a numerical study on the behaviour of suction bucket

A NUMERICAL STUDY ON THE BEHAVIOUR OF SUCTION BUCKETFOUNDATIONS FOR OFFSHORE WIND TURBINES IN DENSE SANDS

UNDER CYCLIC LOADING

A THESIS SUBMITTED TOTHE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES

OFMIDDLE EAST TECHNICAL UNIVERSITY

BY

SEYIT ALP YILMAZ

IN PARTIAL FULFILLMENT OF THE REQUIREMENTSFOR

THE DEGREE OF DOCTOR OF PHILOSOPHYIN

CIVIL ENGINEERING

MAY 2021

Approval of the thesis:



submitted by SEYIT ALP YILMAZ in partial fulfillment of the requirements for thedegree of Doctor of Philosophy in Civil Engineering Department, Middle EastTechnical University by,

Prof. Dr. Halil KalıpçılarDean, Graduate School of Natural and Applied Sciences

Prof. Dr. Ahmet TürerHead of Department, Civil Engineering

Prof. Dr. Bahadır Sadık BakırSupervisor, Civil Engineering, METU

Assoc. Prof. Dr. H.Ercan TasanCo-supervisor, Civil Engineering, AYBU

Examining Committee Members:

Prof. Dr. Sami Oguzhan AkbasCivil Engineering, Gazi University

Prof. Dr. Bahadır Sadık BakırCivil Engineering, METU

Assoc. Prof. Dr. Nejan Huvaj SarıhanCivil Engineering, METU

Assoc. Prof. Dr. Mustafa Tolga YılmazEngineering Sciences, METU

Assoc. Prof. Dr. Abdullah SandıkkayaCivil Engineering, Hacettepe University

Date: 24.05.2021

I hereby declare that all information in this document has been obtained andpresented in accordance with academic rules and ethical conduct. I also declarethat, as required by these rules and conduct, I have fully cited and referenced allmaterial and results that are not original to this work.

Name Surname: Seyit Alp Yılmaz

Signature :

iv

ABSTRACT



Yılmaz, Seyit Alp

Ph.D., Department of Civil Engineering

Supervisor: Prof. Dr. Bahadır Sadık Bakır

Co-Supervisor: Assoc. Prof. Dr. H.Ercan Tasan

MAY 2021, 142 pages

Suction bucket foundations simply consist of a cylinder skirt and a top plate, usually

made of steel and installed by the assist of suction are a relatively new and economi-

cally favorable solution for offshore wind turbines which are exposed to high lateral

loads from winds and waves both of which have cyclic characteristic. Understanding

the behaviour under the effect of complex cyclic load environment is essential to as-

sess the design requirements of bucket foundations. Deformations and pore pressures

may accumulate up to irrecoverable range under cyclic loadings. In this research, a

3D finite element model is developed with ANSYS v.18 software to investigate the

behaviour of bucket foundations in dense sandy soils under cyclic axial compressive

and cyclic lateral loads. Hypoplastic constitutive material model with intergranular

strain which is appropriate to use with non-cohesive soils is adopted to simulate the

material behaviour in cyclic load environment. Special attention was given to the pore

pressure accumulation in and around the foundation. A fully coupled two-phase finite

element model is adopted in which soil consists of a solid phase, the skeleton, and a

fluid phase that fully saturates the skeleton. Coupled pore fluid-structure interaction

v

is solved by the fluid flow by Kozeny-Carman poro-permeability relations and equi-

librium conditions. The frictional behavior at the soil-structure interface is modeled

by contact elements. The effect of the bucket dimensions, cyclic loading amplitude

and frequency, relative density of the soil on the deformation and pore pressure be-

havior was investigated with a numerical parametric study. A set of design charts are

developed according to the findings of the parametric study.

Keywords: cyclic axial load, displacement accumulation, hypoplasticity, pore pres-

sure accumulation, suction bucket foundation

vi

ÖZ

AÇIK DENIZ RÜZGAR TÜRBINLERININ VAKUMLU KOVATEMELLERININ SIKI KUMLARDA DÖNGÜSEL YÜKLER ALTINDA

DAVRANISI ÜZERINE SAYISAL BIR ÇALISMA

Yılmaz, Seyit Alp

Doktora, Insaat Mühendisligi Bölümü

Tez Yöneticisi: Prof. Dr. Bahadır Sadık Bakır

Ortak Tez Yöneticisi: Doç. Dr. H.Ercan Tasan

Mayıs 2021 , 142 sayfa

Vakumlu kova temeller, genellikle çelikten yapılmıs ve vakum yardımı ile monte edi-

len bir silindir etegi ve bir üst plakadan olusur. Döngüsel karakteristiklere sahip rüz-

garlardan hem de dalgalardan yüksek yanal yüklere maruz kalan açık deniz rüzgar

türbinleri için nispeten yeni ve ekonomik olarak uygun bir çözümdür. Kova temelle-

rinin tasarım gereksinimlerini degerlendirmek için karmasık döngüsel yük ortamının

etkisi altındaki davranısı anlamak çok önemlidir. Deformasyonlar ve bosluk suyu ba-

sınçları, döngüsel yüklemeler altında kalıcı degere kadar birikebilir. Bu arastırmada,

ANSYS v.18 yazılımı ile sıkı kumlu zeminlerdeki kova temellerin döngüsel ekse-

nel basınç ve yanal yükler altındaki davranısını arastırmak için bir 3B sonlu eleman

modeli gelistirilmistir. Döngüsel yük ortamında malzeme davranısını simüle etmek

için kohezyonsuz zeminlerde kullanılmaya uygun taneler arası birim deformasyon

esasına dayanan hipoplastik malzeme modeli benimsenmistir. Temel içindeki ve çev-

resindeki bosluk suyu basıncı birikimine özel önem verilmistir. Zeminin katı iskeleti

ve iskeleti tamamen doyuran bir sıvı fazdan olustugu, tamamen eslestirilmis iki fazlı

vii

sonlu eleman modeli benimsenmistir. Iki fazlı bosluk suyu-zemin etkilesimi, Kozeny-

Carman bosluk-geçirgenlik iliskileri ve denge kosulları ile çözülmüstür. Zemin-yapı

arayüzündeki sürtünme davranısı temas elemanları ile modellenmistir. Kova boyutla-

rının, döngüsel yükleme genligi, frekansı ve zeminin relatif sıkılıgının deformasyon

ve bosluk suyu basıncı davranısı üzerindeki etkisi sayısal bir parametrik çalısma ile

arastırılmıstır. Parametrik çalısmanın bulgularına göre bir dizi tasarım abagı gelisti-

rilmistir.

Anahtar Kelimeler: döngüsel eksenel yük, deformasyon birikimi, hipoplastisite, bos-

luk suyu basıncı birikimi, vakumlu kova temel

viii

To my family. . .

ix

ACKNOWLEDGMENTS

I offer my sincere thanks to my supervisors Dr. B. Sadık Bakır and Dr. H. Ercan

Tasan for their guidance. Without encouragement and profound advices, this study

would not be possible.

Proffessor Bakır who directed me to the area of numerical modelling and helped me

take a very good path. The fact that this research environment was in his lead and his

support throughout the process made me come to this day.

I can’t thank enough to Dr. Tasan who offered a gratuitous and infinite support

throughout the research and who did not withhold what he knew and always give

value for my work. His encouragement and contributions made me an engineer and a

researcher of a higher level than I started.

I offer my sincere thanks to the members of examining comittee, Dr. S. Oguzhan

Akbas, Dr. Nejan H. Sarıhan, Dr. M. Tolga Yılmaz and Dr. Abdullah Sandıkkaya for

their valuable guidance and contributions.

I would like to express my sincerest gratitude to my wife Tugba and daughter Defne,

for their endless love and encouragement. Their great patience, support and calmness

keeps me poised and gives power. I also give my great thanks to my father Mehmet,

my mother Berrin and little sisters Aysenur and Begüm for their great love and support

from the beginning of my life. Having a wonderful wife and great family makes the

life meaningful with shared great moments in good and bad days.

I am thankful to Sadun Tanıser, Ali Rıza Yücel, A. Fatih Koç, Serdar Sögüt and Birol

Cankurtaran for their great friendship. It is a blessing to have all these great family of

friends.

I am thankful to the Derya Bahçeci and Çaglar Kerimoglu for sharing their great

experience, knowledge and valuable friendship. I am also thankful to my colleagues

Mustafa Turan and Sera Tirkes from Lava Mühendislik for their valuable friendship.

x

TABLE OF CONTENTS

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

ÖZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

TABLE OF CONTENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi

LIST OF ABBREVIATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiv

CHAPTERS

1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Suction Bucket Foundations . . . . . . . . . . . . . . . . . . . . . . 4

1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.3 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 REVIEW OF LITERATURE . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 Loads and Actions . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Installation of Suction Buckets . . . . . . . . . . . . . . . . . . . . . 15

2.4 Behaviour under Cyclic Loading . . . . . . . . . . . . . . . . . . . . 19

2.4.1 Behaviour under Cyclic Lateral Loading . . . . . . . . . . . . 20

xi

2.4.2 Behaviour under Cyclic Axial Loading . . . . . . . . . . . . . 23

2.5 Design of Suction Buckets . . . . . . . . . . . . . . . . . . . . . . . 27

3 FINITE ELEMENT MODEL . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.1 Simulation of Material Behaviour . . . . . . . . . . . . . . . . . . . 32

3.1.1 Hypoplastic Material Model . . . . . . . . . . . . . . . . . . 33

3.1.1.1 Determination of Parameters . . . . . . . . . . . . . . . 36

3.1.2 Hypoplastic Model for Small Strain Performance . . . . . . . 41

3.1.2.1 Determination of Additional Parameters . . . . . . . . . 41

3.1.3 Theory of Permeability . . . . . . . . . . . . . . . . . . . . . 43

3.1.3.1 Kozeny-Carman Relationship . . . . . . . . . . . . . . 44

3.1.4 Two-Phase Model . . . . . . . . . . . . . . . . . . . . . . . . 45

3.2 Details of Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.3 Verification of Finite Element Model . . . . . . . . . . . . . . . . . 55

3.3.1 Verification of Geometric Modelling, Mesh and Boundary Con-ditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

Prototype Bucket Foundation at Frederikshavn . . . . . . . . . . 57

Prototype Bucket Foundation at Sandy Haven . . . . . . . . . . 57

3.3.2 Verification of Two-Phase Model Implementation . . . . . . . 58

Consolidation of a Finite Layer Under Surface Surcharge . . . . 58

CU Cyclic Triaxial Test on Hochstetten Sand . . . . . . . . . . 59

CU Cyclic Triaxial Test on Toyoura Sand . . . . . . . . . . . . 60

CU Cyclic Triaxial Test on Karlsruher Sand . . . . . . . . . . . 61

3.3.3 Verification of Complete Model with Centrifuge Tests of BucketFoundation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

xii

3.3.3.1 Centrifuge Tests on Fujian Sand . . . . . . . . . . . . . 61

3.3.3.2 Centrifuge Tests on Baskarp Sand . . . . . . . . . . . . 65

3.3.4 Summary of Verification Works . . . . . . . . . . . . . . . . . 66

4 BEHAVIOUR UNDER CYCLIC LOADING . . . . . . . . . . . . . . . . . 69

4.1 Reference Set of Parameters . . . . . . . . . . . . . . . . . . . . . . 71

4.1.1 Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.1.1.1 Saturated Sandy Soil . . . . . . . . . . . . . . . . . . . 71

4.1.1.2 Bucket Foundation . . . . . . . . . . . . . . . . . . . . 72

4.1.1.3 Bucket-Soil Interaction . . . . . . . . . . . . . . . . . 72

4.1.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.1.2.1 Multipod . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.1.2.2 Monopod . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.1.3 Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.1.3.1 Cyclic Axial Compression . . . . . . . . . . . . . . . . 73

4.1.3.2 Cyclic Lateral Loading . . . . . . . . . . . . . . . . . . 74

4.1.3.3 Frequency and Duration of Loading . . . . . . . . . . . 76

4.1.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.2 Studies on Bucket Behaviour under Cyclic Axial Compressive Load . 78

4.2.1 General System Response . . . . . . . . . . . . . . . . . . . . 78

4.2.2 Load Bearing Mechanism . . . . . . . . . . . . . . . . . . . . 81

4.2.2.1 Effect of Cyclic Loading Amplitude, Fcyc . . . . . . . . 82

4.2.2.2 Effect of Cyclic Loading Frequency, f . . . . . . . . . . 85

4.2.2.3 Effect of Aspect Ratio, L/D . . . . . . . . . . . . . . . 87

xiii

4.2.2.4 Effect of Coefficient of Skin Friction, µ . . . . . . . . . 88

4.2.2.5 Effect of Initial Relative Density, Dr of Soil . . . . . . . 89

4.2.3 Effect of the Constitutive Model Improvements on Behaviour . 89

4.2.4 Sensitivity of Results to the Constitutive Model Parameters . . 90

4.3 Studies on Bucket Behaviour under Cyclic Lateral Load . . . . . . . 92

4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

4.4.1 Cyclic Axial Compression . . . . . . . . . . . . . . . . . . . 97

4.4.2 Cyclic Lateral Loading . . . . . . . . . . . . . . . . . . . . . 99

5 DESIGN OF BUCKETS FOR CYCLIC LOADING . . . . . . . . . . . . . 101

6 CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

APPENDICES

A DESIGN CHARTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

CURRICULUM VITAE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

xiv

LIST OF TABLES

TABLES

Table 3.1 Hypoplastic Material Properties of Hochstetten Sand, (Niemunis

and Herle, 1997) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Table 3.2 Parameters of Toyoura Sand, (1) Ochmanski et al. (2014) (2) Hong

et al. (2017) (3) Ng et al. (2015) (4) This Study . . . . . . . . . . . . . . . 60

Table 3.3 Hypoplastic Material Properties of Karlsruher Sand, Wichtmann

and Triantafyllidis (2005) . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Table 3.4 Hypoplastic Material Properties for Fujian Sand, Wang et al. (2018a)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Table 3.5 Hypoplastic Material Properties of Baskarp Sand, Ragni et al. (2020) 66

Table 4.1 Hypoplastic Material Properties with IGS, adopted from Le (2015) . 71

Table 4.2 Model Parameters for Reference System . . . . . . . . . . . . . . . 77

xv

LIST OF FIGURES

FIGURES

Figure 1.1 (a) World consumption (in exajoules), (b) Shares of global pri-

mary energy (BP, 2020) . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Figure 1.2 Offshore wind potential of the great countries identified as the

largest national emitters of CO2 (IEA, 2020) . . . . . . . . . . . . . . . 2

Figure 1.3 Major foundation types of OWTs, from left to right : gravity

based, mono-pile, mono-bucket, piled tripod, piled jacket and bucket

jacket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Figure 1.4 Examples of skirted foundations, buckets of four-legged SBJ to

be installed at in Aberdeen Bay by Kihlström (2019) (left), the three-

legged SBJ installed at Borkum Riffgrund 1 by Ørsted (2019) (right)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Figure 1.5 Typical elements of a suction bucket . . . . . . . . . . . . . . . 6

Figure 1.6 Typical procedure of a suction assisted bucket installation . . . . 6

Figure 1.7 Installation of a suction bucket . . . . . . . . . . . . . . . . . . 7

Figure 2.1 Typical frequency ranges for OWTs, Leblanc (2009) . . . . . . . 15

Figure 2.2 Comparison of the observed rotation fitted with Equation 2.1,

Foglia et al. (2012) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Figure 2.3 Rotation of bucket with respect to center of rotation, Zhu et al.

(2013) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

xvi

Figure 2.4 Failure mechanisms, Senders (2008) . . . . . . . . . . . . . . . 25

Figure 2.5 Design procedure for an offshore wind turbine foundation . . . . 27

Figure 3.1 Determination of critical state parameter from angle of repose,

Herle and Gudehus (1999) . . . . . . . . . . . . . . . . . . . . . . . . 36

Figure 3.2 Determination of exponent n (left), Effect of different values of

hs on calculated compression curves using Equation 3.20 (right), Herle

and Gudehus (1999) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Figure 3.3 Pressure dependent minimum void ratio ed, Herle and Gudehus

(1999) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Figure 3.4 Determination of ed based on Cu at ps = 55 kPa (left), Determi-

nation of emax based on grain angularity, Youd (1973) (right) . . . . . . 38

Figure 3.5 Idealized packing of grains for minimum density, Herle and

Gudehus (1999) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Figure 3.6 Characteristic stiffness for model calibration, Niemunis and Herle

(1997) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Figure 3.7 Correlation of βr, Niemunis and Herle (1997) . . . . . . . . . . 43

Figure 3.8 u20p8 element (Tasan, 2011) . . . . . . . . . . . . . . . . . . . 46

Figure 3.9 Schematic description of multipod and monopod structures . . . 53

Figure 3.10 Element types . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Figure 3.11 FE model of single suction bucket . . . . . . . . . . . . . . . . 54

Figure 3.12 Preliminary calculations for determination of suitable model di-

mensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Figure 3.13 Moment - rotational displacement of bucket at Frederikshavn . . 57

Figure 3.14 Horizontal Load - Rotation of bucket at Sandy Haven . . . . . . 58

xvii

Figure 3.15 Simulation of the consolidation of a finite layer under surface load 59

Figure 3.16 Simulation of undrained triaxial tests on Hochstetten sand, Niemu-

nis and Herle (1997), on Toyoura sand Ishihara (1975), on Karlsruher

sand, Wichtmann and Triantafyllidis (2005) . . . . . . . . . . . . . . . 62

Figure 3.17 Simulation of axial strain vs deviatoric stress relationship for

Karlsruher sand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Figure 3.18 Simulated tests according toWang et al. (2018a) . . . . . . . . . 63

Figure 3.19 Simulation of monotonic test and cyclic test on Fujian Sand . . . 63

Figure 3.20 Simulated tests according to Bienen et al. (2018a,1) . . . . . . . 66

Figure 3.21 Simulation of cyclic centrifuge test on Baskarp sand . . . . . . . 66

Figure 4.1 Description of multipod structure . . . . . . . . . . . . . . . . . 69

Figure 4.2 Description of monopod structure . . . . . . . . . . . . . . . . . 70

Figure 4.3 Loading scheme and legend for resistance components in axial

loading (a) Cyclic loading pattern, (b) Loads on components . . . . . . 74

Figure 4.4 Axial monotonic loading test . . . . . . . . . . . . . . . . . . . 75

Figure 4.5 Loading scheme and legend for resistance components in lateral

loading (a) Cyclic loading pattern, (b) Loads on components . . . . . . 75

Figure 4.6 Lateral monotonic loading test . . . . . . . . . . . . . . . . . . 76

Figure 4.7 Schematic Description of Parametric Analyses . . . . . . . . . . 77

Figure 4.8 Principal behaviours under cyclic loading Goldscheider and Gude-

hus (1976) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

Figure 4.9 Effect of load level on plastic deformations for reference system

(Table 4.2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

xviii

Figure 4.10 Effect of load level on foundation stiffness for reference system

(Table 4.2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

Figure 4.11 Effect of aspect ratio on plastic deformations . . . . . . . . . . . 80

Figure 4.12 Effect of frequency on plastic deformations . . . . . . . . . . . . 81

Figure 4.13 Effect of relative density on plastic deformations . . . . . . . . . 81

Figure 4.14 Load distribution inside the bucket . . . . . . . . . . . . . . . . 82

Figure 4.15 Effect of cyclic loading amplitude on the load share of bucket

components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

Figure 4.16 Effect of load level on accumulation of excess pore pressure

(kPa) for reference system . . . . . . . . . . . . . . . . . . . . . . . . 83

Figure 4.17 Soil displacements inside and around the bucket at the end of

12th cycle relative to 1st cycle under (a) Fcyc = 0.15 Fult and (b) Fcyc =

0.25 Fult . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

Figure 4.18 (a) to (c) Effect of cyclic loading frequency on the pore pressure

development at the end of 12th cycle relative to 1st cycle, (d) to (f) Load

share of bucket components . . . . . . . . . . . . . . . . . . . . . . . 86

Figure 4.19 (a) to (c) Effect of aspect ratio on the load share of bucket com-

ponents in quantity, (d) to (f) Effect of aspect ratio on the load share of

bucket components as relative percentage . . . . . . . . . . . . . . . . 87

Figure 4.20 Effect of skin friction coefficient on the load share of bucket

components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

Figure 4.21 (a) to (c) Effects of initial relative density of soil on the pore

pressure development at the end of 12th cycle relative to 1st cycle, (d) to

(e) Effects of initial relative density of soil on the load share of bucket

components from Dr= 90% to 70% . . . . . . . . . . . . . . . . . . . . 90

Figure 4.22 Effect of the constitutive model improvements on behaviour . . . 91

xix

Figure 4.23 Effect of the constitutive model parameters on behaviour . . . . 91

Figure 4.24 Effect of cyclic lateral loading amplitude on the angular rotation

of bucket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

Figure 4.25 Effect of vertical static load on the angular rotation of the bucket

under cyclic lateral Loading . . . . . . . . . . . . . . . . . . . . . . . . 94

Figure 4.26 Effect of initial permeability on the angular rotation of the bucket

under cyclic lateral Loading . . . . . . . . . . . . . . . . . . . . . . . . 95

Figure 4.27 Effect of initial relative density on the angular rotation of the

bucket under cyclic lateral Loading . . . . . . . . . . . . . . . . . . . . 95

Figure 4.28 Excess pore pressure development in soil after loading cycle of

number N = 1, 6 and 12 for different cyclic loading levels . . . . . . . . 96

Figure 4.29 Deformation of Bucket at the End of 12 Cycle Loading under

Hcyc = 0.15Hult . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

Figure 5.1 Expected cyclic response for L/D = 1.0 bucket in a sandy soil

with kinitial = 1.0x10-4 m/s under a cyclic axial compressive loading fre-

quency f =0.10 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103



quency f =0.05 and 0.20 Hz. . . . . . . . . . . . . . . . . . . . . . . . . 104


under a cyclic axial compressive loading frequency f =0.10 with kinitial

= 1.0x10-3 to 1.0x10-5 m/s . . . . . . . . . . . . . . . . . . . . . . . . . 105

Figure 5.4 Expected cyclic response envelope for L/D = 0.80 to 1.30 buck-

ets in a sandy soil under a cyclic axial compressive loading frequency

f =0.05 to 0.10 Hz with kinitial = 1.0x10-3 to 1.0x10-5 . . . . . . . . . . . 106

xx

Figure A.1 Expected cyclic response for L/D = 0.8 bucket in a sandy soil


quency f =0.05 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126



quency f =0.05 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126



quency f =0.05 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127



quency f =0.10 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127



quency f =0.10 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128



quency f =0.10 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128



quency f =0.20 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129



quency f =0.20 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129



quency f =0.20 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

xxi



quency f =0.05 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130



quency f =0.05 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131



quency f =0.05 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131



quency f =0.10 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132



quency f =0.10 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132



quency f =0.10 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133



quency f =0.20 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133



quency f =0.20 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134



quency f =0.20 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

xxii



quency f =0.05 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135



quency f =0.05 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135



quency f =0.05 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136



quency f =0.10 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136



quency f =0.10 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137



quency f =0.10 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137



quency f =0.20 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138



quency f =0.20 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138



quency f =0.20 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

xxiii

LIST OF ABBREVIATIONS

ABBREVIATIONS

2D 2 Dimensional

3D 3 Dimensional

OWT Offshore wind turbine

L Length of bucket skirt

D Diameter of bucket

Pin Pore pressure inside the bucket

Pout Pore pressure outside the bucket

SBJ Suction bucket jacket

WEC World Energy Council

IEA International Energy Association

UNFCCC United Nations Framework Convention on Climate Change

FE Finite element

JON-SWAP Joint European North Sea Wave Project

API American Petroleum Institute

DNV Det Norske Veritas

CSSR Cyclic Shear Stress Ratio

Ru Relative pore pressure

∆Ru Increase in relative pore pressure

N Number of cycles

N liq Number of cycles to reach liquefaction

T Stress rate tensor

T Cauchy stress tensor

D Stretch rate tensor

xxiv

ψi Scalar functions of invariants and joint invariants of T and D

Ci Material parameters

T* Deviatoric stress

tr Trace operator in algebra

S "structure tensor" or "back stress"

ϕ Critical friction angle

hs Granulate hardness

n Exponent controlling void ratio

α Material parameter

β Material parameter

ed0 Minimum void ratio

ec0 Maximum void ratio

ei0 Critical void ratio

M Stiffness tensor

R Parameter controlling the size of the elastic range

mr Parameter controlling initial shear modulus upon 180o path re-

versal

mt Parameter controlling initial shear modulus upon 90o path re-

versal

βR Parameter controlling the intergranular strain evolution rate

χ Parameter controlling the tangent stiffness degradation

Q Rate of flow

k Darcy’s coefficient of permeability

h3 Head at the begin of soil

h4 Head at the end of soil

Lsample Length of sample

i Hydraulic gradient

CH Hazen’s coefficient

xxv

D10 Particle size that 10% of soil is finer

D60 Particle size that 60% of soil is finer

CC Carman coefficient

g gravity

µw Dynamic viscosity of water

ρw Density of water

DR-C Specific weight

e Void ratio

CK-C Kozeny-Carman coefficient

xxvi

CHAPTER 1

INTRODUCTION

Economic growth and technological development are highly dependent on the energy,

thus the amount of required energy to meet the needs of society is increasing everyday.

Figure 1.1a according to BP (2020) shows the energy consumption all over the world

for transportation, electricity, heating and industry, the majority of which is met with

fossil fuels. In the last 20 years, a considerable increase occurred in the renewable

energy production such that the growth in wind and solar energy is higher than 100%

but still accounted for only less than 15% of the total production (BP, 2020; IEA,

2020; WEC, 2016) as shown in Figure 1.1b.

