of Lp/D, EpIp, e/Lp and soil properties on the pile response

Figure 6 and Figure 7 present pile deflections and bending moment distributions for piles with D = 1-7 m

and φ = 37°, respectively. For D = 7 m the pile behaves very stiffly. In contrast, the pile with D = 1 m

behaves rather flexibly. The depth to the point of zero deflection increases for increasing pile diameter.

Furthermore, the depth of the maximum bending moment increases for increasing pile diameter. Since the

length has been kept constant at 20 m, the slenderness ratio, Lp/D, varies as the pile diameter is varied. It

can, hereby, be concluded that the slenderness ratio has a significant effect on the pile behaviour. A similar

tendency has been observed for other combinations of φ, Es and e/Lp.

Figure 8 illustrate the variation of the initial slope of the p-y curves, Epy* with pile diameter, D, and depth

below soil surface. In practice E*

py has been estimated as the secant stiffness for a pile displacement of 1.5

mm. E*

py is therefore considered as a parameter capturing the initial part of the p-y curves and not as the

small strain stiffness which should be employed when considering dynamic loading. A non-linear increase

of Epy* can be observed for increasing depths, which is in contrast to the linear dependency proposed by API

(2000) and DNV (2010). Further, Epy*

is found to increase for increasing pile diameter (Figure 8). In contrast,

API (2000) and DNV (2010) propose that Epy*

is independent of the pile diameter. The rotation of the pile

12

causes discontinuities in the values of Epy* at depths between approximately 8-17 m as the point of rotation

changes with the size of loading. Therefore, values of Epy* at these depths are left out in the following

figures.

Figure 9, Figure 10 and Figure 11 illustrate the variation of the initial slope of the p-y curves, Epy* with

friction angle, φ, Young’s modulus of elasticity for the soil, Es, and loading eccentricity, e/Lp,, respectively.

According to Figure 9, E*

py is insignificantly influenced by the internal friction angle. Furthermore, Figure 10

indicates that Epy*

increases with increasing values of Young’s modulus of the soil, Es. However, API (2000)

and DNV (2010) suggest that E*

py is independent on the Young’s modulus of elasticity of the soil and instead

dependent on the internal friction angle. However, it should be noted that Young’s modulus of elasticity of

the soil and the internal friction angle are interrelated via the relative density of the sand. Figure 11

indicates that E*

py is independent of the loading eccentricity for e/Lp = 0.5-2.0. The above mentioned trends

have also been observed for other combinations of D, φ and Es.

Figure 12 presents the influence of bending stiffness, EpIp, on the p-y curves. It can be concluded that the p-

y curves are not influenced by EpIp. This is in agreement with Fan and Long (2005), but in contrast to Ashour

and Norris (2000).

4.2 Modified expression for the initial slope of the p-y curves

Figure 8 and Figure 10 indicate that the initial slope of the p-y curves, Epy*, depends on the depth below the

soil surface, x, Young’s modulus of elasticity for the soil, Es, and the pile diameter, D. A modified expression

for the initial stiffness is proposed in Equation 9.

*

,

b c d

spy

ref ref s ref

Ex DE a

x D E

= ⋅ ⋅ ⋅

(9)

13

b, c, and d are dimensionless constants whereas a is a constant specifying the initial stiffness for D = Dref = 1

m, x = xref = 1 m and Es = Es,ref = 1 MPa. Further, x and D should both be inserted in meters and Es in MPa.

Values of a, b, c and d have been found to 1000 kPa, 0.3, 0.5 and 0.8, respectively.

The constants a, c and d have been determined based on least squares fitting. The constant b has due to

the discontinuity of the initial stiffness around the point of zero deflection been determined by visual fitting

of Equation 9 with the FLAC3D

simulations.

Figure 13 shows E*

py normalized with respect to (Es/Es,ref)0.8

for varying values of Young’s modulus of

elasticity for the soil and D = 4 m. It can be observed that Equation 9 provides a reasonable description of

the dependency of the internal friction angle when using d = 0.8. Similar results have been obtained for D =

1-7. The linear variation of Epy* with depth, b = 1, and the non-linear expression proposed be Lesny and

Wiemann (2006), b = 0.6, overestimates E*

py for large depths.

In Figure 14, the normalised E*

py for an internal friction angle of 40°, Es = 74 MPa, and varying pile diameters

is presented as function of depth. A constant bending stiffness has been employed. The proposed

expression for E*

py (Equation 9), produces a reasonable fit. The same tendency has been observed for other

combinations of D, e/Lp and Es.

The expression of E*

py presented in Equation 9 is based on a parametric study in which the soil stiffness, Es,

has been assumed constant with depth. In Figure 15, the initial slope of the p-y curves determined by

means of FLAC3D

and Equation 9 is compared for a situation in which the Young’s modulus of elasticity for

the soil is stress-dependent. Young’s modulus of elasticity, Es, has been varied with confining stress and

relative density according to Equation 10 in which σ’3,ref is a reference minor effective stress of 100 kPa and

Es is given in kPa. The equation is valid for Aalborg University Sand No. 1 and it has been determined based

on triaxial tests (Ibsen et al. 2009).

14

( )

0 58

3

3

1 15 20000σ

σ

= + ⋅

.

,

'.

's D

ref

E I

(10)

The proposed expression of E*

py (Equation 9) is found to produce a reasonable fit. Hence, Equation 9 is also

valid for sands with effective stress dependent stiffness.

When using Equation 9 for the initial slope of p-y curves for investigations of the serviceability limit state,

the authors would recommend employing the initial Young’s modulus of elasticity for the soil, Es ≈ E0.1, as

monopiles used as foundation for offshore wind turbines are exposed to small displacements/rotations.

5. Example - Horns Rev 1

The wind turbine considered in this example is a part of Horns Rev 1 Offshore Wind Farm, built during 2003

and located in the North Sea approximately 30 km west of Esbjerg in Denmark. The wind turbines at the

site are all of the Vestas V80-2.0 MW type with a total assembly weight of 105.6 t. The hub height is 70 m

above MSL and the site is dominated by westerly winds. The foundations are monopiles having a diameter

of 4.0 m. A transition piece with outer diameter of 4.34 m constitutes the transition from the tower to the

monopile, cf. Hald et al. (2009).

5.1 Pile and loads conditions

The steel monopile considered is the foundation for wind turbine 14. The outer diameter is 4 m, the length

is 31.6 m and the wall thickness, wt, and thereby the bending stiffness, EpIp, varies along the pile as shown

in Figure 16. Ep denotes Young’s modulus, and Ip is the second moment of area around a horizontal axis

perpendicular to the pile axis. The monopile has been driven to its final position 31.8 m below the mean

sea level leading to an embedded depth of 21.9 m.

15

The pile behaviour is investigated corresponding to the serviceability limit state (SLS): the horizontal load

H = 2.0 MN and the overturning bending moment M = 45 MNm, both acting at seabed level, whereas the

vertical load is V = 5.0 MN. The SLS-loads are generated from wind and wave loading.

5.2 Soil conditions

The soil profile consists primarily of sand with the stratification and properties summarized in Table 1. ϕ is

the angle of internal friction and ψ is the dilation angle. The friction angle ϕ is determined from cone

penetration tests according to the procedure proposed by Schmertmann (1978). Apart from the silt/sand

layer with organic material all other layers have relatively high angles of internal friction (36.6° < ϕ < 45.4°).

Further, it is assumed that ψ = ϕ – 30°. The unit weight γ and the submerged unit weight γ´ of the soil are,

except in the layer including the organic material, 20 kN/m3

and 10 kN/m3, respectively. In the organic sand

layer, γ/γ´ yields 17/7 kN/m3.

For the FLAC3D

analyses the classical Mohr-Coulomb criterion and a linear elastic material model have been

combined to describe the elasto-plastic material behaviour of the soil. It is assumed that the stiffness of the

soil can be represented by the secant Young’s modulus Es corresponding to an average axial strain of 0.1 %

as well as Poisson’s ratio ν. According to Lunne et al. (1997), this level of strain is reasonably representative

for many well-designed foundations. Es is stress-dependent and it is determined according to Lengkeek

(2003). Apart from the silt/sand layer with organic material, all soil layers have relatively high stiffness

(100 MPa < Es < 168.8 MPa).

The increase in effective soil stresses caused by the scour protection has not been considered in the

numerical analysis.

