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DYNAMICALLY INSTALLED ANCHORS FOR FLOATING OFFSHORE STRUCTURES by MARK DAMIAN RICHARDSON B.E. (Hons), B.Com. This thesis is presented for the degree of DOCTOR OF PHILOSOPHY at THE UNIVERSITY OF WESTERN AUSTRALIA Centre for Offshore Foundation Systems School of Civil and Resource Engineering September 2008

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DYNAMICALLY INSTALLED ANCHORS FOR

FLOATING OFFSHORE STRUCTURES

by

MARK DAMIAN RICHARDSON

B.E. (Hons), B.Com.

This thesis is presented for the degree of

DOCTOR OF PHILOSOPHY

at

THE UNIVERSITY OF WESTERN AUSTRALIA

Centre for Offshore Foundation Systems

School of Civil and Resource Engineering

September 2008

i

ABSTRACT

The gradual depletion of shallow water hydrocarbon deposits has forced the offshore oil

and gas industry to develop reserves in deeper waters. Dynamically installed anchors

have been proposed as a cost-effective anchoring solution for floating offshore

structures in deep water environments. The rocket or torpedo shaped anchor is released

from a designated drop height above the seafloor and allowed to penetrate the seabed

via the kinetic energy gained during free-fall and the anchor’s self weight. Dynamic

anchors can be deployed in any water depth and the relatively simple fabrication and

installation procedures provide a significant cost saving over conventional deepwater

anchoring systems.

Despite use in a number of offshore applications, information regarding the

geotechnical performance of dynamically installed anchors is scarce. Consequently, this

research has focused on establishing an extensive test database through the modelling of

the dynamic anchor installation process in the geotechnical centrifuge. The tests were

aimed at assessing the embedment depth and subsequent dynamic anchor holding

capacity under various loading conditions. Analytical design tools, verified against the

experimental database, were developed for the prediction of the embedment depth and

holding capacity.

Test results in normally consolidated clay indicated zero fluke anchor tip embedment

depths of up to 3 times the anchor length for impact velocities approaching 30 m/s. The

anchor embedment depth was found to depend on both the impact velocity and the

anchor geometry, and resulted in holding capacities of up to 4 times the anchor dry

weight. Given the dependence of holding capacity on penetration depth, optimisation of

the anchor impact velocity suggests the potential for considerably higher capacities.

Long-term sustained and cyclic loading did not significantly influence the holding

capacity, although an increase in the load duration under either sustained or cyclic

loading conditions led to a slight reduction in the anchor capacity. An apparent

threshold sustained loading level was identified, above which the anchor capacity may

be detrimentally affected.

ii

In normally consolidated clay, the dynamic anchor holding capacity increased with time

following installation due to setup. The short-term capacity immediately after

installation depended on the rate of installation, with an increase in the impact velocity

resulting in a comparative reduction in the short-term capacity. Cavity expansion

solutions for the radial consolidation of soil around a solid driven pile provided

reasonable estimates of the increase in capacity of dynamic anchors following

installation.

The centrifuge tests indicated that whilst dynamic anchors were suitable for use in

calcareous soils, extremely low embedment depths (less than the anchor length)

prevented their use in silica sands. Impact velocities of up to 30 m/s resulted in

penetration depths of up to 1.5 times the anchor length in uncemented calcareous sand

samples, corresponding to vertical monotonic holding capacities of 1 – 2 times the

anchor’s dry weight. Given the dependence of embedment depth on impact velocity and

the subsequent dependence of holding capacity on embedment depth, optimisation of

the dynamic anchor impact velocity suggests the potential for higher holding capacities

than were achieved here.

An analytical method based on conventional bearing and frictional resistance theory and

incorporating provisions for viscous enhanced shearing resistance and inertial drag

resistance during penetration was adopted for predicting the dynamic anchor

embedment depth. Similarly a conventional pile capacity calculation technique was

adapted for determining the vertical monotonic holding capacity of dynamic anchors.

Validation of these methods against the test database indicated that they were capable of

providing reasonable estimates of the embedment and holding capacity performance of

dynamically installed anchors in both normally consolidated clay and uncemented

calcareous sand deposits. Combining the embedment and capacity prediction methods

enabled the generation of dynamic anchor design charts.

iii

ACKNOWLEDGEMENTS

First and foremost I would like to take this opportunity to express my sincere gratitude

to Dr Conleth O’Loughlin for encouraging me to pursue this research. Con was always

available to discuss various aspects of the project and remained an important source of

guidance even after leaving the university. A special thank you also to Professor Mark

Randolph; it has been a great privilege to work with Mark and his guidance and advice

have proved invaluable. Thanks also to Dr Christophe Gaudin for helping out in Con’s

absence; Christophe’s input, particularly with the centrifuge tests was greatly

appreciated.

This research would not have been possible without the important contributions of Don

Herley and Bart Thompson. Don and Bart provided immeasurable assistance with the

experimental aspects of the project and lightened the mood with endless stories about

past sporting glories. Thanks also to the workshop, electronics and technical staff who

assisted with the project, especially John Breen, Tuarn Brown, Shane De Catania, Phil

Hortin, Gary Davies, Dave Jones, Frank Tan, Neil McIntosh, Alex Duff and Wayne

Galbraith. In addition, the support provided by Monica Mackman, Wenge Liu and the

rest of the administrative staff is gratefully acknowledged.

I would also like to acknowledge the financial support I received during my

candidature, which consisted of an Australian Postgraduate Award through a linkage

project with Woodside Energy Ltd, a postgraduate top-up scholarship through the

Western Australia Energy Research Alliance (WA:ERA) and an Ad-Hoc scholarship

through the Centre for Offshore Foundation Systems.

It would be remiss of me not to thank my friends. To my friends within the school,

thank you for providing valuable discussion on many of the issues arising during the

project. Thank you also to my friends outside of the university for the often much

needed distraction; but don’t pretend that you are ever going to read this.

A special thank you also to my family, particularly my parents, your guidance,

encouragement, love and understanding, not only over the past few years but throughout

my life has been an inspiration.

iv

Finally, to Rebecca (and Normie and Scoobie), your unwavering love and support has

been a source of strength and encouragement. This work is dedicated to you.

I certify that, except where specific reference is made in the text to the work of others,

the contents of this thesis are original and have not been submitted to any other

university.

Mark Richardson

September 2008

v

TABLE OF CONTENTS

ABSTRACT i

ACKNOWLEDGEMENTS iii

TABLE OF CONTENTS v

NOTATION xiv

CHAPTER 1 - INTRODUCTION 1

1.1 THE OFFSHORE OIL AND GAS INDUSTRY 1

1.2 OFFSHORE DEVELOPMENT SYSTEMS 2

1.2.1 Fixed Platform 2

1.2.2 Compliant Tower 2

1.2.3 Tension Leg Platform (TLP) 3

1.2.4 Semi-Submersible 3

1.2.5 Spar Platform 3

1.2.6 Floating Production Storage and Offloading (FPSO) Facility 4

1.2.7 Subsea System 4

1.2.8 Hybrid Systems 4

1.3 MOORING SYSTEMS 5

1.4 ANCHORING SYSTEMS 6

1.4.1 Anchor Piles 6

1.4.2 Suction Caissons 7

1.4.3 Drag Embedment Anchors 7

1.4.4 Drag-In Plate Anchors 8

1.4.5 Direct Embedment Anchors 8

1.4.6 Dynamically Installed Anchors 9

1.5 RESEARCH OBJECTIVES 10

1.6 THESIS STRUCTURE 12

vi

CHAPTER 2 - LITERATURE REVIEW 15

2.1 INTRODUCTION 15

2.2 SEABED PENETRATION 15

2.2.1 Seabed Strength Characterisation 16

2.2.1.1 Marine Sediment Penetrometer 16

2.2.1.2 Marine Impact Penetrometer 17

2.2.1.3 Doppler Penetrometer 18

2.2.1.4 Free Fall Cone Penetrometer 19

2.2.1.5 Expendable Bottom Penetrometer 19

2.2.2 Nuclear Waste Disposal 20

2.2.3 Embedment Prediction Methods 23

2.2.3.1 Strain Rate Effects 23

2.2.3.2 Inertial Drag 26

2.2.3.3 Young's Method 27

2.2.3.4 True's Method 29

2.2.3.5 Ove Arup and Partners Method 33

2.3 PULLOUT CAPACITY 35

2.3.1 American Petroleum Institute Method 35

2.3.2 Marine Technology Directorate Method 36

2.3.3 Consolidation Effects 38

2.3.4 Long-Term Sustained Loading 40

2.3.5 Cyclic Loading 41

2.4 DYNAMICALLY INSTALLED ANCHORS 42

2.4.1 Torpedo Anchor 42

2.4.2 Deep Penetrating Anchor 44

2.4.3 SPEAR Anchor 46

2.4.4 Physical Modelling 46

2.4.5 Analytical and Numerical Modelling 48

2.5 SUMMARY 49

vii

CHAPTER 3 - EXPERIMENTAL METHODS AND MODELLING 53

3.1 INTRODUCTION 53

3.2 CENTRIFUGE MODELLING 53

3.3 CENTRIFUGE FACILITIES 56

3.3.1 Beam Centrifuge 56

3.3.1.1 Sample Strong-Box 56

3.3.1.2 Actuators 56

3.3.1.3 STOMPI 57

3.3.2 Drum Centrifuge 57

3.3.2.1 Sample Channel 58

3.3.2.2 Tool Table Actuator 58

3.4 SOIL SAMPLES 58

3.4.1 Soil Properties 58

3.4.1.1 Kaolin Clay 58

3.4.1.2 Calcareous Sand 59

3.4.1.3 Silica Flour 60

3.4.2 Sample Preparation 60

3.4.2.1 Kaolin Clay 60

3.4.2.2 Calcareous Sand 62

3.4.2.3 Silica Flour 62

3.5 PENETROMETER DEVICES 63

3.5.1 T-bar Penetrometer 63

3.5.2 Cone Penetrometer 64

3.5.2.1 Calcareous Sand 64

3.5.2.2 Silica Flour 65

3.6 MODEL ANCHORS 65

3.6.1 Zero Fluke Model Anchors 65

3.6.2 Four Fluke Model Anchors 66

3.6.3 Model Anchors with Different Tip Shapes 67

viii

3.6.4 Instrumented Anchor 68

3.6.5 Model Anchors with Different Aspect Ratios 70

3.6.6 Anchor Chain and Release Cord 71

3.7 EXPERIMENTAL APPARATUS 71

3.7.1 Installation Guide 71

3.7.2 Release Mechanism 73

3.7.3 Load Cell 73

3.8 TESTING PROCEDURE 74

3.8.1 Beam Centrifuge 74

3.8.1.1 Dynamic Installation 74

3.8.1.2 Vertical Monotonic Extraction 75

3.8.1.3 Sustained Loading Tests 75

3.8.1.4 Cyclic Loading Tests 76

3.8.1.5 Static Installation 77

3.8.1.6 Monotonic Extraction Following Static Installation 77

3.8.2 Drum Centrifuge 78

3.8.2.1 Dynamic Installation 78

3.8.2.2 Vertical Monotonic Extraction 79

3.9 EXPERIMENTAL PROGRAMME 79

CHAPTER 4 - ANALYTICAL AND NUMERICAL METHODS 81

4.1 INTRODUCTION 81

4.2 DRAG COEFFICIENT 81

4.2.1 Factors Influencing the Drag Coefficient 82

4.2.2 Computational Fluid Dynamics 84

4.2.3 Inertial Drag in Soil 87

4.3 IMPACT VELOCITY 89

4.3.1 Uniform Acceleration Field 89

4.3.2 Centrifuge Acceleration Field 90

ix

4.3.3 Energy Losses 91

4.4 EMBEDMENT DEPTH 91

4.4.1 Calculation Procedure 92

4.4.2 Parameter Values 95

4.5 HOLDING CAPACITY 97

4.5.1 Calculation Procedure 98

4.5.2 Parameter Values 99

4.5.3 Normalised Capacity 101

4.5.4 Anchor Efficiency 101

4.6 CALCAREOUS SAND 101

4.6.1 Embedment Depth 102

4.6.1.1 Calculation Procedure 102

4.6.1.2 Parameter Values 103

4.6.2 Holding Capacity 104

4.6.2.1 Calculation Procedure 104

4.6.2.2 Parameter Values 105

CHAPTER 5 - EXPERIMENTAL RESULTS FOR DYNAMIC

ANCHOR TESTING IN NORMALLY CONSOLIDATED CLAY 107

5.1 INTRODUCTION 107

5.2 BEAM CENTRIFUGE 108

5.2.1 Strength Characterisation Tests 108

5.2.2 Impact Velocity 112

5.2.3 Embedment Depth 114

5.2.3.1 Influence of Impact Velocity 115

5.2.3.2 Influence of Anchor Geometry 116

5.2.3.3 Influence of Surface Water 118

5.2.3.4 Verticality 119

5.2.4 Load Displacement Response 119

5.2.5 Vertical Monotonic Holding Capacity 121

x

5.2.5.1 Influence of Embedment Depth 122

5.2.5.2 Influence of Anchor Geometry 123

5.2.6 Long-Term Sustained Loading 123

5.2.6.1 Normalised Capacity Ratio 125

5.2.6.2 Influence of Load Magnitude 126

5.2.6.3 Influence of Load Duration 128

5.2.7 Cyclic Loading 128

5.2.7.1 Normalised Capacity Ratio 130

5.2.7.2 Influence of Load Magnitude / Amplitude 130

5.2.7.3 Influence of Number of Cycles 132

5.2.8 Static Push Tests 133

5.2.8.1 Static Installation 133

5.2.8.2 Monotonic Extraction Following Static Installation 134

5.2.9 Summary 134

5.3 DRUM CENTRIFUGE 136

5.3.1 Strength Characterisation Tests 136

5.3.2 Impact Velocity 138

5.3.3 Embedment Depth 139

5.3.3.1 Influence of Impact Velocity 140

5.3.3.2 Influence of Anchor Aspect Ratio 141

5.3.3.3 Influence of Anchor Mass 141

5.3.3.4 Combined Influence of Aspect Ratio and Mass 142

5.3.4 Load-Displacement Response 142

5.3.5 Vertical Monotonic Holding Capacity 143

5.3.5.1 Influence of Embedment Depth 144

5.3.5.2 Influence of Anchor Aspect Ratio 144

5.3.6 Setup and Consolidation 145

5.3.6.1 Short-Term Anchor Capacity 147

5.3.6.2 Capacity Increase with Time 148

5.3.6.3 t50 and t90 149

5.3.7 Summary 150

5.4 CONCLUSIONS 152

xi

CHAPTER 6 - EXPERIMENTAL RESULTS FOR DYNAMIC

ANCHOR TESTING IN SILICA AND CALCAREOUS SAND 155

6.1 INTRODUCTION 155

6.2 SILICA SAND 155

6.2.1 Strength Characterisation Tests 156

6.2.2 Impact Velocity 156

6.2.3 Embedment Depth 156

6.3 CALCAREOUS SAND 157

6.3.1 Strength Characterisation Tests 158

6.3.2 Impact Velocity 158

6.3.3 Embedment Depth 159

6.3.4 Load-Displacement Response 160

6.3.5 Holding Capacity 161

6.3.6 Static Push Tests 161

6.4 CONCLUSIONS 161

CHAPTER 7 - COMPARISON OF EXPERIMENTAL AND

THEORETICAL RESULTS 163

7.1 INTRODUCTION 163

7.2 CLAY - BEAM CENTRIFUGE 163

7.2.1 Impact Velocity 163

7.2.2 Embedment Depth 164

7.2.2.1 Back-Calculated Strain Parameter 164

7.2.2.2 Predicted Embedment Depth 166

7.2.2.3 Sensitivity Analysis 167

7.2.3 Holding Capacity 168

7.2.3.1 Predicted Vertical Monotonic Holding Capacity 168

7.2.3.2 Sensitivity Analysis 170

7.2.4 Summary 171

xii

7.3 CLAY - DRUM CENTRIFUGE 172

7.3.1 Impact Velocity 172

7.3.2 Embedment Depth 173

7.3.2.1 Back-Calculated Strain Rate Parameter 173

7.3.2.2 Predicted Embedment Depth 174

7.3.3 Holding Capacity 176

7.3.3.1 Predicted Vertical Monotonic Holding Capacity 176

7.3.3.2 Consolidation Solutions 178

7.3.4 Summary 180

7.4 CALCAREOUS SAND – BEAM CENTRIFUGE 181

7.4.1 Impact Velocity 181

7.4.2 Embedment Depth 182

7.4.2.1 Back-Calculated Strain Rate Parameter 182

7.4.2.2 Predicted Embedment Depth 183

7.4.2.3 Sensitivity Analysis 183

7.4.3 Holding Capacity 184

7.4.3.1 Predicted Vertical Monotonic Holding Capacity 185

7.4.3.2 Sensitivity Analysis 185

7.4.4 Summary 187

7.5 DYNAMIC ANCHOR DESIGN CHARTS 188

7.5.1 0FA – Normally Consolidated Clay 188

7.5.2 4FA – Normally Consolidated Clay 189

7.5.3 0FA – Calcareous Sand 189

7.5.4 Design Example 190

7.6 CONCLUSIONS 191

CHAPTER 8 - CONCLUSIONS AND FURTHER RESEARCH 195

8.1 INTRODUCTION 195

8.2 MAIN FINDINGS 195

8.2.1 Experimental Modelling in Normally Consolidated Clay 195

xiii

8.2.2 Experimental Modelling in Silica and Calcareous Sand 196

8.2.3 Analytical Methods and Design Tools 197

8.3 APPLICATION TO INDUSTRY 198

8.4 RECOMMENDATIONS FOR FURTHER RESEARCH 199

REFERENCES 201

TABLES 215

FIGURES 231

xiv

NOTATION

Roman

a acceleration

Ap projected / cross-sectional area

Apf projected fluke area

As surface area

Asf fluke surface area

B diameter / width

ch horizontal coefficient of consolidation

cv vertical coefficient of consolidation

Cc compression index

CD drag coefficient

CDe effective drag coefficient

CDf drag coefficient in fluid

CD,N drag coefficient in Newtonian fluid

CDs drag coefficient in soil

Ce strain rate coefficient

Co strain rate constant

Cs swelling index

d50 average grain size

D diameter

Deq equivalent diameter

e void ratio

Ef anchor efficiency

Ek kinetic energy

Ep potential energy

f degree of hole closure

fh frequency received at hydrophone

fr frequency

F force / load

Fb bearing resistance force

Fbf bearing resistance force - anchor flukes

Fd inertial drag resistance force

xv

FN normalised capacity

Fr reverse end bearing resistance force

Frf reverse end bearing resistance force - anchor flukes

Fs side friction resistance force

Fsf side friction resistance force – anchor flukes

Fsus sustained load

Fv vertical capacity

g gravitational acceleration

G shear modulus

Gs specific gravity

h distance from pile tip

hd drop height

hd,eq equivalent prototype drop height

hs height above sample surface

hsample sample height

H Hedstrom number

ID relative density (density index)

Ir rigidity index

k undrained shear strength gradient with depth

kp permeability

Kc earth pressure coefficient after equalisation

KL soil viscosity coefficient

Ks lightweight projectile correction factor

L length

Lfluke1 length of fluke segment 1

Lfluke2 length of fluke segment 2

Lfluke3 length of fluke segment 3

Lshaft shaft length

Ltip tip length

LL liquid limit

m mass

Ma Mach number

n gravitational acceleration level

N nose performance coefficient

Nc bearing capacity factor

Ncd dynamic nose bearing capacity factor

xvi

Ncf fluke bearing capacity factor

Nchd dynamic tail bearing capacity factor

NCR normalised capacity ratio

Ned dynamic nose and tail bearing capacity factor

Neq equivalent number of cycles

Nq bearing capacity factor in calcareous sand

Nt nose resistance factor

NT-bar T-bar bearing capacity factor

PL plastic limit

q net bearing resistance

qc cone tip resistance

qcd dynamic cone tip resistance

r radius

Re Reynolds number

Reff effective radius

R0 radius to base of sample

Rf strain rate function

su undrained shear strength

su,ave undrained shear strength averaged over embedded shaft length

su,bf undrained shear strength at the bottom of the flukes

su,pad undrained shear strength at the padeye

su,r remoulded shear strength

su,ref undrained shear strength at reference strain rate

su,sea undrained shear strength at the seabed

su,sf average undrained shear strength over the embedded fluke length

su,tf undrained shear strength at the top of the flukes

su,tip undrained shear strength at the projectile tip

su0 undrained shear strength at the threshold strain rate

S target penetrability constant

Se strain rate factor

Se* maximum strain rate factor

St soil sensitivity

t time

tfluke fluke thickness

T non-dimensional time factor

v velocity

xvii

vave average velocity

vb velocity at the beginning of radius increment

ve velocity at the end of radius increment

vf velocity of sound in fluid

vi impact velocity

vm measured velocity

vref reference velocity

vs ‘static’ penetration velocity

vt terminal velocity

v0 velocity at threshold strain rate

V non-dimensional velocity

wfluke fluke width

W dry weight

Ws submerged weight

YSR yield stress ratio

z depth / displacement

zchain chain length

ze embedment depth

zLC height of load cell above sample surface

zslack anchor chain slack length

Greek

α adhesion factor

αd dynamic side adhesion factor

αfluke fluke adhesion factor

αshaft shaft adhesion factor

β strain rate parameter (power law)

βCALC ratio of shaft friction to effective overburden stress (adhesion factor)

γd dry unit weight

γsat saturated unit weight

γ΄ effective unit weight

γ& strain rate

refγ& reference strain rate

0γ& threshold strain rate

δ pile-soil interface friction angle

∆Ivy relative voids index

xviii

∆r radius increment

∆t interrupt time / time increment

∆u excess pore pressure

∆v velocity increment

∆z depth increment

η porosity

λ strain rate parameter (semi-logarithmic law)

λ΄ strain rate parameter (inverse hyperbolic sine law)

µ absolute viscosity

µp plastic viscosity

ν kinematic viscosity

ρ density

σ΄hc horizontal effective stress after installation and equalization

σ΄hf horizontal effective stress at failure

σ΄v vertical effective stress

σ΄vy vertical effective stress at yield

σ΄v0 in situ vertical effective stress

σ΄v0,ave average in situ vertical effective stress over embedded shaft length

σ΄v0,pad in situ vertical effective stress at padeye

τsf local shear stress at failure

sfτ average shear stress

τy shear stress at yield

φ friction angle

φcv critical state friction angle

φ΄ angle of internal friction

ψ dilation angle

ω angular rotation

Subscripts / Superscripts

ave average

cyc cyclic

m model

max maximum

min minimum

mon monotonic

p prototype

xix

sus sustained

0 original

Abbreviations

API American Petroleum Institute

BRE Building Research Establishment

CFD Computational Fluid Dynamics

CPT Cone Penetration Test

DOIR Department of Industry and Resources

DOMP Deep Ocean Model Penetrator

DPA Deep Penetrating Anchor

EPW Earth Penetrating Weapon

ESP European Standard Penetrometer

FFCPT Free Fall Cone Penetrometer

FLAC Fast Lagrangian Analysis of Continua

FPSO Floating, Production, Storage and Offloading

GME Great Meteor East

IEA International Energy Agency

ISSMGE International Society for Soil Mechanics and Geotechnical Engineering

MCF Multi-Column Floater

MIP Marine Impact Penetrometer

MODU Mobile Offshore Drilling Unit

MSP Marine Sediment Penetrometer

MTD Marine Technology Directorate

NAP Nares Abyssal Plain

NCEL Naval Civil Engineering Laboratory

NEA Nuclear Energy Agency

NNLA Near Normal Load Anchor

OECD Organisation for Economic Cooperation and Development

PERP Photoemitter-Receiver Pair

PVC Polyvinyl Chloride

RGD Rijks Geologische Dienst

SEPLA Suction Embedded Plate Anchor

SPEAR Self-Penetrating Embedment Attachment Rotation

SNL Sandia National Laboratories

STOMPI Sub-Terrain Oil Impregnated Multiple Pressure Instrument

xx

TLP Tension Leg Platform

UWA University of Western Australia

VLA Vertically Loaded Anchor

XBP Expendable Bottom Penetrometer

0FA Zero Fluke Anchor

3FA Three Fluke Anchor

4FA Four Fluke Anchor

1

CHAPTER 1 - INTRODUCTION

1.1 THE OFFSHORE OIL AND GAS INDUSTRY

Global oil demand is expected to increase by 2.5 % to 88.2 mb/d (million barrels per

day) during 2008 (IEA 2007), with long-term forecasts predicting a 40 % increase in

demand by 2030 (Mortished 2006). However oil and gas production from shallow water

sources has decreased significantly over the past 10 years. During this time deepwater

oil production has increased to such a level that it now exceeds shallow water

production in the Gulf of Mexico (Figure 1.1). Figure 1.1 suggests the emergence of a

similar trend for Gulf of Mexico gas production. The shortfall in supply generated by

increased worldwide demand and decreased shallow water production is placing

increased dependence on the discovery and development of deepwater oil and gas

reserves.