Figure 1.1: (a) World consumption (in exajoules), (b) Shares of global primary energy

(BP, 2020)

Consequently, majority of global greenhouse gas emissions is contributed by the

1

energy-related CO2 pollution which in the last centuries caused an almost irreversible

climate change that interests all societies of the world. To prevent the situation from

getting worse, many countries take actions in energy policies such that the govern-

ments under United Nations Framework Convention on Climate Change (UNFCCC)

aims to keep global warming to just below 2oC compared to the pre-industrial level

by 2035 (Letcher, 2017). In addition to pollution and global warming, not all coun-

tries have fossil fuel resources, which create dependency on foreign energy sources.

Today, achievement of this transformation to clean and renewable sources has greater

potential with the new technological developments in wind energy.

Figure 1.2 according to IEA (2020) shows the potential of offshore wind power for the

largest CO2 emitter countries. According to this figure, even if only a small portion

of the total available offshore wind power potential could be tapped, the energy to be

produced would be greater than the total consumption all over the world. With the

recent technological developments and mass production of bigger and more efficient

turbines, offshore wind provides feasible prices for renewable energy and it is also

clean and unlimited resource.

Figure 1.2: Offshore wind potential of the great countries identified as the largest

national emitters of CO2 (IEA, 2020)

2

Feasibility of offshore platforms are highly dependent on a reliable and economic

foundation systems which generally have three main types as gravity-based, piled

and skirted (i.e. suction bucket) foundations all of which are fixed type structures.

For very deep waters, it is possible to use tension leg or low-roll floaters.

Gravity based foundations satisfy the stability with self weight. Mostly suitable for

small to medium scale offshore wind turbines (OWTs) (i.e. < 5 MW) in rather dense

soil conditions and rocky formations in the shallow water depths (i.e < 25 m) where

pile driving is not feasible.

Piles and buckets can be used as mono, jacket and tripod configuration. A jacket

foundation is a three or four-legged steel lattice structure. At the tip of each jacket

leg, there is a pile or bucket support. The turbine tower is mounted on top of the

lattice. Tripods have three legs as the name implies and legs are connected to a central

column to support the tower. Mono-piles and single buckets resist lateral loads and

bending moments. The tripods and jackets on the other hand have their moment arms

so that the piles and buckets are subjected to axial compression and tension forces

under lateral loading of turbine.

Major supporting structures are illustrated in Figure 1.3.

Figure 1.3: Major foundation types of OWTs, from left to right : gravity based,

mono-pile, mono-bucket, piled tripod, piled jacket and bucket jacket

3

Nowadays, piles are most common type for OWTs with over 80% of the total installed

foundations are mono-piles (WindEurope, 2019). Piles have applicability from soft

clays to soft rock types whenever driving is possible. Maximum pile penetration

depth is limited with the capacity of current installation equipments, stiffness of soil

and buckling of the thin walled pile. The equipments may be jack-up vessels or

floating vessels with a crane. A hydraulic hammer, capacity and dimensions of which

depends on the pile and soil conditions, drives the pile into seabed. Typical hammers

can provide 30 to 50 blows per minute. Depending on the penetration by blow and

required depth, duration of driving averages at 4-6 hours. Total installation time is

approximately 1 pile for a day (Energinet.dk, 2015).

In order to achieve the required horizontal and vertical capacity, necessary embed-

ment length may be very long which consequently can increase the material cost

excessively, in addition, driving very deep may not be possible. Besides the econom-

ical concerns and practicability, environmental impact should be taken into account.

During the hammering of pile foundations, the sound and vibrations affect the marine

species deadly (Merchant et al., 2020).

In summary, installation procedure for piles is rather compelling and expensive. Ac-

cording to Oh et al. (2018), 20 to 45% of the total cost of an OWT is foundation

construction cost from shallow to deep waters.

On the other hand, suction bucket foundations have been started to be considered for

OWTs, which offer less cost and installation effort but the experience and information

on the behaviour is relatively less. Here in this study, these bucket foundations are

investigated under cyclic loading conditions to understand further.

1.1 Suction Bucket Foundations

In the last 25 years, a new foundation system called "suction caissons" or "bucket

foundations" have been implemented and started to be used widely. Although it is

qualified as "new", it is only new as a fixed foundation system. Suction buckets are

mostly utilized as anchorage systems which date back to 1950s but it is the first time

that the suction buckets are utilized as fixed foundations alone in early 1990s. Draup-

4

ner E (Europipe 16/11E) and Sleipner T platforms in the North Sea are the pioneer

applications of suction buckets which showed that penetration of walls into very dense

sands is possible by using suction assistance. These successful applications has re-

vealed that construction and material costs can be reduced drastically. Recently, suc-

tion buckets have been deployed in the offshore wind sector with installations taking

place at the Borkum Riffgrund 1 (2014; one position), Borkum Riffgrund 2 (2018;

20 positions) and Aberdeen Bay (2018; 11 positions) offshore windfarms (Ørsted,

2019).

Figure 1.4: Examples of skirted foundations, buckets of four-legged SBJ to be in-

stalled at in Aberdeen Bay by Kihlström (2019) (left), the three-legged SBJ installed

at Borkum Riffgrund 1 by Ørsted (2019) (right)

Suction buckets are simply large cylindrical steel structures, the base is open and the

top is closed (by a top plate) like an upturned bucket. The top plate (or lid) can be a

stiffened flat plate, or a dome. In general, skirt (or wall) length (L) to diameter (D)

ratio can be close to 1 or below (shallow-wide formation) and greater than 1 (narrow-

deep formation) based on the soil conditions. In cohesive soils, L/D ratio tends to

be greater than non-cohesive soils due to installation problems such as piping and

critical gradient. The thickness of the skirt is generally 0.3% to 0.6% of the diameter

(Tran, 2005). Examples of some suction buckets are shown in Figure 1.4 and typical

elements of a suction bucket is illustrated in Figure 1.5.

The suction buckets are favourable due to their relatively simple installation opera-

tion which starts with an initial penetration into the seabed caused by its self weight

as shown in Figure 1.6a. After initial penetration, water that entrapped inside the

bucket is pumped out to develop a difference between outside pressure (Pout) and in-

5

side pressure (Pin) (i.e. suction) as in Figure 1.6b. Lastly, the pump is off and valve

is closed as in Figure 1.6c. The pressure difference results in a force on the bucket to

embed itself as given in the free body diagram in Figure 1.7.

Figure 1.5: Typical elements of a suction bucket

Figure 1.6: Typical procedure of a suction assisted bucket installation

Decreasing the installation time is another important aspect of buckets since daily

rates of vessels and equipments are significant part of the total cost Lacal-Arántegui

et al. (2018).

Before the latest suction bucket jackets mentioned earlier, the suction buckets have

already been employed as foundation for met masts, substations and OWTs (Ibsen,

2008; Kim et al., 2014a; Leblanc, 2009; Oh et al., 2018; Wang et al., 2018b; Zhang

et al., 2007), in addition to pioneer applications in oil industry (Clausen and Tjelta,

1995). Experiences have revealed that construction and material costs can be reduced

6

drastically with reversible and noise free installation process and easy transportation.

Figure 1.7: Installation of a suction bucket

Cyclic loads, induced by wind and waves, play a special role in the design of suc-

tion bucket foundations for OWTs. There is no standard or guideline that is fully

dedicated to suction bucket foundations yet. General offshore structure design stan-

dards are adopted for suction buckets. However, it requires further considerations for

the mobilized suction inside the bucket and cyclic capacity where there is a lack of

experience (Sturm, 2017). Significant research has been recently devoted experimen-

tally (especially centrifuge tests) and numerically. It is very expensive to conduct full

scale tests. In addition, alteration of the soil, geometry and loading conditions are

not achievable. Small scale centrifuge test can fulfil that purpose but this time scaling

problems especially in terms of viscosity of pore fluid and the particle size of soil

which can affect the results significantly. It is essential to support the experiments

with numerical solutions. A significant FEA effort is given to the tensile capacity of

buckets by Achmus and Thieken (2014) with a coupled pore fluid diffusion and stress

analysis but relatively less attention is given to compression side with a FE modelling

sophisticated at this level. Here, this study proposes to focus on this deficiency. Suc-

tion buckets are suitable for dense sandy formation, thus, a material constitutive law

that is appropriate for modelling non cohesive soils is necessary where a non-linear

hypoplastic constitutive model with intergranular strain concept is used for that rea-

son. This concept is accepted to give good results for modelling according to the

previous studies on OWT piles (Tasan, 2011,1) and buckets in tension (Achmus and

Thieken, 2014; Fiumana, 2020). A coupled two-phase model is also adopted here

7

which allows the description of the load-bearing behaviour. Previous studies focus-

ing on the suction buckets under cyclic axial compression with constant permeability

by Tas, an and Akdag (2018) pointed to findings worth studying in this area.

Contribution of this thesis is first to improve the analysis tool by implementing a void-

ratio dependent permeability calculation by Kozeny-Carman equation and also refine

the u-p model by which the compressibility properties of constituents and damping

can be considered. The use of Kozeny-Carman equation is known to give good ap-

proximations to the experimental findings according to finite element and discrete

element simulations for porous media (Achmus and Thieken, 2014; Aubram et al.,

2015; Chrisopoulos et al., 2016; Fiumana, 2020; Lambe and Whitman, 1969; Oh

et al., 2018; Rattez, 2017; Sun, 2020; Tasan, 2011,1; Tas, an and Akdag, 2018; Tasan

and Yilmaz, 2019). This improved tool can be applied to suction buckets to obtain

a good accuracy on the estimation of the behaviour under cyclic loads to achieve

following objectives.

1.2 Objectives

This study aims to investigate the behaviour of suction buckets under cyclic loads and

assess a relation between cyclic loading and failure for design purpose. Due to lack

of experience on cyclic response of OWTs, the behaviour of buckets embedded in

saturated sandy soils subjected to cyclic loading is investigated numerically by using

a sophisticated finite element model mentioned above.

Parts of the work presented in this thesis have been or are in the process of being

published.

• S.Alp Yılmaz, H.Ercan Tasan. (2019). Numerical investigations on the be-

haviour of offshore suction bucket foundations under cyclic axial loading. Pro-

ceedings of the XVII ECSMGE-2019. Reykjavik: The Icelandic Geotechnical

Society. (Published, doi:10.32075/17ecsmge-2019-0019)

• S.Alp Yılmaz, H.Ercan Tasan. (2020). A Numerical Study on the Behaviour

of Offshore Suction Bucket Foundations under Cyclic Lateral Loading. ASCE

8

GEOCONGRESS 2020, Minneapolis, USA.

(Published, doi:10.1061/9780784482810.088)

• S. Alp Yılmaz, H.Ercan Tasan. (2020). A Numerical Study on the Behaviour of

Offshore Suction Bucket Foundations under Cyclic Axial Compressive Loading.

International Journal of Geotechnical Engineering. (Under Review)

In parallel, an additional research was conducted on the effects of installation on

the behaviour of suction buckets under cyclic axial compression but the installation

phase is out of main focus of this thesis study. Details of some important findings are

presented in the literature review.

• H.Ercan Tasan, S.Alp Yılmaz. (2019). Effects of Installation on the Cyclic

Axial Behaviour of Suction Buckets in Sandy Soils. Applied Ocean Research.

(Published, doi:10.1016/j.apor.2019.101905)

1.3 Scope

Organization of the thesis is as follows:

In Chapter 2, a brief review of literature on installation, analysis and design of suction

buckets is given. Main experiences in the installation problems such as critical pres-

sure, piping, liquefying of soil, plug and heave problems are discussed. In addition,

very important findings on the long term behaviour experienced under cyclic loading

of centrifuge tests are presented.

In Chapter 3, the principles of the two-phase model that is used in finite element anal-

ysis where hypoplastic material law with inter-granular strain is adopted for the solid

skeleton and the Kozeny-Carman relationship for the porosity-permeability interac-

tion. Later, some verification efforts are presented and discussed.

In Chapter 4, parametric numerical analysis under cyclic loading are explained. The

response of suction buckets subjected to cyclic axial loads and cyclic lateral loads in

saturated sandy soils are studied with a series of numerical analyses. Main focus is

9

given to the displacement behaviour for tested scenarios and load distribution among

the components of bucket during cyclic loading are discussed.

In Chapter 5, after collecting the results of parametric analyses, it is aimed to obtain

an estimation on the response of a bucket under extreme cyclic loading situations. By

this, a designer would be able to decide if detailed analyses for cyclic loading in case

progressive deformations expected.

In Chapter 6, the discussions are summarized and concluded.

10

CHAPTER 2

REVIEW OF LITERATURE

2.1 Introduction

In this chapter, the state of art in design and installation of suction bucket foundations

is presented which aims to give an overview of the understanding on the behaviour.

Firstly, the permanent and variable loads as well as the environmental actions con-

sidered for the design of a suction bucket are introduced. Later, the construction

stage, (i.e. suction assisted installation) which has a crucial importance on the state

of stresses and properties of soil is discussed. Installation process, challenges and

limits for suction assisted penetration and design for these aspects as well as the

changes in the properties and behaviour of the soil during and after the installation

are presented. Afterwards, developments in the understanding of cyclic response of

the suction buckets in combination with the other loads are discussed in the light of

experimental and numerical studies. Lastly, current design methodologies are pre-

sented for the suction buckets.

2.2 Loads and Actions

The loads that act on an OWT can be categorized into three as permanent, variable

and environmental loads. In this section, these loads are briefly introduced.

Permanent Loads

Gravity loads such as the self weight of the structure, attachments, equipments, ballast

etc. and hydrostatic loads in at rest condition of surrounding environment constitute

11

the permanent loads. Magnitude and location of these loads do not change during

time.

Variable Loads

In contrary to permanent loads, magnitude and position of variable loads change in

time. These loads generally include operational live loads such as actuation loads,

impact from crane operations etc.

Environmental Loads

Environmental loads are long term actions such as wind loads, wave and current loads,

earthquake, tidal effects, snow, ice etc. These loads include high uncertainty. For that

reason, they are quantified with respect to their probability of exceedence.

In general, major long term actions are wind loads, wave loads, mechanical vibra-

tions. The most common property of these loads is their cyclic characteristic. Re-

sponse of foundations to these cyclic effects differs from the monotonic loads and

shall be considered carefully. Identification of the wind and wave loads involve high

amounts of uncertainty. For that reason important simplifications are required.

Wind Loads

For offshore wind turbines, excitation wind is an interaction of dynamics of the tur-

bine and wind field which contains turbulent flow caused by atmospheric turbulence

and flow from nearby turbines disturbing the flow. In practice, usually von-Karman

or the Kaimal spectrum is applied to define wind power. The frequency range for an

energy rich wind turbulence is below 0.1 Hz (Leblanc, 2009).

Wind loads act on all structural parts that are above sea level. Generally, the winds

are distinguished as the gusts that continue less than one minute and the continuous

winds that endure longer.

API requires to determine the design wind criteria to be obtained by considering;

Normal Wind Conditions;

• the frequency of occurrence of continuous wind speed in different directions

12

for each time intervals

• continuity of these wind speeds above the specified thresholds during that time

interval

• expected speed of gusts that are associated with continuous winds

Extreme Wind Conditions;

• location, date, magnitude of the gust and direction of wind data used to obtain

the extreme loads

• projected number of occasions during the service life in combination with a

minimum continuous wind speed

API states that wind loads can be very significant and so should be addressed in detail

for structures in deep waters where dynamic analysis of the wind-structure interaction

is necessary if wind field contains high energy close to the fundamental frequency of

the structure. For fixed steel structures in shallow waters, wind is not a primary source

of problem where structure can be in static condition under wind loads (API, 2014).

Lastly, winds have different coherency with respect to their characteristics. API

(2014) states that smaller elements of platform are dominantly affected by 3-second

gusts which are coherent at short distances where the total response of structures

smaller than 50 m horizontal dimension are more affected by 5 second gusts and

15-second gusts are dominant over larger structures. For structures which require dy-

namic analysis of wind-structure interaction, it can be conservatively assumed that all

frequencies are coherent on the structure.

A recent study by Penner et al. (2020) state that higher forces and displacements occur

for the lower frequency band (0.05 Hz < f < 0.2 Hz) based on the pre-installed and

comprehensive measuring system on a prototype of the suction bucket jacket installed

in the wind park ‘Borkum Riffgrund 1’ (North Sea) in August 2014.

Wave Loads

Characteristics of a wave load is very region specific. For example, Leblanc (2009)

stated that in European coastal waters, tidal currents and wind induced waves are very

13

important. Due to topographical properties of the North Sea, swells and long distance

waves comparably less important. It was also given that, the frequency range varies

between 0.05-0.50 Hz for the energy rich waves and 0.07-0.14 Hz for extreme waves.

As in the case of wind loads, wave loads have dynamic characteristics. For shallow

waters and relatively rigid structures, equivalent static analysis may be appropriate

but for flexible structures in deep waters, detailed dynamic analysis of wave-structure

interaction is required.

In cases where site specific wave data is not available, DNV GL (2016) suggests to

represent spectral density of waves by JON-SWAP (Joint European North Sea Wave

Project) spectrum.

Current Loads

This action is created by winds and tides. DNV GL (2016) suggest to describe current

velocity in cases where field measurements does not exist.

Other Environmental Loads

In this section, dominant loads in offshore environment such as winds and waves are

given importance and went into more detail. There are other environmental loads that

affect the offshore turbines which may of may not be particular to the offshore. These

are;

- Earthquake Loads

Earthquake loads can be considered by response spectra analyses. In cases where

earthquake induced tsunami risk exists, this action shall also be considered in design.

- Marine Growth

Marine growth shall be considered by increasing the dimensions of the structure con-

sidered to account for the growth in hydrodynamic wave and current loads.

- Ice Loads

Ice loads shall be considered if possibility of any interaction with a laterally moving

ice exists. Consideration shall be given to shape and size of the structure and ice mass

14

and its mechanical characteristics.

Wind Turbine Loads

The range of the rotational speed of blades typically between 10-20 rpm for a wind

turbine. The rotation has two fundamental frequencies. First excitation frequency

which corresponds to a full revolution of blades is denoted by 1P (or 1Ω) generally

varies between 0.17 and 0.33 Hz. The second fundamental frequency of blade passing

which is denoted by 3P (or 3Ω) varies between 0.5 and 1.0 Hz.

Figure 2.1: Typical frequency ranges for OWTs, Leblanc (2009)

Leblanc (2009) summarized these typical frequency ranges in as shown in Figure

2.1. It can be simply inferred that, it is a good achievement for a successful design

to obtain natural frequency in between 1P and 3P ranges. That type of designs are

referred as soft-stiff. Leblanc (2009) stated that a soft-soft design (natural frequency

below 1P) may also do not interact with the mechanical excitation, however, fatigue

and strength parameters may get very critical for the design. On the other hand, stiff-

stiff design is also possible but it can be too uneconomical.

2.3 Installation of Suction Buckets

The developments related to the installation stage, which is the most important feature

that highlights the bucket foundations are examined in this section.

The installation of a bucket consists of two stages. At the initial stage, the bucket is

submerged into water and penetrates by self weight. After sufficient penetration, a

seal is formed around the bucket. In second stage, with the pumping out of the water

15

inside the bucket, a pressure difference develops between inside (Pin) and outside

(Pout) of the bucket as described in Section 1.1 and shown in Figure 1.6b. This results

in an additional pressure on top plate and skirt as well as a reduced resistance at the

tip of the bucket so that the bucket can penetrate further to desired depth even in very

dense soils. Schematic illustration of a typical suction bucket installation is already

given in Figure 1.6 and 1.7.

Following paragraphs present the observations and conclusions from small to large

scale laboratory tests as well as numerical studies to comprehend the installation pro-

cedure. In accordance with these studies, design procedures for practical purposes

are presented. Some prominent topics about installation are soil heave, piping limits

and estimation of soil resistance during the installation phase.

Soil heave during the installation by suction often develops in practice. According

to Tjelta (1995), about 5% heaving which is considered to be acceptable, occurred

during the installation of Europipe16/11. However, higher heave ratios are also re-

ported in the literature which obstructs the penetration of the bucket to the desired

depth. Yang et al. (2003) investigated the soil heave during the installation by suction

with small scale tests in silt and noted that high soil heave ratios observed in the tests

in silts which is attributed to seepage gradient that loosens the soil inside the bucket

by upward flow no matter if critical gradient (which may be very high for silts) is

reached or not. As a consequence of high heave ratios, leaving some portion of the

skirt length above the seabed may lead to higher scour around the bucket. Recently,

Klinkvort et al. (2019) presented a simple model to evaluate the degree of plug lift

based on both time to reach steady-state conditions and flow required to generate a

critical gradient.

Failure during installation may develop in case the suction reduces the effective stress

within the bucket excessively, resulting in liquefying of the soil and breaking down

the seal by formation of piping channels. Ibsen and Thilsted (2010) performed large

scale tests (D=L=2 m and D=L=4 m buckets) in three different soil profiles where

the layers consist of homogeneous sand, sand with a thin silt layer at 2.7 m depth

and sand with several thin silt layers. Comparison of the test data and analytical

solutions showed that estimated suction for homogeneous sand is close or greater

16

than the critical which suggests that proposed equations can be used, however, for

the case of single silt layer, the applied suction exceeded the estimated threshold.

It is important to note that in the case of multiple silty layers, the flow boundaries

increased the threshold so high that and the estimated boundary never reached even

in the maximum applied suction.

On the other hand, no piping failure observed in the tests in dense sands which is

explained by the existence of an anti-failure mechanism by Erbrich and Tjelta (1999)

that in dense sands, even if the critical gradient is reached, sand loosens and perme-

ability increases which result in the decrease of the hydraulic gradient and prevents

the failure. Ibsen and Thilsted (2011) presented closed form solutions useful for

evaluation of suction thresholds against piping based on numerical flow analysis to

determine the hydraulic gradients developing in response to the suction applied.

Another aspect of the effect of installation to the long-term behaviour of the bucket as

the state of soil changes during suction assisted penetration. Stapelfeldt et al. (2020)

stated that installation does not have significant effect on the static or cyclic axial

loading of a bucket in sandy seabed based on discussion of a series of centrifuge

tests that investigate the installation and the load transfer mechanisms governing the

response of suction buckets. The soil plug is found rather important that will effect

the actual embedded length of the bucket skirt. However, a comprehensive numeri-

cal set of simulations by Tasan and Yilmaz (2019) showed that the consequences of

soil loosening were particularly substantial regarding the inner and outer skirts load

carrying behaviour. The participation of inner skirt on the load transfer reduced sig-

nificantly due to the excessive pore pressure development in soil inside the bucket

resulting from repetitive loading as the soil gets looser.

Design for Installation

The suction assistance during installation alters the state of soil in and around the

bucket, thus the reason the behaviour of the bucket is greatly affected. This mech-

anism has been studied in detail in Andersen et al. (2008); Bienen et al. (2018a);

Erbrich and Tjelta (1999); Goldscheider and Gudehus (1976); Houlsby and Byrne

(2005); Ragni et al. (2020); Senders and Randolph (2009); Tran (2005). Villalobos

(2006) showed that moment resistance of a bucket installed by jacking is greater than

17

a bucket installed by suction assistance. This emphasizes the requirement for consid-

ering the suction affects in the design for installation (Cotter, 2009).

Generally, CPT resistance is used for estimating the bearing capacity of the buckets

in sand since it is a direct measure of the resistance to penetration into soil (Sturm,

2017). However, some stresses develop around the skirt during installation due to

downward friction on the soil in contact with the surface (Cotter, 2009). In addition,

since bucket skin roughness is different than the CPT rod, the stress development will

be different (w.r.t a CPT cone) around bucket skirt (Andersen et al., 2008). Also due

to greater geometry of bucket skirt, the strains in the soil will be different. For these

reasons, the resistance measured by CPT test requires some modification with respect

to penetration of skirt but a method is not suggested (Andersen et al., 2008).

Schneider et al. (2005) suggested an estimation for the driven piles however the

method does not consider the seepage induced changes in the skin friction around

the bucket which is noted by Houlsby and Byrne (2005) and Cotter (2009) that if the

slight increase at the outside friction is not taken into account, the required suction

will be higher than the estimated. Such a case is an unconservative solution. Seepage

in suction assisted installation in permeable soils is a well identified phenomenon by

Erbrich and Tjelta (1999) and Schneider et al. (2005)

Cotter (2009) proposed an empirical correlation based on effective stresses to CPT

resistance by some confidential data collected in prototype installations in the indus-

try.

Houlsby and Byrne (2005) developed an analytical design procedure for installation

of suction buckets in sands. The penetration is divided into two phases as self-weight

penetration and suction-assisted penetration. For the self weight phase, the resistance

mechanism formed by the friction on the outside and inside of the skirt and the end

bearing at the tip. As a starting point, the conventional pile design accepted. For the

second phase the stress enhancement is considered.

Importance of seepage flow during suction is also mentioned by Stapelfeldt et al.

(2015) by simulating the installation procedure via finite element analyses where

the penetration is modelled a zip like technique but excluding the pore pressure (i.e.

18

jacked installation) which resulted in resistance prediction greater than the actual.

Authors supported that both numerical and analytical (API and DNV) methods pro-

vide conservative but inaccurate results because of neglecting the seepage flow and

its resistance decreasing effect which may result in exceed of piping limits.

Recently, Klinkvort et al. (2019) presented a model that accounts for seepage flow

in unlimited permeable layers that are overlain by one or several impermeable layers.

Seepage flow in the underlying sand layer was assumed to be induced by an incremen-

tal lift of the internal soil plug. That assumption enables the transfer of some of the

differential pressure applied under the top plate to the bottom of the lifted soil plug.

The critical suction is calculated with a single equation and used with an empirical

model to calculate the reduction in penetration resistance. The proposed penetration

model is demonstrated by back-calculating full-scale installations.

Alluqmani et al. (2019) proposed a unified procedure where seepage was first solved

for a normalized bucket geometry, then normalized excess pore pressure was ex-

pressed in terms of polynomial regressions. This resulted into an analytical repre-

sentation of the required suction and also critical suction for piping condition as a

function of normalized penetration depth. Verifications of the proposed formulation

is presented against field tests reported in Houlsby and Byrne (2005).