5.3 Results and discussion

In Figure 17, the calculated deflections are shown for the case in which the pile is subjected to the static

SLS-loads. The pile behaviour has been determined by means of FLAC3D

and the Winkler model approach

16

employing, respectively, the original API p-y curves given by Equations 1-4 (in the following denoted the API

method) and the API p-y curves employing the modified expression for the initial stiffness given in Equation

9 (in the following denoted the modified API method). The deflection patterns predicted by FLAC3D

and the

modified API method have similar shapes. The monopile behaves relatively rigid implying that a “toe kick”

occurs; this is especially pronounced when considering the deflection behaviour predicted by means of

FLAC3D

and the modified API method. Below 14 m the deflection pattern estimated by the API method and

FLAC3D

deviate significantly. FLAC3D

estimates, for example, greater horizontal deflections at the pile toe

compared to the API method (Table 2). The deviation in deflection pattern may be due to the fact that the

initial stiffness, E*

py, provided by the API method is overestimated at great depths. Since the API method

overestimates the stiffness with depth compared to FLAC3D

and the modified API method, the depth for

zero deflection predicted by the API method is located closer to the seabed (Table 2). Furthermore, the

maximum horizontal deflection at seabed level determined by means of the API method is much lower

compared to the deflections predicted by the other methods (Table 2). The above mentioned observations

also apply for other load levels.

The three approaches predict similar distributions of the moment with depth. However, FLAC3D

estimates

slightly lesser and higher moments at moderate and deep depths, respectively, compared to the API

method and the modified API method. The maximum moments determined by the three approaches are

almost identical (Table 2). The depths to the maximum moment are 3.4 m and 2.1 m, respectively, with

FLAC3D

giving rise to the latter value.

The p-y curves at different depths are shown in Figure 18. Except for the depth x = 2.1 m the API method

has a tendency to overestimate the soil resistance, p, at a given deflection, y, compared to the other two

approaches. The pressures, estimated by means of FLAC3D

, mobilised at the depth x = 7.4 m are less than

the pressures at both x = 2.1 m and x = 3.9 m for a given deflection y. This is due to the lower angle of

17

internal friction and the lower Young’s modulus of elasticity of the third layer compared to the first layer

(Table 1). The above mentioned observations also apply for other load levels and depths.

Generally, the modified API method predicts the results obtained by FLAC3D

better than the API method.

The deviations, however, in the results determined by means of FLAC3D

and the modified API method may

be caused by: the traditional uncertainties related to numerical modelling; shortcomings in the method

proposed by Georgiadis (1983), in which layered soil profiles have been taken into account; shortcomings in

the general shape of the p-y curves; and shortcomings in the definition of the ultimate soil resistance.

6. Conclusions

This paper considers large-diameter non-slender monopiles in sand for offshore wind turbines. In design of

such piles the initial part of the p-y curves are especially important. A modified expression for the initial

slope of the p-y curves has been proposed, in which the slope depends on the depth below the soil surface,

the pile diameter and Young’s modulus of elasticity of the soil. This is in contrast to the method

recommended by the American Petroleum Institute (API) in which the initial part of the p-y curves is

independent of Young's modulus of elasticity and the diameter. The reassessment of the p-y curves

recommended by the API is based on three-dimensional numerical analyses and the reassessment is aiming

for a better prediction of the pile behaviour, especially when exposed to SLS loads.

The differences in pile behaviour by employing a Winkler model incorporating the current p-y curves

recommended by API and a modified version in which the expression for the initial slope of the p-y curves

proposed in this paper is employed, respectively, has been evaluated. The assessment is based on a

monopile for an offshore wind turbine at Horns Rev, Denmark. A three-dimensional numerical model of the

pile at Horns Rev has also been established by means of the commercial software package FLAC3D

.

Generally, the modified API method predicts the results obtained by FLAC3D

considerably better than the

API method.

18

7. References

Abbas, J.M., Chik, Z.H. & Taha, M.R. (2008). Single pile simulation and analysis subjected to lateral load.

Electronic Journal of Geotechnical Engineering, 13E, 1–15.

Achmus, M., Kuo, Y.-S. & Abdel-Rahman, K. (2009). Behavior of monopile foundations under cyclic lateral

load. Computers and Geotechnics, 36, No. 5, 725-735.

API (2000). Recommended practice for planning, designing, and constructing fixed offshore platforms –

Working stress design, API RP2A-WSD. American Petroleum Institute, Washington, D.C., USA, 21. Edition.

Ashford, S. A., & Juirnarongrit, T. (2003). Evaluation of pile diameter effect on initial modulus of subgrade

reaction. Journal of Geotechnical and Geoenvironmental Engineering 129, No. 3, 234-242.

Ashour, M., & Norris, G. (2000). Modeling lateral soil-pile response based on soil-pile interaction. Journal of

Geotechnical and Geoenvironmental Engineering 126, No. 5, 420-428.

Bogard, D. & Matlock, H. (1980). Simplified Calculation of p-y Curves for Laterally Loaded Piles in Sand,

Unpublished Report, The Earth Technology Corporation, Inc., Houston, Texas.

Brinkgreve, R. B. J. & Swolfs, W (2007). PLAXIS 3D FOUNDATION, Material Models manual, Version 2.

PLAXIS b.v.

Budhu, M. & Davies, T. (1987). Nonlinear analysis of laterally loaded piles in cohesionless soils. Canadian

Geotechnical Journal 24, No. 2, 289-296.

Carter, D. P. (1984). A non-linear soil model for predicting lateral pile response. Civil Engineering Dept.,

Univ. of Auckland, New Zealand, Rep. No. 359.

Chik, Z. H., Abbas, J. M., Taha, M. R. & Shafiqu, Q. S. M. (2009). Lateral behavior of single pile in

cohesionless soil subjected to both vertical and horizontal loads. European Journal of Scientific Research 29,

No. 2, 194-205.

Cox, W. R., Reese, L. C. & Grubbs, B. R. (1974). Field testing of laterally loaded piles in sand. Proceedings of

the Sixth Annual Offshore Technology Conference, Houston, Texas, USA, pp. 459-464.

DNV (2010). Design of Offshore Wind Turbine Structures, DNV-OS-J101. Det Norske Veritas, Det Norske

Veritas Classification A/S.

Dobry, R., Vincente, E., O'Rourke, M. & Roesset, J. (1982). Stiffness and damping of single piles. Journal of

Geotechnical Engineering, 108, No. 3, 439-458.

Fan, C. C. & Long, J. H. (2005). Assessment of existing methods for predicting soil response of laterally

loaded piles in sand. Computers and Geotechnics 32, 274-289.

FLAC3D

3.1 manual (2006). Fast langrangian analysis of continua in 3 dimensions. Itasca Consulting Group

Inc., Minneapolis, Minnesota, USA.

Georgiadis, M (1983). Development of p-y curves for layered soils. In Proc. of the Conference on

Geotechnical Practice in Offshore Engineering, pp. 536–545.

19

Hald, T., Mørch, C., Jensen, L., Bakmar, C. L. & Ahle, K (2009). Revisiting monopile design using p-y curves –

Results from full scale measurements on Horns Rev. European Offshore Wind 2009, Stockholm, Sweden.

Ibsen, L. B., Hanson, M., Hjort, T. H. & Thaarup, M. (2009). MC parameter calibration for Baskarp Sand No.

15. DCE Technical Report No. 62, Department of Civil Engineering, Aalborg University, Denmark.

Kim, Y. & Jeong, S. (2011). Analysis of soil resistance on laterally loaded piles based on 3D soil-pile

interaction. Computers and Geotechnics 38, 248-257.

Klinkvort, R. T, Leth, C. T. & Hededal, O. (2010). Centrifuge modelling of a laterally cyclic loaded pile.

Proceedings of International Conference on Physical Modelling in Geotechnics, Zürich, Switzerland, pp. 959-

964.

Kramer, S. L. (1996). Geotechnical Earthquake Engineering. Prentice-Hall International Series in Civil

Engineering and Engineering Mechanics, William J. Hall (eds.), ISBN0-13-374943-6.

Lengkeek, H.J. (2003). Estimation of sand stiffness parameters from cone resistance. PLAXIS Bulletin No. 13,

15–19.

Lesny, K. & Wiemann, J. (2006). Finite-element-modelling of large diameter monopiles for offshore wind

energy converters, Geo Congress 2006, Atlanta, Georgia, USA.

Ling, L. F. (1988). Back analysis of lateral load test on piles. Civil Engineering Dept., Univ. of Auckland, New

Zealand, Rep. No. 460.

Lunne, T., Robertson, P.K. & Powell, J.J.M. (1997). Cone penetration testing in geotechnical practice. Blackie

Academic & Professional.

Murchison, J. M. & O'Neill, M. W. (1984). Evaluation of p-y relationships in cohesionless soils. Analysis and

design of pile foundations. Proceedings of a Symposium in conjunction with the ASCE National Convention,

New York, New York, USA, pp. 174-191.