The definition of deepwater has evolved with technology, but today, water depths less

than 500 m are typically considered shallow, with depths of 500 – 1500 m representing

deep water and depths greater than 1500 m classified as ultra deep (Colliat 2002). The

first offshore platform, Superior, was installed in 1947 in the Gulf of Mexico in just 6 m

of water. Since this time the oil and gas industry has been continuously moving into

ever increasing water depths, with the Independence Hub semi-submersible production

facility installed in a record 2440 m of water during February 2007 (Offshore Engineer

2007c). Deepwater activity is currently dominated by developments in the Gulf of

Mexico, West Africa and Brazil, although deepwater exploration and production in the

Asia-Pacific region is also proceeding rapidly. Australia recently became a deepwater

producer when the Enfield development came onstream during 2006 in 600 m of water.

With additional significant natural gas discoveries in water depths of up to 1400 m, such

as the Io, Geryon and Jansz fields (DOIR 2007), further deepwater development in

Australia appears certain.

2

The transition from shallow to deep water has been made possible by advances in

platform and foundation technology. However as the water depths have increased, so to

have the installation and procurement costs, with traditional platforms fixed to the

seabed replaced by floating structures attached to the seabed by mooring lines.

Anchoring systems for these floating structures pose a number of financial and technical

challenges. Hence the current focus is on the development of cost effective and reliable

deepwater mooring techniques.

1.2 OFFSHORE DEVELOPMENT SYSTEMS

Selection of the appropriate development strategy for offshore hydrocarbon deposits is

influenced by a number of factors including water depth, reserve size, proximity to

existing infrastructure, well numbers, operating considerations, economic factors and

anticipated well intervention frequency (French et al. 2006). Offshore structures can be

broadly categorised as fixed platforms, compliant towers, floating structures and subsea

systems. Figure 1.2 shows the various types of offshore development systems currently

in use.

1.2.1 Fixed Platform

Fixed platforms may include tubular steel jackets or concrete gravity structures. Steel

jackets are primarily pile supported, whilst concrete gravity structures achieve stability

by virtue of their immense structural weight and large diameter base. Additional

stability may be provided by the use of base skirts which penetrate several metres into

the seabed. Economic considerations limit the installation of fixed platforms to water

depths approaching 600 m. In Australia, the North Rankin A platform is an example of

a steel jacket fixed platform whilst the Wandoo structure is an example of a fixed

concrete platform.

1.2.2 Compliant Tower

A compliant tower is a slender steel space-frame tower with a piled foundation, which is

very flexible in bending relative to a conventional fixed platform. This flexibility means

that the platform can withstand significant lateral loads by sustaining large lateral

3

deflections. Compliant towers are typically applicable in water depths ranging from 300

– 600 m. The Petronius compliant tower stands in 535 m of water, making it one of the

highest freestanding structures ever built (Chevron 2000).

1.2.3 Tension Leg Platform (TLP)

A TLP consists of a semi-submersible platform moored by vertical tendons connected to

the seafloor (Figure 1.3). The excess buoyancy provided by various hull components

maintains the tension in the mooring system even during storm loading conditions.

TLPs are capable of deployment in water depths of up to 2000 m. In May 2007, the hull

of the Neptune TLP was towed out for installation in approximately 1310 m of water

(Offshore Engineer 2007d).

1.2.4 Semi-Submersible

A semi-submersible production unit typically comprises parallel pontoons connected to

the topside by numerous vertical columns (Figure 1.4). The pontoons and columns can

be filled with water to alter the buoyancy of the system for improved stability under

wave and wind loading. Semi-submersibles can be deployed in a wide range of water

depths for both temporary and permanent operations. The Atlantis semi-submersible

was installed during November 2006 in the Gulf of Mexico in approximately 1870 m of

water (Offshore Engineer 2007a).

1.2.5 Spar Platform

A spar consists of a large diameter, truncated, vertical, cylindrical hull which supports

the platform by means of excess buoyancy (Figure 1.5). Buoyancy chambers located

within the hull enable the buoyancy of the structure to be controlled thereby maintaining

the platform stability. In addition, strakes fitted to the hull minimise lateral movement

due to vortex shedding, improving lateral stability. The spar can be anchored to the

seabed by vertical tethers but more commonly by catenary or taut mooring lines. The

Holstein truss spar was established in 1324 m of water (French et al. 2006), although

SPARs are theoretically capable of being deployed in water depths of up to 3000 m.

4

1.2.6 Floating Production Storage and Offloading (FPSO) Facility

FPSOs comprise a large tanker type vessel fitted with production and storage facilities

(Figure 1.6). The storage capabilities of the FPSO mean that it may be suitable for

marginally economic fields located in remote areas in which pipeline infrastructure does

not exist. Smaller shuttle tankers may be used to transport the hydrocarbons to an

onshore processing facility. FPSOs can be fixed in position or comprise multiple

mooring lines meeting at a single point. The single point mooring allows the tanker to

weathervane to achieve an optimal orientation with regard to the prevailing

environmental conditions. The key advantages of FPSOs relate to their ability to operate

on short term or permanent developments in water depths up to and exceeding 3000 m

(French et al. 2006). The P-50 FPSO is moored in approximately 1240 m of water in the

Albacora Leste field in the deepwater Campos Basin, Brazil (Brandão et al. 2006).

1.2.7 Subsea System

Subsea systems typically comprise either a single subsea well producing to a nearby

platform, or multiple wells producing through a manifold and pipeline system to a

distant production facility. Multi-component seabed facilities such as subsea wells,

manifolds, control umbilicals and flowlines allow subsea systems to recover

hydrocarbons in water depths and conditions that would normally preclude the

installation of a conventional fixed or floating platform. Subsea systems are capable of

operation in any water depth.

1.2.8 Hybrid Systems

Technical innovation in deepwater oil and gas exploration and production has seen the

evolution of hybrid development systems combining the characteristics of traditional

floating production installations. Several different hybrid systems have emerged,

including the MinDOC3 design which is a cross between a semi-submersible and a truss

spar and the MCF (multi-column floater) which is a combination of a semi-submersible

and a cell spar (Offshore Engineer 2007e). The MinDOC3 comprises three vertical

columns arranged in a triangular shape connected to pontoons. The structure appears to

be a semi-submersible but in fact behaves much like a spar in terms of stability. The

MCF is a deep draft semi-submersible with longer columns than conventional semi-

5

submersibles and each column is made up of four smaller diameter, closely spaced

tubular columns similar to those of a cell spar. In addition the development of

cylindrical mono-column floating structures known as MPSOs is challenging the

tradition of converting existing tankers into FPSOs. Hybrid systems continue to emerge

as the industry continues to explore and develop in ever increasing water depths.

1.3 MOORING SYSTEMS

Floating facilities can be anchored to the seabed by catenary, taut-leg or vertical

mooring systems. Vertical moorings are applicable only to TLPs (see Section 1.2.3), in

which the tendons from the TLP arrive vertically at the seabed. Catenary moorings on

the other hand arrive horizontally at the seabed, transmitting predominantly horizontal

loads to the anchoring system whilst taut-leg (or semi-taut leg) moorings arrive at

angles as high as 40° to 50° transmitting both horizontal and vertical load components

(Figure 1.7). The design of taut-leg moorings is therefore governed by the vertical

holding capacity of the anchoring system as opposed to the lateral capacity for catenary

moorings (Ehlers et al. 2004). In a catenary system, the restoring forces are provided by

the self-weight of the mooring lines and the pretension. In a taut-leg system however,

these restoring forces are provided by the elasticity of the mooring lines. Therefore the

use of taut-leg mooring systems is restricted to water depths that are sufficient to ensure

that the mooring line length is capable of providing the required elasticity.

Oil and gas exploration in shallow water has traditionally employed a chain or wire rope

catenary mooring line configuration. However in deepwater operations the weight and

length of the mooring line become limiting factors in the design of the platform (Vryhof

1999). Therefore the move towards deeper waters has seen an associated shift away

from catenary moorings towards taut-leg and vertical mooring systems. Taut-leg and

vertical configurations significantly reduce the mooring footprint (Figure 1.7) resulting

in a substantial decrease in the possibility of the mooring lines encroaching on adjacent

tracts, crossing mooring lines from adjacent facilities or encountering undersea

pipelines (Aubeny et al. 2001). The reduced mooring line length also results in

significant installation cost savings. The increased prevalence of taut-leg and vertical

6

mooring systems has subsequently resulted in the need for cost effective anchoring

systems that can resist high components of vertical load.

1.4 ANCHORING SYSTEMS

Floating facilities can be anchored to the seabed using a number of methods. The choice

of method depends on the size and nature of the facility (i.e. short, medium or long

term), environmental conditions, the mooring system (i.e. catenary or taut-leg), the

geotechnical properties of the seabed and any financial or installation limitations that

may exist. This section provides a brief description of each of the available anchoring

methods.

1.4.1 Anchor Piles

Anchor piles typically comprise a hollow steel tube with a mooring line attached at

some point below the mudline (Figure 1.8). Anchor piles may also be used to anchor

TLP tendons, in which case the TLP tendon attaches to a receptacle at the top of the

pile. Installation may involve vibration or driving by a pile hammer or the pile may be

drilled and grouted into position depending on the site characteristics. Resistance to

applied loads is predominantly provided by the frictional resistance developed between

the pile surface and the surrounding soil. Anchor piles can be accurately installed in a

wide range of seabed soil conditions and are capable of withstanding both horizontal

and vertical loads, making them suitable for catenary and taut-leg as well as vertical

mooring configurations.

Installation costs for anchor piles are extremely high due to the large crane barges and

pile driving equipment required. These installation costs increase dramatically with

increasing water depth. Current technology also limits the operating depth of pile

hammers to approximately 1500 m, with the Constitution spar holding the current depth

record for driven piles at 1564 m (Offshore Engineer 2007b).

7

1.4.2 Suction Caissons

Suction caissons consist of a large diameter, stiffened cylindrical shell with a cover

plate at the top and an open bottom (Figure 1.9). Installation is achieved by a pressure

differential (suction) established within the caisson after initial penetration under the

anchor’s self weight. The pressure differential established by pumping water out from

the caisson’s interior results in a downward force on the top of the caisson, which

slowly pushes the caisson further into the seabed. Suction caissons can be installed

relatively quickly and accurately in either single or multicell units for both fixed and

floating structures. The ability of suction caissons to resist both horizontal and vertical

loads means they can be employed in catenary, taut-leg and vertical mooring systems.

The nature of the suction caisson installation process may make it difficult for the

caisson to penetrate hard layers within the seabed. Furthermore, in stratigraphies

comprising clay overlying sand, the relatively high suction pressure required to

penetrate the sand may cause failure of the soil plug within the anchor (Watson et al.

2006). It is also possible that a thin-walled caisson may buckle due to excessive

underpressure. The large anchor size may require a considerable amount of deck space

during transport and the use of a heavy lift vessel during installation, resulting in higher

installation costs.

1.4.3 Drag Embedment Anchors

A drag anchor comprises a bearing plate (fluke) rigidly attached to a shank which is

designed to self embed when dragged along the seabed by a wire rope or chain (Figure

1.10). The anchor derives its capacity from the bearing resistance of the plate and the

frictional resistance developed along the anchor shank and embedded portion of the

mooring line. Drag anchors exhibit high efficiencies (ratio of capacity to dry weight)

and can be easily removed following installation making them suitable for short to

medium term applications.

Uncertainty exists, however, over the trajectory and final embedment depth of the

anchor during installation. Since the optimal anchor configuration (fluke angle) is

dependent on the soil conditions, layered soil profiles can lead to further installation

uncertainty. Drag embedment anchors are not capable of withstanding vertical loads and

8

as such they are only applicable for catenary mooring line configurations. Furthermore,

significant anchor drag distances may be required to achieve the final embedment depth

in certain soil conditions, resulting in greater site investigation costs and the increased

possibility of interference with existing mooring lines and subsea pipelines.

1.4.4 Drag-In Plate Anchors

Drag-in plate anchors, or vertically loaded anchors (VLAs) were introduced as an

alternative to conventional drag embedment anchors for use in taut-leg mooring

systems. VLAs consist of thin plates and smaller shanks than traditional drag anchors

(Figure 1.11); however a similar installation process is employed. When the fluke has

penetrated to the target depth the shank or bridle is triggered allowing the anchor to

rotate such that the fluke becomes normal to the applied load. The process by which the

anchor orientation changes to this normal configuration is known as keying. VLAs are

capable of withstanding high components of vertical load, making them suitable for use

in taut-leg mooring systems. As with drag embedment anchors, VLAs offer high weight

efficiencies and can easily be retrieved following installation.

Upon keying, VLAs are situated at their maximum possible embedment depth and

during loading can subsequently only experience a decrease in embedment and

therefore capacity. The near normal load anchor (NNLA) provides holding capacities of

up to 95 % of a VLA but is capable of embedding deeper or dragging horizontally at a

constant load without pulling out (Bruce 2007). The installation procedure is similar to

that of the VLA, but upon triggering the NNLA achieves a final fluke angle of

approximately 80° (near normal), thereby enabling the NNLA to embed further and thus

achieve higher capacities when overloaded.

VLAs and NNLAs offer the same disadvantages as conventional drag anchors in terms

of the uncertainty with the installation process and the soil conditions which they are

suited for. Furthermore, there is an additional degree of uncertainty regarding the

triggering process and the final anchor orientation.

1.4.5 Direct Embedment Anchors

Direct embedment anchors comprise a bearing plate attached to a mooring line installed

at the end of a follower either by driving, vibration or suction. The plate anchor is

9

typically installed vertically to minimise installation resistance and, once the target

depth has been achieved, the follower is removed for reuse in later installations. Upon

removal of the follower the anchor chain is tensioned to initiate the keying process

whereby the anchor rotates to an orientation perpendicular to the applied load. The

suction embedded plate anchor (SEPLA, Figure 1.12) is a form of follower embedded

plate anchor in which the plate anchor is installed using a suction caisson (Wilde et al.

2001). Direct embedment anchors combine the benefits of the installation method with

the benefits of the high weight efficiency plate anchors. Installation via a suction

caisson or pile follower enables the anchor to be accurately installed at the target depth

and location. Plate anchors are capable of withstanding both horizontal and vertical

loads allowing them to be used in catenary and taut-leg mooring systems.

Direct embedment anchors have the potential to become damaged during installation in

hard soils. Loss of embedment during keying of the plate anchor is also an issue which

may lead to uncertainty in the final plate anchor embedment (Ehlers et al. 2004,

O’Loughlin et al. 2006). The installation and retrieval of the follower may also create a

zone of weakened soil extending from the plate to the soil surface resulting in

potentially lower capacities (Gaudin et al. 2006, Song et al. 2007).

1.4.6 Dynamically Installed Anchors

Dynamically installed anchors comprise a thick-walled, steel, tubular shaft filled with

scrap metal or concrete and fitted with a conical tip. Steel plates (flukes) may be

attached to the shaft to provide hydrodynamic stability and additional frictional

resistance to imposed uplift forces. The anchor becomes completely buried within the

seabed by dynamic self-weight penetration following free-fall from a specified height

above the seabed. Resistance to environmental uplift loading is predominantly provided

by friction developed at the anchor-soil interface. Two main types of dynamic anchor

exist; the torpedo anchor (Figure 1.13) and the Deep Penetrating Anchor (DPA; Figure

1.14).

The main advantage of dynamic anchors is that they are deployable in essentially any

water depth and, since no external energy source or mechanical interaction is required

during installation, costs are relatively independent of water depth. In addition, the

simple anchor design limits fabrication and handling costs. Dynamic anchors can be

10

accurately deployed and their performance is less dependent on accurate assessment of

the soil shear strength since lower seabed shear strengths permit greater penetration

depths and vice versa. Once installed, dynamic anchors behave in a similar manner to

anchor piles and as such are capable of withstanding both horizontal and vertical load

components, enabling their use in both catenary and taut-leg mooring systems.

Despite the economic advantages afforded by dynamic anchors, a degree of uncertainty

exists in relation to predicting the embedment depth and subsequent capacity. There is

also some concern with verifying the anchor’s verticality following installation. In

addition, this type of anchor may not be suitable for use in sandy soils.

1.5 RESEARCH OBJECTIVES

The need for cost effective deepwater anchoring solutions capable of withstanding both

horizontal and vertical loading components is clear. Conventional anchoring methods

such as anchor piles, suction caissons and drag embedment anchors become relatively

expensive as the water depth increases and as such developmental anchors such as the

dynamically installed anchor are being actively pursued. Dynamically installed anchors

appear to offer the most potential economic benefit of the current anchor concepts due

to the simplicity of the anchor design and the installation method, resulting in the need

for smaller marine vessels and reduced vessel time together with less complex marine

operations (Ehlers et al. 2004). With the exception of a number of field trials, (which

have not been published in detail) very little dynamic anchor performance data exists.

Increased understanding of the geotechnical behaviour of these anchors in varying soil

and loading conditions would evidently lead to increased industry confidence in the

potential of dynamically installed anchors.

Given the lack of performance data currently available and the potential economic

benefit of dynamic anchors to the industry, there exists a clear need for an experimental

study to address the basic issues of predicting the embedment depth and subsequent

holding capacity for a given anchor geometry, anchor drop height and seabed strength

profile. This project therefore aimed to investigate the geotechnical performance of

dynamically installed anchors in normally consolidated clay, calcareous sand and silica

sand. Two main challenges arise concerning the geotechnical performance of dynamic

11

anchors: firstly, determination of the anchor embedment depth for a given drop height

and seabed strength profile; secondly, determination of the subsequent anchor capacity

under various loading conditions. These challenges were addressed in two distinct

phases.

Considering the scarcity of dynamic anchor experimental data, Phase 1 involved the

development of an experimental database through an extensive suite of reduced scale

centrifuge tests on model dynamic anchors. Specifically this was aimed at:

• Investigating the parameters that govern anchor embedment depth, i.e. impact

velocity, anchor shaft length/diameter ratio, anchor fluke geometry, anchor tip

geometry, anchor mass and soil shear strength profile.

• Examining the effect of anchor embedment on anchor capacity under monotonic,

sustained and cyclic loading conditions.

• Quantifying the contribution of consolidation time (duration between anchor

installation and loading) to anchor capacity.

Phase 2 focused on the development of a design tool for the prediction of anchor

embedment depth and subsequent capacity. This design model was based on an

analytical approach validated against the experimental database established in Phase 1.

The specific aims of Phase 2 were to:

• Develop an analytical approach for anchor penetration. The anchor penetration

model is based upon conventional bearing and frictional capacity theory but with

provisions for viscous enhanced shearing resistance and fluid mechanics drag

resistance.

• Apply conventional pile capacity calculation techniques, incorporating end

bearing and shaft friction resistance terms, to the prediction of the vertical

anchor capacity. In this context, the effect of consolidation time on anchor

capacity was also considered.

The outcomes of the project include the attainment of experimental data that has been

used to identify expected dynamic anchor penetrations and capacities as well as the

development of robust and versatile design tools that can be used in routine offshore

engineering practice.

12

1.6 THESIS STRUCTURE

This thesis is presented in 8 chapters, as outlined below:

Chapter 2 reviews the literature relating to dynamically installed anchors. The review

commences with a discussion of seabed penetration research in terms of seabed disposal

of nuclear waste and the assessment of seabed strength properties using free-fall

penetrometers. In the context of dynamic seabed penetration, the strain rate effects on

soil shear strength are also examined. The chapter concludes with a summary of

experimental and numerical work relating to the use of free-fall projectiles as a form of

anchoring system.

Chapter 3 summarises the details of the dynamic anchor experimental programme. The

centrifuge facilities and test apparatus are outlined and the soil properties and sample

preparation procedures are presented. A discussion of the apparatus developed

specifically for the research project is provided with particular focus on the various

model anchors developed.

Chapter 4 details the analytical and numerical techniques adopted in the dynamic anchor

design model. The analytical approach adopted for predicting anchor embedment and

subsequent capacity, based on conventional bearing and frictional capacity theory, is

presented. Consideration of the effects of strain rate and inertial drag during anchor

installation is also provided. Simplified pile capacity calculation techniques are

presented for use in predicting the vertical anchor capacity following installation. The

techniques are subsequently adapted for use in calcareous soil.

Chapter 5 presents the results of the model anchor tests conducted in clay. The

experimental results are presented in terms of impact velocity, embedment depth and

holding capacity. The tests provide information regarding the influence of the aspect

ratio, mass, tip geometry, flukes, consolidation time and cyclic and sustained loading on

the performance of dynamically installed anchors. The test results are compared with

the results of dynamic anchor field trials and previous laboratory and centrifuge model

tests.

13

Chapter 6 presents the results of the model anchor tests conducted in silica and

calcareous sand. The test results are presented in terms of impact velocity, embedment

depth and holding capacity. The experimental results are compared with the results of

known field trials.

Chapter 7 provides a comparison of the experimental data presented in Chapters 5 and 6

with the analytical solutions for the dynamic anchor impact velocity, embedment depth

and holding capacity derived in Chapter 4 for both normally consolidated clay and

calcareous sand. The experimental results are used to validate the proposed methods and

to develop user friendly design tools

Chapter 8 summarises the major research findings and discusses the implications of

these findings with regard to the practical implementation of dynamic anchors in

industry. The chapter also presents recommendations for future work arising from the

outcomes of the research project.

15

CHAPTER 2 - LITERATURE REVIEW

2.1 INTRODUCTION

Literature regarding the behaviour of dynamically installed anchors is limited.