Another aspect of the design is measuring the uncertainties. A recent study presented

by Remmers et al. (2019) quantified variability of geotechnical parameters and incor-

porated it into two existing design methods; the empirical CPT-based method (An-

dersen et al., 2008; Senders and Randolph, 2009) and the theoretical approach by

Houlsby and Byrne (2005).

2.4 Behaviour under Cyclic Loading

Cyclic loading may cause change in foundation stiffness, generation of excess pore

pressure and accumulation of displacements. In consequence, a bucket may fail at a

load that is lower than the expected capacity or lose the functionality by large dis-

placements under cyclic loading (Dutto et al., 2016; Foglia et al., 2012; LeBlanc

et al., 2010; Lin and Liao, 1999; Lombardi et al., 2011; Wang et al., 2017). The ac-

19

cumulated rotation can surpass the acceptable limits so that it can govern the design

(Lin and Liao, 1999) or the natural frequency can slide towards any of the excitation

frequencies due to change in stiffness during cyclic loading (Zhu et al., 2013).

To cover the behaviour, numerous experimental test programs as well as numerical

studies have been conducted under cyclic load cases. Most of the experiments are

small scale tests due to the very large dimensions of suction buckets. However, even

it is rare, large scale prototype and full scale tests also exist. It is an inevitable fact

that structures can be scaled but soil particles cannot. Thus, the true behaviour can

be mispredicted unless necessary measures to eliminate the scale effects in the small

scale tests are taken. For that purpose, centrifuge tests are often used to scale the

laboratory stresses to in situ stress range.

In this section, some leading studies in literature that focused on the cyclic lateral and

cyclic axial loading are briefly reviewed. Important findings are presented.

Excess pore pressure generation and changes in foundation stiffness are major topics

that are focused. In addition, researchers also studied the effects of aspect ratio "L/D",

loading rate and changes in the interface angle during cyclic compression, tension and

cyclic moment.

2.4.1 Behaviour under Cyclic Lateral Loading

Foundation stiffness typically decreases due to cyclic loading (Foglia et al., 2015,1;

Fugro, 2016; Kim et al., 2014b; Lombardi et al., 2011; Lu et al., 2005; Wang et al.,

2017; Zhang et al., 2007). In general, the rate of change slows with increasing number

of cycles after yielding to a minimum stiffness (Wang et al., 2006). Results of a series

of 50g centrifuge tests in loose dry/loose saturated/dense dry and dense saturated sand

conducted by Wang et al. (2017) showed continuously growing lateral displacement

with the increasing number of cycles but at a decreasing rate. The first five cycles

contributed almost 66% of the total displacement. Similarly, according to Foglia et al.

(2012), a displacement accumulation observed in the very first cycles than the rate of

accumulation decreases in the four test conducted on a monopod with 1g, 30000 load

cycles in saturated sand.

20

Although general tendency is as expected, it is effected by many factors such as cyclic

amplitude, direction and frequency of loading. For example, LeBlanc et al. (2010)

showed that accumulated rotation can differ four times with respect to two-way load-

ing according to a series of tests, conducted on small-scale driven piles subjected to

8000 to 60 000 cycles of combined moment and horizontal loading. Similarly, Zhu

et al. (2013) observed that stiffness is mostly affected by characteristics of loading

rather than the number of cycles according to 10000 load cycle test on small scale

monopod in dry sand.

In the light of the experimental observations, empirical relations are possible between

the change of foundation stiffness or the accumulated rotation and number of cycles,

N. Lin and Liao (1999) suggested that accumulated rotation is in proportion to N log-

arithmically. LeBlanc et al. (2010) investigated this by plotting the resulting rotations

with respect to ln(N) and showed that if N<100, the suggestion gives a good fit. For

the number of cycles greater than 500, it is claimed that exponential relation gives

better results than logarithmic fit until 104 cycles. The trend also shows that, this

fitting can be extrapolated further to predict the rotations at fatigue limit cycles (107

cycles). Zhu et al. (2013), extended this subject for suction buckets and investigated

the cyclic accumulated rotations and foundation stiffness under cyclic loading. The

results stands for the drained response of the foundation since the test program per-

formed in dry sand. It is shown that largest increment occurred in the first cycle of

sinusoidal loading. After that, the rotation increased with the number of cycles but the

increment rate decreased. In general, following expression form is suggested for the

prediction of accumulated rotation according to Foglia et al. (2012); LeBlanc et al.

(2010); Lin and Liao (1999); Zhu et al. (2013).

θ

θ1

= A(N)B (2.1)

where A and B are dependent on loading characteristics and relative density of soil.

Similarly variation of stiffness with respect to number of cycles is empirically ap-

proximated by the following form.

21

Figure 2.2: Comparison of the observed rotation fitted with Equation 2.1, Foglia et al.

(2012)

kN = C +Dln(N) (2.2)

where C and D are also dependent on loading characteristics and relative density of

soil.

An example illustration of this form is presented by Foglia et al. (2012) in Figure 2.2.

The figure compares the predicted rotation by the suggested equation in the form of

Equation 2.1 in the three of four test conducted on a monopod with 1g 30000 load

cycles in saturated sand.

Settlement accumulates as well as the rotation. When the location of centre of rotation

examined, it starts a level beneath the skirt and tends to move towards the level of the

skirt according to Figure 2.3. (Zhu et al., 2013).

Another recent study by Zhu et al. (2018) presents the results from 1g bucket tests in

sand, clay and sand over clay seabed profiles under one million cycles of lateral load.

The capacity and rotation response is shown to approach that measured in the sand

seabed when the sand - clay interface is located at or beneath the caisson skirt tip.

22

Figure 2.3: Rotation of bucket with respect to center of rotation, Zhu et al. (2013)

Lateral cyclic loading was seen to increase bucket capacity by up to 30% with a bias

towards clay - dominated seabed profiles and stiffness by up to 50%. Such stiffness

increases need to be considered when assessing the system dynamics for the offshore

wind turbine, as demonstrated in the paper. Dynamic stiffness increase is reported

also by Wang (2017) during the first few hundreds of cycling but decreases thereafter,

leading to little variation in medium dense dry sand, at a centrifugal acceleration of

100g.

Luo et al. (2020) investigated the effect of the irregularity of the wind and wave action

on OWTs where in practice, ‘counting methods’ that decompose the time history of

irregular cyclic loads into a series of cyclic load parcels of uniform amplitude are

applied. The accumulated rotation approximately doubled when the load ordering

changed from ascending to descending, observed according to the varying amplitude

cyclic tests. The variation was related to the densification of soil under low amplitude

cyclic loads.

2.4.2 Behaviour under Cyclic Axial Loading

Multi-leg support structures distribute the lateral loads acting on the OWTs as axial

loads on the legs as compression and tension. Many researches focused on the tensile

or pull-out resistance of the suction buckets such as Bo and Nordahl (2016); Bye et al.

(1995); Feld (2001); Houlsby et al. (2005a,0); Jeong et al. (2020); Nielsen (2019);

23

Rapoport and Young (1985); Sørensen et al. (2017); Ukritchon et al. (2018); Vaitkune

et al. (2017).

Three major topics are ratio of tensile and compressive unit friction, influence of rate

of loading and importance of the reverse end bearing capacity.

Tensile resistance of the bucket consists of self weight of the foundation and the skin

friction at the faces of the skirt in drained conditions (Thieken et al., 2014). The skin

friction resistance in tension generally suggested with a reduction to the compressive

resistance of the skirt. For example, the API suggest a value for the coefficient of

lateral earth pressure, K<1 and introduce limit for unit friction. Another approach

is suggested by Houlsby et al. (2005b) similar to the installation resistance discussed

earlier. The vertical effective stress around the skirt is affected by the frictional forces.

Dependency of the behaviour on the rate of loading under tension is a phenomenon

observed such that as the pull out rate increases the resistance of the foundation also

increases (Byrne and Houlsby, 2004; Vicent et al., 2020b). However, there is no such

observation in the compression side.

Reverse end bearing is another major behaviour described by Senders (2008) as in

the Figure 2.4. As the bucket move upwards, a gap beneath the top plate is formed.

However, for fully undrained conditions, suction forces restrains the formation of any

gap which leads to plug of soil.

Seepage-pore pressure-displacement behaviour under tensile loading is studied nu-

merically by (Dutto et al., 2016; Emdadifard and Hosseini, 2010; Mana et al., 2014;

Thieken et al., 2014; Thijssen and Alderlieste, 2012; Zhang and Cheng, 2017). Thieken

et al. (2014) presented FEA results based on a constitutive model which account for

coupled pore fluid diffusion and partially drained behaviour. Water elements are used

to simulate formation of the gap beneath the top plate. Two main failure limits exists

either cavitation of pore water or fully undrained behaviour as described with reverse

end bearing. It is concluded that increasing pull-out rate would result in higher ten-

sile capacities but large plug rates are necessary to mobilize that capacity. It was

observed that undrained capacity mostly depend on the diameter whereas drained

capacity mostly depend on skirt length of the bucket.

24

Figure 2.4: Failure mechanisms, Senders (2008)

Cyclic loading tends to influence the foundation behaviour in an unfavourable man-

ner (Senders and Randolph, 2009; Versteele et al., 2013). During cyclic loading, a

displacement increment and excess pore pressure increment which implies stiffness

degradation at each cycle is observed by Dutto et al. (2016) with a material model to

numerically simulate the pore pressure development and displacement accumulation

under cyclic load combinations (lateral and vertical) based on Biot (1955). Zhang

and Cheng (2017) stated that accumulation of displacements (both rotation and set-

tlements) and excessive pore pressure development are captured with a model based

on energy dissipation principal based on thermodynamic theory according to Jiang

and Liu (2009) in soil instead of strain rates. Thijssen and Alderlieste (2012) also

reported the similar observations as stiffness degradation due to cyclic displacements

and excess pore pressure accumulation but also claimed that axial cyclic degradation

is only significant in tensile loadings. Contact of top plate to the sea floor mobilize

the end bearing which dramatically increase the capacity of foundation and offered a

method, to capture the excess pore pressure development where high shear stress and

low overburden pressure exists.

Assessment of pore pressure build-up suggested by Thijssen and Alderlieste (2012):

1. per series of wave loads, calculate the cyclic shear strength ratio (CSSR) with

respect to depth.

2. determine the number of cycles to reach liquefaction, N liq versus CSSR rela-

tionship

25

3. calculate the increase of relative pore pressure ∆ Ru from N/N liq

4. for the new (increased) value of Ru, determine the number of equivalent cycles

represented by the CSSR for the next set of wave loads.

5. calculate the relative pore pressure increase ∆Ru for this new load set.

6. repeat from step 4.

Senders (2008) conducted a study on tripod bucket foundations for offshore wind

turbines and investigated the pull-out behaviour of a single bucket of a tripod foun-

dation, assuming the capacity of the whole tripod system was primarily governed by

the pull-out capacity of the windward bucket. Despite the aforementioned research

efforts, existing data are still insufficient to understand the complicated behaviour of

the tripod bucket foundation, including failure mode and cyclic behaviour.

Suction buckets are widely used as anchor systems or tension legs before, but the

OWTs are very sensitive to excessive rotations that mainly designed to be under

compression.The simulation presented showed that the average loading of the suc-

tion buckets is compressive loading and that tensile loading is unlikely to occur un-

der operational conditions and is only sporadic during ultimate loading conditions.

(Senders, 2008)

Cerfontaine et al. (2016) presented the results of a numerical study on suction buckets

under cyclic axial loading and concluded that the problem is mainly partially drained

which mean that the load variation is sustained by positive or negative variations of

PWP within the soil. Accumulation of settlement during the cyclic loading of the

bucket was observed in all calculations.

The measurements obtained in a series of tests on suction buckets in dense sands un-

der vertical cyclic loading by Bienen et al. (2018b) showed significant differences in

the load sharing between bucket skirt and top plate, depending on the drainage char-

acteristics which will be a significant focus of this thesis in the following chapters.

26

2.5 Design of Suction Buckets

Selection of the foundation type for an OWT depends on the water depth, soil and en-

vironmental conditions at the project location. The initial stage of design is to obtain

environmental data at the project site and turbine data. Environmental data should at

least include wave, current, wind, topography and soil conditions. Design and opti-

mization of an OWT foundation is an iterative process until stability is assured under

all load cases under limit states during the service life. Limit states considered in de-

sign are ultimate (ULS), servicability (SLS), accidental (ALS) and fatigue limit states

(FLS). The structural strength of individual members and overall system corresponds

to ULS where allowable deformations to retain functionality of turbine is checked by

SLS. Collision and impact loads are checked in ALS and accumulated stresses and

deformations during service life that may damage functionality are checked in FLS.

Figure 2.5 shows general design procedure as a scheme.

Figure 2.5: Design procedure for an offshore wind turbine foundation

Major design leading property of an support structure is the natural frequency which

represents the dynamic behaviour of the system since wind, wave and mechanical

excitations are dynamic. Coincidence of fundamental frequencies may lead to ampli-

fication of stresses and deformations to the resonance. Typical frequency ranges for

OWTs were shown earlier in Figure 2.1. Structural strength is satisfied by checking

for the yielding of members and controlling the slenderness against local or global

buckling.

27

Foundation stability is satisfied by checking horizontal and vertical capacities. Failure

mode of foundation depends on the loading such that for lateral loading, horizontal

deformation and overturning can be de first failure mode where ultimate vertical load

capacity is fundamental failure mode for axially loaded foundations.

Axial resistance of a piled foundation is summation of skin friction and bearing ca-

pacity at the tip. There is no difference from a regulated pile design. That ultimate

capacity shall be greater than the design demand by an amount of acceptable safety.

General formulation of axial pile resistance, R in a N layer deposit is given in DNV

GL (2016) is as follows;

R = RS +RT =∑

fSiASi + qTAT (2.3)

where i is from 1 to N. f S is unit skin friction, AS is unit skin area, qT is unit tip bearing

and AT is tip area.

To determine side friction in clays, well known effective stress λmethod, total stress α

method or empirical β methods can be used. In sands, friction can be calculated based

on effective overburden stress and corresponding Coulomb friction. End bearing can

be calculated by simplified Terzaghi formulation.

For lateral analysis of piles, most common method is p-y curves. This method gives

the relation of the mobilized resistance for a corresponding deformation along the

pile depth. Pile length is discretized into sub-elements and lateral springs are used

to represent that relationship (Grecu et al., 2020; Randolph, 1981). The relationships

derived from field test are for flexible piles with diameters D from 0.5 to 3 m with

length-to-diameter ratios L/D > 12 in the oil and gas industry. Rigid monopiles with

L/D < 12 and diameters from > 5 m are typically used for OWTs. The effect of load

rate is not concerned in the p-y curve method. In order to incorporate the effect of

load frequency and pore pressure, the coupled equations are needed to illuminate the

behaviour of different states in the soil. Special consideration is required to modify

the method for geometrical scaling as well as incorporating the state of soil. (Achmus

et al., 2016; Bayat et al., 2016; Damgaard et al., 2014; Liingaard, 2006; Lin et al.,

2012; Sørensen et al., 2010)

28

A very powerful method for estimating the behaviour of horizontally loaded piles is

the finite element method (FEM). In this method, soil is modelled as a continuum

with its non-linear behaviour and also structure-soil interface is modelled which can

account for the formation of gap during lateral loading. However, computational

effort to for an accurate modelling is high.

There are some recent studies such as Achmus et al. (2013); Dekker (2014); Jin et al.

(2019); Maniar (2004); Vicent et al. (2020a) that propose either failure envelopes

or equations to quantify lateral and axial ultimate capacity of the buckets based on

parametric numerical studies under monotonic load cases.

State of Art Dimensioning of Offshore Suction Buckets

There is no standard or guideline that is fully dedicated to suction bucket foundations

yet. General offshore structure design standards are adopted for suction buckets.

However, it requires further considerations for the mobilized suction inside the bucket

and cyclic long term capacity where there is a lack of experience on the long term

behaviour of suction bucket foundations for OWTs.

Methods to Assess Cyclic Behaviour of Bucket Foundations

Most design procedures developed for ultimate bearing capacity of soils under static

load conditions. Literature survey on the behaviour of suction buckets revealed that

cyclic bearing capacity may govern the design. It is necessary to pay a special atten-

dance to cyclic bearing capacity.

For foundations which are subjected to cyclic loads in undrained conditions, Ander-

sen and Lauritzsen (1988); Andresen et al. (2008) suggested a design procedure to

calculate the bearing capacity. Two failure modes are stated;

• due to large cyclic shear strains

• due to large average strains

The shear stress consists of two components, average shear stress τ a and cyclic shear

stress τ cy.The average shear stress is summation of initial shear stress (drained) under

at rest condition and the stress added by the self-weight (undrained). Cyclic shear

29

stress has an amplitude of period which is dependent on the loading.

It was observed from the tests on Drammen clay that if stress path at one cycle du-

ration is equally close to failure lines (compression and tension), the expected failure

mode occurs due to large cyclic shear strains. If the path is closer to any of the failure

lines, dominant failure mode would be due to average shear strains.

To consider the combination of cyclic shear strain and average shear strain with re-

spect to number of cycles, envelopes are developed from the cyclic triaxial and direct

shear strength tests.

Europipe 16/11E(1994) and Sleipner T(1996) are frontiers in suction installed bucket

foundations for wind turbines. The geotechnical design basis of these platforms were

presented by Bye et al. (1995).

30

CHAPTER 3

FINITE ELEMENT MODEL

The behaviour of buckets embedded in saturated sandy soils subjected to cyclic axial

compression and cyclic lateral loading are studied by using a sophisticated finite ele-

ment (FE) model, details and the theoretical background of which is presented in this

chapter.

In saturated sandy soils, accumulation of excess pore pressure under cyclic loading

environment and corresponding development of deformations are one of the major

topics for OWT foundations. A FE model should be capable of calculating the ac-

cumulation of deformations in a non-linear manner under small load cycles while

determining the excess pore pressures related to the changes in relative density of soil

(i.e. variable void ratio) during load cycles. This requires coupled analysis of soil

stresses and pore pressures.

In this study, a fully coupled two-phase model is adopted where a non-linear hy-

poplastic constitutive model with intergranular strain concept is used to calculate the

soil part and the Kozeny-Carman relationship is used for porosity-permeability de-

pendence.

The choice of the constitutive model is partially a subjective matter, the capability of

capturing cyclic behaviour of the sandy soils, the number of parameters and practical

implementation of the model are important aspects for consideration. Success of the

hypoplastic constitutive law with intergranular strain is shown by the recent studies

on piles and suction buckets in sandy soils by Achmus and Thieken (2014); Labenski

and Moormann (2017); Stapelfeldt et al. (2015); Tasan (2011); Thieken et al. (2014);

Vogelsang et al. (2017). Especially, the earlier studies by Tasan (2017); Tas, an and

31

Akdag (2018) present important findings on suction buckets that needs to study fur-

ther. Here, the implemented model by Tasan (2011) was taken as the basis where

with some important developments and modifications such as the implementation of

Kozeny-Carman relationship, consideration of damping and compressibility of grains

to capture the behaviour better.

In the following sections, details of the material constitutive law, porosity-permeability

relationship and two-phase model is discussed. Subsequently, details of the FE model

constructed is given. Lastly, verification studies are explained and discussed.

3.1 Simulation of Material Behaviour

Finite element analyses are based on the constitutive material laws which mainly

define the stress-strain relation for the subjected materials by some parameters to dis-

tinguish between different ones. Most of the well-known material models are based

on elasto-plasticity theory. In general, the material has an elastic behaviour up to a

certain yield point and a plastic route after that yield strain. This post-yield behaviour

may be hardening, softening or perfectly plastic depending on the theory which are

commonly called as "yield theories". Most frequently used ones are Mohr-Coulomb,

Drucker-Prager, Von Misses, Tresca yield theories. The yield surfaces have some

problems when implemented in the FE analyses. One of the most important is the

convergence problems which frequently arise as the FE models get larger and com-

plex, due to complexity of mathematical transition from elastic to plastic zones and

flow rules on the yield surfaces.

To overcome these problems, Kolymbas (1988) presented a new constitutive law,

later named as hypoplastic material law which perceive the plastic behaviour without

using a yield surface definition or flow rule. In addition, continuous form of the equa-

tion makes it mathematically simple to implement in FE analyses. In the following

sections, hypoplastic material law developed by Kolymbas (1988) is introduced and

some important improvements by Bauer (1996); Gudehus (1996); Kolymbas et al.

(1995); von Wolffersdorff (1996) are discussed. Then, intergranular strain concept

which was introduced by Niemunis and Herle (1997) to overcome the over-prediction

32

of deformations in small cyclic loadings is presented.

3.1.1 Hypoplastic Material Model

Hypoplastic constitutive model is appropriate for modelling non cohesive soils by

taking into account the influence of stress level and soil density on the soil behaviour.

Stiffness, dilatancy, contractancy and peak friction is followed by the soil state and

the deformation direction. Plastic deformations are simulated without using potential

or switch functions. A single tensorial equation is used to describe plastic as well as

elastic deformations (Kolymbas, 1999).

Directly relating the strain to stress ignores the dependence of stress to strain history

which is physically wrong for soils. For that reason, hypoplasticity connects stress

increments to strain rate. That incremental dependence has to account for behaviour

difference between loading and unloading. The relationship in incremental rate is

non-linear in strain rate (Kolymbas, 1999).

The theory is based on the continuum mechanics. General constitutive equation in

the form of;

T = h(T,D) (3.1)

where D is the stretch rate tensor and T is the Cauchy stress tensor.

According to general representation theorem, Equation 3.1 can be written in the fol-

lowing form in Equation 3.2;

h(T,D) = ψ11 + ψ2T + ψ3D + ψ4T2 + ψ5D

2 + ψ6(TD + DT)

+ψ7(TD2 + D2T) + ψ8(T2D + DT2) + ψ9(T2D2 + D2T2)

(3.2)

where ψi are scalar functions of invariants and joint invariants of T and D.

A rate independent material means that behaviour does not vary with the time scale.

If the creep and relaxation and small rate dependence of clays are omitted, soils can

be assumed as rate independent as a first approximation (Kolymbas, 1988). To be

rate-independent, function h has to be homogeneous with D in the first degree.

33

As a result, the earlier version of the hypoplastic constitutive law is expressed as in

Equation 3.3.

T = C1(trT)D + C2tr(TD)

trTT + C3

T2

trT

√trD2 + C4

T∗2

trT

√trD2 (3.3)

in which the deviatoric stress T* in Equation 3.3 is defined by subtracting the isotropic

part given in Equation 3.4. C1, C2, C3, C4 are material constants.

T∗ = T− 1

3(trT)1 (3.4)

This primary form of the expression lacks on the description of physical difference

between loose and dense materials since it does not account for void ratio. An im-

provement where the influence of stress level and void ratio is considered with ‘struc-

ture tensor’ or ‘back stress’, S is suggested by Kolymbas et al. (1995) as given in

Equation 3.5.

T = C1[(tr(T + S)]D + C2tr[(T + S)D]

tr(T + S)+[

C3T2

trT+ C4

T∗2

trT+ C5

T3

trT2+ C6

T∗3

trT2

]√trD2

(3.5)

where S is defined as in Equation 3.6;

S = s0

1− 1(trTr

p0

)υln 1+er

1+e0

(trT

p0

)υln

1 + e

1 + e0

(trT

p0

)α(3.6)

In later studies, prediction performance is aimed to be improved in other deviatoric

directions than the triaxial test and ease the calibration. In addition Bauer (1996) and

von Wolffersdorff (1996) proposed a relation in between four material constants C1,

C2, C3, C4 by coinciding the deviatoric yield curve with predefined limit state surface

and hypoplastic equation has taken the form of Equation 3.7;

T = fbfe1

trT2(F 2D + α2Ttr(TD) + fdαF (T + T∗)

√trD2) (3.7)

The formulation by von Wolffersdorff (1996) requires determination of 8 parameters

where detailed expressions are given in Equations 3.8 to 3.16 according to Equation

3.7. Critical friction angle ϕc represents a state where the shear stress rate and the

volumetric deformation rate vanish both. Granulate hardness hs depends on the stress

level and used as reference pressure. It does not refer to hardness of the grains. hs

and n are used to describe the shape of the limiting void ratio curves. Exponent α,

34

describes the transition to peak state where axial stress rate is equal to zero. Exponent

β relates the change in stiffness to the change in density and pressure. Incremental

stiffness modulus increases with increasing density and pressure. The remaining three

parameters are Minimum Void Ratio, ed0, Maximum Void Ratio, ei0 and Critical Void

Ratio, ec0. Detailed information on the determination processes of all 8 parameters

will be explained further.

T =T

trT(3.8)

α =

√3(3− sinϕc)

2√

2 sinϕc(3.9)

F =

√1

8tan2 ψ +

2− tan2 ψ

2 +√

2 tanψ cos 3υ− 1

2√

2tanψ (3.10)

tanψ =√

3trT∗2 (3.11)

cos 3υ = −√

6trT∗3

(trT∗2

)3/2(3.12)

fd = (e− edec − ed

)α (3.13)

fe = (ece

)β (3.14)

fb =hsn

(ei0ec0

)β1 + eiei

(3p

hs)1−n(3 + a2 − a

√3(ei0 − ed0

ec0 − ed0

)α)−1 (3.15)

eiei0

=ecec0

=eded0

= exp(−3p

hs)n (3.16)

35

3.1.1.1 Determination of Parameters

Critical Friction Angle, ϕc

Schofield and Wroth (1968) stated that during large monotonic shearing, the critical

state is reached if the shear stress rate and the volumetric deformation rate vanish

both. Which mean (in case of a cylindrical compression);

T1 = T2 = D1 + 2D2 = 0, D1 6= 0 (3.17)

Substituting Equation 3.17 into constitutive equation and using the following defini-

tion of friction angle ϕc in Equation 3.18, a relation between critical friction angle and

parameter α is obtained in Equation 3.19. The subscript 1 denotes the axial direction,

and 2 the radial direction under axial compression T1 > T2.

sinψ = max

(T1 − T2

T1 + T2

)(3.18)

α =

√3(3− sinϕc

2√

2 sinϕc(3.19)

Critical state parameter, ϕc can be predicted by angle of repose (Figure 3.1). Herle

and Gudehus (1999) suggest a small excavation to eliminate the affects of the heap

preparation. It is also stated that angle of repose is sensitive to the grain size distri-

bution. As the grain size decreases, angle of the repose is found to be increasing.