Poulus, H. & Hull, T. (1989). The Role of Analytical Geomechanics in Foundation Engineering. In Foundation

Eng.: Current principles and Practices 2, pp. 1578-1606.

Schmertmann, J.H. (1978). Guidelines for cone penetration test, performance and design. US Federal

Highway Administration, Washington, DC, USA , Report, FHWA-TS-78-209, 145.

Sørensen, S. P. H., Brødbæk, K. T., Møller, M., Augustesen, A. H. & Ibsen, L. B. (2009). Evaluation of the

load-displacement relationships for large-diameter piles in sand. Proceedings of the Twelfth International

Conference on Civil, Structural and Environmental Engineering Computing, Funchal, Madeira, Portugal,

paper no. 244.

Sørensen, S. P. H. & Ibsen, L. B. (2011). Small-scale Quasi-static tests on non-slender piles situated in sand –

Test results. DCE Technical Report No. 112, Department of Civil Engineering, Aalborg University, Denmark.

Sørensen, S. P. H., Brødbæk, K. T., Møller, M. & Augustesen, A. H. (2012). Review of laterally loaded

monopiles employed as the foundation for offshore wind turbines. DCE Technical Report No. 137,

Department of Civil Engineering, Aalborg University, Denmark.

20

Terzaghi, K. (1955). Evaluation of coefficients of subgrade reaction, Geotechnique 5, No. 4, 297-326.

21

Table 1. Soil conditions including average values of the strength and stiffness parameters for each soil layer.

Depth

[m]

φ

[°]

Es

[MPa]

ν

[-]

Sand 0 - 4.5 45.4 130 0.28

Sand 4.5 - 6.5 40.7 114.3 0.28

Sand(silty) 6.5 - 11.9 38.0 100 0.28

Sand(silty) 11.9 - 14.0 36.6 104.5 0.28

Sand/silt/organic 14.0 - 18.2 27.0 4.5 0.28

Sand 18.2 → 38.7 168.8 0.28

22

Table 2. Comparison of the distribution of bending moment, pile deflection and pile rotation calculated by means of FLAC

3D, the API method, and the modified API method, respectively.

FLAC3D

API Mod. API

Max. moment [MNm] 47.1 48.8 48.3

Depth max. moment [m] 2.5 3.0 2.8

Pile deflection, seabed [mm] 14.8 11.4 13.7

Pile deflection, toe [mm] -1.0 -0.6 -2.5

Rotation, seabed [°] 0.12 0.12 0.13

Depth to zero deflection [m] 13.2 9.4 9.8

23

Figure 1. Winkler model approach in which a pile is modelled as a beam on an elastic foundation with spring stiffnesses given by p-y curves. The circles illustrate hinges.

24

Figure 2. Mesh employed for the numerical model.

25

0 0.05 0.1 0.15 0.2 0.25 0.30

1

2

3

4

5

6

Pile head displacement [m]

Ho

rizo

nta

l lo

ad [

MN

]

2660 zones

8022 zones

18828 zones

67480 zones

Figure 3. Load-displacement relationship for D = 4 m, Lp = 20 m, t = 0.05 m, Es = 53 MPa and φ tr = 40° obtained with

2660, 8022, 18828, and 67480 zones.

26

Figure 4. Cross-sectional view of the test setup, after Sørensen and Ibsen (2011).

27

0 0.2 0.4 0.60

200

400

600

800

1000

1200

1400

Hori

zonta

l lo

ad [

N]

Normalised displacement, y/D [−]

D = 40 mm, L/D = 5, P0 = 100 kPa

Measured

FLAC3D

0 0.05 0.1 0.15 0.2 0.250

2500

5000

7500

10000

12500

15000

Hori

zonta

l lo

ad [

N]

Normalised displacement, y/D [−]

D = 100 mm, L/D = 5, P0 = 100 kPa

Measured

FLAC3D

Figure 5. Comparison of numerical simulations and laboratory tests.

28

−0.01 0 0.01 0.02 0.03

0

5

10

15

20

Displacement, y [m]

Dep

th,

x [

m]

D = 1 m

D = 2 m

D = 3 m

D = 4 m

D = 5 m

D = 6 m

D = 7 m

Figure 6. Pile displacement along the pile for φtr = 37°, Es = 59 MPa, D = 1-7 m, wt = 0.05 m, Lp = 20 m and e/Lp = 0.75. The lateral pile deflection at the soil surface is for all the piles approximately 0.025 m.

29

−0.2 0 0.2 0.4 0.6 0.8 1

0

5

10

15

20

Normalised bending moment, M/Mmax

[−]

Dep

th,

x [

m]

D = 1 m

D = 2 m

D = 3 m

D = 4 m

D = 5 m

D = 6 m

D = 7 m

Figure 7. Distribution of bending moment. D = 1-7 m, φ = 37°, Es = 59 MPa, wt = 0.05 m, Lp = 20 m and e/Lp = 0.75.

30

0 100 200 300 400

0

5

10

15

20

Epy

* [MN/m

2]

Depth

, x [

m]

D = 1 m

D = 2 m

D = 3 m

D = 4 m

D = 5 m

D = 6 m

D = 7 m

Figure 8. Variation of Initial stiffness, E

*py, with depth for D = 1-7 m, φ = 37°, Es = 59 MPa, Lp = 20 m and e/Lp = 0.75.

31

0 50 100 150

0

5

10

15

20

Epy

* [MN/m

2]

Dep

th,

x [

m]

φ = 34°

φ = 37°

φ = 40°

φ = 43°

Figure 9. Variation of initial stiffness, E

*py, with depth for varying internal friction angles. D = 5 m, Es = 59 MPa, Lp =

20 m, e/Lp = 0.75.

32

0 100 200 300 400

0

5

10

15

20

Epy

* [MN/m

2]

Depth

, x [

m]

Es = 21 MPa

Es = 35 MPa

Es = 59 MPa

Es = 74 MPa

Es = 93 MPa

Figure 10. Variation of initial stiffness, E

*py, with depth for varying values of the Young’s modulus of elasticity for the

soil. D = 5 m, Lp = 20 m, e/Lp = 0.75 and φ = 37°.

33

0 20 40 60 80 100

0

5

10

15

20

Epy

* [MN/m

2]

Depth

, x [

m]

e/Lp = 0.50

e/Lp = 0.75

e/Lp = 1.00

e/Lp = 1.50

e/Lp = 2.00

0 50 100 150 200 250 300

0

5

10

15

20

Epy

* [MN/m

2]

Depth

, x [

m]

e/Lp = 0.50

e/Lp = 0.75

e/Lp = 1.00

e/Lp = 1.50

e/Lp = 2.00

0 50 100 150 200

0

5

10

15

20

Epy

* [MN/m

2]

Depth

, x [

m]

e/Lp = 0.50

e/Lp = 0.75

e/Lp = 1.00

e/Lp = 1.50

e/Lp = 2.00

0 100 200 300 400 500

0

5

10

15

20

Epy

* [MN/m

2]

Depth

, x [

m]

e/Lp = 0.50

e/Lp = 0.75

e/Lp = 1.00

e/Lp = 1.50

e/Lp = 2.00

Figure 11. Variation of Initial stiffness, E

*py, with depth for varying e/Lp. Top left – D = 2 m, Es = 21 MPa, Lp = 20 m, φ

= 37°. Top right – D = 2 m, Es = 93 MPa, Lp = 20 m, φ = 37°. Bottom left – D = 6 m, Es = 21 MPa, Lp = 20 m, φ = 37°. Bottom right – D = 6 m, Es = 93 MPa, Lp = 20 m, φ = 37°.

34

0 0.01 0.02 0.03 0.04 0.05 0.060

0.5

1

1.5

y [m]

p [

MN

/m]

EpIp = 2.54 ⋅ 10

7 kNm

2

EpIp = 2.54 ⋅ 10

8 kNm

2

EpIp = 2.54 ⋅ 10

9 kNm

2

Figure 12. Comparison of p-y curves for varying pile bending stiffness. D = 4 m, φ = 40°, x = 4 m, Es = 74 MPa, Lp = 20 m and e/Lp = 0.75.

35

0 5 10 15 20 25

0

5

10

15

20

Epy

*/(E

s/E

s,ref)0.8

[MN/m2]

Depth

, x [

m]

b = 0.3

b = 0.6

b = 1.0

Es = 21 MPa

Es = 35 MPa

Es = 59 MPa

Es = 74 MPa

Es = 93 MPa

Figure 13. Normalized initial stiffness, E

*py, with respect to (Es/Es,ref)

0.8 for Es = 21-93 MPa, Lp = 20 m, e/Lp = 0.75 and

D = 4 m. Three continuous curves describing the variation of initial stiffness with depth are shown, b = 0.3, b = 0.6, and b = 1. All curves have been forced through the average normalised initial stiffness in a depth of 1 m.