Dynamically installed anchors emerged during the late 1990s from the need of the oil

and gas industry for a reliable and cost effective deepwater anchoring system. However,

the potential application of dynamically embedded objects for anchoring purposes was

recognised as early as the 1970s (True 1974). Dynamic anchor behaviour is typically

considered in two distinct phases: (i) dynamic installation and (ii) loading and

extraction. The penetration of objects into the seabed has previously been considered in

the measurement of seabed shear strengths and for the disposal of high-level radioactive

waste. Likewise the capacity of anchor piles for offshore foundations has been

extensively investigated. This literature provides a basis for assessing the geotechnical

performance of dynamically installed anchors in both phases of its operation, as is

discussed further below.

2.2 SEABED PENETRATION

Investigation of the penetration of objects into the seabed is not new. Dynamic seabed

penetration has been studied for in situ strength measurement and nuclear waste

disposal purposes since the 1960s. For typical seabed soils in which the shear strength

increases with depth, dynamically installed anchors rely upon the depth of penetration

achieved during installation to achieve their capacity. Accurate prediction of the

dynamic anchor penetration depth is therefore an important consideration in evaluating

the subsequent anchor capacity and hence relative merit of the concept. Embedment

depth prediction methods exist, from earlier work on earth penetrating weapons and

nuclear waste disposal penetrometers, but uncertainty regarding strain rate effects and

inertial drag resistance limit their reliability.

16

2.2.1 Seabed Strength Characterisation

Foundations for offshore structures require detailed information about seabed soil

properties to enable safe and effective design. Seabed sampling is expensive and current

sampling techniques are known to cause significant sample disturbance. Likewise quasi-

static penetration tests for assessing soil strength, such as the Cone Penetration Test

(CPT), are expensive, especially in deep water. During the Earth Penetrating Weapon

(EPW) programme conducted by Sandia National Laboratories (SNL) during the 1960s,

the idea emerged of estimating the strength of the target material by instrumenting

projectiles and recording their deceleration during penetration (Thompson and Colp

1970, Colp et al. 1975). Since that time various penetrometer designs and analysis

techniques have been proposed for the in situ measurement of seabed strength

properties.

2.2.1.1 Marine Sediment Penetrometer

During the 1970s and 80s, SNL in association with Texas A and M University

undertook a seabed strength characterisation research programme resulting in the

development of a Marine Sediment Penetrometer (MSP; Colp et al. 1975; see Figure

2.1). Linked via an umbilical to a surface vessel, onboard accelerometers measured the

MSP deceleration during penetration of the soft seabed sediments. An approximate

method for determining the soil shear strength from penetrometer deceleration

measurements was subsequently proposed (McNeill 1981). The method was based on

the suggestion that there is an apparent constant, which when multiplied by the

deceleration at a given depth yields a close estimate of the soil shear strength at that

depth. Based on the results of field and laboratory tests the relationship between the soil

shear strength and deceleration was defined as:

agLA4

WDs

pu

≈ (2.1)

where su is the soil shear strength, W is the penetrometer weight, D is the penetrometer

diameter, g is the local gravitational acceleration, L is the penetrometer length, Ap is the

projected cross-sectional area of the penetrometer and a is the measured deceleration.

17

This approximate method is limited in its application due to its failure to account for

inertial effects during penetration. In addition no consideration has been given to the

strain rate dependence of soil shear strength, resulting in a discrepancy between the

derived dynamic shear strength profile and the shear strength profile based on low strain

rate laboratory tests. Hence it was recommended that this method not be used for

strength measurements for final design, but rather as a useful tool for the simple and

efficient assessment of soil stratigraphy and the relative strengths of adjacent soil layers

(McNeill 1981).

2.2.1.2 Marine Impact Penetrometer

Dayal and Allen (1973) described the development of an instrumented cone

penetrometer for the direct measurement of in situ strength properties of a soil target.

The Marine Impact Penetrometer (MIP; Figure 2.2) featured an accelerometer and tip

and sleeve load cells for measuring the acceleration/deceleration and tip and side

friction resistances during installation, with data transferred to a surface vessel via an

umbilical. Laboratory and preliminary field tests indicated that the ‘dynamic’ shear

strength profile and the soil stratigraphy could be evaluated directly during MIP

penetration of soft seabed sediments (Dayal et al. 1975). An empirical relationship was

proposed for calculating the static cone pressure and therefore static shear strength from

the dynamic cone pressure values obtained in MIP tests, by applying a correction for

penetration rate effects (Dayal et al. 1975)

=−

sL

c

ccd

v

vlogK

q

qq (2.2)

where qcd is the dynamic cone resistance, qc is the ‘static’ cone resistance, KL is a soil

viscosity coefficient, v is the penetrometer velocity and vs is the ‘static’ penetration

velocity. Values of the soil viscosity coefficient were established experimentally from a

limited number of tests and were found to vary from 0.03 – 1.5, indicating an increase

in the cone resistance per log cycle increase in velocity of 3 – 150 % (Dayal et al.

1975). Subsequent sea trials demonstrated the usefulness of the MIP and the analysis

method for obtaining in situ soil strength profiles in depths of up to 4 m below the

seabed (Dayal 1980). Further field and laboratory tests were recommended to validate

18

the accuracy of this method particularly with regard to values of the soil viscosity

coefficient.

2.2.1.3 Doppler Penetrometer

An expendable dynamic penetrometer for measuring seafloor penetrability and

undrained shear strength in water depths of up to 6000 m was developed by the United

States Naval Civil Engineering Laboratory (NCEL; Beard 1981). The military interest

in dynamic penetrometers initially resulted from research into propellant-embedded

anchors in the deep ocean. Installation of such anchors required information about the

seabed soil shear strength which could be obtained using a dynamic penetrometer. The

penetrometer was designed to embed up to 9 m below the seabed and featured an

acoustic telemetry system, comprising an onboard sound source and a surface

hydrophone and receiver for signal processing. The frequency of the signal received at

the hydrophone and the velocity of sound in the fluid in which the penetrometer was

immersed were used to determine the velocity of the projectile during penetration

according to the Doppler principle:

vv

vff

f

frh +

= (2.3)

where fh is the frequency received at the hydrophone, fr is the frequency of the sound

source, vf is the velocity of sound in the fluid and v is the velocity of the sound source

or penetrometer.

A soil penetration model based on Newton’s second law of motion presented by True

(1976) was used to determine the soil strength from the known penetrometer motion

(Beard 1981). The method accounts for both inertial drag and strain rate effects during

dynamic penetration of fine grained soil targets (see Section 2.2.3.4). More than 50 field

tests were conducted in various seafloor materials in order to demonstrate the feasibility

of the penetrometer and its telemetry system and the soil shear strength determination

method. Derived shear strengths were compared with in situ and laboratory test shear

strength data at the test locations with favourable agreement (Figure 2.3). It was

concluded by Beard (1981) that the Doppler penetrometer appeared to provide

reasonable estimates of the undrained shear strength profile of seabed soils.

19

2.2.1.4 Free Fall Cone Penetrometer

The Free Fall Cone Penetrometer (FFCPT), shown in Figure 2.4 was developed by

Brooke Ocean Technology Ltd. and Christian Situ Geosciences Inc. to obtain

geotechnical and geophysical data from the seabed for a range of different applications

(Brooke Ocean Technology 2007). Onboard acceleration and pressure sensors in

conjunction with a high speed data acquisition system provide continuous data profiles

during penetration. A computer data logger fitted within the instrumentation section of

the penetrometer eliminates the need for an umbilical cord or acoustic data transmission

to the surface. The FFCPT provides information on layering within the sediments and

the undrained shear strength and it is also claimed to provide shear modulus and shear

wave velocity data. Pressure transducers provide the FFCPT with the ability to measure

pore pressures during and after penetration, enabling the consolidation properties of the

soil to be investigated. The use of this type of device is particularly suited to

investigations of pipeline or cable route surveys over large distances as the device is

quick and simple to install.

2.2.1.5 Expendable Bottom Penetrometer

The eXpendable Bottom Penetrometer (XBP) represents the most recent seabed

penetrometer for the measurement of in situ seabed soil strength properties. The XBP is

approximately 215 mm long, 51 mm in diameter and is designed to reach a terminal

velocity of approximately 7 m/s (Aubeny and Shi 2006; Figure 2.5). The penetrometer

is fitted with an accelerometer and decelerations measured upon impact with the seabed

provide a basis for estimating the sediment shear strength. The XBP provides an

advantage over previously devised seabed strength characterisation penetrometers in

that it can be deployed from a moving vessel, making it well suited to seabed

investigations over large survey areas.

Aubeny and Shi (2006) proposed a framework for assessing the soil shear strength from

interpreted XBP deceleration profiles in soft clay. Using static bearing capacity factors

derived from finite element analyses and by accounting for viscous strain rate effects

during penetration, a dynamic bearing capacity factor was determined:

20

λ+=

0ccd v

vlog1NN (2.4)

where Ncd is the dynamic bearing capacity factor, Nc is the static bearing capacity

factor, λ is the strain rate parameter, v is the penetrometer velocity and v0 is the velocity

corresponding to the threshold strain rate. Comparisons of interpreted XBP shear

strength profiles to reference miniature vane shear strength profiles of samples

recovered from Gulf of Mexico test sites indicate that the XBP overestimates the

strength during the initial stages of penetration, possibly because the data interpretation

technique ignores inertial drag effects which may be significant during the early stages

of penetration (Figure 2.6). Additionally the XBP strength decreases rapidly in the final

stages of penetration possibly due to elastic rebound of the soil as the velocity reduces

to zero. Overall it was concluded that the XBP is capable of providing first order

estimates of the strength of soft clay materials, although uncertainty with regard to the

strain rate effects precludes improved accuracy from being obtained (Aubeny and Shi

2006).

2.2.2 Nuclear Waste Disposal

During the late 1970s it was recognised that the world was facing a growing problem

with the management of high-level radioactive waste, with increased waste production

from both commercial and military sources. A coordinated research programme was

established by the Organisation for Economic Co-operation and Development (OECD)

Nuclear Energy Agency (NEA) through the International Seabed Working Group,

investigating the feasibility and safety of disposing of high-level radioactive waste in

deep ocean abyssal plain formations (Murray 1988). One waste disposal option

considered involved the free-fall installation of nuclear waste containers into the

seafloor. Vitrified nuclear waste was to be placed within streamlined projectiles and

released from a vessel and allowed to penetrate the soft seabed sediments (Valent and

Lee 1976). A key consideration in evaluating the feasibility of this concept was ensuring

adequate penetration of the projectiles into the ocean bottom. During the 1980s

extensive analytical and experimental research efforts were directed towards assessing

the technical feasibility of the penetrometer nuclear waste disposal method, both in

terms of hydrodynamic performance and seabed penetrability.

21

In 1981 the Building Research Establishment (BRE) representing the Department of the

Environment commissioned Ove Arup and Partners to carry out a feasibility study of

the seabed penetrometer method for the disposal of high-level nuclear waste (Ove Arup

and Partners 1982). This feasibility study proposed a method for predicting the

penetrometer embedment depth using simplifying assumptions about the free-fall

through water and the penetration resistance of the seabed sediments (see Section

2.2.3.5). Supplementary studies considered the seabed soil properties, ocean bed

seismology, penetrometer collision with seabed objects and the penetrometer path

during embedment. It was found that within the limitations of the embedment prediction

model, free-fall penetrometers could reasonably be expected to achieve the necessary

embedment to be considered for the disposal of radioactive waste.

In March 1983 a collaborative experiment between the BRE, the Commission of

European Communities Joint Research Centre and the Institute of Oceanographic

Sciences at Wormley was conducted in the Great Meteor East (GME) radioactive waste

disposal study area in the eastern Atlantic Ocean (Figure 2.7; Freeman et al. 1984). The

experiments involved the free-fall installation of four, similar Deep Ocean Model

Penetrators (DOMP), commonly referred to as European Standard Penetrators (ESP).

The design of the solid steel 3.25 m long, 0.325 m diameter, 1800 kg projectiles (Figure

2.8) was based on hydrodynamic analysis and indicated likely terminal velocities of

approximately 50 m/s. During the field trials, which later became known as the DOMP I

experiments, the penetrometer velocity was monitored using an acoustic telemetry

system incorporating a transmitter in the projectile and a surface hydrophone. The test

results indicated that in the soft calcareous ooze at the GME test site, tip penetrations of

approximately 30 – 35 m were achievable with ESPs impacting the seabed at 46 – 51

m/s (Freeman et al. 1984).

The DOMP II tests were performed in March 1984 at the Nares Abyssal Plain (NAP)

test site in the western Atlantic Ocean (Figure 2.7) by BRE in collaboration with the

Joint Research Centre, SNL and the Rijks Geologische Dienst (RGD). A total of

seventeen tests were conducted with eight different penetrometer designs, including the

ESP (Freeman and Burdett 1986; Figure 2.9). Several different instrumentation and

telemetry systems were also trialled during the test programme. The test results

22

indicated impact velocities of 45 – 56 m/s resulting in penetration depths of 21 – 35 m

in the soft seabed sediments at the NAP site.

A further fifteen tests were conducted at GME in 1986 with three different penetrometer

designs, including a Type X penetrometer, similar to the ESP (Freeman et al. 1988).

The tests were partially aimed at assessing the influence of the weight and surface finish

of the Type X penetrometers on their penetration performance. Impact velocities of 30 –

68 m/s resulted in tip penetration depths of approximately 29 – 58 m. The surface finish

was found to affect the impact velocity but did not result in destabilising hydrodynamic

forces on the penetrometer during free-fall.

Additional field tests were conducted in late 1986 off the coast of Antibes in the

Mediterranean Sea. A total of nine tests were conducted with five different

penetrometers in soil considerably stiffer and stronger than the sediments encountered at

the GME and NAP test sites. The increased seabed strength resulted in reduced tip

penetrations of only 9 – 15 m (Audibert et al. 2006).

In conjunction with the field trials, the Department of the Environment also

commissioned a series of centrifuge tests to model the free-fall option for nuclear waste

disposal. The tests were conducted at 1:100 scale, with 60 mm long, 6 mm diameter, 13

gram model projectiles representing 6 m long, 0.6 m diameter, 13 tonne prototype

projectiles (Poorooshasb and James 1989). The tests were conducted in kaolin clay to

assess the penetration depth, deformation pattern and degree of hole closure associated

with dynamic projectile penetration. The results indicated that nose penetrations of at

least 305 mm (30.5 m at prototype scale) were achievable with blunt nosed model

penetrometers impacting a normally consolidated clay sample at 40 m/s at 100 g. These

penetrations were in agreement with penetrations observed in the earlier field trials. It

was also found that the simple semi-empirical depth prediction model suggested by Ove

Arup and Partners (1982) (see Section 2.2.3.5) adequately predicted the projectile

penetration depth in the centrifuge tests.

Despite extensive developmental work which established the concept feasibility, seabed

penetrometers were never utilised in the disposal of high-level radioactive waste.

Disposal of nuclear waste in the sea was subsequently banned and as a result research

efforts in the area ceased. However the methods developed to predict penetrometer

23

embedment may be useful in determining the likely penetration depth of dynamic

anchors in soft seabed sediments.

2.2.3 Embedment Prediction Methods

For typical seabed strength profiles in which the shear strength increases with depth, the

dynamic anchor capacity is heavily dependent upon the depth of penetration achieved

during installation. Hence in order to predict the anchor capacity it is first necessary to

be able to predict the anchor embedment depth reliably. Arising from the seabed

strength characterisation and nuclear waste disposal penetrometer studies, several

methods for predicting the penetration depth of objects into soft seafloor sediments have

been proposed. However, dynamic penetration of fine grained soils is believed to

generate viscous strain rate effects and inertial drag resistance forces which are often

difficult to quantify. These methods adopt various approaches towards accounting for

strain rate and inertial drag effects during soil penetration.

2.2.3.1 Strain Rate Effects

It is generally observed that, under undrained conditions, an increase in the strain rate

results in an increase in the shear strength (Casagrande and Wilson 1951, Graham et al.

1983, Sheahan et al. 1996). The dependence of shear strength on the applied rate of

strain has long been recognised and is supported by a large database of vane shear

(Biscontin and Pestana 2001) and triaxial compression tests (Sheahan et al. 1996). The

effect of shear strain rate ( )γ& on the undrained shear strength of clay (su) may be

expressed using a semi-logarithmic function given by:

γγλ+=ref

ref,uu log1ss&

& (2.5)

where su,ref is the undrained shear strength at the reference strain rate (refγ& ) and λ is a

strain rate parameter representing the increase in shear strength per log cycle increase in

strain rate (Graham et al. 1983). There are arguments however, both from physical

principles (Mitchell 1993) and to avoid problems at low strain rates for the use of an

alternative inverse hyperbolic sine function, expressed as

24

γγλ′+= −

0

10uu sinh1ss

&

& (2.6)

Adopting λ’ = λ / ln(10), this expression reverts closely to Equation 2.5 for strain rates

greater than the threshold strain rate (0γ& ), but leads to rapidly decaying strain rate

effects below the threshold rate (Einav and Randolph 2006). Sheahan et al. (1996) noted

the concept of a threshold strain rate below which the rate effect disappears; the

subscript ‘0’ has been used to emphasise that su0 is a true minimum shear strength at

very low strain rates.

The variation in shear strength with strain rate can alternatively be represented by a

power law expression (Biscontin and Pestana 2001):

β

γγ=ref

ref,uu ss&

& (2.7)

The semi-logarithmic function is the most commonly adopted model for analysing rate

effects in clay. Sheahan et al. (1996) reported values of λ from a database of triaxial

compression tests of up to 0.17 for strain rates ranging from 0.0014 – 670 %/hr, while

Biscontin and Pestana (2001) gave values of λ from 0.01 – 0.60 for a database of vane

shear tests conducted at rotation rates of 0.06 – 3000 °/min.

Strain rate effects are an important consideration in assessing the penetration of objects

into the seabed, as they dictate the mobilised shear strength and therefore resistance to

penetration. Whilst the shear strength is known to increase with strain rate, assuming the

deformation pattern remains constant during penetration, it is reasonable to assume that

the strain rate is proportional to the velocity (True 1976). True (1974) was the first to

account for strain rate effects in predicting the penetration of objects into the seabed,

using an empirical approach to determine the strain rate effects from model

penetrometer tests in soft clay (see Section 2.2.3.4). The semi-logarithmic formulation

in Equation 2.5 has since been adopted in centrifuge model tests of dynamic anchors in

kaolin clay (Lisle 2001, Wemmie 2003, Richardson 2003, O'Loughlin et al. 2004b).

Back-calculated values of λ from the centrifuge tests indicate an increase in shear

strength ranging from 3 – 36 % per log cycle increase in anchor velocity. The wide

25

range of back-calculated strain rate parameter values highlights the difficulties

associated with determining strain rate effects in clay.

Strain rates relevant for in situ tests, laboratory tests and operational conditions cover an

extremely wide range, typically 6 to 8 orders of magnitude. Typical strain rates in

triaxial compression tests of 1 %/hr (3 × 10-6 s-1) are generally several orders of

magnitude lower than strain rates for in situ vane tests of approximately 2 × 10-3 s-1

(Einav and Randolph 2006). Strain rates associated with the dynamic installation of

seabed penetrometers may be considered proportional to v/D. Hence for a dynamic

anchor with a diameter of 1.2 m, an average strain rate during installation in the order of

10 s-1 is likely. This represents four and seven fold increases in the order of magnitude

over strain rates for triaxial compression and vane shear tests respectively. It is therefore

difficult to extrapolate potential strain rate effects from laboratory tests for use in

predicting the embedment depth of projectiles in fine grained seabed sediments unless

comparable strain rates are achieved.

Evidence suggests that strain rate effects are not constant for a given material but

actually increase with increasing strain rate. It has been shown that for vane tests

conducted at different rotation rates, the semi-logarithmic function in Equation 2.5 with

λ ≈ 0.1 adequately captures the shear strength rate dependence in the vicinity of the

conventional rotation rate of 0.1 °/s; at higher rates, however, the rate effect increased to

λ ≈ 0.2 (Biscontin and Pestana 2001). An increase in the strain rate effect with

increasing strain rate was also observed in model penetrometer tests by True (1976).

Biscontin and Pestana (2001) noted that the power law rate formulation in Equation 2.7

provided a better fit to their vane data over several log cycles of rotation rate.

Through seabed MIP tests (Section 2.2.1.2), Dayal and Allen (1975) found that the rate

effect for the skin friction component of penetrometer resistance was greater than the

rate effect for the nose bearing resistance component. Therefore it is acknowledged that

separate rate dependent functions for the bearing and frictional resistance during seabed

penetration may be more appropriate than the use of a single rate function for both

resistance components. However it is difficult to differentiate the rate dependence of

each component and as such the bearing and frictional rate effects are typically

combined in a single rate function (O’Loughlin et al. 2004b).

26

2.2.3.2 Inertial Drag

During the seabed penetration of projectiles, soil is displaced from the path of the

advancing projectile. Soil elements are accelerated from rest to a velocity sufficient to

move them out of the path of the projectile. The force required to accelerate the soil

elements is known as an inertial force. The reaction to the inertial force produces a

resistance force on the projectile. Inertial drag resistance in soil is analogous to the

hydrodynamic drag experienced by an object passing through water. Considering the

very soft, viscous clay typically present at the seabed surface it seems reasonable to

assume that an inertial drag force exists during penetration, despite a lack of

experimental justification.

Inertial drag resistance terms have been included in penetration analyses by True (1976)

and Ove Arup and Partners (1983). In each case the inertial drag resistance has been

evaluated using the expression:

2pD2

1d vACF ρ= (2.8)

where CD is the drag coefficient and ρ is the soil density. The most important

consideration in assessing the inertial drag resistance force acting on a projectile during

penetration is the drag coefficient. The drag coefficient is essentially a function of the

projectile geometry and surface roughness (True 1976); however, it is also dependent on

the Reynolds number (Re) of the associated flow.

ν

= vDRe (2.9)

where D is the projectile diameter and ν is the kinematic viscosity of the fluid.

During the transition of a seabed penetrometer from the water into the soil, the viscosity

of the medium through which the projectile is passing will change and as such there will

be an associated change in the Reynolds number. This suggests that there should be

separate drag coefficients for projectile motion through the water and the soil. However

the same drag coefficient is typically adopted for projectiles passing through both

media. This is a reasonable assumption provided the change in Reynolds number is

minimal and given the fact that the inertial drag resistance is expected to account only

for a relatively minor proportion of the total penetration resistance. For a range of

27

projectile velocities and geometries, True (1976) recommended a drag coefficient of 0.7

to account for both soil and water inertia effects. Hydrodynamic studies conducted on

nuclear waste disposal penetrometers during the 1980s indicated considerably smaller

drag coefficients in the order of 0.15 – 0.18 for the ESP (Freeman et al. 1984), whilst

similar studies on Deep Penetrating Anchors (DPAs) indicate a drag coefficient of 0.63

for a four fluke steel anchor in water (Øye 2000).