For very low grain sizes (d < 0.1 mm), parameters such as capillarity, van der Waals

forces and cohesive force cause unrealistically high angles. In those cases, critical

state parameter shall rely on shear tests.

Figure 3.1: Determination of critical state parameter from angle of repose, Herle and

Gudehus (1999)

36

Granulate Hardness, hs and Exponent, n

Granulate hardness depends on the stress level and used as reference pressure (Herle

and Gudehus, 1999). It does not refer to hardness of the grains. It is used to describe

the void ratio with respect to a reference void ratio at zero pressure when utilized with

parameter n as in Equation 3.20.

ep = ep0exp

[−(

3p0

hs

)n](3.20)

In or to determine hs and n, a specimen which is in the loosest possible state with-

out collapsing should be tested under compression. That can be either oedometer or

triaxial test but first is easier to perform. Herle and Gudehus (1999) proposed that ex-

ponent, n can be calculated with respect to void ratios ep2 and ep1 and corresponding

compression coefficients Cc1 and Cc2 for a pressure range ps1 and ps2 as in Equations

3.21 and 3.22 according to Figure 3.2.

n =

ln

(ep1Cc2ep2Cc1

)ln

(ps2ps1

) (3.21)

hs = 3ps

(nepCc

)1/n

(3.22)

Figure 3.2: Determination of exponent n (left), Effect of different values of hs on

calculated compression curves using Equation 3.20 (right), Herle and Gudehus (1999)

37

Minimum Void Ratio, ed0

In Equation (3.16) the relationship between ed and ps is given. Hence, ed0 can be

calculated with respect to ed if hs and n are determined as in Equation 3.23.

ed0 = edexp

[−(

3pshs

)n](3.23)

The void ratio ed can be best determined by small amplitude cyclic shearing (Herle

and Gudehus, 1999). Value of the ed can be much lower than the minimum void

ratio suggested by the standard densification methods (see Figure 3.3). Youd (1973)

showed that ed decreases with increasing non-uniformity, Cu since smaller grains can

fill the gaps between larger ones. The value of ed0 can be predicted using Figure 3.4

(left).

Figure 3.3: Pressure dependent minimum void ratio ed, Herle and Gudehus (1999)

Figure 3.4: Determination of ed based on Cu at ps = 55 kPa (left), Determination of

emax based on grain angularity, Youd (1973) (right)

38

Maximum Void Ratio, ei0

Herle and Gudehus (1999) defined ei0 as the void ratio that can be reached during

an isotropic consolidation in a gravity-free space. It cannot be simulated by tests but

theoretical predictions are proposed by idealized packing of grains (see Figure 3.5).

Figure 3.5: Idealized packing of grains for minimum density, Herle and Gudehus

(1999)

ASTM 4254 and some other standards offer pouring of the dry soil into calibrated

mould. However soil reaches a denser state than theoretical minimum density. Theo-

retically maximum void ratio ei0 is 1.2 times greater than experimental emax for spher-

ical packing and 1.3 times for cubic arrangement (Herle and Gudehus, 1999).

Similar to minimum void ratio, the value of ed0 can be predicted using Figure 3.4

(right).

Critical Void Ratio, ec0

The critical void ratio can be obtained from shear tests together with ϕc but undrained

triaxial tests are more suitable since keeping a homogeneous deformation up to the

critical state is difficult. That void ratio is found to be very close or equal to the

maximum void ratio (Herle and Gudehus, 1999).

In Equation (3.16) the relationship between ec and ps is given. Hence, ec0 can be

calculated with respect to ec if hs and n is determined in Equation 3.24.

ec0 = ecexp

[−(

3pshs

)n](3.24)

39

Exponent α

Exponent α, describe the transition to peak state where axial stress rate is equal to

zero. From constitutive relation, exponent α can be calculated for zero axial stress

rate as in Equation 3.25;

α =

ln

[6 (2+Kp)2+a2Kp(Kp−1−tan νp)

a(2+Kp)(5Kp−2)√

4+2(1+tan νp)2

]ln(e−edec−ed

) (3.25)

where;

Kp =T1

T2

=1 + sinϕc1− sinϕc

(3.26)

tan νp = −D1 + 2D2

D1

(3.27)

sinϕp =

(T1 − T2

T1 + T2

)p

(3.28)

Exponent β

Exponent β relates the change in stiffness to the change in density and pressure.

Incremental stiffness modulus increases with increasing density and pressure (Herle

and Gudehus, 1999). Stress rate in isotropic compression is given in Equation 3.29;

T1 = fs

(3 + a2 − fda

√3)D1 (3.29)

From constitutive relation, exponent β can be calculated as in Equation 3.30;

β =ln(β0

E2

E1

)ln(e1e2

) (3.30)

where β0 is given in Equation 3.31;

β0 =3 + a2 − a

√3fd1

3 + a2 − a√

3fd2

(3.31)

40

3.1.2 Hypoplastic Model for Small Strain Performance

The hypoplastic material model satisfactorily predicts the soil deformation caused by

the rearrangement of the grains. However, researches conducted by Niemunis and

Herle (1997) and Bauer and Wu (1993) have shown that when hypoplastic constitu-

tive Equation is applied to cyclic loading or small deformation problems, excessive

accumulation of deformation is observed and deformations are over-predicted. This

defect brings researchers to focus on the modelling of small strain cyclic behaviour.

Niemunis and Herle (1997) presented an improved hypoplastic constitutive equation

that account for small strain behaviour of dry or fully saturated soils.

The general constitutive relation is given as;

T =M : D (3.32)

where M is the stiffness tensor depending on parameters mT, mR and intergranular

strain, δ. For normalized magnitude of intergranular strain, 0 < ρ < 1,

M = [ρχmT + (1− ρχ)mR]L+ ρχ(1−mT )Lδδ + ρχN δ for δ : D > 0 (3.33)

M = [ρχmT + (1− ρχ)mR]L+ ρχ(1−mT )Lδδ for δ : D 6 0 (3.34)

The equation requires additional 5 parameters. Parameter R defines the size of the

elastic range, in other words constant incremental stiffness, parameters mr and mt

controls the very small strain shear modulus upon 90o and 180o strain path reversals,

respectively. Parameters βr and χ controls the rate of degradation of the stiffness

with strain. Detailed information on the determination processes of all 5 parameters

presented by Niemunis and Herle (1997) is given below.

3.1.2.1 Determination of Additional Parameters

Size of Constant Incremental Stiffness, R

Niemunis and Herle (1997) suggested to use stress strain curves from cyclic tests or

static tests with reversed strains can be used to assess the maximum value of inter-

granular strain. The size of the strain range that stiffness remains approximately

constant is defined with as constant, R. (Figure 3.6)

41

Figure 3.6: Characteristic stiffness for model calibration, Niemunis and Herle (1997)

Parameters mr and mt

It is suggested by Niemunis and Herle (1997) to perform a series of strain controlled

tests (with D = constant (plane strain test) ) where with a reference void ratio and

stress state but varying load history. By this way the increase in the stiffness (see

Figure 3.6) can be modelled with using the constants mR and mT.

Parameters βr and χ

In Figure 3.6, the upper curve is approximated as (E is stiffness);

E = mrE0 ( = ER ) for ε < R

E = E0 + E0()mr − 1)[1− ρχ] for ε > R(3.35)

Non dimensional intergranular strain is obtained for 1D monotonic strain path as in

the following differential form;

dρ

dε= (1− ρβr)/R (3.36)

It is suggested by Niemunis and Herle (1997) to use cyclic tests with small strain.

Single cycle strain accumulation is a function of χ and βr. As a result the parameter

βr can be correlated with the length of εSOM by using Figure 3.7

42

Figure 3.7: Correlation of βr, Niemunis and Herle (1997)

3.1.3 Theory of Permeability

The voids between the grain particles of the soil masses are interconnected. This

interconnection allows the water to travel through the soil by moving from one cell

to another no matter how dense or loose the soil is. Isolated voids are technically

possible but practically almost impossible in naturally formed soils. Even in the finest

clays with plate-shaped particles, electron photomicrograph results reveal that the

voids are interconnected (Lambe and Whitman, 1969). In soil mechanics, this flow is

generally simplified by assuming a straight channel flow rather than cell-to-cell flow.

In late 18th century, Darcy performed the classical test of permeability in which water

passes from a tube of soil. Darcy found by varying the length of the sample that the

rate of flow Q is proportional to head difference per length.

Q = kh3 − h4

LsampleA = kiA (3.37)

where;

• Q = rate of flow

• k = Darcy’s coefficient of permeability

• h3 = head at the begin of soil

• h4 = head at the end of soil

• Lsample = length of sample

43

• i = hydraulic gradient

Size of particles, void ratio, composition, fabric and saturation degree are the main

characteristics of soil that effect the permeability. In late 20th century, Hazen devel-

oped well known relationship to represent the permeability of soil by only considering

particle size as;

k = CHD210 (3.38)

where CH is empirically determined Hazen’s coefficient and D10 is the particle size

that 10 % of the soil is finer. The relationship is developed for loose clean sand with

unifomity D60/D10 is lower than 2. The relation is simple but there is a high deviation

from actual values and CH has the values from 1 to 1000 in the literature for various

test results (Carrier, 2003).

A more elaborated relation was suggested by Kozeny in 1927 and later modified by

Carman in 1937 and took its final form which is known as Kozeny-Carman relation-

ship.

3.1.3.1 Kozeny-Carman Relationship

The relation is developed by dealing the soil as an assembly of capillary tubes of equal

length by Kozeny (1927). Specific surface concept per unit mass of solid is introduced

by Kozeny to express the permeability. Later, Carman (1956) removed the assumption

that fluid moves in a straight channel by introducing Carman coefficient, CC (Chapuis

and Aubertin, 2003). Hence the relation took the following form in Equation 3.39;

k =1

CC

γ

µw

SF

Deff

2 e3

(1 + e)(3.39)

where γ is unit weight of water, µw is dynamic viscosity of water, SF is the shape

factor, Deff effective grain size and lastly e is the void ratio. In this study, the equation

is simplified with combining in a Kozeny-Carman coefficient, CK-C as follows;

k = CK-Ce3

(1 + e)(3.40)

44

where e is void ratio and the coefficient CK-C is dependent on density and dynamic

viscosity of water as well as specific surface.

Carrier (2003) stated three main limitations of Kozeny-Carman relation that must be

considered when applying. First of all, the relation ignores possible electrochemical

reaction between grain particles and the water which may cause a deviation for clay.

Secondly, the relation assumes laminar flow and inertia is ignored which may result

in a deviation for very coarse gravelly soils. Thirdly, a compact soil formation is

assumed in the relation hence it might result in difference in actual and measured

specific surface for extremely irregular shaped particles. On the other hand, based on

permeability test results of very wide range of samples, Chapuis and Aubertin (2003)

stated that using Kozeny-Carman relation is adequate for soils, k of which varies

between 10-1 to 10-11 m/s, where the deviaton from actual value can be between 0.33

to 3.

In the numerical model, hydraulic conductivity of soil was re-calculated at each step

with respect to the void ratio calculated under applied load.

3.1.4 Two-Phase Model

The primary actions considered for the foundation structures in the content of this

study are transient loads such as wind and wave loads. In these kind of problems,

coupled relation between deformation of soil skeleton and the pore water that fill in

the voids between solid particles are very important. Biot (1941), established the in-

teraction relation between solid and the fluid in quasi-static form. Later, Biot (1962),

extended that relationship to the dynamic form.

Zienkiewicz and Shiomi (1984) derived the incremental formation from the basis

theory of Biot (1941). In addition, assumption of incompressible fluid is implemented

by using a penalty formulation. It was assumed that if the problem considered is

a relatively slow speed phenomena, one can neglect the compressive waves in the

fluid. This allows another assumption that the pore pressure and only solid phase

displacements are allowed.

45

Tasan (2011) developed a stable two-phase model for soils with nonlinear material

formulation of the solid phase. The two-phase model is based on the theory of porous

media and described by Zienkiewicz and Shiomi (1984) and Potts (1999). The soil is

divided into into its soil skeleton and water. For this purpose, the principle of effective

stress and the Darcy’s law are used as basis.

One of the main assumptions in that model is that the soil is fully water-saturated.

Secondly, both the fluid phase as well as the single grain as an ingredient of the grain

skeleton are assumed as incompressible. Thirdly, the solid and the fluid phase are

regarded as continuous. Lastly, the balance of momentum equation is developed by

neglecting the accelerations of the relative movement between water and skeleton and

considering Terzaghi’s effective stress principle.

A 3D continuum used defined element u20p8 on the basis of two-phase model is de-

veloped in ANSYS as shown in Figure 3.8, where the displacement field is approxi-

mated using triquadratic interpolation functions and the pressure field is approximated

using trilinear interpolation functions.

Figure 3.8: u20p8 element (Tasan, 2011)

A well-known problem with modelling two-phase elements is the numerical instabil-

ity, which can be observed in the form of pore water pressure oscillations .The choice

of a higher order of displacement field is required to ensure the stability of the coupled

elements (Zienkiewicz et al., 1986).

Numerical studies performed in the scope of this dissertation initiates with some mod-

ifications of the existing tools developed and documented by Tasan (2011). The mod-

46

ifications to the u20p8 element are presented under following topics;

• Damping ratio

• Compressibility of solid grains and fluid

• Kozeny-Carman relationship

Absolute displacement of the solid skeleton u and the pressure of pore fluid p was

main variables of this u-p model in which the balance of momentum of the com-

position was expressed with regard to Terzaghi’s principle of effective stress as in

Equation 3.41 in the previous version of the model by Tasan (2011). Damping is

added to equilibrium in Equation 3.42.

LT (σ′ −mp) + ρb = ρu (3.41)

LT (σ′ −mp) + ρb = ρu + ζu (3.42)

where LT is divergence operator,

LT =

∂/∂x 0 0 ∂/∂y 0 ∂/∂z

0 ∂/∂y 0 ∂/∂x∂/∂z 0

0 0 ∂/∂z 0 ∂/∂y∂/∂x

σT is the effective stress vector as σT=[σxx σyy σzz σxy σyz σxz] where according to

Terzaghi’s effective stress principle;

σ = σ′ −mp

m is the indicator vector as mT = [1 1 1 0 0 0], ρ is density of mixture, b is force

vector,and ζ is the damping ratio.

Mass equilibrium of the fluid phase was expressed by considering linear momentum

as in Equation 3.43 in Tasan (2011).

mTLu +∇T Kp

ηw(−∇p+ ρwb) = 0 (3.43)

47

where ηw is the dynamic viscosity, ρw is the density of the water, Kp is the perme-

ability matrix, ∇p is the gradient of the pore water pressure. In this study, following

stiffness of the solid and fluid phases are taken into account by volumetric striffness

term Q* as in Equation 3.44.

mTLu +∇T Kp

ηw(−∇p+ ρwb) +

p

Q∗= 0 (3.44)

The volumetric stiffness of the solid phase and the fluid were coupled with respect to

porosity of soil n, bulk modulus of solid grains and pore water, Ks and Kw respectively;

1

Q∗=

n

Kw+

1− nKs

(3.45)

Earlier version of the two-phase model considered the case of an isotropic problem.

The permeability matrix was described by Kp = kpI, where I is the unit matrix.

Hydraulic conductivity kd was defined as;

kd =ρwg

ηwkp

In this version of the model, the permeability is allowed to be anisotropic by replac-

ing the unit matrix I. In addition, remember that the permeability kp is updated for

each step of the solution with regarding the void ratio according to Kozeny-Carman

relationship.

In this formulation of u-p model, the balance of momentum equation is simplified by

neglecting the accelerations of relative movement between water and skeleton which

is regarded as valid for most geotechnical problems of saturated soils (Zienkiewicz

et al., 1999). Equations 3.42 and 3.44 were the fundamental differential equations

developed for two-phase element.

An analytically exact solution of the differential Equations 3.42 and 3.44 for all

boundary value problems cannot be determined, so that, these has to be numerically

solved with the help of the FEM. In order to be able to apply the method, it is first

necessary to replace the differential Equations 3.42 and 3.44 with an equivalent in-

tegral representation. If these equations are approximately solved by an approach,

an approximation error remains, which is referred to as a residual. One method of

48

minimizing this error is the weighted residual method. It is required that the approx-

imation error with the help of a weight function becomes zero on average over the

entire area. A special method of weighted residuals that will be used in the following

is the method according to Galerkin. The basic idea of this method is to use the same

approach for both the approximate functions and the weight functions.

The weak form of the differential Equation 3.42 is obtained by multiplying a weight

function wT for boundary Ω as follows;∫Ω

wT(LT (σ′ −mp))dΩ +

∫Ω

wT(ρwb)dΩ −∫Ω

wT(ρwu)dΩ −∫Ω

wT(ζu)dΩ = 0

(3.46)

The first summation term in Equation 3.46 can be calculated as;∫Ω

wT(LT (σ′ −mp))dΩ = −∫Ω


∮Γ

wTσRdΓ (3.47)

where

σR = (σ′ −mp)Tn (3.48)

when Equation 3.47 is substituted into Equation 3.46;∫Ω


∮Γ

wTσRdΓ −∫Ω

wT(ρwb)dΩ

+

∫Ω

wT(ρwu)dΩ +

∫Ω

wT(ζu)dΩ = 0

(3.49)

The weak form of the differential Equation 3.44 is obtained by multiplying a weight

function w (where the weight function w is a scalar function here) for boundary Ω as

follows;∫Ω

wmTLudΩ +

∫Ω

w(∇T Kp

ηw(−∇p+ ρwb)

)dΩ +

∫Ω

wp

Q∗dΩ = 0 (3.50)

The second summation term in Equation 3.50 can be calculated as;∫Ω

w∇T Kp

ηw(−∇p+ ρwb)dΩ = −

∫Ω

w(∇T Kp

ηw(−∇p+ ρwb)

)dΩ

+

∮Γ

w(

Kp

ηw(−∇p+ ρwb)

)TndΓ

(3.51)

49

when qR is defined as;

qR =

(Kp

ηw(−∇p+ ρwb)

)Tn (3.52)

and substituting Equation 3.51 into Equation 3.50 the equation becomes;∫Ω

wmTLudΩ +

∫Ω

w(∇T Kp

ηw∇p)dΩ −

∫Ω

w(∇T Kp

ηwρwb

)dΩ

+

∮Γ

wqRdΓ +

∫Ω

wp

Q∗dΩ = 0

(3.53)

After deriving the weak form of the differential equations, they are spatially dis-

cretized below.

The absolute displacements of any element point of the solid phase are approximated

as follows using the shape function Nu of the general form and the element node

values u:

u = Nuu

The approximation of the pore water pressure of the fluid phase is carried out using

the shape functions Np of the general shape and the element node values pwusing the

following relationship:

pw = Nppw

According to Galerkin’s method, the same approaches are chosen for the weight func-

tions as;

wT = uNuT

w = pwNpT

Here u and pw are the element nodal values of the displacements or the pore water

pressures in the weight function.

The Equations 3.1.4 to 3.1.4 are described with the expansion operator B, which is

called

B = LNu and Bp = ∇Np

50

The resulting Equation 3.49;

u

∫Ω

NuTρNuudΩ +

∫Ω

NuT ζNuudΩ

∫Ω

BTσ′dΩ +

∫Ω

BTDtBudΩ

−∫Ω

BTmNppwdΩ −∫Ω

NuTρbdΩ −

∮Γ

NuTσRdΓ

= 0

(3.54)

and the Equation 3.53;

pw

∫Ω

NpTmTBudΩ +

∫Ω

NpT 1

Q∗NppwdΩ +

∫Ω

BpT Kp

ηwBppwdΩ

−∫Ω

BpT Kp

ηwρwbdΩ −

∮Γ

NpT qRdΓ

)= 0

(3.55)

The global system equations then becomes;M 0

0 0

u

pw

+

C 0

QT S

u

pw

+

K -Q

0 H

u

pw

=

fu

fp

where the mass and coupling matrices are;

M =

∫Ω

NuTρNudΩ, Q =

∫Ω

BTmNpdΩ

The permeability and stiffness matrices are;

H =

∫Ω

BT Kp

ηwBpdΩ, K =

∫Ω

BTDtBdΩ

C =

∫Ω

NuT ζNudΩ, S =

∫Ω

NpT 1

Q∗NpdΩ

Force vector for the solid phase and the fluid phase are;

fu =

∫Ω

NuTρbdΩ +

∮Γ

NuTσRdΓ

fp =

∫Ω

BpTKp

ηwρwbdΩ −

∮Γ

NpT qRdΓ

Here, Dt is the tangential modulus. If the elastic behaviour is considered for the solid

phase, the global system equations then becomes;M 0

0 0

u

pw

+

C 0

QT S

u

pw

+

KE -Q

0 H

u

pw

=

fu

fp

51

where

KE =

∫Ω

BTEBdΩ

E is the elastic modulus.

Implicit Newmark method is adopted for solving a differential equation of the second

order. Available integration algorithm given by Tasan (2011) is also utilized here.

The entire solution can be built from the local element equation systems, taking into

account the compatibility, i.e. the assignment of the local degrees of freedom of the

elements to the global degrees of freedom of the system and solved iteratively by a

suitable method for given initial and boundary conditions taking non-linearities into

account as explained in Tasan (2011).

The implementation takes place in the ANSYS program system, which contains a

large number of elements for various physical problems in its element library. The

user is given the opportunity to expand the element library via interfaces, for exam-

ple, and to implement additional material law formulations (ANSYS, 2018). The

advantage of implementing the elements or substance law formulations in ANSYS is

that the existing preprocessor for creating and mesh the calculation model, the equa-

tion solver for solving the equation systems and the postprocessor for visualizing the

results can be used.

ANSYS provides a number of prepared Fortran routines as an interface. The UserElem

routine is of central importance for the implementation of a finite element. An ele-

ment implementation can be carried out completely through this routine. Substance

law formulations can also be implemented directly in UserElem or in the UserMat

routine provided for this purpose (ANSYS, 2018).

3.2 Details of Modelling

A single bucket of a 4 legged lattice multipod under cyclic axial compression (Figure

3.9 left) and a monobucket under cyclic lateral loading (Figure 3.9 right) were investi-

gated with a three-dimensional FE model by taking the interaction between the bucket

and the surrounding sandy subsoil into account. The dimensions and the parameters

will be discussed in Chapter 4. The model was developed using the finite element

52

software ANSYS (2018). Modified u20p8 element is implemented into UserElem

and hypoplastic material law with intergranular strain is implemented in the routine

UserMat ANSYS (2018) as explained above in detail.

Figure 3.9: Schematic description of multipod and monopod structures

The model consists of soil medium, a steel bucket and contact interface elements

regarding the interaction between the bucket and the surrounding soil.

Two-phase u20p8 element which is presented in the previous section is used to repre-

sent saturated soil medium with saturated unit weight γ′ and initial relative density DR

representing the in situ conditions. The bucket was modelled with higher order 3-D

20-node solid continuum elements "SOLID186" which is defined by 20 nodes having

three degrees of freedom per node: translations in the nodal x, y, and z directions. The

bucket-soil interface was represented by contact and sliding between "CONTA174"

elements and 3-D target surfaces "TARGE170" considering isotropic Coulomb fric-

tion as shown in Figure 3.10. Augmented Lagrange penalty based formulation is

used with all default values according to ANSYS (2018) and the tangential frictional

stress is linearly proportional to the normal stress and calculated by a contact friction

coefficient µ.

The FE model is presented in Figure 3.11 where D and L are diameter and embedded

skirt length of bucket, respectively. Dimensions and mesh density of FE model were

optimized based on the preliminary calculations to avoid boundary effects. An exam-

ple calculation is given for axial loading in Figure 3.12 where effect of model height

diminished for total height Ltotal greater than 9L.

53

Figure 3.10: Element types

21D

10L

L

D

Figure 3.11: FE model of single suction bucket

Figure 3.11 also shows the translational boundary conditions schematically. These

are imposed on the mesh by fixing of nodes at the bottom of the mesh against dis-

placement in all directions, on the plane of symmetry against displacement normal to

that plane and on the periphery of the mesh against displacement in both horizontal

directions. In addition, drainage is allowed on the surface of the model and a hy-

drostatic pore pressure profile that is equal to the initial pressure was applied to the

54

Figure 3.12: Preliminary calculations for determination of suitable model dimensions

edges. The bottom of model is impermeable.

Prior to the first phase of the simulation, a vertical and a horizontal effective stress

as the initial loading is defined for soil to determine the required state variables of

the expanded hypoplastic model. As first, a calculation under gravity loading was

performed with a value of the coefficient of earth pressure at rest k0. For this purpose,

the Poisson’s ratio ν is determined depending on a coefficient of earth pressure at

rest k0 using the relationship ν = k0 / (1+ k0). In the next step, the predefined soil

elements defining the bucket geometry were replaced by bucket elements and thereby

the contact between the bucket and the surrounding soil was activated. Subsequently,

the repetitive load was applied on the bucket. Here the calculated number of loading

cycles is limited to 12 due to the excessive calculation times and the numerical errors

from an implicit calculation strategy as described in Niemunis et al. (2005).

3.3 Verification of Finite Element Model

Verification of the accuracy of the finite element model is essential to rely on the

results. Most appropriate method to validate a finite element analysis is the simulation

of existing laboratory and field tests or to use full scale field tests but such a data is

most often confidential by the owners.

In this chapter of the study, it is aimed to validate the finite element modelling by

means of model geometry, constitutive material model, loading and boundary condi-

55

tions. For that purpose, existing experimental tests documented in the literature are

considered.

3.3.1 Verification of Geometric Modelling, Mesh and Boundary Conditions

In this first section of the chapter, the field tests of buckets at Frederikshavn and

Sandy Haven reported by Houlsby and Byrne (2004) under monotonic loading are

used to validate the finite element model in terms of geometry, boundary conditions

and meshing.