36

0 1 2 3 4 5 6 70

1

2

3

4

5

D [m]

Epy

*/(

a⋅(

x/x

ref)b

(Es/E

s,re

f)d)

FLAC3D

, x = 1

FLAC3D

, x = 2

FLAC3D

, x = 3

FLAC3D

, x = 4

Equation 9, c = 0.5

Figure 14. Normalised initial stiffness for varying pile diameter and for φ = 40°, Es = 74 MPa, Lp = 20 m and e/Lp = 0.75. Further, the bending stiffness has been kept constant for all piles with a bending stiffness corresponding to a steel pile with a pile diameter of 4 m and a wall thickness of 0.05 m.

37

0 100 200 300 400

0

5

10

15

20

Epy

* [MN/m

2]

Dep

th,

x [

m]

D = 3 m, FLAC3D

D = 5 m, FLAC3D

D = 3 m, Equation 9

D = 3 m, Equation 9

Figure 15. Comparison of the initial stiffness, E

*py, determined by means of FLAC

3D and Equation 9. Lp = 20 m, wt =

0.05 m, e/Lp = 0.75, φ = 37° and ID = 80 %.

38

CL

8.2 m

1.5 m

D = 4.0m

Scour protection

7.8 mwt = 52 mmE I = 2.64 10 kNmp p

8 2

4.0 mwt = 50 mmE I = 2.54 10 kNmp p

8 2

4.0 mwt = 40 mmE I = 2.05 10 kNmp p

8 2

4.0 mwt = 30 mmE I = 1.55 10 kNmp p

8 2

11.8 mwt = 50 mmE I = 2.54 10 kNmp p

8 2

Soil profile

x = 0.0 m

x = 4.5 m

x = 6.5 m

x = 11.9 m

x = 14.0 m

x = 18.2 m

Sand

Sand

Sand, silty

Sand, silty

Sand/silt/organic

Sand

Figure 16. Geometry and pile properties of a monopile foundation employed at Horns Rev 1 offshore wind farm.

39

−5 0 5 10 15

0

5

10

15

20

Pile deflection, y [mm]

Dep

th, x [

m]

FLAC3D

API

Mod.API

Figure 17. Pile deflections at maximum horizontal load for the monopile foundation of Wind Turbine 14 at Horns Rev 1.

40

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.020

500

1000

1500

2000

2500

Pile deflection, y [m]

So

il r

esi

stan

ce,

p [

kN

/m]

FLAC3D

(x=2.1m)

FLAC3D

(x=3.9m)

FLAC3D

(x=7.4m)

API (x=2.1m,φ=45.4o)

API (x=3.8m,φ=45.4o)

API (x=7.4m,φ=38o)

Mod.API (x=2.1m,φ=45.4o)

Mod.API (x=3.8m,φ=45.4o)

Mod.API (x=7.4m,φ=38o)

Figure 18. Soil resistance as a function of pile deflection and depth for the monopile foundation of Wind Turbine 14 at Horns Rev 1.

Title:

Experimental Evaluation of Backfill in Scour Holes around Offshore Monopiles.

Authors:

Sørensen, S. P. H., Ibsen, L. B., and Frigaard, P.


2010

Published in:

In Proceedings of the 2nd International Symposium on Frontiers in Offshore Geotech-nics, II ISFOG, Perth, Australia, 8-10 November 2010, Balkema Publishers, A.A. /Taylor & Francis, The Netherlands, pp. 617-622.

Number of pages:

6

Due to copyright, the paper is not included

Title:

Assessment of Scour Design for Offshore Monopiles Unprotected Against Scour.

Authors:

Sørensen, S. P. H., and Ibsen, L. B.


2012

Published in:


Number of pages:

42

Assessment of Scour Design for Offshore Monopiles

Unprotected Against Scour

Søren Peder Hyldal Sørensena,∗, Lars Bo Ibsenb

aDepartment og Civil Engineering, Aalborg University, Sohngaardsholmsvej 57, 9000

Aalborg, Denmark, email: [email protected], tlf: +45 6075 5884, fax: +45 9940 8552bDepartment og Civil Engineering, Aalborg University, Sohngaardsholmsvej 57, 9000

Aalborg, Denmark, email: [email protected]

Abstract

When designing offshore monopiles without scour protection, the stiffness of

the foundation will vary with time due to the dependency of sea conditions

on the scour depth. Currently, design regulations of organizations such as

Det Norske Veritas (DNV) and the International Organization for Standard-

ization (ISO) recommend the use of the most extreme local scour depth as

the design scour depth. This is a conservative approach, because the scour

depth depends on the sea conditions and because the equilibrium scour depth

is low during moderate to extreme wave loading. In this paper the effect of

using expected scour depths when designing for the ultimate limit state and

the fatigue limit state are illustrated by means of a desk study.

Keywords: Scour, backfill, pile, wind turbine foundation, fatigue

1. Introduction

The monopile foundation concept is often employed as the foundation for

offshore wind turbines. The monopile foundation concept consists of a steel

∗Corresponding author

Preprint submitted to Ocean Engineering May 3, 2012

cylinder driven or drilled open-ended into the seabed. Typical dimensions

are: pile diameters of D = 4 − 5 m; pile wall thicknesses of wt ≈ 50 −

120 mm; and embedded pile lengths of Lp = 15 − 30 m. The monopile

foundation concept has for offshore wind turbines mainly been employed

in shallow waters with water depths ranging from approximately 10-25 m

supporting 2-5 MW wind turbines.

Offshore wind turbine foundations are exposed to large lateral loads and

overturning bending moments due to among others waves and wind. Ubilla

et al. (2006) state that the design loading on a 3.5 MW offshore wind turbine

is approximately 6 MN in vertical loading, 4 MN in horizontal loading and

120 MNm in overturning moment. Of these the vertical loading is consid-

ered a static load originating from the selfweight of the wind turbine and

the foundation, while the horizontal loads in contrast are cyclic. The wave

frequency of extreme waves is typically 0.07-0.14 Hz while the energy rich

wind turbulence typically has a frequency less than 0.1 Hz. Monopile foun-

dations for offshore wind turbines are therefore designed such that the first

natural frequency lies within the rotor frequency, 1P, and the blade passing

frequency, 3P. Typically, 1P lies within 0.17-33 Hz, and 3P lies within 0.5-1.0

Hz. Therefore, the first natural frequency of offshore wind turbine is required

to be within a narrow range. Hence, offshore wind turbines are heavily af-

fected of changes in the first natural frequency. Offshore wind turbines are

traditionally designed for a lifetime of 20 years. During the lifetime of an

offshore wind turbine approximately 100 cycles with a large load amplitude

are expected and further 106 − 108 cycles with low or intermediate load am-

plitude are expected. Therefore, the wind turbines and the foundation of

2

the wind turbines should be designed such that fatigue failure of the steel

material is prevented.

Around offshore piles installed in sandy or silty soil erosion of soil material

can occur leading to local scour holes. The scour depth relative to the pile di-

ameter is primarily dependent on the Keulegan-Carpenter number. However,

Shield’s parameter, Froude’s number, the water depth, the bed shape and

the sediment dimensions also influence the scour depth. Generally, the scour

depth, S, is large when currents are dominating and small when waves are

dominating. Several authors have investegated scour around piles (Breuser

et al., 1977; Sumer et al., 1992a,b, 1993; Whitehouse, 1998; Richardson and

Davis, 2001; den Boon et al., 2004). To avoid the generation of scour holes,

scour protection consisting of rock infill can be deployed around offshore

monopile foundations. Deployment of scour protection is however costly.

Furthermore, the deployment requires calm sea conditions. The economic

feasibility of deployment of scour protection, therefore, depends on the site

conditions.

When designing an offshore monopile foundation without scour protec-

tion, scour will occur and the depth of the scour hole will vary with time.

Therefore, the stiffness and capacity of the foundation as well as the natu-

ral frequency of the offshore wind turbine will vary with time. DNV (2010)

suggests the use of the local extreme scour depth for all investigations of the

wind turbine. This seems to be a conservative estimate for both the fatigue

limit state (FLS) as well as the ultimate limit state (ULS), since the scour

depth generally is small when waves are dominating and large when currents

are dominating. The stiffness of the foundation is hereby large when the

3

foundation is exposed to major loads and small when minor loads act on the

foundation.

In this paper a review of the scour/backfilling phenomena is presented.