2.2.3.3 Young's Method

In the early 1960s SNL commenced an earth penetration research programme with the

objective of developing the technology to permit the design of a nuclear earth

penetrating weapon (EPW). As part of this project, empirical equations were developed

to predict the depth of penetration of projectiles into concrete and natural earth

materials. The development of the empirical equations was based on an extensive

database of full scale earth penetration tests and an assumed form of the depth

prediction equation, including assumptions as to which parameters influenced

penetration.

The basic equations first published by Young (1969) have varied little over the past 40

years, although the test database has been expanded and new target materials considered

such as ice, frozen soil and weathered rock. Revised empirical penetration equations

were published by Young (1981) and then later revised again by Young (1997). A

number of assumptions apply to the application of these equations:

• The projectile remains intact during penetration.

• The projectile follows a stable trajectory, i.e. no tumbling or large changes in

direction.

• The impact velocity is less than 4000 ft/s (1219 m/s).

• The equations may not be accurate for penetrations less than approximately three

projectile diameters.

• The equations are not valid for water or air penetration.

• The equations are not valid for armour penetration.

28

• The minimum projectile mass is approximately 5 lbs (2.3 kg) for soil and 10 lbs

(4.6 kg) for rock, concrete, ice and frozen soil targets.

For a uniform layer of soil, the penetration depth can be predicted using Equations 2.10

and 2.11 (Young 1997). For vi < 200 ft/s (61 m/s)

( )2i

5

7.0

ps v1021ln

A

mSNK3.0z −×+

= (2.10)

and for vi ≥ 200 ft/s (61 m/s)

( )100vA

mSNK00178.0z i

7.0

ps −

= (2.11)

where z is the penetration depth in ft, S is the target penetrability constant (see Table

2.1), N is a nose performance coefficient (see Equations 2.13 and 2.14), vi is the impact

velocity in ft/s, m is the projectile mass in lbs, Ap is the cross-sectional area of the

projectile in ft2 and Ks is a correction factor for lightweight projectiles, which for m <

60 lbs (27 kg) is given by:

4.0s m2.0K = (2.12)

For all other projectiles, Ks = 1.

Values of the nose performance coefficient were developed based on soil penetration

test data (Young 1997). For ogive shaped noses

56.0D

L18.0N tip += (2.13)

and for conical shaped noses

56.0D

L25.0N tip += (2.14)

where Ltip is the length of the projectile nose or tip in ft.

A major criticism of the Young penetration equations is that the target or soil

penetrability constant (S) has no physical relevance in terms of standard soil properties.

29

Whilst an extensive database of soil penetration tests exists, it was found to be more

difficult to estimate S for soil media than for rock or concrete. The accuracy of the

proposed empirical equations is heavily dependent on the accuracy with which the value

of S can be determined (Young 1969). Soil penetrability values for a number of typical

soil types are provided in Table 2.1. The value of S is assumed constant for a given

target material despite the fact that the strength of certain materials varies with depth

and strain rate. The Young penetration equations also fail to account for the length of

the projectile, which determines the surface area of the object available to provide

frictional resistance to penetration. Increasing the projectile length would be expected to

increase the frictional resistance and ultimately lead to lower penetration depths.

Consequently this method has rarely been used in predicting the embedment depth of

seabed penetrometers.

Target Material Description S

Dense, dry, cemented sand 2 - 4

Sand without cementation, very stiff and dry clay 4 - 6

Moderately dense to loose sand, no cementation 6 - 9

Soil fill material, various levels of compaction 8 - 10

Silt and clay, low to medium moisture content 5 - 10

Silt and clay, moist to wet 10 - 20

Very soft, saturated clay - very low shear strength 20 - 30

Clay marine sediments - Gulf of Mexico 30 - 60

Table 2.1 Soil penetrability of typical soil types (after Young 1997)

2.2.3.4 True's Method

During the 1970s the NCEL commenced a programme of research investigating the

penetration of projectiles into the seafloor with a view to establishing a new anchoring

technique (True 1974). It was recognised that the phenomenon of penetration into soils

was directly relevant to the performance of direct embedment anchors and that whilst

methods existed for predicting projectile embedment, these relationships were not

necessarily directly applicable to this problem. Accurate depth predictions were found

to be essential in evaluating the holding capacities attainable. A technique was

presented for determining the penetration of projectiles into the seafloor by considering

Newton's second law of motion and the forces acting on the projectile during

30

penetration (NCEL 1985). Early versions of this method (Schmid 1969, Migliore and

Lee 1971) were modified by True (1976) to adapt the technique to velocities up to 400

ft/s (122 m/s). The method considered the static forces resisting projectile penetration

and also accounted for strain rate effects on the soil shear strength, remoulding of the

soil on the sides of the projectile and inertial drag effects as the projectile passed

through the soil (NCEL 1985). The method was considered applicable for objects

impacting the seabed at velocities greater than 3 ft/s (0.9 m/s). At lower velocities,

dynamic effects were considered negligible and static penetration techniques were

recommended.

True’s method, as published in the NCEL Handbook for Marine Geotechnical

Engineering (NCEL 1985), defined the net downward force (F) on the projectile as the

difference between the submerged weight of the projectile (Ws) and the combined soil

resistance terms

dsbs FFFWF −−−= (2.15)

where Fb is the tip or nose bearing resistance, Fs is the side friction or adhesion

resistance and Fd is the inertial drag resistance.

The tip bearing resistance is obtained from:

ptetip,ub ANSsF = (2.16)

where su,tip is the undrained soil shear strength at a depth of D/2 below the projectile tip,

Se is the strain rate factor, Ap is the cross-sectional area of the projectile and Nt is a

dimensionless nose resistance factor given by:

10D

z2.01

L

D2.015Nt ≤

+

+= (2.17)

Assuming no separation between the soil and the side of the projectile during

penetration, the side friction or adhesion resistance is obtained from:

set

ave,us AS

S

sF

= (2.18)

31

where su,ave is the undrained soil shear strength averaged over the length of the projectile

in contact with the soil, St is the soil sensitivity (i.e. the ratio of the undisturbed

undrained shear strength to the remoulded shear strength) and As is the side surface area

of the projectile. True (1976) accounted for separation between the projectile and the

soil by including a side adhesion factor at high penetration velocities. This factor was

not included in the version published by NCEL (1985).

The undrained shear strength of fine grained soils is known to increase with an increase

in strain rate. True (1976) derived an empirical expression for the strain rate factor from

penetration test data

( )[ ]1

CDsvC

11

SS

5.0oeque

*e

e ≥

++

= (2.19)

where Se* is the maximum strain rate factor, Ce is an empirical strain rate coefficient, v

is the velocity of the projectile at the start of the increment (in ft/s), su is the undrained

soil shear strength (in lbf/ft2) equal to su,tip or su,ave depending on whether the expression

is modifying the bearing or frictional resistance, Deq = (4 Ap/π)0.5 is the equivalent

projectile diameter (in ft) and Co is an empirical strain rate constant. For long cylindrical

penetrometers, Se* = 4, Ce = 4 lbf.s/ft2 and Co = 0.11 (NCEL 1985)

The inertial drag force during penetration is given by Equation 2.8.

As the major forces resisting penetration are depth or velocity dependent, an iterative

procedure is used to solve for the projectile penetration. Consequently True’s method

provides an advantage over Young’s empirical method in that a complete velocity

profile with depth is obtained rather than just a final embedment value.

Modifying Newton's second law to eliminate the time term, the net downward force on

the projectile can be related to the deceleration

=dz

dvmvF (2.20)

where m is the penetrometer mass and dv/dz is the instantaneous change in velocity

with depth. Selecting an appropriate depth increment (∆z), the change in velocity can be

determined as:

32

∆=∆i

ii v

F

m

zv (2.21)

The velocity for the (i+1)th increment is therefore estimated as

i1i1i v2vv ∆+= −+ (2.22)

However, in order to commence the iterative calculation procedure, the velocity of the

projectile at the end of the first increment (v1) must be approximated as:

( )

−−−

+= 1d1s1b1s

001 FFFW

m

z

v

1vv (2.23)

where v0 is the impact velocity of the penetrometer and Ws1, Fb1, Fs1 and Fd1 are the

submerged weight, bearing resistance, side friction resistance and inertial drag

resistance values for the first penetration increment. This approximation is then used to

calculate the inertial drag force and the first iteration can be completed. The process

continues until a negative velocity is obtained, in which case the penetration depth is

calculated by interpolating between the last two velocity values.

−∆+=

+1ii

ii vv

vzzz (2.24)

A flow chart outlining the calculation procedure for this method is shown in Figure

2.10.

True’s method was subsequently modified to include the semi-logarithmic rate function

(Lisle 2001, Wemmie 2003, Richardson 2003, O'Loughlin et al. 2004b, Cunningham

2005, Aubeny and Dunlap 2003, Shi 2005, Aubeny and Shi 2006) presented in Section

2.2.3.1 and expressed as:

( ) dsbfs2

2

FFFRWdt

zdm −+−= (2.25)

where Rf is the strain rate function in terms of penetration velocity given by

λ+=

reff v

vlog1R (2.26)

33

where vref is the velocity at which the reference penetration resistance was assessed.

In both the original formulation (NCEL 1985) and the modified version (Lisle 2001,

Wemmie 2003, Richardson 2003, O'Loughlin et al. 2004b, Cunningham 2005), the

strain rate parameter was back-analysed from penetrometer test data. However,

significant variation in the strain rate parameter was identified across test series,

demonstrating the uncertainty associated with strain rate effects in fine grained soils.

This uncertainty, particularly at very high strain rates, ultimately results in uncertainty

in the prediction of penetrometer embedment depths. Strain rate effects have been

discussed in more detail in Section 2.2.3.1.

2.2.3.5 Ove Arup and Partners Method

A method for calculating penetrometer embedment was proposed as part of the

feasibility study commissioned by the Department of the Environment investigating the

use of free-fall penetrometers for the disposal of high-level radioactive waste in seabed

sediments (Ove Arup and Partners 1982). The method involved the development of

separate equations for partial and full embedment. Upon full embedment the

accelerating force acting on the projectile can be related to semi-empirical soil

parameters, through the governing differential equation:

222

2

BzAdt

zdm +=− (2.27)

where t is the time after installation and A2 and B2 are given by:

ded

2

2 DLkkN4

DA απ+π= (2.28)

( )( ) ssea,udsea,ued

2

2 W2

LksDLkLsN

4

DB −

+απ++π= (2.29)

and

t

chdcded S

NNN += (2.30)

where Ned is a dynamic nose and tail bearing capacity factor, Ncd is a dynamic nose

bearing capacity factor, Nchd is a dynamic tail resistance factor, St is the soil sensitivity,

34

αd is the dynamic side adhesion factor, su,sea is the undrained shear strength at the seabed

and k is the undrained shear strength gradient such that the undrained shear strength at

any depth, z, below the seabed is given by

kzss sea,uu += (2.31)

Ove Arup and Partners (1982) adopted closed-form solutions of the differential equation

(Equation 2.27) to predict the final penetrometer embedment depth; however,

Poorooshasb and James (1989) present the predicted penetration depth with time after

installation as:

( )( ) ( )KtsinK

v1Ktcos

A

Bz i

2

2 +−= (2.32)

where

m

AK 22 = (2.33)

The projectile velocity can be determined by differentiating Equation 2.32 with respect

to time, which when combined with the displacement data provides a complete

penetration velocity profile with depth given by

( ) ( )KtcosvKtsinKA

Bv i

2

2 +

−= (2.34)

This method attempts to account for the soil strength dependence on strain rate by

utilising empirically derived dynamic bearing resistance and side adhesion factors. The

side adhesion factor was shown to vary with velocity, approaching very low values at

high velocities, indicating a certain degree of separation between the soil and projectile

(Poorooshasb and James 1989). No consideration of inertial drag effects during

penetration of the soil was provided. Many of these shortcomings were detailed in a

follow up report by Ove Arup and Partners (1983).

35

2.3 PULLOUT CAPACITY

Dynamic seabed penetrometers for in situ strength measurement and nuclear waste

disposal purposes were largely expendable in nature. Consequently very little

information exists regarding the pullout capacity of objects penetrating the seabed

following free-fall installation. However, geometric similarities between dynamically

installed anchors and driven piles suggest that the anchor capacity may be assessed

using conventional pile capacity techniques. Despite discrepancies in the rate of

installation between dynamic anchors and driven piles, these techniques provide a basis

for considering the expected anchor capacity and the effects of the installation rate on

this capacity. Two methods are in common use for predicting the capacity of offshore

piles in clay:

1. American Petroleum Institute (API) method (API 2000)

2. Marine Technology Directorate (MTD) method (Jardine and Chow 1996)

For both methods the ultimate vertical tensile capacity (Fv) is calculated as the sum of

the submerged weight of the pile (Ws) and the end bearing (Fb) and shaft friction (Fs)

resistances:

sbsv FFWF ++= (2.35)

For piles in tension the tip bearing resistance is often ignored, providing conservative

capacity estimates; however a reverse end bearing mechanism may generate

considerable short-term resistance to tension loading and should be considered in the

analysis. Consolidation following installation and long-term sustained and cyclic

loading conditions are also likely to affect the capacity. These effects are important

considerations in the accurate prediction of capacity, and at present are not wholly

addressed by either the API or MTD method.

2.3.1 American Petroleum Institute Method

According to API recommended guidelines for pile capacity in cohesive soils (API

2000), the tip bearing resistance is given by

36

ptip,ucb AsNF = (2.36)

where Nc = 9 is the tip bearing capacity factor, su,tip is the undrained shear strength at the

pile tip and Ap is the projected area of the pile.

In addition, the shaft friction resistance generated by a pile is given by

save,us AsF α= (2.37)

where su,ave is the average shear strength over the embedded pile shaft length, As is the

embedded surface area of the pile and α has been determined from empirical

correlations with an extensive database of pile test results compiled by Randolph and

Murphy (1985) and can be expressed as

For 1s

v

u ≤σ′

1s

5.05.0

v

u ≤

σ′=α

(2.38)

For 1s

v

u >σ′

1s

5.025.0

v

u ≤

σ′=α

(2.39)

where σ′v is the vertical effective stress.

The API design method is simple to apply, and as such remains widely used in the

offshore industry.

2.3.2 Marine Technology Directorate Method

The MTD method (Jardine and Chow 1996) was devised to address some of the

reported weaknesses of the API method and is currently becoming more widely used in

Europe. The penetration of closed ended piles is analogous to the penetration of a cone

penetrometer. Hence it appears logical that the unit base resistance for a pile will be

linked to the unit cone tip resistance. The MTD load test database suggests that for

undrained loading, the pile bearing resistance should be estimated as:

pcb Aq8.0F = (2.40)

37

where qc is the unit cone tip resistance. It should be noted that the value of qc adopted in

Equation 2.40 should be the cone tip resistance averaged over 1.5 pile diameters above

and below the pile tip.

The MTD method uses empirical correlations based on soil properties derived from high

pressure oedometer tests to determine the shaft friction resistance. The horizontal

effective stress after installation and equalisation (σ′hc) is given by:

0vchc K σ′=σ′ (2.41)

where σ′v0 is the in situ vertical effective stress and Kc is given by

[ ]20.0

42.0vyc r

hYSRI870.0YSR016.02.2K

∆−+= (2.42)

where h is the vertical distance from the pile tip, r is the pile radius and YSR is the yield

stress ratio given by

0v

vyYSRσ′σ′

= (2.43)

where σ′vy is the yield stress and

( )tvy SlogI =∆ (2.44)

A lower limit of h/r = 8 should be used in Equation 2.42, with the shaft resistance

assumed constant for a vertical distance of four diameters from the pile tip. Load tests

indicate that the horizontal effective stress typically drops by approximately 20 %

during loading; hence the horizontal effective stress at failure (σ′hf) is given by

hchf 8.0 σ′=σ′ (2.45)

The local shear stress (τsf) is then estimated as

δσ′=τ tanhfsf (2.46)

where δ is the interface friction angle, which can be determined from interface ring

shear tests. Ultimately the shaft friction resistance can be expressed as

38

ssfs AF τ= (2.47)

where sfτ is the average shear stress along the embedded shaft length.

The MTD method is more difficult to apply than the API method since it requires the

use of more sophisticated soil properties. However, the design correlations reflect the

processes governing pile capacity more closely. In particular the effects of friction

fatigue are captured by the decay of Kc in Equation 2.42 with increasing h/r. The

influence of the yield stress ratio and soil sensitivity is captured by empirical

correlations. The MTD method was calibrated against a large database of recent load

tests, and is therefore likely to give more accurate estimates of pile capacity than the

API method, if information regarding the appropriate input parameters is available.

2.3.3 Consolidation Effects

The capacity of piles in fine grained soils is known to increase with time following

installation (Soderberg 1962). During pile (and dynamic anchor) installation, significant

excess pore pressures are generated in the soil in the vicinity of the pile due to the

combined effects of changes in mean effective stress due to shearing and increases in

total stress as soil is forced outwards to accommodate the volume of the pile (Randolph

2003). The low effective stress in the soil leads to low frictional resistance in the short

term. Subsequent to installation however, the excess pore pressures gradually dissipate

and the shear strength of the soil increases due to the combined effects of thixotropy and

consolidation. This time dependent increase in capacity is known as setup.

Evidence suggests that generally, the capacity of piles in clay immediately following

driving ranges from approximately 25 – 45 % of the ultimate pile capacity (Esrig et al.

1977, Bogard and Matlock 1990). However, Seed and Reese (1957) (as cited in Fleming

et al. 1985) reported much lower short-term capacities of approximately 10 % of the

long-term pile capacity (see Figure 2.11). Observations made in laboratory tests on

dynamic anchors indicate short-term capacities of approximately 30 % of the anchor

capacity after complete consolidation (Figure 2.12; Audibert et al. 2006).

Soderberg (1962) showed that the consolidation time was proportional to the square of

the horizontal dimension of the foundation (D) and inversely proportional to the

39

horizontal coefficient of consolidation (ch). Hence the consolidation time (t) is often

expressed in terms of a non-dimensional time factor (T) given by:

2

h

D

tcT = (2.48)

It is generally recognised that for large offshore piles, setup times to achieve full

capacity may be of the order of 1 – 2 years in fine grained seabed soils (Mirza 1999).

By contrast, Jeanjean (2006) has reported 90 % consolidation times for suction caissons

of approximately 30 days. Randolph (2003) showed that dissipation times for open

ended piles and suction caissons are one to two orders of magnitude shorter than for a

closed-ended pile of the same diameter, since the key dimension is the ‘equivalent

diameter’, determined by the volume of steel per unit length of pile. Pipe piles of 2 to 3

m diameter and with a wall thickness of 2.5 % of the diameter have an equivalent

diameter of 0.7 to 1 m. Suction caissons of 5 to 8 m diameter, with wall thicknesses of

0.5 to 1 % of the diameter, have similar equivalent diameters (0.7 – 1.6 m). It appears

therefore that the time required for a dynamic anchor to develop its ultimate capacity

will be significantly longer than that required for a thin-walled suction caisson.

Analytical studies of DPAs conducted by Lieng et al. (1999) reported times for 90 %

consolidation for the anchor shank (shaft) of approximately 180 days (see Figure 2.13),

corresponding to a non-dimensional time factor of T90 = 1.89 with ch = 5.5 m2/yr and D

= 1.2 m. In soil with a similar coefficient of consolidation, 90 % consolidation times of

approximately 30 days for suction caissons with equivalent diameters of 0.7 – 1.6 m,

result in significantly lower T90 values of between 0.18 and 0.92.

Cavity expansion theory describes changes in stresses, pore pressures and displacements

caused by the expansion and contraction of cylindrical or spherical cavities in soil (Yu

2000). Modelling pile installation as the undrained expansion of a cylindrical cavity, the

effective and total stress changes during both the expansion of the cavity and

subsequent consolidation of the soil around the pile, can be estimated (Randolph et al.

1979). Randolph and Wroth (1979) presented a closed form solution for the radial

consolidation of soil around a driven pile, leading to the development of a realistic

method for modelling the dissipation of excess pore pressures following installation.

The dissipation of the excess pore pressures is governed by the extent of the pore

pressure zone surrounding the pile which is quantified by the rigidity index, Ir = G/su

40

(where G is the shear modulus of the soil). Theoretical consolidation curves for a solid

driven pile at typical values of Ir ranging from 50 to 500 (Randolph 2003) are presented

in Figure 2.14. These indicate non-dimensional consolidation times for 50%

consolidation of T50 = 0.42 to 2 and 90% consolidation of T90 = 6 to 32. The range of

T90 values is significantly higher than the back-calculated value of T90 = 1.89 from the

analytical studies of DPA consolidation, suggesting that even longer consolidation times

are likely for dynamic anchors than have been reported by Lieng et al. (1999).

The effects of setup in offshore foundation design are well recognised but often not

adequately accounted for. Both the short-term capacity and the time required for

capacity regain are important considerations in assessing the performance of the

anchoring system. Information regarding setup following the seabed penetration of

projectiles is limited and as such experience with piles and other offshore foundations

should be utilised to provide a better understanding of the effects of setup on the

capacity of dynamically installed anchors.

2.3.4 Long-Term Sustained Loading

Offshore foundations are subjected to sustained loading, which may govern the design

in deepwater, particularly in the Gulf of Mexico where loop currents may continue for

periods of several days or even weeks (Eltaher et al. 2003, Clukey et al. 2004). Apart

from loop currents, anchor piles may also be subjected to sustained loading in the form

of pre-tension in TLP tendons (see Section 1.2.3). It has been reported that sustained

tensile loading of 30 % of the ultimate pile capacity may be sufficient to induce a creep

related pile failure (Edil and Muchtar 1988).

Sustained loading may lead to a reduction in the foundation capacity due to the adverse

effects of creep on the soil shear strength. Conversely, longer duration loading may lead

to further consolidation of the soil surrounding the foundation resulting in higher shear

strengths and therefore higher capacities. Hence any examination of the influence of

sustained loading on the capacity of dynamically installed anchors should consider the

effects of both creep and consolidation. Analysis of the response of suction caissons in

clay to sustained axial tensile loading indicates a reduction in the caisson capacity

(Huang et al. 2003, Clukey et al. 2004, Chen 2005), which may be attributed partly to

creep and partly to a reduction in the passive suction, developed from the upward

41

motion of the caisson under tensile loading, due to the dissipation of negative excess

pore pressures (Huang et al. 2003).

Very little information exists regarding the behaviour of dynamically installed

projectiles under long-term sustained loading. Lieng et al. (1999) state that in order for

DPAs to be a viable concept the anchor must be capable of withstanding long-term

static loads of up to 3 MN, as opposed to 4 - 5 MN under short-term loading. A single

long-term sustained loading test conducted on a model dynamic anchor in the centrifuge

indicated a 19 % increase in capacity for sustained loads of up to 95 % of the short-term

capacity (Lisle 2001). It is recognised however that this increase in capacity may be due

to post-installation consolidation effects, and as such it is difficult to conclude what

effect the sustained loading had on the ultimate anchor capacity. It is clearly evident that

further research examining the effects of long-term sustained loading on dynamically

installed anchor capacity is necessary.