The model diameter is roughly selected as 7D and the model height is 3L where D

is the bucket diameter and the L is the skirt length. At the bottom of the model, dis-

placements in all directions are constrained. At the outermost surface, only horizontal

translations are constrained. At the symmetry plane, the displacements normal to the

plane are restrained.

Elasto-plastic Mohr-Coulomb model is used for soil for simplicity since only mesh-

ing and geometrical modelling is questioned. Oedometric modulus is defined with

respect to stress state. Geometric non-linearity is considered to account for high de-

formations by updating the deformed node locations at load steps. Stress dependency

of oedometric modulus is defined as;

Es = κσat(σmσat

)λ (3.56)

where, σat = 100 kPa, σm = Stress State at Reference Location, κ and λ are coeffi-

cients.

In the first phase calculations, soil stresses were calculated under gravity loading

only. At rest earth pressure coefficient is applied. In the next phase, bucket elements

activated and overlapping soil elements were deactivated ignoring the stress changes

during the installation of buckets. At the third phase, vertical loading was applied. Fi-

nally, horizontal load is applied with varying eccentricity to obtain M-θ relationship.

A load controlled scheme was used for variation of cases.

56

Prototype Bucket Foundation at Frederikshavn Houlsby and Byrne (2004) re-

ported details of the tests on fully operational 3 MW wind turbine on a suction bucket

prototype with aspect ratio of 1.0 (D = L = 2.00 m, ts = 12 mm.). V = 37.3 kN

load is applied monotonically at 17.4 m eccentricity. Achmus et al. (2013) sum-

marized the material properties for back calculation as; effective unit weight of the

soil, γ’ = 9.00 kN/m3, oedometric stiffness coefficient κ = 500, λ = 0.57, Poisson’s

Ratio µ= 0.25, angle of internal friction, φ = 37.0o. Figure 3.13 shows the moment-

rotational displacement behaviour comparison between Frederikshavn test and nu-

merical simulation.

Figure 3.13: Moment - rotational displacement of bucket at Frederikshavn

Prototype Bucket Foundation at Sandy Haven Houlsby and Byrne (2004) re-

ported details of the tests on nearshore suction bucket prototype with aspect ratio of

0.625 (D = 2.50 m, L = 4.00 m, ts = 20 mm.). Varying horizontal loads H were ap-

plied at 14.5 m eccentricity. Achmus et al. (2013) summarized the material properties

for back calculation as; effective unit weight of the soil, γ’ = 9.00 kN/m3, oedometric

stiffness coefficient κ = 400, λ = 0.60, Poisson’s Ratio µ = 0.25, angle of internal fric-

tion, φ = 35.0o. Figure 3.14 shows the horizontal load-rotation behaviour comparison

for Sandy Haven between numerical simulation.

A very good agreement of results is observed. The efforts up to this point indicates

a successful geometric modelling and healthy working mesh with adequate boundary

conditions.

57

Figure 3.14: Horizontal Load - Rotation of bucket at Sandy Haven

In the next step, verification effort is continued with implementing cyclic loads and

considered constitutive law which in this case is hypoplastic law of von Wolffersdorff

(1996) with intergranular strain developed by Niemunis and Herle (1997). To ac-

count for the interaction of pore-fluid and soil skeleton, two-phase model developed

by Tasan (2011), later improved in this study as presented in previous paragraphs

is utilized which mainly includes Kozeny-Carman relationship for the variation of

permeability.

3.3.2 Verification of Two-Phase Model Implementation

Consolidation of a Finite Layer Under Surface Surcharge

To start with the verification of correct implementation of the two-phase element to

the ANSYS (2018) program, the consolidation of a fully saturated, cohesive layer

under surface surcharge load which was studied by Booker (1974) was simulated

as a benchmark. In this study, the soil is elastic. The thickness of the fully saturated

cohesive material is 4.00 m. An impermeable and rigid layer exist beneath the soil. To

decrease the computation time, symmetry was taken into account and only a quarter

of total area is modelled with outer boundary is 5 times greater than the loaded width.

Drainage of the pore water is allowed only from the surface. Young’s modulus for

the soil was given as 40 MPa and problem was solved for Poisson’s ratio µ of 0.25 as

summarized in left of Figure 3.15.

58

The comparison of the simulations and the study of Booker (1974) is given in Fig-

ure 3.15 which shows a very good agreement for settlement of the layer during the

time considered. In the early stages after loading, the stresses are transferred to pore

fluid and as the time lapses, the effective stress increased gradually which implies a

successful working coupled element.

16m4m

4m

4m16m

10 kPa

E = 40 MPa

v = 0.25

ki= 2x10-6m/s

10−4

10−2

100

102

0

0.2

0.4

0.6

0.8

1

Time (s)

Deg

ree

of

Co

nso

lid

atio

n, U

Booker (1974)

FE Simulation

Figure 3.15: Simulation of the consolidation of a finite layer under surface load

In the next phase, it is aimed to check the coupling with hypoplastic constitutive law

with intergranular strain. Three cyclically loaded undrained triaxial experiments (CU)

were modelled with a u20p8 for single element FE tests.

CU Cyclic Triaxial Test on Hochstetten Sand

The calculation was performed for the initial void ratio e0 = 0.695 and isotropic cell

pressure p0 = 300 kPa. Comparison of the numerical simulation and experimental

results of undrained triaxial compression with symmetric deviatoric stress cycles of

30 kPa at 0.10 Hz frequency are shown in Figure 3.16a which shows a very good

agreement. This result is accepted as an indication of the working coupled element.

Hypoplastic material properties of dense Hochstetten sand is given by Niemunis and

Herle (1997) in Table 3.1 which is applied to the u20p8 element, details of which

is discussed early in this chapter. A single rectangular element was modelled with

constraining at the bottom just to avoid translation and singularity and loaded with a

cell pressure at each face with the information given above.

59

Table 3.1: Hypoplastic Material Properties of Hochstetten Sand, (Niemunis and

Herle, 1997)

φc(o) hs (GPa) n ed0 ec0 ei0 α β mR mT Rmax βR χ

(1) 33 1.00 0.25 0.55 0.95 1.05 0.25 1.00 5.0 2.0 1e-4 0.50 6.00

CU Cyclic Triaxial Test on Toyoura Sand In addition to Hochstetten Sand, cyclic

triaxial tests on Toyoura sand were also studied. Toyoura sand is widely researched

in the literature and employed in many labaratory tests. Hypoplastic material parame-

ters were suggested by Herle and Gudehus (1999). Later, Hong et al. (2017); Ng et al.

(2015); Ochmanski et al. (2014) suggested Hypoplastic material parameters with in-

tergranular strain. The summary of previous researches on the parameters are given

in Table 3.2 with the parameters assessed in this study.

Table 3.2: Parameters of Toyoura Sand, (1) Ochmanski et al. (2014) (2) Hong et al.

(2017) (3) Ng et al. (2015) (4) This Study


(1) 30 2.60 0.27 0.61 0.98 1.10 0.14 3.00 8.0 2.0 2e-5 0.10 1.00

(2) 31 2.60 0.27 0.61 0.98 1.10 0.11 4.00 8.0 4.0 2e-5 0.15 1.00

(3) 30 2.60 0.27 0.61 0.98 1.10 0.50 3.00 8.0 4.0 3e-5 0.20 1.00

(4) 31 2.60 0.27 0.61 0.98 1.10 0.50 1.00 8.0 2.0 3e-5 0.10 1.00

In this study, a curve fitting effort was performed to assess the input parameters of

Toyoura sand. For that purpose 3 cyclic triaxial tests were used. Ishihara (1975)

performed stress controlled cyclic triaxial test on a loose sample of 5 cm diameter

and 10 cm height with a void ratio of 0.737. It was stated that freshly boiled sand

was used to obtain the loose sample. p′-q′ diagram for the test was aimed to simulate

where p′ is mean effective stress ((σa+2σr)/3) and q′ is the deviatoric stress (σa-σr).

The calculation was performed for the initial void ratio e0 = 0.737 and isotropic cell

pressure p0 = 210 kPa. Comparison of the numerical simulation and experimental

results of undrained triaxial compression with symmetric deviatoric stress cycles of

68.6 kPa at 1.00 Hz frequency are shown in Figure 3.16b.

60

CU Cyclic Triaxial Test on Karlsruher Sand A cyclic triaxial CU test with loose

Karlsruher sand specimen which has almost no fines content with a mean grain size

d50 = 0.14 mm and a uniformity coefficient Cu = 1.50. Initial relative density was

0.27. An isotropic cell pressure, p′ = 200 kPa followed by symmetric deviatoric stress

cycles, q = 30 kPa was applied. The material parameters are given in Table 3.3.

The p′-q diagram from experimental test where p′ is mean effective stress ((σa+2σr)/3)

and q is the deviatoric stress (σa-σr) is given in Figure 3.16c. FE calculations show a

satisfactory agreement with experimental results.Table 3.3: Hypoplastic Material Properties of Karlsruher Sand, Wichtmann and Tri-

antafyllidis (2005)


(1) 33.1 4.00 0.27 0.68 1.05 1.21 0.14 1.00 5.0 2.0 1e-4 0.50 6.00

It is better to approximate the stress-strain behaviour as well. However, data is not be

available for all the tests simulated here. Axial strain – deviatoric stress diagram is

plotted and compared for Karlsruher sand in Figure 3.17. Number of cycles to failure

and critical state angle (observed from stress path) is approximated well.

3.3.3 Verification of Complete Model with Centrifuge Tests of Bucket Founda-

tion

3.3.3.1 Centrifuge Tests on Fujian Sand

Until this stage, individual verification studies showed good agreements with the ex-

perimental data. To carry the verification process further and ensure reliability of

simulations, a cyclic centrifuge test will be simulated in which a combination of all

previous individual works will be included. Real scale testing for OWT structures are

not convenient to conduct. Laboratory tests on the other hand may be inappropriate to

simulate the problems of this kind of scale. Centrifuge modelling helps to overcome

the disadvantages of scale by amplifying the stress level.

Wang et al. (2018a) performed geotechnical centrifuge test to study the behaviour

of monopod and tripod suction bucket foundations under monotonic and cyclic load

61

Figure 3.16: Simulation of undrained triaxial tests on Hochstetten sand, Niemunis

and Herle (1997), on Toyoura sand Ishihara (1975), on Karlsruher sand, Wichtmann

and Triantafyllidis (2005)

Figure 3.17: Simulation of axial strain vs deviatoric stress relationship for Karlsruher

sand

conditions. Four centrifuge tests were carried out on medium dense dry Fujian sand,

at 100 g centrifugal acceleration. First two tests involved monotonic loading to obtain

moment-rotation response and other two tests involved one-way cycling loading.

The buckets were installed at 1 g acceleration. The actuator, the load cell and the

62

laser displacement sensor installed at the loading height. The views of the centrifuge

model package is given in Figure 3.18. The monopod and tripod buckets were placed

in the middle of the model container. The container dimensions were 1200 x 950

mm. Mean particle diameter was 0.17 mm, and coefficient of uniformity (Uc) was

1.57. The relatively density of the sand was 60%. The maximum and minimum

void ratios of the sand are 0.952 and 0.607, respectively. The model tripod bucket

foundation was made of aluminium alloy with an elastic modulus of 72 GPa and a

Poisson’s ratio of 0.3. The thickness of bucket skirt was chosen to be 4 mm (0.4 m in

prototype). Diameter (DMonopod) is 150 mm (15 m in prototype) and aspect ratio (L/D)

is 1.

D = 15m

L = 15m

θ

E = 72 GPa

ν = 0.30

Test 1

Test 2

h

x

z

Number of Cycles N

H [MN]

Test 2

Time

F

Test 1

Hmax

0

Figure 3.18: Simulated tests according toWang et al. (2018a)

Figure 3.19: Simulation of monotonic test and cyclic test on Fujian Sand

Wang et al. (2018a) performed four stress paths controlled drained triaxial tests on the

63

Table 3.4: Hypoplastic Material Properties for Fujian Sand, Wang et al. (2018a)


(1) 32.50 2.00 0.34 0.61 0.95 1.14 0.08 1.80 8.0 4.0 1e-4 0.40 0.80

Fujian silica to calibrate the hypoplastic material properties. All the calibrated model

parameters were summarized in Table 3.4.

Two centrifuge tests with dry Fujian sand with relative density Dr = 0.60 was simu-

lated. Two-phase u20p8 elements were used for the modelling the sand. To simulate

dry soil, fixing the pore pressure degree of freedom to zero is possible. However, in

order to check the two-phase model, a coefficient CK-C according to Equation 3.40

was assumed high enough to numerically prevent any pore pressure development in

soil.

A bucket with an outer diameter D = 15 m, skirt length L = 15 m and a wall thick-

ness t = 0.40 m was subjected to lateral loads at a height h = 31.5 m as shown in

Figure 3.18. Bucket was modelled with a linear elastic material model where Young’s

modulus E = 72 GPa and Poisson′s ratio v = 0.30. Wall friction angle of 23tan(φc) was

assumed at the contact surfaces.

In first analysis, the bucket was subjected to monotonic load. The calculated moment-

rotation response is given in Figure 3.19a. In further analysis, the bucket was sub-

jected to horizontal one-way cyclic loading with a maximum load amplitude Hmax =

1270 kN. The centrifuge test included series of 1000 cycles at 10, 20, 30, 40 and 50

percent of ultimate load. Numerically it is impractical and unreliable to solve that

amount of cycles since there would be a stress accumulation at the model boundaries

which will result in inaccuracy of deformations after a certain cycle. In general, it

is acceptable to rely on the numerical simulations up to 10-20 cycles, after that, the

model dimensions must be very large which is computationally impracticable.

It is beneficial to be note here that, 10-20 cycles (the study will focus on 12 cycles

only in parametric simulations) may be considered more than enough to benefit some

important interpretations such that, according to typical decomposition of storm time

histories by Schjetne et al. (1979) and Andersen and Lauritzsen (1988), the peak

value can only occur once or for a couple of times. 100s and 1000s of repetitions

64

is possible for very low amplitudes. This is also valid for NGI’s equivalent cycle

method or rainflow method. According to this, a couple of times expected peak loads

are covered more than expected times. This study does not aim to simulate the service

level daily cycles with million repetitions but largest amplitude components of design

storms. For this purpose, 12 cycle simulation may be assumed as enough to get

an idea with expecting largest accumulation at the early cycles under high cyclic

amplitude loadings Senders and Randolph (2009).

Bucket rotation - number of cycle response presented in Figure 3.19b was focused

for only first few cycles to avoid numerical error accumulation. Comparison of both

simulations shows a good agreement with test results.

3.3.3.2 Centrifuge Tests on Baskarp Sand

A series of 100g centrifuge tests presented by Bienen et al. (2018a,1) on saturated

Baskarp sand with relative density Dr = 0.98. Material properties adopted according

to Ragni et al. (2020) are given in Table 3.5.

A bucket with an outer diameter, D = 8 m, skirt length L = 4 m and a wall thickness

t = 0.05 m was subjected to axial compressive loads. (see Figure 3.20)

Bucket was modelled with a linear elastic material model where Young’s modulus

E = 70 GPa and Poisson’s ratio v = 0.30. Friction of coefficient, Coefficient of fric-

tion, µ = 2/3 tan(φc) was assumed at the contact surfaces. The bucket was subjected

to cyclic axial compression with a mean 4 kPa and ± 14 kPa cyclic stress amplitude.

Axial displacement number of cycle response presented in Figure 3.21. When the

sheared soil adjacent to the bucket skin is examined closely, the slope of the volumet-

ric strain vs. shear strain showed an angle of dilation of approximately 14o. However,

according to Byrne and Houlsby (2004), the dilation angle of the soils saturated with

silicon oil reduces 2-3o which may result in an inevitable difference for simulation

of the centrifuge tests. Nevertheless, the comparison of simulation shows a good

agreement with test results according to Figure 3.21.

65

Table 3.5: Hypoplastic Material Properties of Baskarp Sand, Ragni et al. (2020)


(1) 31.5 2.30 0.30 0.39 0.69 0.79 0.13 1.00 1.4 2.2 1e-4 0.40 0.80

Figure 3.20: Simulated tests according to Bienen et al. (2018a,1)

Figure 3.21: Simulation of cyclic centrifuge test on Baskarp sand

3.3.4 Summary of Verification Works

In this section, it is aimed to verify that the model geometry, mesh quality and two-

phase model work sufficiently good to rely on the results of the parametric study that

will follow this chapter.

In that purpose;

• Monotonic tests at Fredericshavn and Sandy Haven are simulated to check the

mesh and geometry.

• Analytical solution of consolidation tests by Booker (1974) is used as a bench-

66

mark test for the two-phase model.

• Undrained cyclic triaxial tests on Hochstettenn, Toyoura and Karlsruher sand

are simulated to check the constitutive material model with two-phase model.

• Laterally loaded monotonic and cyclic centrifuge test on Fujian Sand are sim-

ulated to check the overall combination of model, mesh, material model and

two-phase model.

• Axially loaded cyclic centrifuge test on Baskarp Sand is simulated to check the

overall combination of model, mesh, material model and two-phase model.

In conclusion, the agreement of simulation with these laboratory and field tests indi-

cated that the numerical studies based on that FE model can be used to interpretation

of behaviour of suction bucket foundations.

67

CHAPTER 4

BEHAVIOUR UNDER CYCLIC LOADING

The response of suction buckets subjected to cyclic axial compressive and lateral

loads in saturated sandy soils is studied with a series of parametric numerical analyses

as explained in this chapter. Firstly, a single leg of a multi-pod in Figure 4.1 under

cyclic axial compression, later a mono-pod in Figure 4.2 under cyclic lateral loading

are studied.

Figure 4.1: Description of multipod structure

69

The numerical analyses performed through a 3D finite element model described in

Chapter 3. The model require the definition of geometry, material properties, loading

information and lastly the boundary conditions.In order to perform a parametric study,

a reference set of parameters are determined based on a preliminary design of an OWT

with power rating of 8 MW (see Section 4.1), which define geometry of foundation,

soil characteristics and loading. Then, effect of individual parameters are studied

by varying them separately in a suitable range as schematically described in Figure

4.7. Details of determination of parameters and selecting the range of variation is

discussed in Section 4.1.

Figure 4.2: Description of monopod structure

After collecting the results, following topics are focused on;

• deformation response during cyclic loading

• the changes in load transfer via components of bucket which are top plate, outer

and inner skirt as well as the tip of bucket depending on the number of load

cycles

70

4.1 Reference Set of Parameters

Firstly, a reference set of parameters are determined as given in Table 4.2. Later, the

parameters are modified separately around that set with a suitable range. Selection of

the reference parameters and the variation range is explained below.

4.1.1 Material

4.1.1.1 Saturated Sandy Soil

A poorly graded medium to coarse sand with a characteristic grain size, d50 = 0.55 mm

and a coefficient of uniformity, Cu = 3.3 was adopted. The hypoplastic material pa-

rameters of the test sand are given in Table 4.1 which are adopted from Le (2015).

The sand has similar characteristics with the North Sea sand and material properties

for the numerical model are known. Dense to very dense sand often characterises the

sea bed and suction bucket foundations (Houlsby and Byrne, 2005; Stapelfeldt et al.,

2020; Tjelta, 1995).

Table 4.1: Hypoplastic Material Properties with IGS, adopted from Le (2015)


31.50 2.30 0.3 0.39 0.69 0.79 0.13 1.00 4.4 2.2 1e-4 0.40 0.80

Porosity-permeability relation is considered with Kozeny-Carman coefficient CK-C

which is related to void ratio e and the permeability of soil k according to Equation

3.40.

For sands, soil permeability assumed to vary between 10-3m/s to 10-5m/s. This range

is also practicable for suction bucket installation according to earlier studies by Houlsby

and Byrne (2005) and Tran (2005). In the reference system, the initial permeability

is selected as kinitial=1.0x10-4m/s. Than it is varied between 10-3m/s to 10-5m/s. Ac-

cording to the changes in the stress state during the calculations, the permeability is

automatically updated.

71

Hence, the Kozeny-Carman coefficient CK-C to control the porosity permeability rela-

tionship is obtained as 0.00159 according to Equation 3.40 for the reference system.

During the parametric study, this value is varied between 0.0159 to 0.000159. This

value is artificially generated to study the effect on the deformation behaviour. Actual

value is dependent on the unit weight γw, viscosity of the water µ, shape factor SF,

effective grain size Deff and the Carman coefficient Cc according to Equation 3.39.

γw / µ is approximately 9.9 x 10-4 and 7.6 x 10-4 1/cm.s for water at 20oC and 10oC,

respectively. The coefficient Cc is taken as 5. Shape factor varies between 6 to 8.4

for round to coarse grained soils (Chapuis and Aubertin, 2003). Combining these

together, the permeability of a sand with Deff = 0.55 mm can be estimated between

4 x 10-4 m/s to 2 x 10-3 m/s with respect to the roughness of grains and temperature.

Accordingly, the simplified CK-C is between 0.0165 to 0.004. However, in this study,

a wider range with respect to the physical correspondence is used.

OWT foundations are mostly installed on dense to very dense sands (Houlsby and

Byrne, 2005; Stapelfeldt et al., 2020; Tjelta, 1995). For that reason, relative density

Dr of soil is studied between 70% to 90% in the study. In reference system the initial

relative density is selected as 80% for which the initial void ratio einitial is calculated

as 0.45.

4.1.1.2 Bucket Foundation

The foundation is modelled with the skirt and top plate without the upper structure

which may be a lattice as in Figure 4.1 or tower as in Figure 4.2. The loads are applied

on top surface of the top plate. For bucket steel, linear elastic material behaviour

with Young’s modulus, E = 200 GPa and Poisson’s ratio, v = 0.20 is assumed. A

numerically rigid top plate is defined considering the stiffeners.

4.1.1.3 Bucket-Soil Interaction

Coefficient of friction between sand and steel depend on the relative size, shape and

surface roughness of the sand grains as well as steel surface properties. Effect of the

coefficient of contact friction is studied by using µ=0.20, 0.30 and 0.40.

72

4.1.2 Geometry

4.1.2.1 Multipod

A single bucket of a 4 legged multipod shown in Figure 4.1 is modelled with FE to

investigate the behaviour under cyclic axial compressive loads. A bucket under axial

compression is an axis-symmetric problem however, considering the other cases in

this study (such as horizontal loading), a half cylinder medium was modelled with

three dimensional elements by utilizing ANSYS (2018) software.

According to preliminary estimations, the bucket dimensions are selected as D = L =

10 m. Later, to investigate the affect of aspect ratio, the skirt length is varied between

8 m to 13 m. For all cases, the bucket diameter is kept constant.

4.1.2.2 Monopod

Similar to multipod, bucket of a monopod shown in Figure 4.2 is modelled with

FE to investigate the behaviour under cyclic lateral loads. Again with preliminary

estimations, the bucket dimensions are selected as D = L = 10 m. As in the case for

multipod, the effect of aspect ratio is studied by changing skirt length, L between 8 m

to 13 m with keeping bucket diameter constant.

4.1.3 Loading

4.1.3.1 Cyclic Axial Compression

Considering the nacelle, hub, blades, tower and lattice of an 8 MW OWT, a static

dead load of 20 MN is estimated. Approximate values of dead weights of nacelle and

rotor with hub is 4.8 MN, tower is 6.5 MN, transition piece and lattice structure for

30 m water depth is 8.7 MN assumed according to Kiełkiewicz et al. (2015). This

load is distributed evenly to all four legs of the lattice as Vstat = 5 MN. Weight of the

bucket itself is calculated in the analysis.

A sinusoidal lateral load is assumed which idealizes the wind, wave and current loads

73

that act on the bucket. As the lattice structure transforms lateral loads as compression

and tension on the individual legs, the axial load pattern shown in Figure 4.3 is applied

on top of the bucket. The minimum value of cyclic loading is Fmin = 5 MN which

is dead load and maximum value Fmax is determined according to Fcyc where Fmax =

Fcyc + Fmin.

The cyclic amplitude Fcyc is determined with respect to the static ultimate loading

capacity Fult shown in Figure 4.4. A displacement ratio criteria of 10% D is selected

according to Moormann (2016) as failure limit to obtain bearing capacity. The dis-

placement ratio, uz/uz,ult is defined as the ratio of accumulated axial displacement, uz

to static ultimate displacement, uz,ult. Before the cyclic analysis, ultimate axial load-

ing capacity, Fult is calculated with monotonic loading test as 101.6 MN for reference

set of parameters in Table 4.1 where D = L = 10 m. For other scenarios of L = 8 m and

L = 13 m, Fult is calculated as 89.7 MN and 116.4 MN, respectively. In conclusion,

the applied cyclic loading amplitude Fcyc is varied between Fcyc = 0.05 Fult to 0.25

Fult during cyclic loading.

Fstat+ΔFcyc

FoutFin

Ftop

FinFout

uz

FtipFtip

Figure 4.3: Loading scheme and legend for resistance components in axial loading

(a) Cyclic loading pattern, (b) Loads on components

4.1.3.2 Cyclic Lateral Loading

Considering the nacelle, hub, blades and tower of an 5 MW OWT, a static dead load

Vstat = 10 MN is applied on the monopod. A similar idealization on lateral load

explained before is repeated here.

The minimum value of cyclic loading Hmin = 0 which indicates one-way loading and

maximum value Hmax = Hcyc + Hmin. One-way loading is commonly accepted and

74

Figure 4.4: Axial monotonic loading test

the majority of lateral load tests reported in the literature are one-way loaded but it

is expected that larger displacements will occur under two-way loading according to

LeBlanc et al. (2010). Thus one-way results can show a bottom line. Figure 4.5

describes the loading scheme and the corresponding loads obtained on elements.

The cyclic amplitude Hcyc is determined with respect to the static ultimate loading

capacity Hult which is determined from load-rotation curve in Figure 4.6 as Mult =

338.90 MNm for the reference soil-bucket-system reference set of parameters in Ta-

ble 4.1 where D = L = 10 m. Corresponding lateral force Hult is 11.30 MN for an

eccentricity ecc = 30 m from the top plate. For other scenarios of L = 8 m and L

= 13 m, Hult is calculated as 200.8 MN and 580.6 MN, respectively with keeping

eccentricity constant at ecc = 30 m.