Current knowledge regarding the equilibrium scour depth, the timescale of

scour and backfilling, and the properties of backfilled soil material is as-

sessed. An adaptive scour design approach is presented in which the time

variation of scour depth is included in the FLS- and ULS-design. The po-

tential savings are illustrated for a design example. The objective of the

adaptive scour design approach is not to provide design methods for offshore

monopiles unprotected against scour, but merely to illustrate potential sav-

ings by accounting for the variation of scour depth with the sea conditions

in the design.

2. Review of scour/backfilling phenomena

Installing a vertical cylinder in the offshore environment causes significant

changes to the waterflow resulting in one or more of the following phenomena:

contraction of flow at the side edges of the pile; formation of a horse-shoe

vortex at the base in front of the pile; formation of lee-wake vortices behind

the pile; generation of turbulence; occurance of wave breaking; occurance of

wave reflection; and occurence of wave diffraction. These phenomena increase

the capacity of the local sediment transport causing the formation of local

scour holes. Scour occurs when the near bed shear stress exceeds the critical

shear stress at which sediment starts to move.

In addition to local scour natural instabilities can cause rise and fall of

the seabed level, for instance, sand waves. Furthermore, scour can also occur

4

over a large area. These phenomena are typically denoted general scour. The

present paper focuses on changes in the seabed level arising from local scour.

2.1. Equilibrium scour depth

The scour depth around offshore piles depends on the sea condition. Gen-

erally currents leads to large scour holes while waves leads to smaller scour

holes. For a given sea state an equilibrium scour depth exists. The process

in which the scour depth increases is denoted scouring, while the process in

which the scour depth decreases is denoted backfilling.

Current induced scour has been studied extensively. Breuser et al. (1977)

presented the following equation for the equilibrium scour depth, S∞,c, around

a circular cylindar in steady currents:

S∞,c

D= α tanh

(

h

D

)

(1)

where α is the depth independent equilibrium scour depth and h is the water

depth. To obtain expected values of the scour depth α = 1.3 should be

employed. Høgedal and Hald (2005) suggests α = 1.75 as a conservative

design value of the current generated equilibrium scour depth. Based on

physical experiments for the Q7 Offshore Wind Farm in The Netherlands,

den Boon et al. (2004) adjusted Eq. (1):

S∞,c

D= αK1 tanh

(

K2

h

D

)

(2)

where K1 and K1 are correction factors accounting for depth limitation and

sediment grading.

5

Sumer et al. (1992b) determined the mean value and the standard devia-

tion of the equilibrium scour depth from the experimental data from Breuser

et al. (1977):

S∞,c

D= 1.3 (3)

σS∞,c/D = 0.7 (4)

Det Norske Veritas has in their design regulation DNV (2010) adopted the

mean value of the equilibrium scour depth, cf. Eq. (3). The International

Organization for Standardization has adopted a scour depth of 1.5D in their

recommendations, cf. ISO (2007).

Sumer et al. (1992b) investigated scour around piles under the presence of

waves. They found that the existence and the extension of both the vortex

shedding at the lee side of a pile as well as the horseshoe vortex at the

upstream side of the pile are governed primarily by the Keulegan-Carpenter

number. The Keulegan-Carpenter number is defined as:

KC =UmT

D(5)

where Um denotes the maximum value of the outer oscillatory flow velocity

and T is the wave period. Sumer and Fredsøe (2001) indicate that the peak

wave period, Tp, should be used for irregular waves.

The horseshoe vortex and the vortex shedding at the lee side of the pile

increase the capacity of the local sediment transport. Hereby, these vortices

lead to the formation of local scour holes, and the Keulegan-Carpenter num-

ber, KC, is governing for the equilibrium scour depth. Based on several

6

small-scale tests, Sumer et al. (1992b) proposed the following dependency

between the equilibrium scour depth around a pile in waves, S∞,w, and the

Keulegan-Carpenter number:

S∞,w

D= S∞,c (1− exp (−0.03(KC − 6))) , KC ≥ 6 (6)

The equilibrium scour depth increases for increasing values of KC and ap-

proaches a constant value equal to the current generated scour depth for

large values of KC.

Sumer and Fredsøe (2001) investigated scour around piles in combined

waves and current through experimental modelling. From their study they

introduced the dimensionless parameter Ucw:

Ucw =Uc

Uc + Um(7)

where Uc is the undisturbed current velocity at a distance y = D/2 from the

bed. The dimensionless parameter Ucw describes whether currents or waves

are dominating. For a current only condition, Ucw takes a value of 1, and

for a waves only condition, Ucw takes a value of 0. Based on their tests,

they proposed the following expression for the equilibrium scour depth in

combined waves and current:

S∞,cw

D=S∞,c

D(1− exp (−A(KC − B))) , KC ≥ B (8)

where S∞,c is the equilibrium scour depth for a current dominated sea state

7

and A and B are constants depending on Ucw:

A = 0.03 +3

4U2.6cw (9)

B = exp (−4.7Ucw) (10)

Høgedal and Hald (2005) compared data for the scour depth around ex-

isting unprotected monopiles for offshore wind turbines at the Scroby Sands

Offshore Wind Farm with the expressions of Breuser et al. (1977), den Boon

et al. (2004) and Sumer et al. (1992b), cf. Eq. (1), (2) and (6). They

found that the equilibrium scour depth proposed by Sumer et al. (1992b)

overestimates the scour depth for shallower water (h/D <3). Further, they

concluded that the expressions for the equilibrium scour depth proposed by

Breuser et al. (1977) and den Boon et al. (2004) provides accurate estimates

of the scour depth.

2.2. Prediction of scour depth

In order to predict the scour depth accurately based on a time series

with given wave and current conditions, it is necessary to have an accurate

estimation of the equilibrium scour depth and further an accurate estimation

of the time scale, T , of both the scour and the backfilling process. Sumer

et al. (1992a) investigated the timescale of scour in waves and current through

physical modelling. For currents, they presented 18 tests with pile diameters

varying from 30-510 mm, while they presented 28 tests with pile diameters

of 10-40 mm on the timescale for piles in waves. Based on their experiments

they found that the scour depth during the scour process varies with time,

8

t, as follows:

S = S∞ (1− exp(−t/T )) (11)

where T is the time scale of scour. Sumer et al. (1992a) found that the

timescale in currents is dependent on the ratio between the boundary-layer

thickness, δ, and the pile diameter as well as the Shields parameter, Θ, while

the time scale in waves is dependent on the Keulegan-Carpenter number and

the Shields parameter:

T = T ∗D2

(g(s− 1)d)0.5(12)

T ∗ =1

2000

δ

DΘ−2.2 , current (13)

T ∗ = 10−6

(

KC

Θ

)3

, waves (14)

T ∗ denotes the normalised time scale, g denotes the acceleration due to grav-

ity, s denotes the specific grain density and d denotes the sediment grain size.

Shields parameter can be determined by:

Θ =U2f

(s− 1)gd, current (15)

Θ =U2fm

(s− 1)gd, waves (16)

where Uf is the undisturbed friction velocity and Ufm is the maximum value

of the undisturbed bed shear velocity.

Hartvig et al. (2010) investigated both the scour and the backfilling pro-

cess around piles in the offshore environment through physical modelling.

Initially, they proposed Eq. (17) and (18) for the development of the scour

9

depth, S, with time and the scour voloume, V , with time, respectively.

S = S∞ + (S0 − S∞) exp (−t/TS) (17)

V = V∞ + (V0 − V∞) exp (−t/TV ) (18)

S0 denotes the initial scour depth at t = 0, V0 denotes the initial scour

volume at t = 0, V∞ denotes the equilibrium scour volume, TS denotes the

time scale for the change in scour depth and TV denotes the time scale for

the change in scour volume. The equations account for both the scour and

the backfilling process. From the physical modelling they found that initially

the scour depth decreases slowly while the scour volume decreases quickly

during the backfill process of a minor scour hole. In contrast, the scour depth

decreases quickly while the scour volume decreases slowly during the backfill

process of a large scour hole. These findings illustrate that the shape of the

scour hole changes during the backfilling process. The change of the scour

shape is not included in Eq. (17) and (18). In spite that Eq. (17) and (18)

do not include the change of the scour shape, the equations can be a useful

tool to predict the variation of scour depth or scour volume with time due to

their simple structure. Hartvig et al. (2010) found that backfilling is faster

for combined waves and current than for waves only. For KC = 3, Θ = 0.2

and D = 0.1 m, they determined the normalised time scale for the change in

scour volume, V , during backfilling in waves to 3.9. By means of Eq. (14)

which was developed for the scour process, the normalised time scale, tV ,

of backfilling should be 0.0034. This illustrates that the equations for the

time scale of scour cannot be employed for the backfilling process. Similarly,

10

Fredsøe et al. (1992) found for pipelines that the time scale for the backfilling

process is different from the time scale for the scour process. Hartvig et al.