2.3.5 Cyclic Loading

Floating offshore structures will also be subjected to cyclic loads due to the influence of

wind, waves, and currents. Under extreme storm conditions these loads are significant

and may lead to failure of the foundation system. Cyclic environmental loads may result

in two potentially compensating effects: cyclic degradation of soil shear strength due to

the accumulation of excess pore pressures (Sangrey 1977, Eltaher et al. 2003, Huang et

al. 2003) and soil strength increase due to loading rate effects (Huang et al. 2003,

Poulos 1988). In field tests on piles in clay, Bjerrum (1973) and Bea (1980) indicated

that the rate of load application has a significant impact on the pile capacity; the higher

the loading rate, the greater the pile capacity. In situations where relatively rapid cyclic

loading is being applied to a pile, the beneficial effects of the high loading rate may

offset the effects of cyclic degradation. Hence simultaneous consideration of the effects

of both cyclic degradation and rate of loading are necessary in order to assess the

response of piles to cyclic loading.

Bea et al. (1982) suggested that cyclic loading results in a maximum of only 10 – 20 %

reduction in axial pile load capacity, but with a definite trend of increasing pile head

settlement with increasing number of cycles and level of cyclic loading. It is also

recognised that two-way cyclic loading (compression and tension) is likely to have a

42

more significant impact on pile capacity and stiffness than one-way cyclic loading

(tension only). Small-scale laboratory and field tests on piles in clay suggest that

reductions in capacity significantly greater than 20 % may occur, particularly in piles

subjected to two-way cyclic loading (Holmquist and Matlock 1976, Steenfelt et al.

1981).

Despite substantial research into the cyclic response of anchor piles, no previous studies

investigating the behaviour of dynamically installed anchors or seabed penetrometers to

cyclic loading have been undertaken. Given the requirements for offshore structures to

withstand extreme cyclic loading events, an evaluation of the performance of dynamic

anchors under cyclic loading conditions is considered essential.

2.4 DYNAMICALLY INSTALLED ANCHORS

Commercial development of dynamic seabed penetrometers as an offshore anchoring

system commenced in the late 1990s, as a direct result of the oil and gas industry need

for a cost effective deepwater anchor. Dynamically installed anchors have since been

identified as the most promising, present day, deepwater anchoring concept in terms of

the cost and complexity of installation (Ehlers et al. 2004). Several different forms of

dynamically installed anchor have been devised, the most notable of which are the

torpedo anchor, which has seen widespread use offshore Brazil, and the Deep

Penetrating Anchor, which has been the subject of field trials in Norwegian waters.

Although the torpedo anchor and Deep Penetrating Anchor are essentially identical

concepts, their respective developments in Brazil and Europe are addressed separately

below.

2.4.1 Torpedo Anchor

The torpedo anchor originated in 1996 (Medeiros 2001, 2002) as a cost effective

anchoring system for flexible risers and floating structures in soft seabed sediments.

Torpedo anchors feature a tubular steel pile, with or without vertical steel fins, fitted

with a conical tip and filled with scrap chain or concrete (Medeiros 2001, 2002; Figure

2.15). The anchor becomes completely buried within the seabed sediments by self

weight dynamic penetration following free-fall through the water column from drop

43

heights of up to 150 m. Loads are applied to the anchor via a mooring line attached to a

padeye located at the top of the anchor, with resistance predominantly provided by

friction developed at the anchor-soil interface.

Full scale field tests (Figure 2.16) were performed in the Campos Basin, offshore Brazil

in water depths of up to 1000 m to analyse the penetration performance and holding

capacity of torpedo anchors (Medeiros 2001, 2002). From a drop height of 30 m above

the seabed, finless 762 mm diameter, 12 m long torpedo anchors with a dry weight of

400 kN achieved average tip penetrations of:

• 29 m in normally consolidated clay;

• 13.5 m in overconsolidated clay;

• 15 m in uncemented calcareous sand;

• 22 m in 13 m of fine sand overlying normally consolidated clay.

The average embedment depth measured in the sand overlying clay is somewhat

surprising given the embedments measured in the other soil types.

Full scale load tests in normally consolidated clay indicate that for an average tip

embedment of 20 m, horizontal loading at the seabed of 762 mm diameter, 12 m long,

240 kN dry weight torpedo anchors resulted in capacities of 3.7 – 4.6 times the anchor

dry weight immediately following installation, increasing by a factor of approximately 2

after ten days consolidation (Medeiros 2001, 2002). For an average tip embedment of

29 m, 45° loading of 1.07 m diameter, 12 m long, 620 kN dry weight torpedo anchors

resulted in capacities of 3.1 – 3.4 times the dry weight immediately after installation,

with a setup factor of approximately 2 after eighteen days. Vertical pullout tests of the

620 kN dry weight torpedo anchor indicated an average capacity of 1.3 times the dry

weight immediately after installation, with a setup factor of 2.5 – 2.75 after ten days.

Following the results of these load tests, torpedo anchors were certified for use on

floating platforms in soft clay.

Medeiros (2001, 2002) reported the first application of torpedo anchors for the

anchoring of flexible risers using 762 mm diameter, 12 m long finless torpedo anchors.

The use of torpedo anchors for flexible risers significantly reduces flexible flowline

length, since without anchoring the floating facility movement must be resisted by

44

friction developed between the flowline and the soil. Reduced flowline length results in

considerable cost savings and may actually lead to the financial viability of previously

unexploitable fields. Medeiros (2002) reported significant cost savings from the

installation of more than 90 torpedo anchors for flexible riser applications. Similar

anchors have also been used successfully to anchor mono-buoys and ships in shallow

water. In addition, a larger torpedo anchor with four vertical fins was produced for

anchoring mobile offshore drilling units (MODUs) and a 1.07 m diameter, 15 m long,

950 kN torpedo anchor with larger fins was developed for use on floating production

systems. Recently, the P-50 FPSO became the first floating facility to be permanently

moored using torpedo anchors. P-50 is situated in 1240 m of water in the Albacora

Leste field in the Campos Basin and adopted a specifically designed and tested 960 kN

torpedo anchor (Brandão et al. 2006).

Limited torpedo anchor test data and analysis is available in the public domain. It is

likely that this is due to intellectual property issues. The little information that is

available is difficult to assess due to a lack of detail in the published geotechnical soil

properties at each test site. Torpedo anchors represent the only current, full scale,

commercial application of dynamic seabed penetrometers for anchoring purposes, with

extensive use in Brazilian waters.

2.4.2 Deep Penetrating Anchor

Deep Penetrating Anchors (DPAs) were first proposed in 1999 as a simple and cost

effective alternative to conventional deepwater anchoring systems for floating structures

(Lieng et al. 1999). Conceptually similar to the torpedo anchor, the DPA features a dart-

shaped, thick-walled steel cylinder with flat plates (flukes) attached to its upper section

(Figure 2.17). At prototype scale the DPA is 10 – 15 m long, with a diameter of

approximately 1.2 m and weighing in the order of 50 – 100 tonnes. The anchor is

lowered to a predetermined height above the seabed and then released and allowed to

free-fall (Figure 2.18). The anchor subsequently penetrates the seabed sediments via self

weight and the kinetic energy gained during free-fall. Once installed the majority of the

uplift resistance is provided by the friction developed at the anchor-soil interface.

Lieng et al. (1999) employed the semi-empirical method proposed by True (1974) to

evaluate the potential embedment depth of DPAs in soft clay seabed sediments (Section

45

2.2.3.4). The anchor capacity was estimated using the American Petroleum Institute

(API 2000) guidelines for pile capacity (Section 2.3.1) and these predictions were

compared with results from three dimensional finite element analyses (Lieng et al.

2000). Associated hydrodynamic studies investigated the drag, terminal velocity and

hydrodynamic stability of the DPA during free-fall through the water column (Øye

1999). The results of the feasibility study indicated that the DPA was a viable solution

for the deepwater mooring of floating offshore structures, concluding that (Ehlers et al.

2004):

• The DPA is deployable in practically any water depth.

• The DPA is applicable for taut-leg mooring, because long-term loading of the

anchor does not reduce the short-term undrained capacity.

• The anchor/soil system shows greater ductility to loading than anchor solutions

that are situated near the mudline, which may experience sudden failure and

anchor pullout due to loss of suction from consolidation effects.

• The anchor chain does not alter the behaviour of the anchor during descent and

the anchor velocity is not noticeably reduced due to chain drag.

During 2004 several 1:3 reduced scale model DPA field tests were conducted in

Trondheim Fjord, Norway in over 300 m of water (Figure 2.19). Instrumented and

‘dummy’ DPAs, 4.4 m long, 0.4 m in diameter and weighing 27 kN were installed and

left for various periods of time prior to extraction. The instrumented DPA contained

devices for measuring the anchor inclination, acceleration and soil pore pressures. The

results of these tests are yet to be published.

The DPA concept is currently limited in its application due to a lack of field and

laboratory data. Consequently, uncertainty exists regarding the installation behaviour of

the DPA, both in terms of the depth of penetration and the final anchor orientation.

Ultimately this lack of data prevents the calibration of theoretical embedment and

capacity models, thereby further restricting the commercial development of the concept.

46

2.4.3 SPEAR Anchor

Zimmerman and Spikula (2005) proposed a dynamically installed anchor design,

identified as the self-penetrating embedment attachment rotation (SPEAR) anchor (also

known as a MIG anchor). The SPEAR anchor is arrow shaped with a padeye located at

approximately half the anchor height that is capable of rotating 360° around the shaft to

orient itself with the direction of loading. The anchor is fitted with retractable fluke fins

(Figure 2.20) allowing the anchor to be adjusted to rotate into the soil and begin diving

at a preferred tension level (Zimmerman 2007). Upon the application of a significant

tensile load, the anchor begins to rotate until the lateral resistance of the lower fins

becomes equal to the lateral resistance of the upper fins. At this stage the anchor

performance is governed by the axial capacity and the anchor dives deeper into the soil.

Under extreme loading the anchor will continue to dive until the required capacity is

achieved.

A full scale field test conducted in the Gulf of Mexico in soft to medium clay using a 9

m long, 3 m fin span anchor with a dry mass of 34,019 kg was recently undertaken

(Zimmerman 2007). The results of the test demonstrated the stability of the anchor

during free-fall.

2.4.4 Physical Modelling

An initial attempt at physically modelling the dynamic anchor installation process was

undertaken by Massey (2000) in kaolin clay at 1 g. Although not able to replicate

prototype impact velocities of 20 – 25 m/s (Lieng et al. 1999) with 1:200 scale model

anchors (based on the idealised DPA design by Lieng et al. 1999), an understanding of

the relationship between anchor impact velocity, penetration depth and holding capacity

was obtained and provided a means of assessing the feasibility of the concept.

A system for centrifuge modelling was then developed (Lisle 2001) allowing prototype

stresses and velocities to be replicated using zero, three and four fluke 1:200 scale

model anchors (Figure 2.21) in the beam centrifuge at The University of Western

Australia (Wemmie 2003, Richardson 2003, O'Loughlin et al. 2004a, O'Loughlin et al.

2004b). These centrifuge tests indicated an approximately linear increase in embedment

with impact velocity and an increase in embedment with decreasing anchor surface area

47

(i.e. number of flukes; Figure 2.22). Somewhat surprisingly, however, the three fluke

model anchors demonstrated higher capacities, normalised by the anchor’s projected

area and the average undrained shear strength over the embedded anchor length, than

the four fluke anchors despite a lower available surface area (Wemmie 2003). Sample

size restrictions in the beam centrifuge limited the number of tests which could be

performed in any one sample. The testing apparatus was therefore adapted for use in the

drum centrifuge, which afforded a sample plan area almost four times larger than that

available in the beam centrifuge (Cunningham 2005). The drum centrifuge apparatus

was used to perform a parametric study on the influence of anchor geometry (diameter

and aspect ratio, i.e. anchor length to diameter ratio) and mass on the geotechnical

performance of dynamically installed anchors (Figure 2.23; Cunningham 2005,

Richardson et al. 2006). The tests highlighted the importance of the anchor mass on the

penetration depth and subsequent holding capacity.

Laboratory testing of DPAs has also been undertaken at the University of Dundee. The

1:200 scale model 1 g tests focused primarily on assessing the relationship between the

kinetic energy of the anchor and the embedment depth with particular attention paid to

the influence of anchor geometry and mass (Nelson 2004, O'Baxter 2005, Small 2007).

Supplementary studies investigated the pullout behaviour of model DPAs under

inclined loading conditions. A series of 1 g experiments conducted in kaolin clay at The

University of Texas at Austin also investigated the influence of anchor geometry and

mass on the embedment and capacity performance of torpedo piles (Audibert et al.

2006). As part of the study the effects of setup following installation were investigated

and indicate a capacity immediately after installation of approximately 30 % of the

ultimate anchor capacity (Figure 2.12).

Given the expense of full scale field trials, physical modelling of dynamic anchor

processes, particularly in the centrifuge, provides a cost effective method for evaluating

anchor performance and the applicability of proposed embedment and capacity

prediction models. To date, however, a relatively small database of model tests exists

and consequently uncertainty remains regarding the geotechnical behaviour of

dynamically installed anchors.

48

2.4.5 Analytical and Numerical Modelling

Much of the dynamically installed anchor research to date has been experimental in

nature. However, in several studies the anchor performance has also been evaluated

using analytical and numerical techniques. In most instances, the anchor embedment

depth has been assessed using True’s method (Section 2.2.3.4) or slight variations on

this (Lieng et al. 1999, Medeiros 2001, Lisle 2001, Medeiros 2002, Wemmie 2003,

Richardson 2003, Araujo et al. 2004, O’Loughlin et al. 2004b, Cunningham 2005,

Audibert et al. 2006, Small 2007). Accounting for both strain rate effects and inertial

drag has been found to be the most reliable embedment prediction method for

dynamically installed anchors. With regard to the anchor capacity, API (2000)

recommended guidelines for pile capacity (Section 2.3.1) have typically been used

(Lieng et al. 1999, Lisle 2001, Wemmie 2003, Richardson 2003, O’Loughlin et al.

2004b, Cunningham 2005, Audibert et al. 2006). The anchor capacity has also been

assessed using three dimensional finite element analyses (Lieng et al. 2000, Medeiros

2001, Medeiros 2002). A potential drawback of the analytical and finite element

capacity prediction methods, however, is that they fail to account for the effects of the

dynamic anchor installation process on the soil and therefore the anchor capacity.

Despite this, these methods have been found to provide reasonable predictions of the

anchor capacity when compared with the results of field and laboratory tests.

Einav et al. (2004) presented numerical analysis of the complete penetration process of

an anchor through the soil stratum. The finite difference approach (implemented in

FLAC; Itasca 2000) incorporated a contact interface formulation in an explicit time-

marching large strain Lagrangean analysis and incorporated a separate equation of

motion to solve for the incremental changes in anchor velocity. The rate-dependent

model assumed a logarithmic increase in soil shear strength due to strain rate effects

(Section 2.2.3.1) whilst the effects of inertial drag were ignored. The numerical results

were validated against experimental data from centrifuge model tests presented in a

companion paper (O'Loughlin et al. 2004a). Somewhat unexpectedly the numerical

analysis indicated that immediately following the cessation of anchor movement within

the soil, negative excess pore pressures exist around the upper portion of the anchor.

Such an effect may detrimentally influence the anchor capacity during consolidation.

49

Unlike the analytical penetration prediction methods presented in Section 2.2.3, which

only produce a velocity profile with depth during penetration, a recently developed

computational fluid dynamics (CFD) approach also provides information about the

pressure and shear distributions along the anchor (Raie and Tassoulas 2006). The CFD

method is capable of modelling the complete installation event including the release and

free-fall through the water column, the transition from the water into the seabed and the

subsequent motion of the anchor through the soil. Utilising a non-Newtonian Bingham

plastic fluid model with a non-zero shear stress at zero strain rate, good agreement was

obtained between the CFD method of Raie and Tassoulas (2006) and the results of

model penetration tests reported by True (1976).

Analytical and numerical methods provide a useful and necessary tool in the

development of the dynamically installed anchor concept. However, calibration of these

methods against experimental field and laboratory test data is necessary. Hence

extending the database of dynamic anchor field and laboratory tests will complement

the development and validation of such analytical techniques.

2.5 SUMMARY

Despite recent research efforts, the concept of dynamically installed anchors is still in its

relative infancy. Dynamically installed anchors have started to be used as anchoring

systems for flexible risers, ships, MODUs and even FPSOs, building on experience

gained with seabed penetrometers for in situ seabed strength measurement and also

studies for the disposal of high-level radioactive waste. With an installation process

which is relatively independent of water depth, they provide a comparative advantage

over conventional deepwater anchoring techniques. However, further development of

the concept, particularly in relation to the application of embedment and capacity

prediction techniques, is required before dynamic anchors achieve widespread

application. This chapter has presented the literature relevant to the development and

implementation of dynamically installed anchors for floating offshore structures,

highlighting shortcomings in current understanding in relation to the objectives of the

current research project.

50

Seabed penetration of projectiles has been considered in various contexts since the

1960s. Much of the earlier available literature is concerned with the development of

instrumented marine penetrometers for the assessment of in situ soil strength properties

or with the use of seabed penetrometers for the disposal of high-level radioactive waste.

Field and laboratory tests of this nature brought about the development of semi-

empirical methods for predicting the penetration depth of streamlined objects into the

seafloor. These methods have demonstrated the importance of considering strain rate

effects and inertial drag resistance during penetration of fine grained seabed soils.

Various methods that account for these effects have since been proposed, mostly based

on empirical fits to experimental test results. A better understanding of the influence of

these effects on the penetration depth of seabed penetrometers is required.

Literature concerning the pullout capacity of seabed penetrometers is scarce. Hence pile

capacity techniques have been adopted to evaluate the capacity of projectiles following

dynamic installation. Based on empirically derived parameters from extensive pile test

databases these methods provide reasonable estimates of the capacity of dynamically

installed anchors at model scale. It is important, however, to consider the effects of

setup due to consolidation and cyclic and sustained loading. These effects are likely to

have a significant impact on anchor capacity.

Two main forms of dynamic anchor exist: the torpedo anchor and the Deep Penetrating

Anchor. Originating at approximately the same time, the main difference between the

two is in the detailed anchor geometry. Torpedo anchors either have no fins or adopt

narrow vertical fins that extend most of the length of the anchor shaft; DPAs on the

other hand incorporate wider fins extending to approximately half the anchor length.

They also differ in terms of the stage of development. Extensive field trials of torpedo

anchors have been carried out, leading to their implementation in a wide variety of

applications as anchors for flexible risers, ships and FPSOs. DPA development,

however, has been limited to analytical studies and a small number of reduced scale

field trials. The cost of field trials has resulted in a move towards physical modelling of

dynamic anchors, both in the laboratory and in the centrifuge. These studies have

investigated the relationship between impact velocity, embedment depth and holding

capacity and sought to optimise the anchor design through consideration of the effects

of anchor mass and geometry. With the aim of providing a reliable design tool, the

51

experimental aspects of dynamic anchor research have been complemented by the

application of analytical embedment and capacity prediction techniques developed for

seabed penetrometers and piles. However, the relatively small amount of data available

has thus far limited the calibration of these methods.

This literature review has highlighted several potential shortcomings in the conceptual

development of dynamically installed anchors:

• A lack of experimental data, both from field and laboratory tests, has resulted in

limited understanding of the soil mechanics processes involved in dynamic

anchor installation.

• A lack of experimental data has restricted the calibration and application of

embedment and capacity prediction models.

• Quantifying and formulating the strain rate dependence of undrained shear

strength in the context of dynamic anchor penetration prediction models is not

straightforward, particularly in view of the several orders of magnitude

difference in strain rate between dynamic anchor installation and standard

laboratory and in situ tests.

• Greater understanding of the inertial drag effects in soil is required to enable

accurate prediction of the anchor embedment depth.

• Setup effects due to post-installation consolidation require examination to permit

accurate prediction of anchor capacity.

• Assessment of the dynamic anchor capacity under cyclic and long-term

sustained loading is essential for further development of the concept.

Dynamically installed anchors have been identified as an attractive option for the

mooring of floating structures in deepwater environments. However, a general lack of

data regarding their performance means that further research is required before

widespread application can be achieved.

53

CHAPTER 3 - EXPERIMENTAL METHODS AND

MODELLING

3.1 INTRODUCTION

Given the lack of available dynamically installed anchor data, a major objective of the

present research was to establish a database of dynamic anchor centrifuge model tests.

The test results would then be used to develop design methods for dynamically installed

anchors. This chapter describes the experimental equipment and methodology adopted

in compiling this database. The chapter introduces the basic principles and scaling laws

of centrifuge modelling and describes the centrifuge facilities used throughout the study.

The soil properties and sample preparation procedures are presented and the

experimental apparatus detailed. A summary of the various model anchors is provided

and the test procedures in both the beam and drum centrifuges are outlined. The chapter

concludes with an overview of the tests conducted during the experimental programme.

3.2 CENTRIFUGE MODELLING

Full scale field testing in offshore geotechnical engineering is often prohibitively

expensive and model tests performed at laboratory scale may be misleading as the

stresses due to self weight may be one or two orders of magnitude lower than those at

prototype scale. As geotechnical behaviour is in many instances dictated by stress level

and stress history (Taylor 1995), it is important to replicate the in situ stresses in the

laboratory model. Geotechnical centrifuge modelling provides a convenient and

economical method for achieving stress and strain similitude between the model and

prototype.

The fundamental principle of centrifuge modelling involves the accurate replication of

prototype body forces and stress conditions in a reduced scale laboratory model, by

54

subjecting a model reduced in scale by a factor n, to a radial acceleration field equal to

ng, where g is the acceleration due to the Earth’s gravitational field (i.e. g = 9.81 m/s2).

That is, if the same soil is used in the model and prototype, for a model subjected to an

inertial acceleration field of ng, the vertical stress at a depth hm will be identical to that

in the corresponding prototype at a depth hp = nhm. This basic scaling law of centrifuge

modelling has been used in conjunction with dimensional analysis to derive scaling laws

for extrapolation of model test results to prototype conditions. A summary of the

common scaling relationships in centrifuge modelling is presented in Table 3.1.

Parameter Scaling Relationship

(model/prototype)

Acceleration n

Length 1/n

Area 1/n2

Volume 1/n3

Mass 1/n3

Stress 1

Strain 1

Force 1/n2

Velocity 1

Density 1

Time (consolidation) 1/n2

Table 3.1 Centrifuge scaling laws (after Schofield 1980, Taylor 1995)

The inertial acceleration field at a radius, r, generated by the angular rotation, ω, of the

centrifuge results in a normal component of acceleration given by

rng 2ω= (3.1)

The variation in centrifuge acceleration with radius results in a stress discrepancy

between the model and prototype. Schofield (1980) showed that this discrepancy could

be minimised by equating the relative magnitudes of the over and under-stresses, by

using an effective radius, i.e. the radius at which the target acceleration level is

achieved, equal to

sample0eff h3

2RR −= (3.2)

55

where Reff is the effective radius, R0 is the radius to the base of the sample and hsample is

the sample height.

Figure 3.1 shows a comparison of the stress variation with depth for the centrifuge

model and the corresponding prototype. It should be noted that the non-linear variation

in stress in the model is exaggerated for clarity. The maximum error in the vertical

stress is given by hsample/6Reff (Taylor 1995). For a sample height of 230 mm and an

effective radius of 1607 mm in the University of Western Australia (UWA) beam

centrifuge, the maximum error is 2.4 %. Similarly for a sample height of 165 mm and

an effective radius of 530 mm in the UWA drum centrifuge, the maximum stress

variation is 5.2 %. Hence the error in the stress profile is relatively minor in both

centrifuges.