Vstat

Ftop

Fin

_C

Fo

ut_

C

Ftip_CFtip_T

Number of Cycles, N

Horizontal Force, H

0

Hmax

f

Hcy

c

D = 10m

L = 10m

ecc

x

z

H [MN]

Mcyc

=Hcyc

x ecc

Hcyc

Compression Side Tension Side

∆θ

∆x

∆z

Fo

ut_

T

Fin

_T

V [MN]

Figure 4.5: Loading scheme and legend for resistance components in lateral loading

(a) Cyclic loading pattern, (b) Loads on components

75

Figure 4.6: Lateral monotonic loading test

4.1.3.3 Frequency and Duration of Loading

Number of load cycles for natural events can be hundreds, however, this duration is

not practicable to simulate numerically. On the other hand, most critical part of devel-

opment of deformations under extreme load conditions (i.e. high cyclic amplitudes)

occurs at the initial cycles. For that reason, 12 cycle duration is assumed as an appro-

priate number to avoid excessive calculation times and the numerical errors from an

implicit calculation strategy as described in Niemunis et al. (2005).

The period of cycles in natural actions assumed to vary between 5 to 20 seconds

according to Senders and Randolph (2009) and Penner et al. (2020). Calculations

performed for f = 0.05, 0.10 and 0.20 Hz.

4.1.4 Summary

Cyclic loading amplitude, Fcyc and frequency, f of cyclic loading; KC coefficient,

CK-C (i.e. permeability) and relative density Dr of soil; aspect ratio, L/D of bucket

and friction coefficient, µ were varied with respect to reference system in Table 4.2 to

study the effects on load-bearing mechanism, deformations and the stresses in soil.

The main focuses were dedicated on general system response and load transfer be-

tween the components of the bucket depending on the cyclic axial compressive load.

76

Figure 4.7: Schematic Description of Parametric Analyses

Table 4.2: Model Parameters for Reference System

Paremeter min Reference max

Bucket Diameter, D - 10 m -

Skirt Length, L 8 m 10 m 13 m

Skirt Thickness, t - 0.05 m -

Static Axial Load, Fmin - 5 MN -

Cyclic Load Frequency, f 0.05 Hz 0.10 Hz 0.20 Hz

Kozeny Carman Coefficient, CK-C 0.000159 0.00159 0.0159

Relative Density, Dr 70% 80% 90%

Friction Coefficient, µ 0.20 0.30 0.40

77

4.2 Studies on Bucket Behaviour under Cyclic Axial Compressive Load

4.2.1 General System Response

Goldscheider and Gudehus (1976) described the principal behaviours of a structure

under cyclic loading as in Figure 4.8. Shakedown response where a plastic defor-

mation occurs in initial stages but as the number of cycles increase accumulation of

plastic deformation stops and response becomes elastic. For higher load levels, ac-

cumulation may not be necessarily stop but it is possible that rate of increase slows

which is called as attenuation response. Lastly, for very high cyclic load levels, sys-

tem progressively tends to collapse. That behaviour is called progressive failure.

Figure 4.8: Principal behaviours under cyclic loading Goldscheider and Gudehus

(1976)

In this part, deformation - cycle graphs for the test scenarios are obtained. In order

to interpret the displacement behaviour in a comparable manner, the displacement

ratio, uz/uz,ult which is defined as the ratio of accumulated axial displacement, uz

to static ultimate displacement, uz,ult is plotted on the y axis. The cycle number is

plotted on the x axis. Each graph shows the deformation-cycle curves for cyclic load

amplitudes Fcyc = F/Fult corresponding to the given set of parameters. In each figure,

only the parameter shown on the graph is changed with respect to the reference set of

parameters in Table 4.2.

Figure 4.9 is obtained for the reference system. For all load levels, the highest in-

crease of plastic deformations was calculated at the first cycle of loading. The defor-

mations remained nearly unchanged during the rest of the cycles and it can be called

shakedown behaviour for cyclic loads up to a maximum amplitude of Fcyc = 0.05 Fult.

78

Figure 4.9: Effect of load level on plastic deformations for reference system (Table

4.2)

The increase of deformations decreased with loading cycle but it never reached zero

for 0.05 Fult < Fcyc < 0.25 Fult which is called as attenuation. The deformations has

increased progressively and system failed to stabilize for Fcyc > 0.25 Fult which is

called as progressive failure.

The load deformation relations for the 3 different loading amplitude tests are plotted

on Figure 4.10(a) for the reference system. The cyclic axial load Fcyc is normalized

with respect to static ultimate load bearing capacity Fult and and cyclic loading ratio

(Fcyc/Fult) plotted on y axis. The axial displacement ratio (uz/uz,ult) is given in x axis.

The stiffness variation during the test cycles are calculated according to Figure 4.10(a)

and plotted on Figure 4.10(b). To compare, the stiffness calculated for each case

is normalized with respect to initial stiffness. Parallel to previous discussion, it is

observed that after initial compaction at first loading cycle, a stiffness degradation

was calculated for the cases of attenuation as well as progressive failure in contrary

to shakedown case.

Axial deformation - load cycle graphs are calculated for varying parameters in Figure

4.11 to Figure 4.13 to show the effect of the selected parameter on the deformation

response.

In Figure 4.11 it is shown that for longer skirt length, the displacement accumulation

slows down due to increased capacity and also the path of the excess pore pressure

79

Figure 4.10: Effect of load level on foundation stiffness for reference system (Table

4.2)

0 2 4 6 8 10 120

0.01

0.02

0.03

0.04

Number of Cycles, N

uz/u

z,u

lt

L/D=0.80

L/D=1.0

L/D=1.30Progressive Failure

Attenuation

Fcyc

= 0.15Fult

Figure 4.11: Effect of aspect ratio on plastic deformations

to dissipate increases which allows more water to seep out. In contrary, as the skirt

length decreases, the excess pore pressure increases rapidly in and around the bucket

which results in accumulation of larger displacements eventually leading to progres-

sive failure.

In Figure 4.12 it is shown that the effect of frequency is relatively less significant

with respect to other parameters. Although all three cases showed attenuation be-

haviour as in the reference system according to Figure 4.12, highest displacements

were calculated for f = 0.20 Hz which is showed a shift towards progressive failure

zone.

In Figure 4.13 the displacement behaviour was heavily affected from relative den-

80

sity of soil. As the relative density of soil decreased, the bucket response shifted

towards progressive failure whereas dense soil showed a shakedown-like behaviour

under same cyclic load.

0 2 4 6 8 10 120

0.01

0.02

0.03

0.04

Number of Cycles, N

uz/u

z,ult

f=0.05 Hz

f=0.10 Hz

f=0.20 HzProgressive Failure

Attenuation

Fcyc

= 0.15Fult

Figure 4.12: Effect of frequency on plastic deformations

0 2 4 6 8 10 120

0.01

0.02

0.03

0.04

Number of Cycles, N

uz/u

z,u

lt

DR

=0.90

DR

=0.80

DR

=0.70

Progressive Failure

Attenuation

Figure 4.13: Effect of relative density on plastic deformations

4.2.2 Load Bearing Mechanism

The changes in proportions of the axial loads transferred by the bucket components

with increasing loading cycle number are dependent on the parameters of cyclic soil-

bucket-interaction problem which is discussed in this section.

The load carried by the components of the bucket shown in Figure 4.14 is determined

81

Fstat+ΔFcyc

FoutFin

Ftop

FinFout

uz

FtipFtip

Figure 4.14: Load distribution inside the bucket

by summation of the loads in global z direction at the corresponding nodes at the

surface. Each individual load is either plotted against load step (Fi - N) to interpret

the distribution quantitative or the ratio of the component load to total applied load

(100 x Fi/Fcyc - N) is plotted against number of load cycle to show the relative changes

in the distribution.

The effects of cyclic loading amplitude Fcyc, frequency f, bucket aspect ratio D/L,

coefficient of skin friction µ and soil initial relative density Dr on the cyclic suction

bucket behaviour are discussed as follows.

4.2.2.1 Effect of Cyclic Loading Amplitude, Fcyc

In the previous section, loading amplitudes that result in shakedown, attenuation and

progressive failure were described. In this part, the chances in the load distribu-

tion among the bucket components in the previously described cases are investigated

further. It was determined that shakedown behaviour can be observed for cyclic

loads up to a maximum amplitude of Fcyc < 0.05 Fult, progressive failure occurs for

Fcyc > 0.25 Fult and attenuation behaviour occur in between. The load carried by in-

dividual parts of the bucket is calculated for 0.05, 0.15 and 0.25 Fult which correspond

to previously classified characteristic bucket responses.

Figure 4.15 shows the load share - cycle relationship both in quantity (1st row) and

as percentage of total load (2nd row). The middle column is given for the reference

system with Fcyc = 0.15 Fult which shows an attenuation behaviour. The neighbouring

columns are calculated by keeping all the parameters except cyclic load amplitude

82

0 5 10

0

10

20

Lo

ad S

har

e (M

N)

0 5 10

Fcyc

= 0.15 Fult

(15.24 MN)

FTop Plate

FIn

FOut

FTip

0 5 10

0 5 10−50

0

50

100

150

Lo

ad S

har

e (%

)

0 5 10Number of Cycles, N

FTop Plate

FIn

FOut

FTip

0 5 10

(a) (c)(b)

(d) (f)(e)

Fcyc

= 0.25 Fult

(25.40 MN)Fcyc

= 0.05 Fult

(5.08 MN)

Figure 4.15: Effect of cyclic loading amplitude on the load share of bucket compo-

nents

Fmin

Fmax

0 2 4 6 N

Fmin

Fmax

0 1 N

Fmin

Fmax

0 2 4 6 8 10 12 N

Fcyc

= 0.05Fult

Fcyc

= 0.15Fult

Fcyc

= 0.25Fult

(a)

(d)

(g)

(b)

(e)

(h)

(c)

(f)

(j)

650 10 30 8550

Δp [kPa]

Figure 4.16: Effect of load level on accumulation of excess pore pressure (kPa) for

reference system

83

Fcyc. The Fcyc is 0.05 Fult on the left (shakedown case) and 0.25 Fult on the right

(progressive failure case).

Figure 4.16 shows the excess pore water pressure developed at the end of 1st, 6th and

12th cycle for the cases shakedown, attenuation and progressive failure, calculated for

reference system with model parameters in Table 4.2. The excess pore pressure is

calculated by subtracting the pore pressure at t=0 seconds from the time of interest.

In shakedown case, changes in load transfer were insignificant according to Figure

4.15 a and d. Only a slight transfer from the increase occurred from the top plate

to outer skin of bucket due to initial plastic settlement. According to Figure 4.16, no

significant excess pore pressure is developed either. It indicates that there was enough

time to dissipate for the excess pore pressure demand imposed by loading (under Fcyc

= 0.05 Fult) for the particular set of parameters of the reference system in Table 4.2.

In attenuation case, some excess pore pressure develop according to Figures 4.16 d to

f. The amount of pressure and the area of spreading increases. It is observed that the

excess pore pressure significantly dissipates under the bucket tip level until the end of

calculations and does not spread around the bucket.

Due to the decrease of effective stresses inside the bucket, as a function increase of

excess pore pressure in Figure 4.16 d to f, proportions of the axial loads transferred

by the top plate, outer surface and tip of skirt increased and inner surface of skirt

decreased with ascending load cycles as shown in Figure 4.15 b and e. However, the

transfer is mostly towards the top plate since the outer skin friction has a certain limit

and more importantly, the top plate share increases significantly due to total stress

since the water is entrapped beneath.

When the load shares looked closer for the case of attenuation in Figure 4.15 b and e

(Fcyc = 0.15 Fult), it can be seen that shares for inner skirt have negative values (after

3rd cycle) which did not change significantly at high number of cycles (N = 7 to 12).

This negative friction force indicated existence of a downward force. This can be re-

lated reduction in soil effective stresses as well as loosening of soil regarding the pore

pressure development. During unloading, the loads transferred via top plate to soil

inside the bucket decreases, thus a greater upward movement demand occurred in soil

84

relative to bucket due to the existing excess pore pressure. In Figure 4.17 a, the rela-

tive displacements in soil at the end of 12th cycle are plotted with respect to initiation

of cyclic loading and the displacement of the bucket was pointed also. The darkest

contour represents the larger upward movement demand which additionally acts to

the bucket and increases the sharing ratio for top plate and tip. This situation gets

even more evident in the case of progressive failure (Fcyc = 0.25 Fult). During unload-

ing, a greater upward soil movement relative to the bucket was calculated also in the

soil outside of bucket which can be traced back to excess pore pressure accumulation

as a result of high cyclic loading amplitude. In Figure 4.17 b, it was shown that the

upward movement demand has influenced a wider and deeper area and also developed

at the outside of bucket, as a result, upward movement was greater in magnitude.

In the case of progressive failure, in addition to inside, outside friction forces were

also substantially reduced in Figure 4.15 c and f. This was related to the flow of water

from interior to outside of bucket which caused an accumulation of pore pressure in

Figure 4.16 h and j thus reduced the effective stresses in soil.

0 5 15 25 96 125(mm)

0 2.5 5 7.5 21 35(mm)

Bucket Bucket

Fcyc

= 0.15 Fult

Fcyc

= 0.25 Fult

(a) (b)

.

Figure 4.17: Soil displacements inside and around the bucket at the end of 12th cycle

relative to 1st cycle under (a) Fcyc = 0.15 Fult and (b) Fcyc = 0.25 Fult

4.2.2.2 Effect of Cyclic Loading Frequency, f

Common frequency range of wave loads were considered to investigate the effect of

the cyclic loading frequency. Calculations performed for f = 0.05, 0.10 and 0.20 Hz.

The rest of the loading, soil and bucket parameters were kept same according to Table

4.2. Within the scope of the studied loading frequencies, it was found that the avail-

85

f = 0.10 Hz f = 0.20 Hzf = 0.05 Hz

0 2.5 5 10 17.5 30

(a) (c)(b)

Δp [kPa]

0 5 10−40

−20

0

20

40

60

80

100

Load Share (%

)


FTop Plate

FIn

FOut

FTip

0 5 10

(d) (e) (f)

Figure 4.18: (a) to (c) Effect of cyclic loading frequency on the pore pressure devel-

opment at the end of 12th cycle relative to 1st cycle, (d) to (f) Load share of bucket

components

able time between two successive cyclic loads had an influence on the load share of

bucket components in the calculated duration (12 cycles).

It was concluded from the excess pore pressure diagrams at the end of 12th cycle given

in Figure 4.18 a to c that high cyclic load frequency results in higher pore pressure

development due to smaller time interval for dissipation. It can be interpreted in

the load share variation given in Figure 4.18 d to f that lower friction forces were

calculated as frequency of loading gets higher and share of top plate and skirt tip

were increased. In addition, the accumulation of excess pore pressure at the outside

of bucket and reduction of outer skin friction initiated in earlier cycles for loading

with higher frequencies.

On the other hand, the displacement behaviour was not affected from loading fre-

quency of the studied range. All three cases showed attenuation behaviour as in the

reference system according to Figure 4.12. However, highest displacements were

calculated for f = 0.20 Hz which is a shift towards progressive failure.

86

4.2.2.3 Effect of Aspect Ratio, L/D

0 5 10

0

4

8

12

16

Load

Sh

are

(MN

)L/D=1.30

0 5 10

L/D=1.0

0 5 10

L/D=0.80

0 5 10

0

50

100

Lo

ad S

har

e (%

)


FTop Plate

FIn

FOut

FTip

0 5 10

(a)

(e) (f)(d)

(c)(b)

FTop Plate

FIn

FOut

FTip

Figure 4.19: (a) to (c) Effect of aspect ratio on the load share of bucket components

in quantity, (d) to (f) Effect of aspect ratio on the load share of bucket components as

relative percentage

In this part of study, the bucket diameter kept constant (D = 10 m) and the skirt

length L was varied as 8 m, 10 m and 13 m. Although the ultimate load capacity

was affected by skirt length, the cyclic loading amplitude was adopted as 15.24 MN

to be comparable with the reference system. Further parameters were not changed

according to Table 4.2.

It was found that total load share of skin friction (Fin + Fout) was increased and shares

of the top plate and skirt tip were decreased as skirt was elongated according to Figure

4.19 a to c. In addition, a greater load transfer was observed in quantity from friction

to bearing resistance with increasing aspect ratio (from right to left). This can be

related to increasing friction capacity due to skirt length.

As in the earlier discussions, friction forces developed inside the bucket tends to

transfer to other components due to excess pore pressure development. This load

was dominantly shared by top plate and tip for short skirted buckets (Figure 4.19 f)

and by outer skin for long skirted buckets (Figure 4.19 a).

87

0 5 10

0

4

8

12

16

Lo

ad S

har

e (M

N)

μ= 0.40

0 5 10

μ= 0.30

0 5 10

μ= 0.20

0 5 10

0

50

100

Lo

ad S

har

e (%

)


FTop Plate

FIn

FOut

FTip

0 5 10

(a) (c)(b)

(d) (f)(e)

FTop Plate

FIn

FOut

FTip

Figure 4.20: Effect of skin friction coefficient on the load share of bucket components

In addition, the displacement behaviour was heavily affected by the aspect ratio of

studied range. As the length of skirt decreased, the bucket response shifted towards

progressive failure, whereas long skirted bucket showed a shakedown-like behaviour

under same cyclic load.

4.2.2.4 Effect of Coefficient of Skin Friction, µ

Coefficient of friction between sand and steel depend on the relative size, shape and

surface roughness of the sand grains as well as steel surface properties. In this section,

affect of the coefficient of contact friction was studied by using µ=0.20, 0.30 and 0.40.

All other parameters given for reference system in Table 4.2 were kept same.

Similar to previous discussions of skirt length, total share of skin friction (Fin + Fout)

decreased as skin friction coefficient decreases as shown in Figure 4.20 a to c. Dur-

ing cyclic loading, the friction forces started to decrease due to excess pore pressure

determined in Figure 4.16 d to f and this load was dominantly shared by top plate and

tip for low friction surfaces (Figure 4.20 c and f) but by outer skin for high friction

surfaces (Figure 4.20 a and d).

88

On the other hand, the displacement behaviour was not affected from contact friction

coefficient within the studied range. All three cases showed attenuation behaviour

as in the reference system. However, highest displacements were calculated for µ =

0.20.

4.2.2.5 Effect of Initial Relative Density, Dr of Soil

In this section, by keeping the Kozeny-Carman coefficient, C constant, relative den-

sity, Dr was varied by changing the initial void ratio, ei. Further parameters accord-

ing to Table 4.2 were not changed. Since two-phase model considers the porosity-

permeability dependency, initial permeability of soil was also varied depending on

the relative density.

To be comparable with the reference system, results under the same cyclic load am-

plitude, Fcyc = 15.24 MN is given in Figure 4.21. With increasing relative density,

less friction reduction occurred at the interior of bucket which can be attributed to

the reduced pore pressure development according to Figure 4.21 a and d. In addition,

outer skin friction increased up to a number of cycles before excess pore pressure

develops at the outside of bucket than start to decrease. This case observed in earlier

cycles for the loose soil in Figure 4.21 c and f and the loose soil showed a behaviour

similar progressive failure case where top plate dominantly shared the loads.

4.2.3 Effect of the Constitutive Model Improvements on Behaviour

The effect of porosity permeability change is relatively less when this range of high

relative density. However, effect is visible around 70% relative density with loading

amplitude Fcyc > 0.15Fult. Figure 4.22 shows that different behaviour observed for

D = L = 10 m, k = 10-3 m/s, Fcyc = 0.15 Fult with f = 0.10 Hz. Old model did not

allowed increase of permeability w.r.t increasing void ratio and earlier progress of

deformations are observed. But remember that the damping and compressibility are

other two differences between two models.

In addition, with less axial load and more number of cycles, the effect would be more

89

10 20 30 4050

Δp [kPa]

(a) (c)(b)

DR = 0.90 D

R = 0.80 D

R = 0.70

.

0 5 10−40

−20

0

20

40

60

80

100

Load Share (%

)


FTop Plate

FIn

FOut

FTip

0 5 10

(d) (f)(e)

Figure 4.21: (a) to (c) Effects of initial relative density of soil on the pore pressure

development at the end of 12th cycle relative to 1st cycle, (d) to (e) Effects of initial

relative density of soil on the load share of bucket components from Dr= 90% to 70%

visible where with KC model, the settlement of soil in a cycle causes a reduction in

its permeability whereby the drainage affected adversely. It is expected to observe

less settlement due to increasing pore stress that will resist. However, in this study,

large cyclic amplitudes are studied for extreme events and model is not capable to

accurately estimate tens or hundreds of cycles.

4.2.4 Sensitivity of Results to the Constitutive Model Parameters

IGS parameters are varied to study the sensitivity of the results. The IGS parameters

have important effect especially βr and ψ which controls the strain evolution rate and

the stiffness degradation. But these are material dependent and they are changed here

without a physical correspondence. Since the cyclic response is mainly related to the

applied stress level and the pore water dissipation rate, the material parameter is not

related to deformation behaviour itself. But it can be claimed that with lower ψ and

higher βr lead to development of high deformations.

Figure 4.23 show the effect of the IGS parameters on the deformation response of the

90

0 2 4 6 8 10 120

0.01

0.02

0.03

0.04

Number of Cycles, N

uz/u

z,u

lt

Tasan(2011)

This Study

Progressive Failure

Attenuation

Fcyc

= 0.15Fult

Figure 4.22: Effect of the constitutive model improvements on behaviour

reference model given in the thesis.

In conclusion, these material dependent information was not considered to link to

the deformation behaviour. This information most probably won’t be available for a

designer at a preliminary design stage that this thesis aims to give information for.

0 2 4 6 8 10 120

0.01

0.02

0.03

0.04

Number of Cycles, N

uz/u

z,ult

0.05

0.06mT=2.2, mR=4.4, Rmax=0.001, βR=0.2, χ=6.0

mT=2.2, mR=4.4, Rmax=0.001, βR=0.5, χ=3.0

mT=2.2, mR=4.4, Rmax=0.001, βR=0.5, χ=6.0

mT=4.0, mR=4.4, Rmax=0.001, βR=0.2, χ=6.0

mT=4.0, mR=4.0, Rmax=0.001, βR=0.2, χ=6.0

Figure 4.23: Effect of the constitutive model parameters on behaviour

91

4.3 Studies on Bucket Behaviour under Cyclic Lateral Load

The bucket response in saturated sandy soil was studied under cyclic lateral load-

ing with FE simulations described earlier. The related changes in load transfer via

components of bucket were focused. A poorly graded, medium to coarse sand with

a characteristic grain size d50 = 0.55 mm and a coefficient of uniformity Cu = 3.30

was considered. The hypoplastic material parameters of the sand used is given in

Table 4.1. A Kozeny-Carman coefficient CK-C = 0.00159 (i.e. initial permeability,

kinit=10-4m/s) was calculated according to Carrier (2003).

The steel bucket was modelled as a linear elastic material with Young’s modulus E =

200 GPa and Poisson’s ratio v = 0.20. The reference bucket has a diameter D = 10 m,

skirt length L = 10 m and wall thickness t = 0.05 m. The stiffeners on top plate were

considered by modelling a numerically rigid top plate.

Considering the nacelle, hub, blades and tower of an 8 MW OWT, a static dead load

Vstat = 10 MN was applied before cyclic loading. This was followed by a sinusoidal

lateral load which idealizes the wind, wave and current load that act on the bucket.

Loading scheme is given in Figure 4.5. The minimum value of cyclic loading Hmin =

0 and the loading frequency f = 0.10 Hz. The number of loading cycle was limited

with 12. Before the cyclic tests, the ultimate lateral load capacity was determined

from load-rotation curve as Mult = 338.90 MNm for the reference soil-bucket-system

with a monotonic loading test where a lateral force Hult = 11.30 MN was applied with

eccentricity ecc = 30 m from the top plate.

General System Response

Under cyclic loading, a structure can exhibit one of the following behaviours given

in Figure 4.8 according to Goldscheider and Gudehus (1976). Elastic response where

the cyclic load amplitude is low that no plastic deformation occurs, shakedown re-

sponse where a plastic deformation occurs in initial stages but as the number of cycles

increase accumulation of plastic deformation stops and response becomes elastic. In

other words, the system stabilizes. For higher load levels, accumulation may not be

necessarily stop but it is possible that rate of increase slows which is called as attenu-

ation response. Lastly, for very high cyclic load levels, system progressively tends to

92

collapse. That behaviour is called progressive failure.

0 2 4 6 8 10 120

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Bu

cket

Ro

tati

on

(R

adia

ns)

Hcyc

=%05Hult

,Vstat

=10MN

Hcyc

=%15Hult

,Vstat

=10MN

Hcyc

=%25Hult

,Vstat

=10MN

Figure 4.24: Effect of cyclic lateral loading amplitude on the angular rotation of

bucket

Principal behaviours can be identified from the angular rotation-cyclic loading num-

ber graphs shown in Figure 4.24 to 4.27. According to Figure 4.24 which is calculated

for a bucket with aspect ratio D/L = 1.0 (with D = L = 10m) and a sand with initial

relative density DR = 80% under 10 MN of static vertical load. It was observed that

the response is highly dependent on cyclic loading amplitude. The highest increase

of plastic deformations was calculated at the beginning of the cyclic loading for low

amplitude loading. For cyclic loads up to a maximum amplitude of Mcyc = 0.05Mult,

the deformations remained nearly unchanged during the rest of loading cycles and

the case of shakedown was calculated. For 0.25Mult > Mcyc > 0.05Mult, the increase

of deformations decreased with loading cycles but it never reached zero. This case is

called as attenuation. For Mcyc > 0.25Mult, the deformations were increased progres-

sively and the system failed to stabilize, which is called as progressive failure.