(2010) conducted a rather limited number of tests regarding the time scale of

backfill with only one type of waves only sea condition, one type of combined

waves and current sea condition and one size of pile diameter. Hence, further

tests are needed for investigation of the time scale of backfill.

Sørensen et al. (2010) conducted a large-scale tests on the time scale

of backfilling around a pile in waves. The pile had a diameter of 0.55 m.

An irregular wave series with KC = 9 and Θ = 0.4 was generated. The

normalised time scale was found to 0.015. The Keulegan-Carpenter number

and Shields Parameter for the test by Hartvig et al. (2010) and Sørensen et al.

(2010) are in the same order of magnitude. However, the normalised time

scale is approximately 260 times larger for the small-scale test by Hartvig

et al. (2010) than for the large-scale test of Sørensen et al. (2010). This

illustrates that the scaling of small scale tests on the backfilling process might

be subject to uncertainties and that more research is needed regarding the

backfilling process.

2.3. Properties of backfilled soil material

Sørensen et al. (2010) investigated the relative density of backfilled soil

material around a pile in waves based on physical modelling. A scour hole

with a scour depth of 1.3D was manually prepared around a pile with a

diameter of 0.55 m. After the preparation of the scour hole an irregular

wave series with KC = 9 and Θ = 0.4 was generated causing backfilling.

After reaching a new equilibrium scour depth, the relative density, ID, of the

backfilled soil material was determined to 65-80 % corresponding to dense

11

sand. Only one test concerning the relative density of backfill was conducted.

Hence, the result is only indicative since the influence of several parameters

needs investigation: the Shields parameter, the Keulegan-Carpenter number,

the dimensionless parameter Ucw, the time period of backfilling, etc. The

relative density of offshore sand near the mudline is often very dense, mainly

due to compaction from waves (Augustesen et al., 2009). Therefore, it is

expected that the relative density of the backfilled soil material compacts

with time. However, the time frame needed for such a compaction is currently

not known. For sand, the strength and stiffness increases for increasing values

of the relative density. Therefore, the findings of Sørensen et al. (2010)

indicate a significant stiffness and strength of the backfilled soil material.

3. Adaptive scour design

When designing offshore monopile foundations unprotected against scour,

design regulations such as DNV (2010) and ISO (2007) recommend that the

local extreme scour depth is employed as design scour depth. This, however,

seems to be a conservative assumption due to the following reasons:

• Extreme local scour normally occurs for a current only situation.

• For combined waves and current and for waves only, the local equilib-

rium scour depth is considerably less than for current only.

• The hydrodynamic loads in ULS and FLS are mainly governed by

waves.

Therefore, the local scour depth is small when the hydrodynamic loads are

large, and the local scour depth is large when the hydrodynamic loads are

12

small.

Høgedal and Hald (2005) conducted a desk study on appropriate scour

depths for the fatigue limit state (FLS) and the ultimate limit state (ULS).

The Scroby Sands Offshore Wind Farm was used as reference for their desk

study. They determined the equilibrium scour depth for possible combina-

tions of the significant wave height, Hs, and the undisturbed current velocity,

UC , by means of Eq. (2) and Eq. (8). From statistical analyses they found

that the scour depth should be 0.63D, 0.05D and 0.61D for respectively

FLS, ULS with extreme waves and ULS with other extreme loads. In their

analyses they assumed that changes in the scour depth occured immedi-

ately. This assumption is non-conservative, which Høgedal and Hald (2005)

also recognised. The large-scale test on backfill presented by Sørensen et al.

(2010), however, illustrate that the backfilling process is fast for a large-scale

monopile in a sea state with extreme waves. The error of not accounting for

the time scale of scour and backfilling might therefore be minor. The desk

study conducted by Høgedal and Hald (2005) was based on the sea conditions

at the Scroby Sands Offshore Wind Farm. Hence, the design scour depths

can not be employed directly for other offshore wind farms.

Combining the findings of Sørensen et al. (2010) regarding the relative

density of backfilled soil material with the desk study of Høgedal and Hald

(2005), the following assumptions might be reasonable for respectively FLS-

and ULS-design:

• FLS - A local extreme scour hole has been developed and afterwards

the scour depth has been reduced due to backfilling. The design scour

depth depends on the site characteristics and can be expected to be in

13

the order of 0.63D. The backfilled soil material has a relative density

of 65-80 %.

• ULS, extreme waves - A local extreme scour hole has been developed

and afterwards the scour depth has been reduced due to backfilling.

The design scour depth depends on the site characteristics and can be

expected to be in the order of 0.05D. The backfilled soil material has

a relative density of 65-80 %.

• ULS, other extreme load - A local extreme scour hole has been devel-

oped and afterwards the scour depth has been reduced due to backfill-

ing. The design scour depth depends on the site characteristics and can

be expected to be in the order of 0.61D. The backfilled soil material

has a relative density of 65-80 %.

4. Example - Design of monopile foundations for offshore wind

turbines based on revised scour adaptive design approach

The potential savings by accounting for the variation of scour depth with

time is illustrated for a wind turbine foundation at the Horns Rev 1 Offshore

Wind Farm. The Horns Rev 1 Wind Farm is located in the North Sea west

of Esbjerg, Denmark. The Wind Farm was built in 2002 and consists of 80

Vestas V80/2 MW wind turbines. Wind turbine 14 is used as example. The

mean water level is 9.0 m at the location of wind turbine 14. The following

five scour/backfilling conditions have been considered:

• Condition 1 - No scour has yet occured.

14

• Condition 2 - A local extreme scour depth of 1.3D is assumed for both

FLS and ULS design. This assumption follows the guidelines of DNV

(2010).

• Condition 3 - A local extreme scour hole with a depth of 1.3D has been

backfilled to a scour depth of 0.63D and 0.05D for respectively FLS

and ULS. The relative density of the backfilled soil material is assumed

to be 0 %.




to be 65 %.




to be 80 %.

For condition 3–5 the design scour depths reported by Høgedal and Hald

(2005) for the Scroby Sands Offshore Wind Farm has been adopted. These

design scour depths are based on the conditions at Scroby Sands and they

are therefore not applicable for the Horns Rev 1 Offshore Wind Farm. How-

ever, since the objective of the current study is merely to illustrate potential

savings by accounting for the time variation of scour/backfilling they have

been adopted.

The first and second natural frequency are determined for condition 1-5.

Accurate predictions of especially the first and second natural frequency are

15

important in order to predict the magnitude of the dynamic load amplifica-

tion. The fatigue life and the maximum pile stresses in the ultimate limit

state during extreme waves is compared for condition 2-5.

4.1. Geometry of pile and tower

Monopiles have been employed as the foundation of the wind turbines

at the Horns Rev 1 Offshore Wind Farm. These monopiles have an outer

diameter of 4.0 m, a total length of 30.0-32.7 m and embedded lengths of

approximately 20-25 m. Transition pieces with outer diameters of 4.34 and

wall thicknesses of 0.09 m constitutes the transition between pile and tower.

The wall thickness, wt, of the monopile for wind turbine 14 varies with depth

as shown in fig. 1. Hereby also the pile bending stiffness, EpIp, varies with

depth. The monopile foundation for wind turbine 14 has a length of 31.6 m

and the embedded length is 21.9 m.

[Figure 1 about here.]

4.2. Soil properties

The soil properties has been determined based on an extensive test pro-

gramme including geotechnical borings, cone penetration tests and triaxial

tests. The soil profile at wind turbine 14 consists primarily of sand. The soil

conditions and parameters are summarised in tab. 1, where ϕp denotes the

peak friction angle, ψ denotes the angle of dilation and ν denotes Poisson’s

ratio. The friction angle has been determined based on the CPT’s according

to the procedure proposed by Schmertmann (1978). The dilatancy angle has

been determined as:

ψ = ϕp − ϕc (19)

16

where ϕc = 30◦ denote the critical state friction angle. The effective unit

weight has for all the sand layers been assumed to be γ′ = 10 kN/m3. For

the organic soil layer the effective unit weight is γ′ = 7 kN/m3.

[Table 1 about here.]

4.3. Loading conditions

For an offshore wind turbine foundation, several load combinations needs

to be investigated. This paper adresses two of these load combinations:

the ultimate limit state with a 50-year wave height and the fatigue limit

state. These two load combinations are shown in tab. 2 where N denotes

the number of load cycles, M denotes the overturning bending moment, H

denotes the horizontal load and V denotes the vertical load.