The inertial radial acceleration is directed towards the axis of rotation of the centrifuge

and consequently in the horizontal plane, there is a change in its direction relative to

vertical across the width of the model, resulting in a lateral component of acceleration

(Taylor 1995). This lateral component of acceleration can become significant if testing

is conducted near a side wall of the model container. For this reason, in the beam

centrifuge, dynamic anchor test events were restricted to the centreline of the sample. In

the drum centrifuge, each point on the sample surface is normal to the axis of rotation

and hence no lateral acceleration component exists.

In order to achieve homologous stresses and strains in the model and prototype, model

tests are generally conducted in soil that is similar in grain size to the prototype soil.

Relative to the size of the foundation being modelled, the grain size of the model soil

will therefore be a factor of n greater than in the prototype. Grain size effects are

generally not observed provided that the ratio of the smallest significant dimension of

the problem (B) to the average grain size (d50) is greater than 35, i.e. B/d50 > 35

(ISSMGE TC2 2007). For tests in clays, silts and fine sands the model is usually large

enough relative to the soil particle size that no effect exists. However, for coarser

grained materials, particle size effects may become significant.

56

3.3 CENTRIFUGE FACILITIES

3.3.1 Beam Centrifuge

The fixed beam Acutronic Model 661 geotechnical beam centrifuge at The University

of Western Australia (UWA) was installed in 1989 and features a swinging platform

with a radius of 1.8 m. The centrifuge, shown in Figure 3.2, is rated to a capacity of 40

g-tonnes, with a maximum payload of 200 kg at the maximum acceleration level of 200

g. Test packages placed on the swinging platform are balanced by a movable counter

weight at the opposite end of the beam. The centrifuge is housed in a specially

constructed circular reinforced concrete chamber. The chamber is air conditioned to

maintain a constant temperature and to avoid seasonal variations. This facility is

described in detail by Randolph et al. (1991).

Since its installation, the beam centrifuge at UWA has undergone a number of upgrades,

particularly in relation to the control software and data acquisition systems. The control

software was written in-house and enables efficient operation of the centrifuge and

actuators. The test package is monitored in-flight by an onboard flight computer,

incorporating a 16 bit data acquisition system and data is transferred to the centrifuge

control room via a wireless network connection. This allows real time monitoring of test

and centrifuge performance data.

3.3.1.1 Sample Strong-Box

Beam centrifuge soil samples were contained within rectangular, aluminium strong-

boxes with internal dimensions measuring 650 mm long, 390 mm wide and 325 mm

high (Figure 3.3). Drainage holes at the base of the box allowed drainage or saturation

of the sample in-flight and an external standpipe enabled the sample water level to be

maintained during testing.

3.3.1.2 Actuators

The test programme was undertaken using electronic actuators (Figure 3.4) with two

degrees of freedom (horizontal and vertical). Powered by 30 V DC variable speed

servo-motors, the actuators have maximum horizontal and vertical strokes of 180 mm

57

and 250 mm respectively. Both axes have a maximum velocity of 3 mm/s and

displacements are monitored using high resolution optical encoders. The actuators

provide loading capabilities of 2 kN horizontally and 6.5 kN vertically. Control software

enables the actuators to perform both monotonic and cyclic loading under either

displacement or load control conditions.

3.3.1.3 STOMPI

During self weight consolidation in the beam centrifuge, the sample pore pressures were

monitored using the Sub-Terrain Oil impregnated Multiple Pressure Instrument

(STOMPI). STOMPI features five individual pore pressure transducers located at 50

mm intervals along a stainless steel shaft. The device was placed within the sample and

secured to the top flange of the strongbox, providing measurements of the pore

pressures at various sample depths. STOMPI is shown in Figure 3.5.

3.3.2 Drum Centrifuge

The drum centrifuge facility at UWA was established in 1997 (Figure 3.6). The

centrifuge has a diameter of 1.2 m and is capable of achieving a maximum rotational

speed of 850 rpm, representing a maximum acceleration level of 485 g at the bottom of

the channel. Two concentric shafts connected to a precision servo motor enable the

central tool table to be rotated differentially from the sample channel. The tool table

actuator is also capable of being stopped while the channel remains spinning,

eliminating the need for reconsolidation time between tests. A detailed description of

the drum centrifuge facility is provided by Stewart et al. (1998).

The drum centrifuge is fitted with two onboard data acquisition systems: one on both

the channel and tool table. Digital signals from each computer are transferred to a single

data acquisition computer in the control room, where the data is stored and transferred

to a second computer for real time graphics display. Rotation of the channel is computer

controlled and monitored and the tool table features a second onboard computer for

actuator control.

58

3.3.2.1 Sample Channel

The sample containment channel shown in Figure 3.7 has a diameter of 1.2 m and is 300

mm wide (vertically) and 200 mm deep (radially). The channel is driven by a 15.5 kW

440 V AC motor via a drive belt. Transducers located 50, 75 and 100 mm from the base

of the channel enable pore pressures to be monitored in-flight.

3.3.2.2 Tool Table Actuator

The central tool table actuator (Figure 3.8) is capable of vertical, radial and

circumferential actuation. The vertical and radial axes are driven by lead screws

powered by 60 V DC brushless servo motors fitted with 88:1 harmonic drive gearboxes

and have a continuous load rating of 10 kN. The circumferential axis is controlled by a

7.5 kW Dynaserv servo motor and has a torque rating of 500 Nm. The vertical and

radial velocities are limited to 3 mm/s with maximum strokes within the test zone of

156 mm and 227 mm respectively.

3.4 SOIL SAMPLES

Centrifuge model tests were conducted primarily in kaolin clay samples although

dynamic anchor performance was also assessed in uncemented calcareous sand and

silica flour samples. The following sections summarise the geotechnical properties and

sample preparation procedure for each soil type.

3.4.1 Soil Properties

3.4.1.1 Kaolin Clay

Kaolin clay is often used in centrifuge modelling due to its isotropic nature and

relatively short consolidation time. The properties of UWA kaolin clay have previously

been characterised by Stewart (1992). These properties have been combined with the

results of a standard Rowe cell test, conducted by the author, in Table 3.2.

The coefficient of consolidation depends on the stiffness and permeability of the soil

and hence varies with the effective stress level and void ratio. The variation in the

59

coefficient of vertical consolidation (cv) with vertical effective stress measured in the

Rowe cell test is shown in Figure 3.9. The value of cv listed in Table 3.2 is an average

calculated at a prototype depth of 20 m (i.e. σ′v = 130 kPa). Piezocone dissipation tests

in kaolin clay reported by Randolph and Hope (2004) demonstrated coefficients of

consolidation which were approximately 2.2 times larger than those measured in Rowe

cell tests. Based on these results it is assumed that the horizontal coefficient of

consolidation is given by

vh c2.2c = (3.3)

Property Value

Specific gravity, Gs 2.60

Effective unit weight, γ' (kN/m3) 6.5

Liquid limit, LL (%) 61

Plastic limit, PL (%) 27

Angle of internal friction, φ' (°) 23

Compression index, Cc 0.47

Swelling index, Cs 0.10

Normally consolidated undrained strength ratio, (su/σ′v0)NC 0.18

Coefficient of consolidation at σ′v = 130 kPa, cv (m2/yr) 3.2

Table 3.2 Engineering properties of kaolin (after Stewart 1992)

3.4.1.2 Calcareous Sand

Property Value

Specific gravity, Gs 2.73

Minimum dry unit weight, γd,min (kN/m3) 7.46

Maximum dry unit weight, γd,max (kN/m3) 10.1

Minimum void ratio, emin 1.65

Maximum void ratio, emax 2.59

Porosity, η (%) 62 - 72

Friction angle, φ (°) 40

Table 3.3 Engineering properties of North Rankin uncemented calcareous sand

(after Richardson et al. 2005)

Calcareous sands originate from biological processes such as the sedimentation of

skeletal debris and coral reef formation and are characterised by highly angular and

60

brittle particles and the presence of varying degrees of cementation (Murff 1987). Sand

recovered from the seabed in the vicinity of the North Rankin platform, off the North

West coast of Western Australia, was used to prepare the uncemented calcareous sand

centrifuge samples. The properties of this sand have been reported by Richardson et al.

(2005) and are presented in Table 3.3.

3.4.1.3 Silica Flour

The properties of silica flour have been extensively investigated by Bruno (1999) and

are summarised in Table 3.4.

Property Value

Specific gravity, Gs 2.66

Mean particle size, d50 (µm) 45

Voids ratio, e 0.57 - 1.30

Minimum saturated density, γsat,min (kN/m3) 16.9

Maximum saturated density, γsat,max (kN/m3) 22.0

Permeability, kp (m/s) 2 x 10-6

Average peak friction angle (ID = 76 %), φ'max (°) 42.8

Average critical state friction angle (ID = 76 %), φcv (°) 37.8

Average dilation angle (ID = 76 %), ψ (°) 5.3

Table 3.4 Engineering properties of silica flour (after Bruno 1999)

3.4.2 Sample Preparation

3.4.2.1 Kaolin Clay

Kaolin clay samples were prepared as a slurry by combining commercially available

kaolin clay powder with water at a moisture content of 120 % (i.e. twice the liquid limit;

see Table 3.2). During mechanical mixing, the slurry was de-aired under vacuum to

ensure a high degree of sample saturation.

For the beam centrifuge samples, the slurry was placed manually within the strong-box

on top of a 10 mm deep sand drainage layer. A layer of water was maintained above the

sample surface during sample preparation to avoid ingress of air into the sample.

Internal sand ‘standpipes’ were placed in the corners of the strong-box in order to

facilitate flow between the free water surface and the external standpipe (connected to

61

the base drainage layer), thereby avoiding an increase in pore pressure beneath the low

permeability clay layer. Water was added to the sample in-flight to compensate for

losses due to evaporation.

For the drum centrifuge samples, the mixed and de-aired slurry was transferred to a

hopper and positioned above the centrifuge (Figure 3.10). The hopper was connected by

a hose and rotating coupling to a PVC nozzle attached to the actuator (Figure 3.11).

Prior to placement of the slurry a 10 mm deep sand drainage layer was placed at the

bottom of the channel. Due to the orientation of the sample containment channel the

slurry was placed with the channel spinning at 20 g in order to prevent the slurry from

spilling out. The nozzle was rotated relative to the channel at a rate of 3 °/s such that the

slurry was distributed uniformly within the channel. The centrifugal force ensured the

slurry formed a level sample surface as it was poured. A layer of water was maintained

above the sample surface to prevent ingress of air during sample placement and water

was added to the sample in-flight to compensate for evaporation losses.

Normally consolidated samples were prepared by self weight consolidation in the

centrifuge at an average acceleration level of 200 g. In the beam centrifuge STOMPI

(Section 3.3.1.3) was used to monitor the progression of consolidation through the

dissipation of excess pore pressures, whilst in the drum centrifuge this information was

provided by pore pressure transducers situated in the channel (Section 3.3.2.1).

In order to achieve a sufficient sample height it was necessary to ‘top-up’ the sample

with slurry, following consolidation of the previous layer. Typically two top-ups were

required to achieve the target consolidated sample height of 230 mm in the beam

centrifuge and 165 mm in the drum centrifuge.

Note that beam centrifuge sample, Box 6 was prepared according to the method

proposed by Chen (2005) for the production of a clay sample with an artificially high

sensitivity. The sensitivity (St) is defined as the ratio of the undisturbed shear strength

(su) to the fully remoulded shear strength (su,r), St = su / su,r. Kaolin clay typically

exhibits sensitivities of approximately 2 – 2.5, however Chen (2005) demonstrated

sensitivities measured using cyclic T-bar tests of approximately 4 – 5. The sample was

prepared by dissolving a dispersing agent (sodium polymetaphosphate) in water for 24

hours at a concentration of 15 g/L. The kaolin slurry was then prepared at a moisture

62

content of 70 % using the hydrated sodium polymetaphosphate. Unfortunately the

sample preparation procedure did not produce a sample with increased sensitivity (see

Section 5.2.1).

3.4.2.2 Calcareous Sand

The preparation of uncemented calcareous sand samples for the beam centrifuge is

outlined in Richardson et al. (2005). Calcareous sand recovered from the seabed near

the North Rankin platform was dried and sieved to remove particles larger than 0.3 mm.

The sieved material was then dry mixed to ensure a uniform distribution of particles

throughout the sample. Following mixing the sand was loosely placed in a centrifuge

strong-box and saturated via the drainage holes in the bottom of the box. The strong-box

was then placed on a vibrating table at a low speed setting for approximately 1 hour.

Drainage at the bottom of the sample was provided via a woven, felt drainage blanket

overlying a 10 mm deep layer of coarse sand.

A total of three uncemented calcareous sand samples were produced. In order to save

sample preparation time the second calcareous sand sample (Box 8) was prepared by

reconstituting the original sample (Box 7). This was achieved by carefully hand mixing

the sample under water to avoid ingress of air. The sample was then placed back on the

vibrating table for approximately 30 minutes. However, due to inconsistencies between

cone penetration test (CPT) profiles in the original and reconstituted samples, the

reconstitution method was not deemed effective and consequently the test results from

Box 8 have been excluded from the analysis (see Section 6.3.1).

3.4.2.3 Silica Flour

The single silica flour beam centrifuge sample was prepared by loosely placing

commercially available silica flour in a strong-box over 10 mm layers of coarse and fine

sand. Following placement of the silica flour, the sample was saturated via the drainage

holes in the bottom of the box. The sample was then placed on a vibrating table at low

speed for approximately half an hour.

63

3.5 PENETROMETER DEVICES

3.5.1 T-bar Penetrometer

Soil characterisation tests in kaolin clay were conducted using a T-bar penetrometer

(Stewart and Randolph 1991). T-bar penetrometer tests were conducted in-flight and

provided a continuous profile of shear strength with depth. The major advantage of the

T-bar over other penetrometers such as the cone, is that the soil is allowed to flow

around and over the T-bar during penetration, therefore the soil overburden pressure is

equilibrated above and below the bar and as such the need for corrections is largely

avoided (Stewart and Randolph 1994).

The T-bar used in the beam centrifuge tests is shown in Figure 3.12. It comprises a 5

mm diameter, 20 mm long cylinder attached at right angles to the end of a vertical shaft.

A load cell at the tip of the shaft measures the T-bar penetration resistance. A similar T-

bar penetrometer was used in the drum centrifuge tests.

T-bar tests were carried out before and after dynamic anchor tests in each sample to

monitor any change in the sample strength with time. The T-bar was installed at a rate

of 1 mm/s, ensuring undrained conditions. The transition from partially drained to

undrained conditions has been shown to occur at a non-dimensional velocity (V) of

approximately 30 (Finnie and Randolph 1994), where

vc

vDV = (3.4)

where v is the penetration velocity, D is the penetrometer diameter (i.e. 5 mm) and cv is

the coefficient of consolidation. House et al. (2001), however, suggested a lower

undrained non-dimensional velocity limit of 10 from T-bar penetrometer tests. Hence

for a penetration velocity of 1 mm/s and an average coefficient of consolidation of 3.2

m2/yr (0.10 mm2/s; Table 3.2), the non-dimensional velocity is approximately 50, which

is greater than the lower bound value of 10 required for undrained conditions.

The net bearing resistance, q, during T-bar penetration can be correlated to the

undrained shear strength, su, by a T-bar bearing capacity factor, NT-bar, where

64

ubarT sNq −= (3.5)

The analytical value of NT-bar depends on the roughness of the T-bar. Plasticity solutions

for the limiting pressure acting on a cylinder displaced laterally in fine grained soil give

a value of approximately 12 for a rough bar, and a value of 9 for a smooth bar

(Randolph and Houlsby 1984). Stewart and Randolph (1991) recommend a T-bar factor

of 10.5, representing an average of the rough and smooth cases.

Cyclic T-bar tests have been used to measure the sensitivity of clay (Watson et al. 2000,

Chen 2005). The cyclic T-bar tests were conducted by monotonically installing the T-

bar to a depth of approximately two-thirds the sample height at a rate of 1 mm/s. An

average measurement of the maximum undisturbed shear strength (su) was made during

the initial penetration stroke of the test, however it should be noted that the actual

undisturbed shear strength is mobilised ahead of the penetrometer with the soil

softening towards a partially remoulded strength behind the T-bar (Yafrate and DeJong

2005). Subsequent vertical cycles of the T-bar over an interval of 30 mm were

considered sufficient to cause remoulding of the soil. Full remoulding in the cycling

zone typically occurred within 10 cycles, however, a total of 25 cycles were performed

in each test. Following cycling, the T-bar was monotonically installed to its final depth

before monotonic extraction at a rate of 1 mm/s. The cyclic T-bar profile is often

asymmetrical and this can have a significant impact on the calculated sensitivity. This

has been accounted for by taking the zero strength as the mid-point between the

penetration and extraction loops in the final cycle of the test. In addition, by assessing

the sensitivity at the mid depth of the cycling interval the influence of limit variations

was minimised.

3.5.2 Cone Penetrometer

3.5.2.1 Calcareous Sand

Cone penetrometer tests (CPTs) were used to assess the variation in cone tip resistance

with depth in the uncemented calcareous sand samples. The 60° cone angle, 10 mm

diameter model cone penetrometer used in the beam centrifuge tests is shown in Figure

3.13. Due to the brittle and collapsible nature of the calcareous sand a cone

penetrometer with a relatively low tip resistance capacity of 25 MPa was selected in

65

order to maximise the data resolution. The cone penetrometer was installed at a rate of 1

mm/s.

3.5.2.2 Silica Flour

CPTs in the silica flour sample were conducted with a 60° cone angle, 7 mm diameter

cone penetrometer (Figure 3.14). Significantly higher tip resistances were expected in

the silica flour sample than in the calcareous sand and as such a cone with a capacity of

100 MPa was utilised. De Nicola (1996) showed that negligible difference in the

measured cone tip resistance was observed for penetration rates of between 0.25 and 3

mm/s in silica flour samples. Hence in order to maintain consistency with the calcareous

sand CPTs, an installation rate of 1 mm/s was adopted.

3.6 MODEL ANCHORS

The geotechnical performance of dynamically installed anchors was investigated

experimentally using 1:200 reduced scale model anchors. For the most part, tests were

conducted with zero fluke anchors in order to simplify the subsequent analysis, although

several other anchor designs were also tested.

3.6.1 Zero Fluke Model Anchors

A standard zero fluke anchor (0FA) geometry was adopted for the centrifuge tests, as

shown in Figure 3.15. The model and corresponding prototype anchor dimensions are

summarised in Table 3.5.

Dimension Symbol Model Prototype

Anchor length L 75 mm 15 m

Anchor diameter D 6 mm 1.2 m

Tip length Ltip 11.4 mm 2.28 m

Shaft length Lshaft 63.6 mm 12.72 m

Projected shaft area, Ap = πD2/4 Ap 28.3 mm2 1.13 m2

Shaft surface area, As = πD(L – Ltip) As 1199 mm2 48.0 m2

Table 3.5 Zero fluke anchor dimensions

66

The 0FA comprised an ellipsoidal shaped tip (Figure 3.16), with two dimensional

coordinates given by

1b

y

a

x2

2

2

2

=+ (3.6)

where a = 3 mm is the anchor radius; and b = 11.4 mm is the anchor tip length.

Anchor Segments Mass

Tip Shaft Padeye Model (g)

Prototype (x 103 kg)

E0-1 brass brass 14.8 118.4

E0-2 brass brass 14.5 116.0

E0-3 brass aluminium aluminium 8.2 65.6

E0-4 aluminium aluminium brass 6.2 49.6

E0-5 aluminium aluminium aluminium 5.4 43.2

Table 3.6 Zero fluke model anchor properties

Brass (density 8400 kg/m3) and aluminium (density 2700 kg/m3) model anchor

segments were used interchangeably in order to alter the anchor mass (Figure 3.17).

Figure 3.17 illustrates two different anchor designs. Early tests were conducted with an

anchor incorporating a combined tip and shaft section with a separate padeye. This

design was later modified to increase the range of potential anchor masses by

fabricating separate tip and shaft components. Five different mass 0FAs were used in

the experimental programme and are detailed in Table 3.6. The first letter of the anchor

designation specifies the tip shape (i.e. ‘E’ identifies the tip as being ellipsoidal) and the

following number specifies the number of flukes.

3.6.2 Four Fluke Model Anchors

Model four fluke anchors (4FAs) were fabricated based on the idealised DPA design

suggested by Lieng et al. (2000). Clipped delta type flukes with a forward swept trailing

edge were adopted and can be seen in Figure 3.18. The same 0FA ellipsoidal tip shape

was utilised. The model and corresponding prototype dimensions are summarised in

Table 3.7.

67

Dimension Symbol Model Prototype

Anchor length L 75 mm 15 m

Anchor diameter D 6 mm 1.2 m

Tip length Ltip 11.4 mm 2.28 m

Fluke length - segment 1 Lfluke1 10 mm 2.0 m

Fluke length - segment 2 Lfluke2 24 mm 4.8 m

Fluke length - segment 3 Lfluke3 3 mm 0.6 m

Fluke width wfluke 9 mm 1.8 m

Fluke thickness tfluke 0.4 mm 0.08 m

Projected fluke area Apf 14.4 mm2 0.58 m2

Fluke surface area Asf 2196 mm2 87.8 m2

Total projected area Ap 42.7 mm2 1.71 m2

Total surface area (excluding tip) As 3395 mm2 135.8 m2

Table 3.7 Four fluke anchor dimensions

As with the 0FAs a modular 4FA design was adopted with interchangeable tip, shaft

and padeye sections in both brass and aluminium. The aluminium flukes were

permanently attached to the shaft segment. Four separate 4FAs were used in the test

programme and they are detailed in Table 3.8.

Anchor Segments Mass

Tip Shaft Padeye Flukes Model (g)

Prototype (x 103 kg)

E4-1 brass brass brass aluminium 15.5 124.0

E4-2 aluminium brass brass aluminium 12.7 101.6

E4-3 brass aluminium aluminium aluminium 9.6 76.8

E4-4 aluminium aluminium aluminium aluminium 6.8 54.4

Table 3.8 Four fluke model anchor properties

3.6.3 Model Anchors with Different Tip Shapes

An investigation into the influence of anchor tip shape was conducted by fabricating

three 0FAs with different tip geometries. The tip shapes included a 15° cone, a tangent

ogive and a flat headed cylindrical pile (Figure 3.19). Each anchor was constructed from

brass with the model and corresponding prototype dimensions specified in Table 3.9.

68

Dimension Symbol Model Prototype

Anchor length L 75 mm 15 m

Anchor diameter D 6 mm 1.2 m

Tip length - cone Ltip 22.8 mm 4.6 m

Tip length - ogive Ltip 22.8 mm 4.6 m

Tip length - flat Ltip 0 mm 0 m

Shaft surface area - cone, As = πD(L – Ltip) As 984 mm2 39.4 m2

Shaft surface area - ogive, As = πD(L – Ltip) As 984 mm2 39.4 m2

Shaft surface area - flat, As = πD(L – Ltip) As 1414 mm2 56.5 m2

Projected shaft area Ap 28.3 mm2 1.13 m2

Table 3.9 Dimensions of anchors with varying tip geometry

The anchor masses are presented in Table 3.10. Every effort was made to ensure

equivalent anchor masses with the reference anchor E0-1 (see Table 3.6). Unfortunately

it was not possible to reduce the mass of the flat tipped anchor in line with the other

anchors, without exceeding safe wall thickness limits. The anchors in Table 3.10 are

designated as ‘C’ for the conical tip, ‘O’ for the ogive tip and ‘F’ for the flat tip.