93

0 2 4 6 8 10 120

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Number of Cycles, N

Bu

cket

Ro

tati

on

(R

adia

ns)

H

cyc=%15H

ult,V

stat=2MN

Hcyc

=%15Hult

,Vstat

=10MN

Hcyc

=%15Hult

,Vstat

=20MN

Hcyc

=%25Hult

,Vstat

=2MN

Hcyc

=%25Hult

,Vstat

=10MN

Hcyc

=%25Hult

,Vstat

=20MN

Figure 4.25: Effect of vertical static load on the angular rotation of the bucket under

cyclic lateral Loading

It can be expected that static vertical load can affect this behaviour. In Figure 4.25,

0.15Mult and 0.25Mult loadings are re-calculated under a very low (Vstat=2 MN) and

very high (Vult=20 MN) static vertical loads. It was observed that the effect is low

when compared to the amount of cyclic loading amplitude.

In addition, effect of permeability is calculated by increasing the coefficient CK-C

to 0.00159 from 0.0159 (i.e. kinit=10-4 to 10-3m/s) as explained in Section 4.1.1.1.

It was observed in Figure 4.26 that under faster drainage conditions, the amount of

cyclic load amplitude to result in progressive failure increases significantly. The sys-

tem showed attenuation behaviour even under 0.25 of Mult.

Lastly, initial relative density has an important effect on the bucket behaviour accord-

ing to Figure 4.27. Under same conditions except initial relative density, two different

behaviours distinguished under 0.15Mult. For looser soils, a faster accumulation of ex-

cess pore pressure is determined during load cycles which shifts the system behaviour

to progressive failure under lower cyclic loading amplitudes.

94

0 2 4 6 8 10 120

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Number of Cycles, N

Buck

et R

ota

tion (

Rad

ians)

H

cyc=%15H

ult, C

K−C = 0.00159

Hcyc

=%15Hult

, CK−C

= 0.0159

Hcyc

=%25Hult

, CK−C

= 0.00159

Hcyc

=%25Hult

, CK−C

= 0.0159

Figure 4.26: Effect of initial permeability on the angular rotation of the bucket under

cyclic lateral Loading

0 2 4 6 8 10 120

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Number of Cycles, N

Buck

et R

ota

tion (

Rad

ians)

H

cyc=%15H

ult, D

r=0.80

Hcyc

=%15Hult

, Dr=0.70

Figure 4.27: Effect of initial relative density on the angular rotation of the bucket

under cyclic lateral Loading

95

The load transfer was affected by changes in the effective stresses at soil-bucket-

interfaces which were highly dependent on drainage conditions, in other words, ex-

cess pore pressure accumulation as well as the rotation of bucket which changes the

normal forces on these interfaces.

Δp [kPa]

650 10 30 8550

0 2 4 6 N

0

Hmax

0 1 N 0 2 4 6 8 10 12 N

0

Hmax

0

Hmax

(a)

(d)

(b)

(e)

(c)

(f)

Mcyc

= 0.15Mult

Mcyc

= 0.25Mult

Figure 4.28: Excess pore pressure development in soil after loading cycle of number

N = 1, 6 and 12 for different cyclic loading levels

The excess pore pressure developed with respect to the initial pore pressure state,

calculated after applying static dead load was illustrated for an attenuation case (Mcyc

= 0.15Mult) in Figure 4.28(a), (b) and (c) and for an progressive failure case (Mcyc

= 0.25Mult) in Figure 4.28(d), (e) and (f) after the end of cycles N=1,6,12. It is

observed that the excess pore pressure initiates around the inner skirt near the tip

and at the right side towards the lateral load direction (loads applied right to left

in this case). In attenuation case, larger excess pore pressure developed on tension

side (right side in terms of loading) according to Figure 4.28(b), due to translation

of bucket through applied lateral load. After a certain number of cycles, the excess

pore pressure spread more evenly according to Figure 4.28(c). During loading phase

of cycles of progressive failure case, due to amount of rotation and translation of the

96

bucket (see Figure 4.29 for deformed shape), some portion of the structure weight acts

as normal compression to outer skin of skirt on compression side and inner skin of

skirt on tension side which cause a larger excess pore pressure around these surfaces

according to Figure 4.28(e) and (f).

In overall, as the loading amplitude increases, the bucket tends to translate and rotate

in the direction of applied force and settle down due to decreasing effective stresses

(Figure 4.29). This movement result in lower and more eccentric rotation centre as

the load amplitude increases. Eventually, overturning of bucket occurs if eccentricity

is greater than the bucket radius.

-0.20 -0.12 -0.04 0.04 0.200.12 0.28 0.36 0.520.44

Displacement Vector Sum [m]

Undeformed Shape

∆θ

∆x∆z

Hcyc

Figure 4.29: Deformation of Bucket at the End of 12 Cycle Loading under Hcyc =

0.15Hult

4.4 Conclusions

4.4.1 Cyclic Axial Compression

The behaviour of a bucket in saturated sandy soil was investigated with focusing on

the load transfer between top plate, skirt and tip due to the cyclic axial compressive

97

loading.

Numerical studies led to the following results for general response of buckets under

cyclic axial compressive loads:

• The bucket response can be classified in shakedown and attenuation as well as

progressive failure.

• The cyclic loads are predominantly transferred into the soil via top plate and

the outer skirt for the case of shakedown.

• In the case of attenuation and progressive failure, a greater soil movement rela-

tive to bucket is determined due to the pore pressure accumulation in soil which

causes additional loads on bucket skirt.

It was concluded from the parametric analyses on the effect of KC coefficient, load

frequency, aspect ratio of bucket, skin friction coefficient and initial relative density

of soil that:

• Cyclic loading amplitude is the most major parameter along the investigated

cases which govern the total stresses as well as pore pressure development.

• Cyclic loading frequency determines the time allowed for dissipation of the

excess pore pressure developed at a cycle before next cycle occurs. It was

observed that lower pore pressure developed as frequency of loading decreases

but the identified displacement response (i.e. attenuation) was not changed

within the investigated number of cyclic loading.

• Aspect ratio and coefficient of friction at contact surfaces have significant affect

on initial load shares on which the amount of load transfer is highly dependent.

Long skirted or high friction surfaces have greater friction developed at the

initial stage and during cyclic loading.

• As aspect ratio decreased, the bucket response shifted towards progressive fail-

ure whereas long skirted bucket showed a shakedown-like behaviour under

same cyclic load.

98

• Relative density was also a major parameter. As the relative density decreased,

higher excess pore pressure developed and soil tend to liquefy which result in a

response similar to progressive failure. Dense sand tends to a shakedown-like

behaviour.

4.4.2 Cyclic Lateral Loading

The behaviour of a bucket in saturated sandy soil was investigated and the numerical

studies led to the following results:

• The bucket response can be classified depending on the cyclic loading level as;

shakedown, attenuation and progressive failure.

• Cyclic loading amplitude and initial relative density of the soil are two major

factors that determine the behaviour.

• The behaviour is very sensitive to excess pore pressure development, i.e., the

drainage. When the excess pore pressure cannot drain fast, the progressive

displacements take place in early cycles.

• The cyclic range of the study is limited to 12 cycles, however, large portion of

the total deformations can be captured in this range under extreme loads.

99

CHAPTER 5

DESIGN OF BUCKETS FOR CYCLIC LOADING

Suction buckets are used to be employed as anchor systems or tension legs where

pull-out capacity, pull-out rate dependency and reverse end bearing mechanisms were

widely studied. However, in this research, suction buckets employed as OWT foun-

dations are focused. Even more specially, suction buckets of multi-leg support struc-

tures are focused where the lateral loads acting on the OWTs are distributed as axial

loads on the legs as compression and tension. OWTs are very sensitive to excessive

rotations thus mainly designed to be under compression. According to Senders and

Randolph (2009) average loading of the suction buckets is compressive loading and

that tensile loading is unlikely to occur under operational conditions.

As discussed in Chapter 2, cyclic loading may cause change of foundation stiffness,

generation of excess pore pressure, accumulation of displacements. In consequence,

a bucket may fail at a load that is lower than the expected capacity or lose the func-

tionality by large displacements under cyclic loading. That means the accumulated

rotation can surpass the acceptable limits so that it can govern the design or the nat-

ural frequency can slide towards any of the excitation frequencies due to change of

stiffness during cyclic loading.

An offshore wind turbine design includes many parties as meteorologist, physical

oceanographer, structural, mechanical, aerodynamic, hydrodynamic and geotechnical

engineer. Here, it is aimed to inform the designers about the expected deformation

behaviour of foundation under cyclic axial compressive loading, due to soil, loading

and geometrical conditions. For this purpose a group of design charts are developed

as the result of this research.

101

Deformation response of the buckets under cyclic axial compressive loading are dis-

cussed in Chapter 4 in detail. Three major behaviours are identified according to

Goldscheider and Gudehus (1976) as shakedown, attenuation and progressive failure.

Here, these principal behaviours are described according to Aboustait (1994) as fol-

lows;

• the behaviour is safe (or shakedown) if plastic strain rate is zero after the bucket

attains the cyclic state

σ (x,T) = σ(x,t+T) and εP(x,T)=0

• the behaviour is progressing failure if plastic strain rate greater than zero after

the bucket attains the cyclic state

σ (x,T) = σ(x,t+T) and ε P(x,T)>0

• the behaviour is attenuation if plastic strain increment is less or equal to zero

after the bucket attains the cyclic state

δεP(x,T)≤0

The major factors that affect the behaviour dominantly are the cyclic loading ampli-

tude and initial relative density. For that reason, a contour plot is prepared where the

x axis is the initial relative density and the y axis is the cyclic loading amplitude.

To use benefit of the proposed charts, following information shall be gathered, calcu-

lated or estimated first;

• Amplitude of cyclic axial compression, Fcyc

• Static ultimate load bearing capacity, Fult

• Relative density of in-situ soil, DR

• Permeability coefficient, k

The cyclic loading amplitude is the leading parameter of the design since it determine

the capacity demand. Thus, according to the proposed capacity of the turbine, height

102

of the nacelle, depth of the water and specific conditions of the environment, a lat-

eral load should be determined and distributed over the legs according to preliminary

assumption span between buckets.

It is found that initial relative density of the soil had significant effect on the behaviour

of foundation. It is determined in Chapter 4 that if the soil is dense, less compaction

occurs under compressive loading and so the void ratio changes less. Eventually, the

permeability of the soil does not differ significantly that allow excess pore pressure to

dissipate relatively faster. Due to less disturbance of the effective stresses at the foun-

dation, the load distribution among the component of the bucket as well as the overall

deformation behaviour is less effected. As the relative density of soil decreased, the

bucket response shifts towards progressive failure side whereas in case of denser soils

response shifts towards shakedown side if all other parameters are same.

Here, a design chart is presented for a L/D = 1.0 bucket in a sandy soil with perme-

ability coefficient of kinitial = 1.0x10-4 m/s under a cyclic loading frequency f =0.10 Hz

in Figure 5.1.

L/D = 1.0, kinitial

= 10−4

m/s, f = 0.10 Hz

Initial Relative Density, Dr

Cycl

ic A

xia

l C

om

pre

ssio

n A

mp

litu

de

F

cyc /

Fult

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25

Figure 5.1: Expected cyclic response for L/D = 1.0 bucket in a sandy soil with kinitial

= 1.0x10-4 m/s under a cyclic axial compressive loading frequency f =0.10 Hz.

103

A single chart is not satisfactory to cover enough scenarios. Thus, affects of other

parameters are necessary such as frequency of loading, f. In this research, common

frequency range of wind and wave loads are covered with f = 0.05 to 0.20 Hz. It is

found that the available time between two successive cyclic loads had an influence on

the load share of bucket components in the calculated duration (12 cycles). Relatively

higher displacements are calculated for high frequency loading which also shows a

shift towards progressive failure. The same chart in the previous reference case is

developed for different frequencies as shown in Figure 5.2.

L/D = 1.0, kinitial

= 10−4

m/s, f = 0.05 Hz


Cy

clic

Axia

l C

om

pre

ssio

n A

mp

litu

de

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25

L/D = 1.0, kinitial

= 10−4

m/s, f = 0.20 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mp

litu

de

F

cyc /

Fult

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25

Figure 5.2: Expected cyclic response for L/D = 1.0 bucket in a sandy soil with kinitial

= 1.0x10-4 m/s under a cyclic axial compressive loading frequency f =0.05 and 0.20

Hz.

104

In addition to initial relative density, initial void ratio or initial permeability of the

soil has affect on the behaviour to determine the amount of the stress to dissipate by

the flow in the pores. The same chart in the previous reference case is developed for

different initial permeability coefficients as shown in Figure 5.3.

L/D = 1.0, kinitial

= 10−3

m/s, f = 0.10 Hz


Cy

clic

Axia

l C

om

pre

ssio

n A

mp

litu

de

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25

L/D = 1.0, kinitial

= 10−5

m/s, f = 0.10 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mp

litu

de

F

cyc /

Fult

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25

Figure 5.3: Expected cyclic response for L/D = 1.0 bucket in a sandy soil under a

cyclic axial compressive loading frequency f =0.10 with kinitial = 1.0x10-3 to 1.0x10-5

m/s

105

All these charts only represent an aspect ratio L/D=1.0. The same effort can be ap-

plied to a shallow wide formation L/D = 0.80 and a narrow deep formation L/D =

1.30.

Initial relative density and the cyclic axial compression amplitude are main parame-

ters that compose the axes of the charts. Aspect ratio, coefficient of initial permeabil-

ity and cyclic loading frequency are the side parameters that fill the charts.

For each side parameters, three charts are developed. First is the reference parameter,

second and third are the boundaries of the studied range. In total, 33 = 27 design

charts are available and presented in Appendix A as follows;

• L/D= 1.0, f =0.05, 0.10, 0.20 Hz, k=0.001, 0.0001, 0.00001 m/s (9 charts)

• L/D= 0.8, f =0.05, 0.10, 0.20 Hz, k=0.001, 0.0001, 0.00001 m/s (9 charts)

• L/D= 1.3, f =0.05, 0.10, 0.20 Hz, k=0.001, 0.0001, 0.00001 m/s (9 charts)

The following figure presents an envelope for all the generated charts for simplicity.

0

0.05

0.10

0.15

0.20

0.25

Shakedown Zone

Progressive Failure Zone


Cyc

lic

Axi

al

Com

pre

ssio

n A

mpli

tude,

Fcy

c/F

ult

0.70 0.850.800.75 0.90

Figure 5.4: Expected cyclic response envelope for L/D = 0.80 to 1.30 buckets in a

sandy soil under a cyclic axial compressive loading frequency f =0.05 to 0.10 Hz with

kinitial = 1.0x10-3 to 1.0x10-5

106

When these set of informations are collected, a designer can use the design charts that

are produced with the parametric analyses in this study as follows;

For example, in case of a set of parameters that fit in Figure 5.1, if the relative density

of soil is determined as 85% for a very stiff soil but a cyclic load amplitude that is

equal to 15% of static ultimate load capacity is calculated, a designer shall expect high

plastic deformations and these deformations may be progressive. Further detailed

analyses are required or the buckets and the support structure shall be re-dimensioned

such that a lower Fcyc/Fult occurs. If a lower load amplitude is estimated lets say as

9% of static ultimate load capacity then the designer should not expect high plastic

deformations. Deformations will probably attenuate. In this case no detailed analyses

will be required provided that it is in allowable limits.

The behaviour of a bucket in saturated sandy soil under cyclic axial compression

is investigated focusing on the deformation response. This study might be a useful

light for a designer with all the preliminary informations on geometry, soil and load

environment in consideration of cyclic failure risks.

107

CHAPTER 6

CONCLUSIONS

Suction bucket foundations which simply consist of a cylinder skirt and a top plate,

usually made of steel and installed by the assist of suction are a relatively new and

economically favourable solution for OWTs which are exposed to high lateral loads

from winds and waves. Understanding the behaviour under the effect of complex

cyclic load environment is essential to assess the design requirements of bucket foun-

dations. Deformations and pore pressures may accumulate up to irrecoverable range

under cyclic loadings.

In this study, a 3D finite element model is developed with ANSYS v.18 software

to study the behaviour of bucket foundations in sandy soils under cyclic axial com-

pressive loads and cyclic lateral loads. Hypo plastic constitutive material model with

intergranular strain which is appropriate to use with non-cohesive soils is adopted to

simulate the material behaviour in cyclic load environment. A fully coupled two-

phase finite element model is used in which soil consists of a solid phase, the skele-

ton, and a fluid phase that fully saturates the skeleton. Coupled pore fluid-structure

interaction is solved by the fluid flow by Kozeny-Carman poro-permeability relations

and equilibrium conditions. The frictional behaviour at the soil-structure interface is

modelled by contact elements. Verification of the numerical model is also discussed.

Parametric numerical analysis are performed under cyclic loading. The response of

suction buckets subjected to cyclic axial loads and cyclic lateral loads in saturated

sandy soils is studied. Main focus is given to the displacement behaviour for tested

scenarios and load distribution among the components of bucket during cyclic loading

are discussed.

109

Under cyclic axial loading, the bucket response is determined for each test scenario as

shakedown, attenuation and progressive failure. It was observed that the cyclic loads

are predominantly transferred into the soil via top plate and the outer skirt for the case

of shakedown. However, in the case of attenuation and progressive failure, a greater

soil movement relative to bucket is determined due to the pore pressure accumulation

in soil which causes additional loads on bucket skirt (see Figure 4.17).

The effect of the problem parameters such as KC coefficient, load frequency, aspect

ratio of bucket, skin friction coefficient and initial relative density of soil are also

studied. Cyclic loading amplitude is one the most important parameter along the in-

vestigated cases which govern the total stresses as well as pore pressure development.

Relative density is also a major parameter. As the relative density decreased, higher

excess pore pressure developed and soil tend to liquefy which result in a response sim-

ilar to progressive failure. Dense sand tends to a shakedown-like behaviour. Other pa-

rameters are found to have a secondary effect. For example cyclic loading frequency

determines the time allowed for dissipation of the excess pore pressure developed at

a cycle before next cycle occurs and it is observed that lower pore pressure developed

as frequency of loading decreases but displacement response was not changed within

the investigated number of cyclic loading. Aspect ratio and coefficient of friction at

contact surfaces have significant affect on initial load shares on which the amount of

load transfer is highly dependent. Long skirted or high friction surfaces have greater

friction developed at the initial stage and during cyclic loading. As aspect ratio de-

creased, the bucket response shifted towards progressive failure whereas long skirted

bucket showed a shakedown-like behaviour under same cyclic load.

Although the main focus is dedicated to cyclic axial compression, the behaviour of a

bucket in saturated sandy soil under cyclic lateral loading is also studied and similar to

axial loading case, principal deformation responses are identified according to cyclic

loading amplitude. In this case, the major parameters are the cyclic loading amplitude

and initial relative density of the soil. The behaviour is found to be very sensitive to

excess pore pressure development, i.e., permeability. When the excess pore pressure

cannot drain fast, the progressive displacements take place in early cycles.

After collecting the results of parametric analyses, an estimation on the response of a

110

bucket under extreme cyclic loading is evaluated for all test scenarios and presented

as a chart. By these charts given in Chapter 5 and Appendix A, a designer would

be able to decide if detailed analyses for cyclic axial compressive loading is required

in other words any progressive deformations expected with only preliminary design

information available.

The improvements implemented to the u-p element was effective on the results with

comparably low relative density cases. In addition, with less axial load and more

number of cycles, the effect would be more visible where with KC model, the set-

tlement of soil in a cycle causes a reduction in its permeability whereby the drainage

affected adversely. However, in this study, large cyclic amplitudes are studied for

extreme events and model is not capable to accurately estimate tens or hundreds of

cycles.

111

BIBLIOGRAPHY

Aboustait, B. (1994). Incremental collapse of subgrades.

Achmus, M., Akdag, C. T., and Thieken, K. (2013). Load-bearing behavior of suction

bucket foundations in sand. Applied Ocean Research, 43:157–165.

Achmus, M., Terceros, M., and Thieken, K. (2016). Evaluation of p-y approaches

for large diameter monopiles in soft clay. Proceedings of the International

Offshore and Polar Engineering Conference, 2016-January:805–816.

Achmus, M. and Thieken, K. (2014). Numerical simulation of the tensile resistance

of suction buckets in sand. Journal of Ocean and Wind Energy, 1(4):231–239.

Alluqmani, A. E., Naqash, M. T., and Harireche, O. (2019). A standard formulation

for the installation of suction caissons in sand. Journal of Ocean Engineering

and Science, 4(4):395–405.

Andersen, K. H., Jostad, H. P., and Dyvik, R. (2008). Penetration Resistance of Off-

shore Skirted Foundations and Anchors in Dense Sand. Journal of Geotechni-

cal and Geoenvironmental Engineering, 134(1):106–116.

Andersen, K. H. and Lauritzsen, R. (1988). Bearing capacity for foundations with

cyclic loads. Publikasjon - Norges Geotekniske Institutt, 114(175):540–555.

Andresen, L., Jostad, H. P., Andersen, K. H., and Skau, K. (2008). Finite element

analyses in offshore foundation design. 12th International Conference on Com-

puter Methods and Advances in Geomechanics 2008, 5:3247–3262.

ANSYS (2018). Theory Reference for the Mechanical APDL and Mechanical Appli-

cations. ANSYS.

API (2014). API_2A-WSD_Recommended Practice for Planning, Designing and

Constructing Fixed Offshore Platforms, volume 22. American Petroleum In-

stitute, Washington DC.

Aubram, D., Rackwitz, F., and Savidis, S. A. (2015). Holistic Simulation of Geotech-

nical Installation Processes, volume 77.

Bauer, E. (1996). Calibration of a comprehensive hypoplastic model for granular

materials. Soils and Foundations, 36(1):13–26.

113

Bauer, E. and Wu, W. (1993). A hypoplastic model for granular soils under cyclic

loading, in modern approaches to plasticity, ed. d.kolymbas. pages 247–258.

Bayat, M., Andersen, L. V., and Ibsen, L. B. (2016). P-Y-Y’ Curves for Dynamic

Analysis of Offshore Wind Turbine Monopile Foundations. Soil Dynamics and

Earthquake Engineering, 90:38–51.

Bienen, B., Klinkvort, R. T., O’Loughlin, C. D., Zhu, F., and Byrne, B. W. (2018a).

Suction caissons in dense sand, part I: Installation, limiting capacity and

drainage. Geotechnique, 68(11):937–952.

Bienen, B., Klinkvort, R. T., O’Loughlin, C. D., Zhu, F., and Byrne, B. W. (2018b).

Suction caissons in dense sand, part II: Vertical cyclic loading into tension.

Geotechnique, 68(11):953–967.

Biot, M. A. (1941). General theory of three-dimensional consolidation. Journal of

Applied Physics, 12(2):155–164.

Biot, M. A. (1955). Theory of elasticity and consolidation for a porous anisotropic

solid. Journal of Applied Physics, 26(2):182–185.

Biot, M. A. (1962). Mechanics of deformation and acoustic propagation in porous

media. Journal of Applied Physics, 33:1482–1498.

Bo, L. and Nordahl, B. (2016). Testing of Axially Loaded Bucket Foundation with

Applied Overburden Pressure. Technical report, Aalborg University, Aalborg

SV.

Booker, J. (1974). The consolidation of a finite layer subject to surface loading.

International Journal of Solids and Structures, 10(9):1053 – 1065.

BP (2020). Statistical Review of World Energy, 2020 | 69th Edition. Bp, 69:66.

Bye, A., Erbrich, C., Rognlien, B., and Tjelta, T. I. (1995). Geotechnical design of

bucket foundations. Proceedings of the Annual Offshore Technology Confer-

ence, 1995-May:869–883.

Byrne, B. W. and Houlsby, G. T. (2004). Experimental Investigations of the Response

of Suction Caissons to Transient Combined Loading. Journal of Geotechnical

and Geoenvironmental Engineering, 130(3):240–253.

Carman, P. (1956). Flow of Gases Through Porous Media. Academic Press, New

York.

Carrier, W. D. (2003). Goodbye, hazen; hello, kozeny-carman. Journal of geotechni-

cal and Geoenviromental Engineering.

114

Cerfontaine, B., Collin, F., and Charlier, R. (2016). Numerical modelling of transient

cyclic vertical loading of suction caissons in sand. Geotechnique, 66(2):121–

136.

Chapuis, R. P. and Aubertin, M. (2003). On the use of the kozeny-carman equation

to predict the hydraulic conductivity of soils. Canadian Geotechnical Journal,

40(3):616–628.

Chrisopoulos, S., Osinov, V. A., and Triantafyllidis, T. (2016). Dynamic problem for

the deformation of saturated soil in the vicinity of a vibrating pile toe. Lecture

Notes in Applied and Computational Mechanics, 80:53–67.

Clausen, C. J. F. and Tjelta, T. I. (1995). Offshore platforms supported by bucket

foundations. IABSE congress report, pages 819–829.

Cotter, O. (2009). The installation of suction caisson foundations for offshore renew-

able energy structures. Phd thesis, the University of Oxford.

Damgaard, M., Bayat, M., Andersen, L. V., and Ibsen, L. B. (2014). Assessment

of the dynamic behaviour of saturated soil subjected to cyclic loading from

offshore monopile wind turbine foundations. Computers and Geotechnics,

61:116–126.

Dekker, M. J. (2014). The Modelling of Suction Caisson Foundations for Multi-

Footed Structures. Master thesis, Norwegian University of Science and Tech-

nology.

DNV GL (2016). DNVGL-ST-0126 : Support structures for wind turbines.

Dutto, P., Baessler, M., and Geissler, P. (2016). Suction bucket foundation for wind

energy turbines. In Proceedings of the ASME 2016 35th International Con-

ference on Ocean, Offshore and Arctic Engineering OMAE2016, pages 1–8,

Busan. ASME.

Emdadifard, M. and Hosseini, S. M. M. (2010). Numerical modeling of suction

bucket under cyclic loading in saturated sand. Electronic Journal of Geotech-

nical Engineering, 15 C:1–16.

Energinet.dk (2015). Technical project description for offshore wind farms (200 mw).

Erbrich, C. T. and Tjelta, T. I. (1999). Installation of bucket foundations and suc-

tion caissons in sand - geotechnical performance. Annual Offsore Technology

Conference, pages 725–736.