4.4. Winkler model approach

The Winkler model approach, originally formulated by Winkler (1867),

has been employed to determine the pile behaviour. In the Winkler model

approach, the pile is modelled as a beam on an elastic foundation in which

the interaction between pile and soil is modelled as a series of uncoupled

springs. The stiffnesses of these springs is governed by the so-called p–y

curves, describing the soil resistance acting on the pile wall, p, against the

pile deflection, y. The Winkler model approach is illustrated in fig. 2.


17

The p–y curve formulation proposed by O’Neill and Murchison (1983) and

validated against a database of field tests on piles in sand by Murchison and

O’Neill (1984) has been employed. The formulation is a modification of the

p–y curve formulation originally proposed by Reese et al. (1974). Both formu-

lations are based on the field tests presented by Cox et al. (1974) on flexible

piles. Design regulations such as API (2000), ISO (2007) and DNV (2010)

has adopted the p–y curve formulation proposed by O’Neill and Murchison

(1983). The p–y curve formulation is given in eq. (20)

p(y) = Apu tanh(kx

Apuy) (20)

A is a dimensionless correction factor depending on the type of loading and

the ratio between the depth and the pile diameter. pu is the theoretical

ultimate soil resistance, k is the initial modulus of subgrade reaction and x

is the depth below seabed. The initial slope of the p–y curves is governed by:

E∗

py =dp

dy|y=0 = kx (21)

Hereby, the initial slope of the p–y curves is proportional to the depth below

seabed. The initial modulus of subgrade reaction, k, and the ultimate soil

resistance, pu, both depends on the friction angle of the soil. Furthermore,

pu depends on the depth below seabed and the effective vertical stress.

The soil stratification at wind turbine 14 consists of layered soil. The

p–y curve formulation proposed by O’Neill and Murchison (1983) is valid for

homogeneous soils. According to Georgiadis (1983) and Yang and Jeremic

(2005), the p–y curves should be modified to account for layered soils. The p–

18

y curves has been modified due to layered soil based on the method proposed

by Georgiadis (1983) in which equivalent depths are determined for all layers

beneath the upper soil layer.

The presence of scour holes is in the p–y curves accounted for by reduction

of the effective soil stresses as suggested by ISO (2007) and API (2008).

Hereby, the ultimate soil resistance, pu, is reduced. The initial slope of the

p–y curves is not reduced for local scouring. The reduction of the effective

soil stresses is illustrated in fig. 3. Lin et al. (2010) emphasized that the soil

beneath a scour hole will be overconsolidated. Taking this into account when

calculating p–y curves for the interaction between pile and soil would increase

the ultimate soil resistance, pu. This phenomena has not been accounted for

in the current study.


4.5. Natural frequency

The first and second undamped natural frequency has been determined for

wind turbine 14 by means of the Winkler model approach. The initial slope

of the p–y curves has been employed as stiffness of the soil-pile interaction.

This assumption seems valid for minor vibrations of the wind turbine. For

large vibrations the non-linear soil behaviour should be accounted for. In

the p–y curve formulation proposed by O’Neill and Murchison (1983) cyclic

loading only affects the correction factor A. Hence, the initial slope of the

p–y curves does not change due to cyclic loading. LeBlanc et al. (2010) found

based on small-scale tests on non-slender piles that the secant stiffness of the

unloading path increases with the number of cycles. They conducted tests

19

on piles situated in sand with a relative density of 4-38 %. Whether their

findings are valid for dense to very dense sands has not been clarified. The

effect of the number of cycles on the stiffness of the soil-pile interaction has

not been accounted for in the current study.

The first and second undamped natural frequency of wind turbine 14 is

in tab. 3 and 4 shown for varying scour/backfilling conditions. The first

natural frequency decreases with approximately 5 % when a scour hole of

1.3D has been formed while the second natural frequency decreases with

approximately 10 %. With a scour depth of 0.63D corresponding to a typical

scour depth during fatigue loads the first natural frequency is approximately

3 % lower than the natural frequency prior to scour, while the first natural

frequency decreases with approximately 1.5 % when the scour depth is 0.05D

corresponding to the estimate on the design scour depth for the ultimate

limit state with extreme wave loads. The relative density of the backfilled

soil material has a significant effect on the first and second natural frequency

of the wind turbine. An increase in relative density give rise to an increase

of the natural frequencies of the wind turbine.



4.6. ULS-design

The ultimate limit state design has been investigated for wind turbine 14

for extreme wave loading by means of the Winkler model approach. The soil

parameters from tab. 1 have been implemented directly.

20

The pile bending moment and the maximum cross-sectional von Mises

stress is in fig. 4 and fig. 5 shown for varying scour/backfilling conditions.

Further, the results are summarised in tab. 5. The von Mises stresses, σm,

is determined as:

σm =√

3J2 (22)

where J2 is the second deviatoric stress invariant.




Scour increases the maximum pile bending moment and the depth below

original seabed to the maximum pile bending moment significantly. Fur-

ther, the maximum cross-sectional von Mises sresses increases significantly

for depths larger than 5 m due to the presence of scour. Backfilling sig-

nificantly decreases the maximum cross-sectional von Mises stresses. For a

depth of 10 m below the original seabed the maximum cross-sectional von

Mises stress is 105.2 MPa prior to scouring, 202.3 MPa for a scour depth of

1.3D and 120.0 MPa when a scour hole with a depth of 1.3D has been beck-

filled with sand material with a relative density of 80 % to a new scour depth

of 0.05D. This illustrates that the stresses in the monopile is significantly

lower when employing the design scour depth proposed by Høgedal and Hald

(2005) than when employing a design scour depth of 1.3D as recommended

by DNV (2010).

21

4.7. FLS-design

The fatigue limit state is investigated for a longitudinal welding along

the monopile. Hence, the welding is parallel to the direction of the applied

stress. The welding is categorised as a category C1 welding.

In the current study on the fatigue limit state design, the dynamic am-

plification of stresses due to resonance has not been included. Normally,

dynamic stress amplifications has a significant influence on the fatigue limit

state. However, since the purpose of the study is merely to illustrate the

effect on the FLS-design by adopting a design scour depth accounting for the

actual variations in scour depth, the wind turbine dynamics have not been

included. DNV (2011) proposes the use of S–N curves when investigating

the fatigue life. S–N curves describe the number of cycles, N , at which

failure occurs versus the stress level, ∆σ. The following S–N curve can be

employed for steel:

log(N) = log(a)−m log

(

∆σ

(

t

tref

)k)

(23)

where N is the number of cycles, log(a) is the intercept of the logN axis, m

is the negative inverse slope of the S–N curve, ∆σ is the stress range inserted

in MPa, t is the thickness through which a crack will most likely grow and

tref is a reference thickness. For a steel welding of category C1 located in

seawater, with cathodic protection and exposed to more than 106 cycles the

following parameters can be adopted: m = 5.0, log(a) = 16.081, tref = 25

mm and k = 0.15. For the considered welding, t can be taken as the wall

thickness of the pile. In the current study the stress range at failure has not

22

been reduced by resistance factors.

In fig. 6 and tab. 6 the maximum cross-sectional von Mises stress relative

to the fatigue capacity at N = 107 cycles, σm/σN=107 , is shown for varying

scour/backfill conditions. It can be observed that for x > 5 m, σm/σN=107

is significantly affected by the scour/backfill conditions. Adopting a design

scour depth of 0.063D and a relative density of the backfilled soil material of

ID = 80 % instead of adopting the extreme local scour depth of 1.3D in the

fatigue limit state design causes a decrease in σm/σN=107 of 0 %, 2 %, 24 %

and 37 % at depths below the original seabed of 2 m, 5 m, 10 m and 15 m,

respectively.



5. Conclusions

Around vertical cylinders in the offshore environment scouring will take

place. Due to changing sea conditions, the scour depth will vary with time.

Hereby, also the stiffness and strength of a monopile foundation in the off-

shore environment will vary with time. The Horns Rev 1 Offshore Wind

Farm has been used as example in a desk study to illustrate potential sav-

ings by accounting for the variation in scour depth when designing monopile

foundations that are unprotected from scour development. The desk study

indicated that significant savings in the amount of steel material used for

the foundation can be achieved if accounting for the time variation of scour

depth in FLS- and ULS-design. The design scour depths adopted in the desk

23

study was based on the statistical wave and current data at the Scroby Sands

Offshore Wind Farm. Naturally this leads to large uncertainties since the spe-

cific site conditions affects the variation of scour depht significantly. Further,

the time scale of scouring and backfilling was assumed to be zero which is is

a non-conservative assumption. The actual time scale of scouring and back-

filling needs to be accounted for when determining design scour depths. The

study therefore do not provide guidelines for the design of monopile foun-

dations exposed to scour. However, the desk study illustrates that further

research regarding backfilling can lead to significant savings. Especially the

following issues needs further investigation:

• The time scale of backfilling needs further investigation. Untill now the

time scale has only been investigated for a limited variation of param-

eters such as the Keulegan Carpenter number, the Shields parameter,

the current velocity, etc.