Anchor Segments Mass

Tip Shaft Padeye Model (g)

Prototype (x 103 kg)

C0-1 brass brass 14.7 117.6 O0-1 brass brass 14.8 118.4 F0-1 brass brass 15.5 124.0

Table 3.10 Properties of model anchors with varying tip geometry

3.6.4 Instrumented Anchor

An instrumented model zero fluke anchor was designed and developed to measure the

anchor deceleration during penetration experiments in the centrifuge. Two identical

instrumented anchors were fabricated, incorporating a tip load cell and a miniature

accelerometer. The instrumented anchors were of similar design to the 0FAs described

in Section 3.6.1 and comprised the same ellipsoidal shaped tip (Figure 3.20). A slight

discrepancy in mass between the two instrumented anchors was identified (Table 3.11).

The ‘I’ in the anchor designation specifies that the anchors are instrumented.

69

The instrumentation was contained within a small section of the anchor just behind the

tip (Figure 3.20). Strain gauges placed on the walls of this section acted as an axial tip

load cell. A miniature piezoelectric accelerometer was installed inside the hollow strain

gauged section. Piezoelectric accelerometers rely on a property exhibited by certain

materials where a voltage is generated across the material when it is stressed. Therefore

when exposed to an acceleration, a test mass stresses the piezoelectric material by a

force, F = ma, resulting in a voltage being developed across the material. Measuring this

voltage provides a measurement of the acceleration. The instrumented anchor

accelerometer was designed to withstand accelerations of up to 1000 g.

Anchor Segments Mass

Tip Shaft Padeye Model (g)

Prototype (x 103 kg)

IE0-1 brass brass 14.3 114.4 IE0-2 brass brass 14.8 118.4

Table 3.11 Model instrumented anchor properties

The shaft of the model anchor was bored out to allow a single instrumentation cable

incorporating the data signals from both the load cell and accelerometer to pass up

through the middle of the anchor, exiting at the padeye. A small metal loop soldered to

the end of the anchor acted as a padeye for attachment of the anchor chain and release

cord. Strain relief for the instrumentation cable was provided with a grub screw located

near the padeye.

The instrumented anchor was designed and developed with the ultimate objective of

measuring the deceleration of model anchors during dynamic installation in the

centrifuge. Measurement of the deceleration would allow a velocity profile to be

obtained, which would subsequently aid calibration of theoretical resistance models

during anchor penetration. Unfortunately the high noise environment in the centrifuge

and damage to the instrumentation prevented any usable data from being obtained from

the instrumented model anchors. As such, no discussion or analysis of the data

measured by the instrumentation will be presented. However since the impact velocity,

embedment depth and holding capacity are measured independently of the anchor

instrumentation, the external data recorded for the instrumented model anchor tests will

be incorporated in the analysis presented in later chapters.

70

3.6.5 Model Anchors with Different Aspect Ratios

The influence of the aspect ratio (length to diameter ratio, L/D) on the performance of

dynamic anchors was assessed via a series of tests with 6, 9 and 12 mm diameter, zero

fluke model anchors with aspect ratios ranging from 1 – 14 (see Figure 3.21). Details of

the anchors are summarised in Table 3.12. In order to provide a smooth transition

between L/D = 1 and higher aspect ratios, both the anchor tip and padeye were

hemispherical in shape (see Figure 3.22). Consequently, the anchors in Table 3.12 have

been designated as ‘H’ for their hemispherical tip shape. The model anchors were

fabricated with interchangeable tip and padeye sections, such that the aspect ratio could

be altered simply by changing the central shaft section. The limited sample depth in the

drum centrifuge prevented all of the model anchors from being fabricated from brass

(density = 8400 kg/m3). In order to investigate anchors with higher aspect ratios,

without embedments exceeding the sample depth, a number of anchors were fabricated

from aluminium with a density of approximately 2700 kg/m3.

The influence of the aspect ratio was objectively assessed by comparing the

performance of two pairs of anchors with identical masses but different aspect ratios:

• Anchors H0-5 (L/D = 4) and H0-13 (L/D = 12) with a mass of 4.7 grams

• Anchors H0-15 (L/D = 1) and H0-18 (L/D = 3) with a mass of 3.0 grams

The anchor mass was varied by drilling out material from the middle of the central shaft

section of the anchor.

The use of brass and aluminium also allowed the behaviour of anchors with identical

aspect ratios but different masses to be compared, thereby providing an assessment of

the influence of anchor density on the dynamic anchor performance. Accordingly, four

individual groups of anchors were developed:

• Anchors H0-5 (m = 4.7 g) and H0-7 (m = 1.4 g) with L/D = 4

• Anchors H0-6 (m = 7.4 g), H0-8 (m = 2.3 g) and H0-9 (m = 1.9 g) with L/D = 6

• Anchors H0-12 (m = 5.0 g) and H0-13 (m = 4.7 g) with L/D = 12

• Anchors H0-17 (m = 11.4 g) and H0-18 (m = 3.0 g) with L/D = 3

71

3.6.6 Anchor Chain and Release Cord

Initial model anchor tests were conducted with an anchor chain comprising nylon

coated, stainless steel wire fishing trace. The 0.45 mm diameter wire had a capacity of

approximately 250 N. This wire was selected as it provided sufficient tensile capacity

whilst minimising potential adverse effects from stretching and unravelling during

loading. In later tests braided fishing line, with a diameter of 0.7 mm and a maximum

capacity of approximately 900 N, was adopted. The braided line was favoured over the

steel wire due to its higher capacity, improved flexibility and similar stretch resistance.

Release of the model anchor in-flight was achieved via a release cord and an electrically

activated release mechanism (see Section 3.7.2). The release cord comprised a braided

fishing line with a capacity of approximately 230 N.

Apart from tests involving the instrumented model anchors, the anchor chain and

release cord were secured to the anchor via knots tied in the end of the cables. The

cables were passed through the top of a stainless steel insert, tied in a knot and

positioned in a cavity at the base of the insert. The small diameter hole in the top of the

insert prevented the cables from being pulled out during loading. The threaded insert

was then screwed directly into the back of the padeye section of the anchor. The anchor

chain and release cord attachment is shown in Figure 3.23.

3.7 EXPERIMENTAL APPARATUS

3.7.1 Installation Guide

Dynamic anchors are partially dependent on their impact velocity with the seabed in

order to achieve the target embedment depth. Equivalent prototype impact velocities of

up to 20 – 25 m/s (Lieng et al. 1999) were achieved in the centrifuge by allowing the

model anchors to free-fall under the influence of the high acceleration field in the

centrifuge from low drop heights. However the rotational nature of the acceleration field

in the centrifuge means that the model anchors must be installed through a guide to

prevent lateral movement of the anchor during installation.

72

Separate guides were fabricated for the 0FAs and the 4FAs. The slotted cylindrical

installation guide for the 0FAs was manufactured from aluminium with an internal

diameter of 6.5 mm, thereby providing nominal clearance to the 6 mm diameter model

anchor. The open slot along the entire 375 mm length of the guide allowed continuous

access for the model anchor chain. The 0FA guide is shown in Figure 3.24. Similar

guides were also fabricated for the 9 and 12 mm diameter anchors described in Section

3.6.5.

The 4FAs were installed using a guide fabricated from PVC incorporating a 0.85 mm

wide slot and a 6 mm diameter groove machined into the centre of the front face of the

guide. The anchor was positioned with a fluke in the slot and the shaft against the

groove. To prevent the anchor from falling away from the guide two PVC rails were

attached to the guide with brackets. These rails did not interfere with the anchor chain or

the movement of the anchor down the guide. The 4FA guide is shown in Figure 3.25.

Measurement of the model anchor velocity at the point of impact with the sample

surface is important in terms of the test analysis. Early tests utilised a single

PhotoEmitter-Receiver Pair (PERP; see the left side of Figure 3.26a) located one anchor

length back from the tip of the guide to measure the anchor velocity. As an object

passes the PERP and breaks the light beam passing between the emitter on one side of

the guide and the receiver on the other side of the guide, a voltage is recorded. The

duration of this voltage increase, known as the interrupt time, ∆t, can be used in

conjunction with the length of the object passing the PERP, L, to determine an average

velocity, vave.

t

Lvave ∆

= (3.7)

For the 0FAs the interrupt time was measured for the entire anchor length. However for

the 4FAs, since the beam was broken by the anchor fluke in the guide slot, the known

fluke length passing the PERP was used to determine the anchor velocity. The PERP

output for a typical model anchor drop test in the centrifuge is shown on the left side of

Figure 3.26b.

Use of a single PERP, however, was not deemed to provide sufficient accuracy for the

velocity calculated by Equation 3.7. Consequently an installation guide comprising

73

multiple PERPs positioned at 10 mm intervals along the guide was developed (see right

side of Figure 3.26a). The anchor velocity was calculated by measuring the time

required for both the anchor tip and padeye to pass consecutive PERPs. Coupled with

the fixed PERP spacing this information could be used to calculate multiple velocities

during the installation of the model anchor. Not only did the reduction in distance over

which the velocity was calculated lead to improved accuracy, but the multiple velocities

allowed a partial anchor velocity profile to be generated as opposed to a single velocity

point for the single PERP guide. A comparison of the velocities derived from the single

and multiple PERP guides is shown in Figure 3.26c.

Figure 3.26c shows that for two separate tests conducted from the same drop height of

250 mm, the single PERP guide records a velocity of 21.2 m/s. With the PERP located

100 mm above the sample surface the velocity is therefore representative of the anchor

velocity at an average height of 62.5 mm above the sample surface, based on an anchor

length of 75 mm (Table 3.5). At a similar height above the sample surface the multiple

PERP guide provides a slightly higher velocity of 22.3 m/s. However, the multiple

PERP guide suggests an interpolated impact velocity of 26.3 m/s, which is 24 % higher

than the single PERP velocity, demonstrating the inaccuracy associated with measuring

the impact velocity with the single PERP guide configuration.

3.7.2 Release Mechanism

Release of the model anchors in-flight was achieved with a release mechanism

developed by Wemmie (2003) (Figure 3.27). Prior to the test, the release cord was

positioned over a 30 Ω resistor and clamped in place to prevent premature movement of

the anchor in the centrifuge acceleration field. Activation of the release mechanism

resulted in a voltage being supplied to the resistor. This voltage was sufficient to cause

the resistor to burn through the release cord, thereby effecting release. The release

mechanism was attached to the top of the installation guide.

3.7.3 Load Cell

The load displacement response of the model anchors during extraction was measured

using a 1.7 kN load cell mounted in-line with the vertical axis of the actuator in the

beam centrifuge and the radial axis of the actuator in the drum centrifuge. The anchor

74

chain passed over a metal loop which was attached to the load cell by a connecting

screw (Figure 3.28).

3.8 TESTING PROCEDURE

The experimental programme predominantly comprised model anchor drop tests. These

tests were conducted in two distinct phases; installation and extraction. Typically

extraction involved vertical monotonic loading of the anchor to failure, although in

some instances this also involved vertical cyclic or sustained loading. Dynamic anchors

are expected to be subjected to predominantly inclined loading and not only vertical

loading as is the case here. However, results from finite element studies reported by

Lieng et al. (1999) suggest that dynamic anchors have ample horizontal capacity and

failure is governed by the vertical capacity. In addition to the drop tests a small number

of static installation tests were conducted. Each test in this study was performed at a

centrifuge acceleration level of 200 g.

3.8.1 Beam Centrifuge

3.8.1.1 Dynamic Installation

The test arrangement in the beam centrifuge is shown in Figure 3.29, with the

installation guide bolted to the actuator tower and the release mechanism attached via a

bracket to the top of the guide. The model anchor was fitted with both an anchor chain

and a release cord and positioned within the installation guide with the anchor tip at the

required drop height above the sample surface. The anchor chain was then connected to

the load cell and the release cord clamped over the resistor in the release mechanism.

The impact velocity of the anchor could be altered by adjusting the initial vertical

position of the anchor within the guide prior to release.

At the required centrifuge acceleration level, the release mechanism was activated from

the control room and after several seconds the anchor was released. Fast-logging data

acquisition software enabled the data from the PERPs to be logged at rates of up to 100

kHz during installation. The software was automatically activated when the anchor

75

passed a designated trigger PERP. A pre-trigger incorporated in the software enabled

the recording of data for a specified time prior to the trigger point.

To minimise interaction effects between adjacent test sites, a spacing of 5 anchor

diameters was adopted, corresponding to 30 mm for the 6 mm diameter 0FA. Similarly

in order to avoid interaction effects with the strong-box boundaries a minimum spacing

of 10 anchor diameters was adopted.

3.8.1.2 Vertical Monotonic Extraction

To allow consolidation of the soil surrounding the embedded anchor, various soak

periods were permitted following installation. Then, before extraction took place, the

actuator was driven horizontally 43 mm to account for the offset between the

installation guide and the vertical axis of the load cell. Extraction of the anchor was

initiated by driving the actuator vertically upwards away from the sample surface at a

constant rate sufficient to ensure undrained conditions. Undrained conditions occur

when the non-dimensional velocity (V) is greater than 10 (House et al. 2001), where V

is given by Equation 3.4. For D = 6 mm (Table 3.5) and cv = 3.2 m2/yr (0.10 mm2/s;

Table 3.2) an extraction rate greater than 0.17 mm/s is sufficient to ensure undrained

conditions, hence a rate of 0.3 mm/s was adopted in all model anchor tests.

The anchor embedment depth, ze, was determined from the initial vertical position of

the load cell above the sample surface, zLC, the length of the anchor chain, zchain, the

amount of slack removed from the anchor chain prior to the onset of a significant tensile

load, zslack, and the model anchor length, L (Figure 3.30), as

Lzzzz slackLCchaine +−−= (3.8)

The reliability of this method was verified by comparison with several direct

measurements.

3.8.1.3 Sustained Loading Tests

Long-term sustained loading of the model anchors was performed under load control

conditions. Following installation and consolidation, vertical sustained loads were

applied with a magnitude equal to a proportion of the maximum capacity measured in

the reference monotonic loading test. The load magnitude and duration were varied

76

between tests. If failure was not observed under the sustained loading sequence, the

anchor was loaded monotonically to failure at a rate of 0.3 mm/s in displacement

control. Failure was identified as excessive vertical displacement under the applied

sustained load.

3.8.1.4 Cyclic Loading Tests

Cyclic loading tests were also performed under load control conditions. Following

installation and consolidation, vertical cyclic loading sequences were applied with the

minimum and maximum cyclic loads specified as proportions of the maximum capacity

measured in the reference monotonic loading test. The load magnitude, duration and

frequency were varied between tests. Since mooring lines for floating offshore

structures are not capable of transmitting compression loads to the foundation system,

the model anchors were subjected to one-way cyclic tensile loading only. The cyclic

loading was applied using a sinusoidal wave form.

Floating structures such as semi-submersibles have natural periods of vibration of the

order of 100 seconds or more in deepwater (El-Gharbawy and Olson 1999). Low

frequency cyclic loads are often applied to these structures by the wind, current, wave

drift and tide, although higher frequency environmental loads from wave and storm

loading may result in cyclic loading frequencies of 5 to 20 times the natural frequency

of the structure. Therefore cyclic loading periods of between 5 and 100 sec can be

expected for floating offshore structures in deepwater. In the centrifuge, time

(consolidation) is scaled by a factor n2 to be representative of prototype conditions

(Table 3.1). Hence prototype cycling periods of 5 – 100 sec represent model periods of

0.000125 – 0.0025 sec, corresponding to frequencies of 400 – 8000 Hz at the test

acceleration level of 200 g. However the centrifuge actuator is limited to a maximum

displacement rate of 3 mm/s. Therefore in order to achieve these test frequencies, the

cyclic load magnitude would need to be realised over a displacement of 0.000375 –

0.0075 mm, which is not physically possible. However, providing the model frequency

is sufficient to ensure undrained conditions, exact replication of the prototype cyclic

loading frequencies is not required.

For nominally undrained conditions, elapsed times for equivalent cyclic loading events

should be less than the time required for approximately 20 % consolidation, i.e. t ≤ t20.

77

Assuming a horizontal coefficient of consolidation of ch = 0.17 mm2/s (ch = 5.5 m2/yr;

see Section 3.4.1.1) and an anchor diameter of D = 6 mm (Table 3.5), cavity expansion

solutions for the consolidation of soil around a solid driven pile in clay indicate a time

for 20 % consolidation of t20 ~ 24 sec (Randolph and Wroth 1979), based on a non-

dimensional time factor of T20 ~ 0.12, where

2

h

D

tcT = (3.9)

For a typical number of equivalent cycles for a cyclic loading sequence, Neq = 10,

undrained conditions will therefore be achieved if the cyclic loading frequency is

greater than 0.42 Hz (i.e. fr ≥ Neq/t20). The actual frequency achievable is somewhat

dependent on the stiffness of the load displacement response of the model anchor.

Cyclic loading frequencies achieved in the centrifuge ranged from 0.3 to 1.5 Hz. Hence

in the tests conducted at frequencies lower than 0.42 Hz, partially drained conditions

may be experienced.

If failure was not observed under the cyclic loading sequence, the model anchor was

subsequently loaded monotonically to failure under displacement control conditions at a

rate of 0.3 mm/s.

3.8.1.5 Static Installation

Static installation tests were conducted in order to assess the static penetration resistance

during dynamic anchor installation. The ‘T’ piece was removed from the T-bar

penetrometer (Section 3.5.1) and the model anchor padeye was screwed directly on to

the T-bar shaft. The anchor was then installed quasi-statically in-flight at a rate of 1

mm/s. Upon reaching the required depth, the anchor was then extracted at the same rate

without any setup period between anchor installation and extraction.

3.8.1.6 Monotonic Extraction Following Static Installation

A single test was conducted in which the model anchor was extracted monotonically

following static installation. The test was aimed at assessing the extraction load

displacement response of a dynamic anchor following static installation. An adaptor was

manufactured which attached to the T-bar shaft (Figure 3.31). The anchor was

positioned within the adaptor with the anchor chain passing through a hole in the top of

78

the adaptor. The anchor was then pushed into the sample at a rate of 1 mm/s with the

centrifuge stationary. When the required anchor penetration was achieved, the adaptor

connected to the T-bar shaft was removed, leaving the model anchor in place within the

sample. The anchor chain was connected to the load cell and the centrifuge ramped up.

Following reconsolidation vertical monotonic extraction of the anchor was performed at

a rate of 0.3 mm/s.

3.8.2 Drum Centrifuge

3.8.2.1 Dynamic Installation

The test arrangement in the drum centrifuge is shown in Figure 3.32. The installation

guide and load cell were mounted on an aluminium plate attached to the centrifuge

actuator tool connection. The model anchor was positioned in the installation guide at

the required drop height and the release cord and anchor chain were attached to the

release mechanism and load cell respectively. In the drum centrifuge, the model anchor

was positioned with the actuator stationary and raised but the channel still spinning.

Following positioning of the anchor the actuator was lowered (vertically) and ramped

up to the channel speed before being positioned circumferentially at the test site. The

actuator was then driven out to its radial test limit. This radial displacement was taken

into account when positioning the model anchor at the required drop height in the

installation guide.

Subsequent activation of the release mechanism resulted in release of the anchor in-

flight. The fast logging software in the drum centrifuge enabled the PERP data to be

recorded at a maximum rate of 22.5 kHz. Combined with a manual software trigger, the

lower capabilities of the drum centrifuge software, compared with the beam centrifuge,

resulted in decreased velocity accuracy and increased possibility that the installation

PERP data would be missed. As in the beam centrifuge tests, various soak periods were

provided following installation. Once again, a test spacing of 5 anchor diameters was

adopted, resulting in 30 mm and 120 mm between adjacent test sites for the 0 and 4FAs

respectively.

79

3.8.2.2 Vertical Monotonic Extraction

Prior to extraction, the actuator was rotated 10° relative to the channel to account for the

offset of the load cell from the installation guide (Figure 3.32). Vertical monotonic

extraction of the model anchors was then conducted by driving the actuator radially

back in towards the centre of rotation at a rate of 0.3 mm/s (see Section 3.8.1.2). The

anchor embedment depth was determined using the same method as outlined for the

beam centrifuge (see Equation 3.8).

3.9 EXPERIMENTAL PROGRAMME

All testing was conducted at a centrifuge acceleration level of 200 g. A total of 6 beam

centrifuge and 2 drum centrifuge, normally consolidated kaolin clay samples were

prepared for this study. In addition 3 uncemented calcareous sand samples and 1 silica

flour sample were produced for testing in the beam centrifuge. The sample details are

summarised in Table 3.12, including the number of strength characterisation (T-bar tests

or CPTs) and dynamic anchor tests conducted in each sample.

Centrifuge Sample Soil Type T-bars / CPTs

Anchor Tests

Beam Box 1 NC clay 6 12

Box 2 NC clay 6 11

Box 3 NC clay 6 16

Box 4 NC clay 4 16

Box 5 NC clay 8 15

Box 6 NC sensitive clay 17 11

Box 7 Calcareous sand 2 10

Box 8 Calcareous sand# 4 4

Box 9 Calcareous sand 4 7

Box 10 Silica flour 4 2

Drum Drum 1 NC clay 13 66

Drum 2 NC clay 13 72 # sample reconstituted from Box 7

Table 3.12 Summary of centrifuge sample details

81

CHAPTER 4 - ANALYTICAL AND NUMERICAL

METHODS

4.1 INTRODUCTION

The extensive dynamic anchor test database established during the experimental

programme has been complemented by the application of associated analytical and

numerical techniques. This chapter details the methods adopted in the evaluation of

dynamic anchor impact velocities, embedment depths and holding capacities in both

normally consolidated clay and calcareous sand. Accurate prediction of the anchor

embedment depth and holding capacity are of particular importance in the assessment of

the performance of dynamically installed anchors.

4.2 DRAG COEFFICIENT

Any object moving through a fluid will experience drag, i.e. a net force in the direction

of flow due to the pressure and shear forces on the surface of the object (Young et al.

1997). The drag force comprises a pressure drag component due to the pressure

exhibited on the front and back faces of the object and a friction drag component due to

the shear stresses acting along the walls of the object. Generally the effects of pressure

and friction drag are combined and an overall drag coefficient (CD) is defined as:

2p2

1

dD vA

FC

ρ= (4.1)

where Fd is the combined pressure and friction drag resistance force, ρ is the fluid

density, Ap is the projected cross-sectional area of the object and v is the velocity.

Previous studies of seabed penetrometers have identified a range of drag coefficient

values; as follows

82

• True (1976) CD = 0.7, for cylindrical penetrometers with a pointed nose;

• Freeman et al. (1984) CD = 0.15 – 0.18, for European Standard Penetrators

(ESP) at velocities of 10 – 50 m/s;

• Freeman and Hollister (1988) CD = 0.030 + 0.0085 L/D, lower bound to nuclear

waste disposal test data;

• Øye (2000) CD = 0.63, for four fluke DPAs;

• Fernandes et al. (2005) CD = 0.33, for torpedo anchors.