Feld, T. (2001). Suction buckets, a new innovative foundation concept, applied to

115

offshore wind turbines. PhD thesis, Aalborg University.

Fiumana, N. (2020). Active suction anchors for offshore renewable energies in sand.

PhD thesis, The university of Western Australia.

Foglia, A., Gottardi, G., Govoni, L., and Ibsen, L. B. (2015). Modelling the drained

response of bucket foundations for offshore wind turbines under general mono-

tonic and cyclic loading. Applied Ocean Research, 52:80–91.

Foglia, A., Ibsen, L. B., Andersen, L. V., and Roesen, H. R. (2012). Physical mod-

elling of bucket foundation under long-term cyclic lateral loading. Proceedings

of the International Offshore and Polar Engineering Conference, 4:667–673.

Fugro (2016). Effects of Cyclic Loading on Suction Bucket Foundations for Off-

shore Wind Turbines. Technical report, Bureau of Safety and Environmental

Enforcement, Sterling, Virginia.

Goldscheider, M. and Gudehus, G. (1976). Einige bodenmechanische Probleme bei

Küsten und Offshore-Bauwerken. Vorträge zur Baugrundtagung, pages 507–

522.

Grecu, S., Ibsen, L. B., and Barari, A. (2020). Winkler springs for axial response of

suction bucket foundations in cohesionless soil. Soils and Foundations, (xxxx).

Gudehus, G. (1996). A comprehensive constitutive equation for granular materials.

Soils and Foundations, 36(1):1–12.

Herle, I. and Gudehus, G. (1999). Determination of parameters of a hypoplastic

constitutive model from properties of grain assemblies. Mechanics of Cohesive-

frictional Materials, 4(5):461–486.

Hong, Y., Koo, C. H., Zhou, C., Ng, C. W. W., and Wang, L. Z. (2017). Small

Strain Path-Dependent Stiffness of Toyoura Sand: Laboratory Measurement

and Numerical Implementation. International Journal of Geomechanics,

17(1):04016036.

Houlsby, G. and Byrne, B. (2004). Calculation procedures for installation of suction

caissons. Technical report, University of Oxford Department of Engineering

Science, Oxford.

Houlsby, G., Kelly, R., Huxtable, J., and Byrne, B. W. (2005a). Field trials of suc-

tion caissons in clay for offshore wind turbine foundations. Géotechnique,

55(4):287–296.

Houlsby, G. T. and Byrne, B. W. (2005). Design procedures for installation of suction

116

caissons in sand. Proceedings of the Institution of Civil Engineers: Geotechni-

cal Engineering, 158(3):135–144.

Houlsby, G. T., Kelly, R. B., and Byrne, B. W. (2005b). The tensile capacity of suction

caissons in sand under rapid loading. Frontiers in Offshore Geotechnics, ISFOG

2005 - Proceedings of the 1st International Symposium on Frontiers in Offshore

Geotechnics, (August):405–410.

Ibsen, L. B. (2008). Implementation of a new foundations concept for Offshore Wind

farms. In 15th NGM, number September, pages 19–33, Sandefjord.

Ibsen, L. B. and Thilsted, C. L. (2010). Numerical study of piping limits for in-

stallation of large diameter buckets in layered sand. Numerical Methods in

Geotechnical Engineering - Proceedings of the 7th European Conference on

Numerical Methods in Geotechnical Engineering, pages 921–926.

Ibsen, L. B. and Thilsted, C. L. (2011). Numerical study of piping limits for suc-

tion installation of offshore skirted foundations and anchors in layered sand.

Frontiers in Offshore Geotechnics II - Proceedings of the 2nd International

Symposium on Frontiers in Offshore Geotechnics, pages 421–426.

IEA (2020). Global Energy Review 2019. Global Energy Review 2019.

Ishihara, K. (1975). Undrained deformation and liquefaction of sand under cyclic

stresses. Soils and Foundations, 15:29 – 44.

Jeong, Y. H., Kim, J. H., Manandhar, S., Ha, J. G., Park, H. J., and Kim, D. S. (2020).

Centrifuge modelling of drained pullout and compression cyclic behaviour of

suction bucket. International Journal of Physical Modelling in Geotechnics,

20(2):59–70.

Jiang, Y. and Liu, M. (2009). Granular solid hydrodynamics. Granular Matter,

11(3):139.

Jin, Z., Yin, Z. Y., Kotronis, P., and Li, Z. (2019). Advanced numerical modelling

of caisson foundations in sand to investigate the failure envelope in the H-M-V

space. Ocean Engineering, 190(August):106394.

Kiełkiewicz, A., Marino, A., Vlachos, C., Maldonado, F. J. L., and Lessis, I. (2015).

The Practicality and Challenges of Using XL Monopiles for Offshore Wind Tur-

bine Substructures. University of Strathclyde.

Kihlström, L.-M. (2019). Offshore wind: suction buckets reduce cost and underwater

noise, vattenfall.

117

Kim, D. H., Lee, S. G., and Lee, I. K. (2014a). Seismic fragility analysis of 5MW

offshore wind turbine. Renewable Energy, 65:250–256.

Kim, D.-J., Choo, Y. W., Kim, J.-H., Kim, S., and Kim, D.-S. (2014b). Investigation

of Monotonic and Cyclic Behavior of Tripod Suction Bucket Foundations for

Offshore Wind Towers Using Centrifuge Modeling. Journal of Geotechnical

and Geoenvironmental Engineering, 140(5):04014008.

Klinkvort, R. T., Sturm, H., and Andersen, K. H. (2019). Penetration model for

installation of skirted foundations in layered soils. Journal of Geotechnical


Kolymbas, D. (1988). Eine konstitutive Theorie für Böden und andere körnige Stoffe.

Veröffentlichung des Institutes für Bodenmechanik und Felsmechanik der Uni-

versität Fridericana in Karlsruhe.

Kolymbas, D. (1999). Introduction to Hypoplasticity (Advances in Geotechnical En-

gineering and Tunneling). A.A.Balkema, Rotterdam, first edit edition.

Kolymbas, D., Herle, I., and Von Wolffersdorff, P. A. (1995). Hypoplastic constitu-

tive equation with internal variables. International Journal for Numerical and

Analytical Methods in Geomechanics, 19(6):415 – 436.

Kozeny, J. (1927). Über kapillare Leitung des Wassers im Boden. Akad. Wiss., pages

271–306.

Labenski, J. and Moormann, C. (2017). Numerical simulation of the lateral bearing

behavior of open steel pipe piles with regard to their installation method. In IC-

SMGE 2017 - 19th International Conference on Soil Mechanics and Geotech-

nical Engineering, number September 2017, pages 2305–2308, Seoul.

Lacal-Arántegui, R., Yusta, J. M., and Domínguez-Navarro, J. A. (2018). Offshore

wind installation: Analysing the evidence behind improvements in installation

time. Renewable and Sustainable Energy Reviews, 92(April):133–145.

Lambe, W. T. and Whitman, R. V. (1969). Soil Mechanics. John Wiley & Sons.

Le, V. H. (2015). Zum Verhalten von Sand unter zyklischer Beanspruchung mit Po-

larisationswechsel im Einfachscherversuch. PhD thesis, des Grundbauinstitutes

der Technischen Universität Berlin.

Leblanc, C. (2009). Design of Offshore Wind Turbine Support Structures Selected.

Phd thesis, Aalborg University.

LeBlanc, C., Houlsby, G. T., and Byrne, B. W. (2010). Response of stiff piles in sand

118

to long-term cyclic lateral loading. Geotechnique, 60(2):79–90.

Letcher, T. M. (2017). Why Wind Energy? Elsevier Inc.

Liingaard, M. (2006). Dynamic Behaviour of Suction Caissons. Phd thesis, Aalborg

University.

Lin, S.-S. and Liao, J.-C. (1999). Permanent Strains of Piles in Sand due to Cyclic

Lateral Loads. Journal of Geotechnical and Geoenvironmental Engineering,

125(9):798–802.

Lin, W. C., Huang, T. Y., Tseng, W. C., Kuo, Y. S., Ho, Y. L., and Tsai, B. (2012).

Revision and application of the p-y curves to monopile foundations in cohe-

sionless soil. pages 589–596.

Lombardi, D., Cox, J. A., and Bhattacharya, S. (2011). Long-term performance of

offshore wind turbines supported on monopiles and suction caissons. Proceed-

ings of the 8th International Conference on Structural Dynamics, EURODYN

2011, (July):3506–3510.

Lu, X., Wang, S., and Zhang, J. H. (2005). Experimental study of pore pressure and

deformation of suction bucket foundations under horizontal dynamic loading.

China Ocean Engineering, 19(4):671–680.

Luo, L., O’Loughlin, C. D., Bienen, B., Wang, Y., Cassidy, M. J., and Morgan, N.

(2020). Effect of the ordering of cyclic loading on the response of suction

caissons in sand. Géotechnique Letters, 10(2):303–310.

Mana, D. S., Gourvenec, S., and Randolph, M. F. (2014). Numerical modelling of

seepage beneath skirted foundations subjected to vertical uplift. Computers and

Geotechnics, 55:150–157.

Maniar, D. R. (2004). A Computational Procedure for Simulation of Suction Caisson

Behavior Under Axial and Inclined Loads. Phd thesis, The University of Texas

at Austin.

Merchant, N. D., Andersson, M. H., Box, T., Le Courtois, F., Cronin, D., Holdsworth,

N., Kinneging, N., Mendes, S., Merck, T., Mouat, J., Norro, A. M., Ollivier, B.,

Pinto, C., Stamp, P., and Tougaard, J. (2020). Impulsive noise pollution in

the Northeast Atlantic: Reported activity during 2015–2017. Marine Pollution

Bulletin, 152(August 2019):110951.

Moormann, C. (2016). Design of piles – German practice Geological overview. In

International Symposium on Design of Piles in Europe, number April, pages

119

1–35, Leuven,. ISSMGE - ETC 3.

Ng, C. W. W., Boonyarak, T., and Mašín, D. (2015). Effects of Pillar Depth and

Shielding on the Interaction of Crossing Multitunnels. Journal of Geotechnical


Nielsen, S. D. (2019). Finite element modeling of the tensile capacity of suction

caissons in cohesionless soil. Applied Ocean Research, 90(May):101866.

Niemunis, A. and Herle, I. (1997). Hypoplastic model for cohesionless soils with

elastic strain range. Mechanics of Cohesive-frictional Materials, 2(4):279–299.

Niemunis, A., Wichtmann, T., and Triantafyllidis, T. (2005). A high-cycle accumula-

tion model for sand. Computers and Geotechnics, 32(4):245 – 263.

Ochmanski, M., Modoni, G., Bzowka, J., Croce, P., and Russo, G. (2014). Numer-

ical modelling of tunnelling supported by jet grouting canopies. In Incontro

Annuale dei Ricercatori di Geotecnica 2014, number July, Chieti e Pescara.

Oh, K. Y., Nam, W., Ryu, M. S., Kim, J. Y., and Epureanu, B. I. (2018). A review

of foundations of offshore wind energy convertors: Current status and future

perspectives. Renewable and Sustainable Energy Reviews, 88:16–36.

Ørsted (2019). Our experience with suction bucket jacket foundations Ørsted. Tech-

nical report.

Penner, N., Grießmann, T., and Rolfes, R. (2020). Monitoring of suction bucket jack-

ets for offshore wind turbines: Dynamic load bearing behaviour and modelling.

Marine Structures, 72(May 2019).

Potts, D. M. (1999).

Ragni, R., O’Loughlin, C., Bienen, B., Cassidy, M., and Stanier, S. (2020). Ob-

servations during suction bucket installation in sand. International Journal of

Physical Modelling in Geotechnics, 20(3):132–149.

Randolph, M. F. (1981). The response of flexible piles to lateral loading. Geotech-

nique, 31(2):247–259.

Rapoport, V. and Young, A. G. (1985). Uplift capacity of shallow offshore founda-

tions. In Clemence, S. P., Uplift Behavior of Anchor Foundations in Soil.

Rattez, H. (2017). École Doctorale Science Ingénierie et Environnement Hadrien

Rattez Couplages Thermo-Hydro-Mécaniques et localisation dans les milieux

de Cosserat Application à l ’ analyse de stabilité du cisaillement rapide des

failles. PhD thesis, De l’Université Paris-Est.

120

Remmers, J., Reale, C., Pisanò, F., Raymackers, S., and Gavin, K. (2019). Geotech-

nical installation design of suction buckets in non-cohesive soils: A reliability-

based approach. Ocean Engineering, 188(August):106242.

Schjetne, K., Andersen, K. H., Lauritzsen, R., and Hansteen, O. E. (1979). Foun-

dation engineering for offshore gravity structures. Marine Geotechnology,

3(4):369–421.

Schneider, J., Lehane, B., and xu, X. (2005). The UWA-05 method for prediction of

axial capacity of driven piles in sand.

Schofield, A. and Wroth, P. (1968). Critical state soil mechanics.

Senders, M. (2008). Suction Caissons in Sand As Tripod Foundations for Offshore

Wind Turbines. Phd thesis, The University of Western Australia.

Senders, M. and Randolph, M. F. (2009). CPT-Based Method for the Installation

of Suction Caissons in Sand. Journal of Geotechnical and Geoenvironmental

Engineering, 135(1):14–25.

Sørensen, E. S., Clausen, J., and Damkilde, L. (2017). Comparison of numerical

formulations for the modeling of tensile loaded suction buckets. Computers

and Geotechnics, 83:198–208.

Sørensen, S., Ibsen, L., and Augustesen, A. (2010). Effects of diameter on initial

stiffness of p-y curves for large-diameter piles in sand. Numerical Methods in

Geotechnical Engineering - Proceedings of the 7th European Conference on

Numerical Methods in Geotechnical Engineering, pages 907–912. cited By 38.

Stapelfeldt, M., Bienen, B., and Grabe, J. (2020). The influence of the drainage

regime on the installation and the response to vertical cyclic loading of suction

caissons in dense sand. Ocean Engineering, 215(September 2019):107105.

Stapelfeldt, M., Bubel, J., and Grabe, J. (2015). Numerical investigation of the in-

stallation process and the bearing capacity of suction bucket foundations. In

Proceedings of the International Conference on Offshore Mechanics and Arctic

Engineering - OMAE, volume 1, pages 1–10, NL. ASME.

Sturm, H. (2017). Design Aspects of Suction Caissons for Offshore Wind Turbine

Foundations. Proceedings of TC 209 workshop at the 19th ICSMGE: Founda-

tion Design of Offshore Wind Structures, pages 45–63.

Sun, W. (2020). Upscaling lattice Boltzmann and discrete element simulations for

porous media. In Wu, W. and Pastor, M., editors, Point based numerical meth-

121

ods in geomechanics, pages 189–242.

Tasan, H. E. (2011). Zur Dimensionierung der Monopile-Gründungen von Offshore-

Windenergieanlagen. Ph.d. thesis, Technische Universität Berlin, Fakultät VI -

Planen Bauen Umwelt.

Tasan, H. E. (2017). Behavior of free and fixed-head offshore piles under cyclic

lateral loads. Uludag University Journal of The Faculty of Engineering, 22(1).

Tas, an, H. E. and Akdag, C. T. (2018). The influence of cylic loading frequency

on the behaviour of suction-bucket foundations for offshore structures. Teknik

Dergi/Technical Journal of Turkish Chamber of Civil Engineers, 29(3):8411–

8431.

Tasan, H. E. and Yilmaz, S. A. (2019). Effects of installation on the cyclic ax-

ial behaviour of suction buckets in sandy soils. Applied Ocean Research,

91(April):101905.

Thieken, K., Achmus, M., and Schröder, C. (2014). On the behavior of suction buck-

ets in sand under tensile loads. Computers and Geotechnics, 60:88–100.

Thijssen, R. and Alderlieste, E. (2012). Cyclic loading of suction caissons. Plaxis

Bulletin.

Tjelta, T. (1995). Geotechnical experience from the installation of the europipe jacket

with bucket foundations. Annual Offsore Technology Conference, pages 897–

908.

Tran, M. N. (2005). Installation of Suction Caissons in Dense Sand and the Influence

of Silt and Cemented Layers. Phd thesis, The University of Sydney.

Ukritchon, B., Wongtoythong, P., and Keawsawasvong, S. (2018). New design equa-

tion for undrained pullout capacity of suction caissons considering combined

effects of caisson aspect ratio, adhesion factor at interface, and linearly increas-

ing strength. Applied Ocean Research, 75:1–14.

Vaitkune, E., Ibsen, L. B., and Nielsen, B. N. (2017). Bucket foundation model testing

under tensile axial loading. Canadian Geotechnical Journal, 54(5):720–728.

Versteele, H., Stuyts, B., Cathie, D., and Charlier, R. (2013). Cyclic loading of caisson

supported offshore wind structures in sand. 18th International Conference on

Soil Mechanics and Geotechnical Engineering: Challenges and Innovations in

Geotechnics, ICSMGE 2013, 3:2411–2414.

Vicent, S., Kim, S. R., and Hung, L. C. (2020a). Evaluation of horizontal and vertical

122

bearing capacities of offshore bucket work platforms in sand. Applied Ocean

Research, 101(April):102198.

Vicent, S., Kim, S. R., Van Tung, D., and Bong, T. (2020b). Effect of loading rate on

the pullout capacity of offshore bucket foundations in sand. Ocean Engineer-

ing, 210(May 2019):107427.

Villalobos, F. A. (2006). Model Testing of Foundations for Offshore Wind Turbines.

Phd thesis, University of Oxford.

Vogelsang, J., Huber, G., and Triantafyllidis, T. (2017). Stress paths on displacement

piles during monotonic and cyclic penetration. Lecture Notes in Applied and

Computational Mechanics, 82:29–52.

von Wolffersdorff, P. A. (1996). Hypoplastic relation for granular materials with

a predefined limit state surface. Mechanics of Cohesive-Frictional Materials,

1(3):251–271.

Wang, L. Z., Wang, H., Zhu, B., and Hong, Y. (2018a). Comparison of monotonic

and cyclic lateral response between monopod and tripod bucket foundations in

medium dense sand. Ocean Engineering, 155(June 2017):88–105.

Wang, X. (2017). Centrifuge modelling of seismic and lateral behaviors of suction

bucket foundations for offshore wind turbines. Phd thesis, Case Western Re-

serve University.

Wang, X., Yang, X., and Zeng, X. (2017). Centrifuge modeling of lateral bearing be-

havior of offshore wind turbine with suction bucket foundation in sand. Ocean

Engineering, 139(May):140–151.

Wang, X., Zeng, X., Li, J., Yang, X., and Wang, H. (2018b). A review on recent

advancements of substructures for offshore wind turbines. Energy Conversion

and Management, 158(September 2017):103–119.

Wang, Y., Lu, X., Wang, S., and Shi, Z. (2006). The response of bucket foundation

under horizontal dynamic loading. Ocean Engineering, 33(7):964–973.

WEC (2016). World Energy Resources 2016. World Energy Council 2016, pages

6–46.

Wichtmann, T. and Triantafyllidis, T. (2005). Über den Einfluß der Korn-

verteilungskurve auf das dynamische und das kumulative Verhalten nichtbindi-

ger Böden. Bautechnik, 82(6):378–386.

WindEurope (2019). Offshore wind in Europe, Key trends and statistics 2019.

123

WIndEurope, 3(2):14–17.

Yang, S. L., Grande, L. O., Qi, J. F., and Feng, X. L. (2003). Excessive Soil Plug and

Anti-failure Mechanism of Bucket Foundation during Penetration by Suction.

Proceedings of the International Offshore and Polar Engineering Conference,

5:1206–1211.

Youd, T. (1973). Factors controlling maximum and minimum densities of sands, in

stp523-eb evaluation of relative density and its role in geotechnical projects

involving cohesionless soils, ed. e. selig and r. ladd. pages 98–112.

Zhang, J. H., Zhang, L. M., and Lu, X. B. (2007). Centrifuge modeling of suction

bucket foundations for platforms under ice-sheet-induced cyclic lateral load-

ings. Ocean Engineering, 34(8-9):1069–1079.

Zhang, Z. and Cheng, X. (2017). Predicting the cyclic behaviour of suction caisson

foundations using the finite element method. Ships and Offshore Structures,

12(7):900–909.

Zhu, B., Byrne, B. W., and Houlsby, G. T. (2013). Long-Term Lateral Cyclic Re-

sponse of Suction Caisson Foundations in Sand. Journal of Geotechnical and

Geoenvironmental Engineering, 139(1):73–83.

Zhu, F. Y., O’Loughlin, C. D., Bienen, B., Cassidy, M. J., and Morgan, N. (2018). The

response of suction caissons to long-term lateral cyclic loading in single-layer

and layered seabeds. Geotechnique, 68(8):729–741.

Zienkiewicz, O. C., Chan, A. H. C., Pastor, M., Schrefler, B. A., and Shiomi, T.

(1999). Computational Geomechanics with Special Reference to Earthquake

Engineering. Wiley.

Zienkiewicz, O. C., Qu, S., Taylor, R. L., and Nakazawa, S. (1986). The patch test

for mixed formulations. International Journal for Numerical Methods in Engi-

neering, 23(10):1873–1883.

Zienkiewicz, O. C. and Shiomi, T. (1984). Dynamic behaviour of saturated porous

media; the generalized biot formulation and its numerical solution. Inter-

national Journal for Numerical and Analytical Methods in Geomechanics,

8(1):71–96.

124

APPENDIX A

DESIGN CHARTS

Once these information is collected, a designer can use the design charts that are

produced with the parametric analyses in this study as follows;

Similar to the ones as Chapter 5, various graphics (total 27 charts) are developed for

cyclic axial compression for the following scenarios.

• L/D= 1.0, f=0.05, 0.10, 0.20 Hz, k=0.001, 0.0001, 0.00001 m/s (9 charts)

• L/D= 0.8, f=0.05, 0.10, 0.20 Hz, k=0.001, 0.0001, 0.00001 m/s (9 charts)

• L/D= 1.3, f=0.05, 0.10, 0.20 Hz, k=0.001, 0.0001, 0.00001 m/s (9 charts)

The behaviour of a bucket in saturated sandy soil was investigated focusing on the

deformation response.

Considering that the bucket foundations are more suitable for multi-legged formations

rather than mono foundations, in the design part, cyclic axial loading was the focus.

This study might be a useful light for a designer with all the preliminary informations

on geometry, soil and load environment in consideration of cyclic failure risks.

125

L/D = 0.80, kinitial

= 10−3

m/s, f = 0.05 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25

Figure A.1: Expected cyclic response for L/D = 0.8 bucket in a sandy soil with kinitial

= 1.0x10-3 m/s under a cyclic axial compressive loading frequency f =0.05 Hz.L/D = 0.80, k

initial = 10

−4 m/s, f = 0.05 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25



126


= 10−5

m/s, f = 0.05 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25



initial = 10

−3 m/s, f = 0.10 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25



127


= 10−4

m/s, f = 0.10 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25



initial = 10

−5 m/s, f = 0.10 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25



128


= 10−3

m/s, f = 0.20 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25



initial = 10

−4 m/s, f = 0.20 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25



129


= 10−5

m/s, f = 0.20 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25



initial = 10

−3 m/s, f = 0.05 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25



130

L/D = 1.0, kinitial

= 10−4

m/s, f = 0.05 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25



initial = 10

−5 m/s, f = 0.05 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25



131

L/D = 1.0, kinitial

= 10−3

m/s, f = 0.10 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25



initial = 10

−4 m/s, f = 0.10 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25



132

L/D = 1.0, kinitial

= 10−5

m/s, f = 0.10 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25



initial = 10

−3 m/s, f = 0.20 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25



133

L/D = 1.0, kinitial

= 10−4

m/s, f = 0.20 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25



initial = 10

−5 m/s, f = 0.20 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25



134


= 10−3

m/s, f = 0.05 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25



initial = 10

−4 m/s, f = 0.05 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25



135


= 10−5

m/s, f = 0.05 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25



initial = 10

−3 m/s, f = 0.10 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25



136


= 10−4

m/s, f = 0.10 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25



initial = 10

−5 m/s, f = 0.10 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25



137


= 10−3

m/s, f = 0.20 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25



initial = 10

−4 m/s, f = 0.20 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25



138


= 10−5

m/s, f = 0.20 Hz


Cycl

ic A

xia

l C

om

pre

ssio

n A

mpli

tude

F

cyc /

Fu

lt

Progressive

Attenuation

Shakedown

0.7 0.75 0.8 0.85 0.90

0.05

0.1

0.15

0.2

0.25



139

CURRICULUM VITAE

PERSONAL INFORMATION

Surname, Name: Yılmaz, S. Alp

Nationality: Turkish (TC)

Date and Place of Birth: 23.09.1987, Ankara

Marital Status: Married

Phone: 0 505 6548031

EDUCATION

Degree Institution Year of Graduation

M.Sc. Structural Mechanics, METU 2014

B.S. Civil Engineering, METU 2010

High School Cumhuriyet H.School, Ankara 2005

PROFESSIONAL EXPERIENCE

Year Place Enrollment

2010 - 2021 Lava Engineering Ltd.Co Design Engineer

2021 - Still Sunko Proje Inc. Design Manager

141

PUBLICATIONS

Thesis

Yılmaz, S.Alp (2014). Reliability Based Evaluation of Seismic Design of Turkish

Bridges by Using Load and Resistance Factor Method, Masters Thesis, METU

International Journal Publications

Tasan,H.Ercan, Yılmaz, S.Alp (2019). Effects of Installation on the Cyclic Axial

Behaviour of Suction Buckets in Sandy Soils, Applied Ocean Research

International Conference Publications

Yılmaz, S.Alp, Tasan,H.Ercan (2019). Numerical investigations on the behaviour of

offshore suction bucket foundations under cyclic axial loading, Proceedings of the

XVII ECSMGE-2019.

Yılmaz, S.Alp, Tasan,H.Ercan (2020). A Numerical Study on The Behaviour of Off-

shore Suction Bucket Foundations under Cyclic Lateral Loading, Proceedings of the

GEOCONGRESS 2020

142

a numerical study on the behaviour of suction bucket

Documents