• Since the strength and stiffness of cohesionless materials are highly

dependent on the relative density, the relative density of backfilled soil

material needs to be studied comprehensively. The effect of parameters

such as the Keulegan-Carpenter number, the Shields parameter, the

current velocity, the grain size distribution and the time of backfilling

on the relative density needs to be investigated.

• The scaling of small-scale tests on backfilling needs further investiga-

tion. The time scale of backfill found from the small-scale tests reported

by Hartvig et al. (2010) deviate from the time scale found from large-

scale tests reported by Sørensen et al. (2010). For the two tests the

24

Keulegan-Carpenter number and the Shields parameter were of similar

magnitude. Whether, the deviation is due to scale effects needs further

investigation.

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28

List of Figures

1 Details of the monopile foundation for wind turbine 14 at theHorns Rev 1 Offshore Wind Farm. . . . . . . . . . . . . . . . . 31

2 Winkler model approach . . . . . . . . . . . . . . . . . . . . . 323 Reduction of effective soil stresses due to the presence of scour,

after ISO (2007) and API (2008). SG denotes the scour depthdue to general scour and SL denotes the scour depth due tolocal scour. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4 Distribution of bending moment,M , under ULS-load for vary-ing scour/backfilling conditions. . . . . . . . . . . . . . . . . . 34

5 Distribution of maximum cross-sectional von Mises stress, σm,under ULS-load for varying scour/backfilling conditions. . . . 35

6 Variation with depth for the maximum cross-sectional vonMises stress relative to the fatigue capacity at N = 107 cy-cles for varying scour/backfilling conditions. . . . . . . . . . . 36

29

CL

9.7m

D = 4.0m

7.8 m

wt = 52 mm

E I = 2.64 10 kNmp p

8 2

4.0 m

wt = 50 mm

E I = 2.54 10 kNmp p

8 2

4.0 m

wt = 40 mm

E I = 2.05 10 kNmp p

8 2

4.0 m

wt = 30 mm

E I = 1.55 10 kNmp p

8 2

11.8 m

wt = 50 mm

E I = 2.54 10 kNmp p

8 2

Figure 1: Details of the monopile foundation for wind turbine 14 at the Horns Rev 1Offshore Wind Farm.

30

Figure 2: Winkler model approach

31

Figure 3: Reduction of effective soil stresses due to the presence of scour, after ISO (2007)and API (2008). SG denotes the scour depth due to general scour and SL denotes thescour depth due to local scour.

32

0 20 40 60 80 100 120

0

2

4

6

8

10

12

14

16

18

20

Moment [MNm]

Dep

th [

m]

No scourS/D = 1.3S/D = 0.05, I

D = 0 %

S/D = 0.05, ID

= 65 %

S/D = 0.05, ID

= 80 %

Figure 4: Distribution of bending moment, M , under ULS-load for varyingscour/backfilling conditions.

33

0 20 40 60 80 100 120 140 160 180 200

0

2

4

6

8

10

12

14

16

18

20

σm

[MPa]

Dep

th [

m]


D = 0 %

S/D = 0.05, ID

= 65 %

S/D = 0.05, ID

= 80 %

Figure 5: Distribution of maximum cross-sectional von Mises stress, σm, under ULS-loadfor varying scour/backfilling conditions.

34

0 10 20 30 40 50 60 70 80 90 100 110

0

2

4

6

8

10

12

14

16

18

20

σm

/σN=10

7 [%]

Dep

th [

m]


D = 0 %

S/D = 0.63, ID

= 65 %

S/D = 0.63, ID

= 80 %

Figure 6: Variation with depth for the maximum cross-sectional von Mises stress relativeto the fatigue capacity at N = 107 cycles for varying scour/backfilling conditions.

35

List of Tables

1 Soil profile with average values of the soil parameters for eachsoil layer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2 Design loads at the seabed for wind turbine 14. . . . . . . . . 393 The first natural frequency, fn,1, and the change in fn,1 due to

scour/backfilling. The relative density in the table relates tothe relative density of the backfilled soil material. . . . . . . . 40

4 The second natural frequency, fn,2, and the change in fn,2 dueto scour/backfilling. The relative density in the table relatesto the relative density of the backfilled soil material. . . . . . . 41

5 Comparison of maximum pile bending moment, Mmax, depthto maximum pile bending moment and maximum cross-sectionalvon Mises stress, σm, under ULS-load for varying scour/backfillingconditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

6 Maximum cross-sectional von Mises stress relative to the fa-tigue capacity at N = 107 cycles. . . . . . . . . . . . . . . . . 43

36

Table 1: Soil profile with average values of the soil parameters for each soil layer.

Soil Description Depth ϕp ψ νlayer [m] [◦] [◦] [-]1 Sand 0-4.5 45.4 15.4 0.282 Sand 4.5-6.5 40.7 10.7 0.283 Sand to silty sand 6.5-11.9 38.0 8.0 0.284 Sand to silty sand 11.9-14.0 36.6 6.6 0.285 Sand/silt/organic 14.0-18.2 27.0 0.0 0.286 Sand 18.2- 38.7 8.7 0.28Backfill 1 Sand, ID = 0 % 27.0 0.0 0.28Backfill 2 Sand, ID = 65 % 36.8 6.9 0.28Backfill 3 Sand, ID = 80 % 39.0 9.0 0.28

37

Table 2: Design loads at the seabed for wind turbine 14.

N M H V[MNm] [MN] [MN]

ULS, extreme waves 1 95.0 4.6 5.0FLS 107 28.0 1.4 5.0

38

Table 3: The first natural frequency, fn,1, and the change in fn,1 due to scour/backfilling. The relative density in the table relatesto the relative density of the backfilled soil material.

SD= 0 S

D= 1.3 S

D= 0.05, S

D= 0.05, S

D= 0.05, S

D= 0.63, S

D= 0.63, S

D= 0.63,

ID = 0 % ID = 65 % ID = 80 % ID = 0 % ID = 65 % ID = 80 %fn,1[Hz] 0.293 0.279 0.281 0.288 0.290 0.280 0.285 0.286Change [%] 0.000 -5.046 -4.364 -1.671 -1.125 -4.569 -2.966 -2.591

39

Table 4: The second natural frequency, fn,2, and the change in fn,2 due to scour/backfilling. The relative density in the tablerelates to the relative density of the backfilled soil material.

SD= 0 S

D= 1.3 S

D= 0.05, S

D= 0.05, S

D= 0.05, S

D= 0.63, S

D= 0.63, S

D= 0.63,

ID = 0 % ID = 65 % ID = 80 % ID = 0 % ID = 65 % ID = 80 %fn,2 [Hz] 1.626 1.458 1.478 1.566 1.586 1.473 1.524 1.537Change [%] 0.000 -10.357 -9.127 -3.696 -2.472 -9.410 -6.286 -5.468

40

Table 5: Comparison of maximum pile bending moment, Mmax, depth to maximum pile bending momentand maximum cross-sectional von Mises stress, σm, under ULS-load for varying scour/backfilling conditions.

Mmax Depth for σmMmax x = 2 m x = 5 m x = 10 m x = 15 m

[MNm] [m] [MPa] [MPa] [MPa] [MPa]No scour 105.2 3.3 171.0 162.4 105.2 52.6S/D = 1.3 129.3 8.8 206.5 189.6 202.3 152.0S/D = 0.05, ID = 0 % 115.5 6.1 173.4 182.7 154.8 96.4S/D = 0.05, ID = 65 % 108.5 4.7 172.2 171.8 126.3 70.4S/D = 0.05, ID = 80 % 107.6 4.2 172.0 169.2 120.0 64.9

41

Table 6: Maximum cross-sectional von Mises stress relative to the fatigue capacity atN = 107 cycles.

σm/σN=107

x = 2 m x = 5 m x = 10 m x = 15 m[%] [%] [%] [%]

No scour 85.6 81.5 52.3 24.9S/D = 1.3 86.9 95.9 101.2 70.5S/D = 0.63, ID = 0 % 86.9 95.0 85.1 52.5S/D = 0.63, ID = 65 % 86.9 94.0 78.3 45.7S/D = 0.63, ID = 80 % 86.9 93.8 76.6 44.1

42

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