Discrepancies between the drag coefficients determined in these studies are not

unexpected as the drag coefficient is a function of the object shape, surface roughness,

Reynolds number and fluid compressibility.

4.2.1 Factors Influencing the Drag Coefficient

The drag coefficient of an object is dependent on its shape; the blunter the object, the

larger the drag coefficient. Conversely streamlined bodies exhibit smaller drag

coefficients. Figure 4.1 shows the difference in drag coefficient between a blunt

cylinder and a streamlined object, in an axial flow regime. The cylinder has a drag

coefficient which is approximately three times larger than that of the streamlined object

across the complete range of aspect ratios considered. Figure 4.1 also indicates a

decrease in drag coefficient with increasing aspect ratio (L/D), up to approximately L/D

= 2 – 3. Subsequently the drag coefficient becomes relatively constant at higher aspect

ratios, increasing slightly due to increased frictional drag resistance.

Generally, the drag on streamlined projectiles increases with increasing surface

roughness. However, for extremely blunt bodies the drag is independent of the surface

roughness, since the shear stress is not in the upstream flow direction and contributes

nothing to the drag. For blunt bodies like a cylinder or sphere, an increase in surface

roughness can actually lead to a decrease in drag as the increased roughness may cause

the boundary layer to become turbulent, resulting in a considerable drop in pressure

drag and only a slight increase in friction drag (Young et al. 1997).

The Reynolds number (Re) reflects the ratio of inertia to viscous effects and can be

defined as

83

ν

= vDRe (4.2)

where D is the diameter of the object and ν is the kinematic viscosity of the fluid. A

dynamic anchor with D = 1.2 m (see Table 3.5) travelling through water with ν = 10-6

m2/s (at 20 °C) at typical velocities of 10 – 30 m/s results in Reynolds numbers of

approximately 107 – 108. At low Reynolds numbers, the flow is laminar in nature and

friction drag dominates, whilst at high Reynolds numbers, inertia effects dominate and

the flow may become turbulent. The variation in the drag coefficient for a smooth

sphere and cylinder with Reynolds number is illustrated in Figure 4.2. For many shapes

there is a sudden change in the drag coefficient when the boundary layer becomes

turbulent. The Reynolds number at which this transition occurs is a function of the body

shape. For streamlined bodies, the drag coefficient will increase when the boundary

layer becomes turbulent because most of the drag is due to the shear force, which is

greater for turbulent flow than for laminar flow. On the other hand, the drag coefficient

for a relatively blunt object will decrease when the boundary layer becomes turbulent,

due to lower pressure drag resistance (Young et al. 1997). For a dynamic anchor falling

through sea water, the anchor diameter and fluid viscosity are essentially constant;

hence the Reynolds number will vary only with the object velocity.

If the velocity of the object is sufficiently large, compressibility effects may become

significant and the drag coefficient becomes a function of the Mach number (Ma)

f

a v

vM = (4.3)

where vf is the velocity of sound in the fluid. For low Mach numbers, i.e. Ma < 0.5,

compressibility effects are negligible and the drag coefficient is essentially independent

of the Mach number. Given that the speed of sound in seawater is approximately 1500

m/s, a dynamically installed anchor would have to be travelling at approximately 750

m/s for compressibility effects to become a consideration. This is at least an order of

magnitude greater than the typical range of dynamic anchor impact velocities.

84

4.2.2 Computational Fluid Dynamics

The drag coefficients for the zero fluke model anchors described in Section 3.6 were

determined using the Computational Fluid Dynamics (CFD) package, FLUENT. The

problem geometry and mesh were first created using GAMBIT and then loaded into the

FLUENT solver for analysis. Using FLUENT’s segregated solver and a laminar viscous

model, the drag coefficient was first calculated for a two dimensional, smooth, axis-

symmetric sphere. This permitted verification of the FLUENT results against the

theoretical solutions shown in Figure 4.2. The fluid was modelled as water with a

density of ρ = 998.2 kg/m3 and a viscosity of µ = 0.001003 kg/m.s. The problem domain

extended five diameters in the upstream direction, 20 diameters downstream and 10

diameters laterally (see Figure 4.3), and was meshed using a quad pave mesh. The

upstream boundary condition was set as a velocity inlet whilst downstream the

boundary was specified as an outflow. The analysis was conducted at a range of flow

velocities to evaluate the variation in drag coefficient with Reynolds number. The drag

coefficient for the smooth sphere obtained from the FLUENT analysis (according to

Equation 4.1) is shown in Figure 4.4 together with the theoretical drag coefficient

values from Figure 4.3. Good agreement is achieved between the calculated and

theoretical drag coefficient for Reynolds number values approaching 105. At this stage,

the flow undergoes a transition from laminar to turbulent flow. It should be noted that it

was not possible to model the transition to turbulence in FLUENT and as such it was

not possible to capture the theoretical change in the drag coefficient during this

transition. However, for typical dynamic anchor velocities of 10 – 30 m/s, the

approximate corresponding Reynolds number values of Re = 107 – 108 indicate that,

according to Figure 4.2, the flow will be fully turbulent and no longer undergoing

transition. Figure 4.2 indicates that the fully turbulent drag coefficient is similar to the

drag coefficient prior to the transition. Hence the FLUENT analysis was deemed to

provide a reliable method for calculating the drag coefficient of the dynamic anchors.

Upon verification of the drag coefficient for the case of the smooth sphere, the problem

geometry was altered to represent the four different zero fluke model anchor shapes, i.e.

ellipsoid nose, conical nose, ogive nose and flat nose (Figure 4.5). Again the problem

was defined in a two dimensional, axis-symmetric manner, with similar mesh

characteristics and domain extents as adopted for the case of the smooth sphere. The

85

model anchor drag coefficients were determined assuming a smooth anchor surface, i.e.

the effects of surface roughness were ignored. Flow velocities of up to 60 m/s were

selected in order to capture the likely range of velocities encountered during the free-fall

of dynamically installed anchors through the water column. The drag coefficients from

the FLUENT analysis for each of the model anchors are shown in Table 4.1, for flow

velocities of 1 – 60 m/s representing Reynolds number values of approximately 1 × 106

to 7 × 107.

CD

Anchor Tip 1 m/s 10 m/s 20 m/s 30 m/s 60 m/s Average

E0 ellipsoid 0.24 0.24 0.24 0.24 0.24 0.24

C0 cone 0.23 0.22 0.22 0.22 0.22 0.22

O0 ogive 0.22 0.22 0.22 0.22 0.22 0.22

F0 flat 0.88 0.88 0.88 0.88 0.88 0.88

Table 4.1 Zero fluke anchor drag coefficients

The calculated drag coefficients for the ellipsoid and flat nosed model anchors compare

favourably with the drag coefficients of the cylinder and streamlined object presented

by Hoerner (1965) in Figure 4.1. At the dynamic anchor aspect ratio of 12.5, Figure 4.1

indicates drag coefficients of approximately 0.25 and 0.83 for the streamlined object

and cylinder respectively, compared with 0.24 and 0.88 from the FLUENT analysis. Not

surprisingly, the blunt shape of the flat nosed anchor results in a significantly higher

drag coefficient when compared with the other three anchor shapes. This difference is

observable in the velocity contours presented in Figures 4.6 – 4.9, where at higher

velocities the flat nosed anchor develops a larger wake zone. The velocity contours also

support the results presented in Table 4.1 which suggest very similar drag coefficients

for the ellipsoid, conical and ogive shaped noses.

Table 4.1 also demonstrates that, for each of the anchors, the drag coefficient is

essentially constant for velocities in the range of 1 – 60 m/s. However, Figure 4.10

shows significantly higher drag coefficients for velocities below 1 m/s. The change in

the drag coefficient at lower velocities is highlighted by the change in the velocity

contours presented in Figures 4.6 – 4.9. At low velocities, the flow is viscous and

essentially no wake forms behind the anchor. As the velocity increases, a wake begins

to develop and with further increases in velocity this wake narrows and the drag

86

resistance is dominated by pressure effects. Since a dynamically installed anchor will

only spend a very short amount of time at velocities less than 1 m/s, the increase in drag

coefficient at lower velocities was not considered and the average drag coefficient for

velocities between 1 and 60 m/s has been adopted in the analysis.

FLUENT was also used to determine the drag coefficients for the model anchors with

varying aspect ratios (see Section 3.6.5). As for the 0FAs, the drag coefficient adopted

in the analysis was the average drag coefficient for velocities between 1 and 60 m/s.

These drag coefficients are presented in Table 4.2. It is evident that the drag coefficient

decreases with increasing aspect ratio before reaching a constant value of CD = 0.23 for

L/D ≥ 4. This is not surprising considering that at high velocities (or Reynolds number)

the drag is dominated by pressure effects on the front and back faces of the anchor.

Consequently frictional effects are minimal and increasing the length of the shaft

section whilst maintaining the same frontal area will have very little influence on the

drag coefficient. It is also apparent that the drag coefficients at higher aspect ratios

agree well with the drag coefficients for the ellipsoid, conical and ogive nosed 0FAs

presented in Table 4.1. This is to be expected given the similarities in anchor shape.

L/D CD

1 0.35

1.5 0.26

2 0.25

3 0.24

4 0.23

6 0.23

8 0.23

10 0.23

12 0.23

14 0.23

Table 4.2 Drag coefficient for model anchors with varying aspect ratio

Attempts were made to replicate the results obtained in the two dimensional axis-

symmetric analysis using the three dimensional capabilities of GAMBIT and FLUENT.

The meshing and calculation procedures however, proved time consuming and often did

not converge on a suitable solution. Hence no results were obtained from the three

dimensional analysis. Consequently no drag coefficients have been determined for the

87

four fluke model anchor and as such a value of CD = 0.63 has been adopted in

subsequent analysis, based on the results of similar CFD studies on DPAs (Øye 2000).

It should also be noted that no attempt was made to model the additional drag resistance

contributed by the anchor chain.

4.2.3 Inertial Drag in Soil

Despite a lack of experimental evidence supporting the existence of inertial drag

resistance in soil, True (1976), Freeman and Burdett (1986), Ove Arup and Partners

(1983), Lisle (2001), Wemmie (2003), Richardson (2003) and O’Loughlin et al.

(2004b) adopt an inertial drag resistance term (Fd) to predict the penetration depth of

objects into the seabed. In each case the inertial drag resistance has been formulated in a

similar manner as the hydrodynamic drag resistance

2pD2

1d vACF ρ= (4.4)

The inclusion of a drag term may be considered appropriate in view of the very soft

viscous clay often encountered at the surface of the seabed (O’Loughlin et al. 2004b).

However, in contrast to the vast amount of information regarding common fluids like

water, very little is known about the inertial forces experienced by objects moving

through soft seabed soil materials. These seafloor materials may exhibit non-Newtonian

behaviour; in fact, clay-water mixtures have been found to behave as Bingham plastics

(Houwink 1952, Pazwash and Robertson 1969, Pazwash 1970, Robertson and Pazwash

1971), defined by a non-zero yield stress and a plastic viscosity. Objects passing

through a Bingham plastic material may experience drag forces that are considerably

higher than those experienced when moving through a Newtonian fluid such as water.

Robertson and Pazwash (1971) define the drag coefficient of an object passing through

a Bingham plastic material as being of the form

2e

N,DDR

HKCC += (4.5)

where CD,N is the drag coefficient of the object in a Newtonian fluid at a Reynolds

number Re, K is an empirically derived coefficient dependent on the object shape and H

is the Hedstrom number defined as

88

2p

2yLH

µρτ

= (4.6)

where ρ is the fluid density, τy is the yield stress of the material, L is the object length

parallel to the flow direction and µp is the plastic viscosity. Consequently separate drag

coefficients may be necessary to account for the drag resistance to dynamic anchor

motion through the water column and through the seabed sediments. True (1976)

acknowledged the notion of separate drag coefficients for projectile motion through

fluid and soil materials by defining an effective drag coefficient (CDe)

fDsDf

DsDe v11

CCCC

+−+= (4.7)

where CDs and CDf are the drag coefficient in the soil and fluid respectively and vf is

given by

δ+

ρ=

pt

sceu

2De2

1f

AS

ANSs

vCv (4.8)

where su is the undrained shear strength, Se is the strain rate factor (see Section 2.2.3.4),

Nc is the bearing capacity factor for the projectile tip, δ is a side adhesion factor, As is

the surface area of the projectile, St is the soil sensitivity and Ap is the projected area of

the projectile.

Since CDe appears on both sides of Equation 4.7, an iterative procedure or algebraic

manipulation is required to derive the effective drag coefficient explicitly. The function

describing CDe provides an approximation for the transition between the geotechnical

and inertial effects. At low velocities, the soil drag coefficient dominates as the inertia

forces are small and the soil deformations follow typical bearing capacity mechanisms.

By contrast, at high velocities, the inertia forces are large and soil deformations tend

towards a pattern of fluid flow. The function assumes values of CDs and CDf for the

extreme cases of static and rapid penetration respectively but is limited in its

applicability in that both geotechnical and inertial effects are combined in a single

expression. True (1976) subsequently adopted an effective drag coefficient of 0.7 for the

analysis of cylindrical penetrometers. Whilst it is possible to model Bingham plastic

89

materials in FLUENT, this analysis has not yet been undertaken. Hence the analysis

presented in later chapters assumes that the drag coefficients for dynamic anchors

moving through soil are equivalent to the drag coefficients of these anchors moving

through water, i.e. CDs = CDf. It is acknowledged that this may create some inaccuracies

in the embedment depth analysis. However inertial drag effects are expected to

comprise only a relatively small proportion of the total resistance to penetration and

therefore this is not likely to have a substantial influence on the calculated embedment

depths.

4.3 IMPACT VELOCITY

The dynamic anchor velocity at impact with the seabed has a substantial influence on

the depth of penetration achieved. As the impact velocity was measured during the

centrifuge tests, accurate prediction of the impact velocity was not necessary. It is

interesting to note, however, the variation in impact velocity due to the non-uniform

acceleration field in the centrifuge and to compare the theoretical impact velocities with

the velocities measured in the experimental programme.

4.3.1 Uniform Acceleration Field

In a uniform acceleration field, the theory of conservation of energy can be used to

estimate the velocity of a dynamic anchor at the point of impact with the seabed. Prior

to release, the anchor possesses potential energy (Ep) based upon its height above the

seabed (hd), given by

dp mghE = (4.9)

where m is the anchor mass and g is the gravitational acceleration. Following release,

this potential energy is converted into kinetic energy (Ek), with

22

1k mvE = (4.10)

where v is the anchor velocity. According to the conservation of energy, assuming there

are no energy losses from the system, at the point of impact, all the potential energy

prior to release will have been converted into kinetic energy. Therefore the idealised

90

dynamic anchor impact velocity (vi) can be found by equating the potential energy to

the kinetic energy and rearranging to give:

di gh2v = (4.11)

The variation in impact velocity with drop height for a uniform acceleration field is

shown in Figure 4.11a.

4.3.2 Centrifuge Acceleration Field

In the centrifuge, the acceleration field is not uniform (see Section 3.2). During free-fall,

the model anchor experiences a gravitational acceleration (a) which increases with

radius (r) from the rotational axis of the centrifuge, expressed as:

ra 2ω= (4.12)

where ω is the rotational velocity of the centrifuge. Therefore, an incremental approach

is adopted whereby the acceleration is assumed constant over small radius intervals

(∆r). A linear equation of motion can then be used to determine the anchor velocity at

the end of each increment (ve)

ra2vv 2be ∆+= (4.13)

where vb is the velocity at the beginning of the increment. This incremental approach is

continued until the anchor reaches the sample surface, thereby providing an idealised

impact velocity.

Given the different radii of the beam and drum centrifuges, the relationship between the

drop height and idealised impact velocity will be different for each centrifuge. The

variation in impact velocity with drop height for the beam and drum centrifuges is

shown in Figure 4.11a. It should be noted that these theoretical impact velocities have

been obtained at an acceleration level of 200 g with an average sample height of 230

mm in the beam centrifuge and 165 mm in the drum centrifuge. Similarly effective radii

of 1607 mm and 530 mm were adopted for the beam and drum centrifuge calculations

respectively.

91

In Figure 4.11a the prototype drop heights are a factor of 200 times (i.e. gravitational

acceleration level, n) larger than the model drop heights, as given by the centrifuge

scaling laws in Section 3.2. However, due to the non-uniform acceleration field in the

centrifuge, an anchor installed from a prototype drop height of hd,p will achieve a higher

impact velocity than an anchor installed in the centrifuge from a drop height of hd,m =

hd,p/n. Hence the impact velocity analysis in the following chapters has been presented

in terms of equivalent prototype drop heights. These represent the drop height, at

prototype scale (i.e. uniform acceleration field), required for a dynamic anchor to

achieve the same impact velocity as a model anchor installed from a given drop height

in the centrifuge. Due to the different centrifuge radii the equivalent prototype drop

heights in the beam and drum centrifuges will be different (see Figure 4.11b).

4.3.3 Energy Losses

The above calculations are based on the assumption that no energy losses occur during

free-fall, i.e. all of the potential energy prior to release is converted into kinetic energy.

Hence they represent idealised impact velocities. Any external force acting on the

anchor during free-fall will cause an energy loss. During installation at prototype scale

the major external force acting on the anchor will be hydrodynamic drag. The energy

dissipated by this drag force will result in lower impact velocities than predicted by

Equation 4.11. In the centrifuge, only a nominal water layer exists on top of the soil

sample and as such the effects of hydrodynamic drag are expected to be minimal.

Instead, the anchor will experience a small amount of aerodynamic drag and frictional

resistance between the anchor and the installation guide (Section 3.7.1). Therefore

energy will also be dissipated during the free-fall stage of installation in the centrifuge

resulting in lower impact velocities than those predicted using the method outlined in

Section 4.3.2.

4.4 EMBEDMENT DEPTH

The holding capacity of dynamically installed anchors, in soil in which the shear

strength increases with depth, is directly dependent on the depth of penetration achieved

during installation. Hence in order to be able to accurately predict the anchor holding

92

capacity it is first necessary to be able to predict the expected embedment depth. From

studies investigating the penetration of objects into earth media (Young 1969, True

1976) it is apparent that the major factors influencing the embedment depth of an object

are the:

• shape (tip shape, aspect ratio, etc.)

• mass (density)

• impact velocity

• strength characteristics of the soil.

In Section 2.2.3, several methods were outlined for predicting the penetration depth of

objects into the seabed. In this study a modified version of True’s method (see Section

2.2.3.4) has been adopted for calculating the penetration depth of model dynamic

anchors in the centrifuge.

4.4.1 Calculation Procedure

True’s method is based on Newton’s second law of motion through consideration of the

forces acting on the anchor during penetration. The differential equation governing the

motion of the anchor through the soil is given by:

( ) dsbfs2

2

FFFRWdt

zdm −+−= (4.14)

where m is the anchor mass, z is the penetration depth below the seabed, t is the time

after impact with the seabed, Ws is the submerged weight of the anchor in soil, Rf is the

rate function, Fb is the end bearing resistance, Fs is the frictional resistance and Fd is the

inertial drag resistance.

It should be noted that the anchor embedment depth has been calculated assuming the

anchor remains vertical during installation. In addition, the cavity created by the passage

of the anchor through the soil is assumed to remain largely open following installation.

Poorooshasb and James (1989) used radiographs to show that cylindrical projectiles

consistently left open pathways when installed dynamically in kaolin clay in the

centrifuge, despite closed entrance craters. The radiographs showed that in some cases

the pathway extended continuously from the rear of the anchor to the sample surface,

whilst in other cases the pathway consisted of interconnected or discrete voids. Based

93

on these observations it has been assumed that during dynamic anchor installation in the

centrifuge, partial hole closure exists (see Figure 4.12b) despite a closed entrance crater.

Hence no reverse end bearing term is included in Equation 4.14 with the additional

resistance created by any hole closure accounted for by the inertial drag resistance term.

Figure 4.13 shows the forces acting on the anchor during penetration. The end bearing

resistance has been formulated as:

ptip,ucb AsNF = (4.15)

where Nc is the tip bearing capacity factor, su,tip is the undrained shear strength at the

anchor tip and Ap is the projected cross-sectional area of the anchor tip. In addition the

frictional resistance has been expressed as:

save,us AsF α= (4.16)

where α is the shaft adhesion factor, su,ave is the undrained shear strength averaged over

the embedded shaft length and As is the surface area of the embedded anchor shaft.

When considering the embedment depth of anchors with flukes, additional bearing and

frictional resistance terms should be included to account for their contribution to the

total penetration resistance (Figure 4.14). It is expected that full closure will occur

behind the anchor flukes due to their relatively small thickness and the apparent plane

strain conditions encountered. Hence a reverse end bearing term should be included to

account for the resistance generated by the topside of the anchor flukes (Frf), given by:

pftf,ucfrf AsNF = (4.17)

where Ncf is the bearing capacity factor of the flukes, su,tf is the undrained shear strength

at the top of the anchor flukes and Apf is the total projected area of the flukes. The

bearing resistance generated by the underside of the anchor flukes (Fbf) can be

expressed as:

pfbf,ucfbf AsNF = (4.18)

where su,bf is the undrained shear strength at the bottom of the flukes. The contribution

of the anchor flukes to the frictional resistance (Fsf) is given by:

94

sfsf,usf AsF α= (4.19)

where su,sf is the average shear strength over the embedded fluke length and Asf is the

embedded fluke surface area.

The inertial drag resistance of the soil to the penetration of dynamically installed

anchors has been formulated using Equation 4.4.

The strain rate dependence of the soil shear strength has been accounted for by adopting

either the semi-logarithmic rate function (see Section 2.2.3.1) given by:

γγλ+=ref

f log1R&

& (4.20)

or the power rate function (see Section 2.2.3.1) expressed as:

β

γγ=ref

fR&

& (4.21)

where λ and β are the strain rate parameters for the respective formulations, γ& is the

strain rate and refγ& is the strain rate at which the reference (‘static’) undrained shear

strength was determined. The strain rate is assumed to be proportional to v/D, where v

is the penetration velocity and D the diameter. Hence the reference strain rate from the

T-bar penetrometer tests (v = 1 mm/s and D = 5 mm, see Section 3.5.1) is refγ& = 0.2 s-1.

A finite difference approach was adopted to solve Equation 4.14, thereby producing a

velocity profile with penetration depth. The incremental acceleration (ai) can be

calculated as:

( )

m

FFFRWa disibifs

i

−+−= (4.22)

where Fbi, Fsi and Fdi are the incremental values of the bearing, frictional and inertial

resistance forces. From this, the incremental penetration depth can be determined using

a central difference solution:

1iii2

1i zz2atz −+ −+∆= (4.23)

95

where ∆t is the specified time increment. Calculation of the penetration depth at the end

of the first increment (z1) using Equation 4.23 requires an estimate of the depth one time

increment prior to impact (z-1). This depth has been calculated assuming a constant

velocity, i.e. z-1 = -∆t v0. Subsequently, the velocity at the end of the first increment can

be determined as:

( )

t

zzv i1i

1i ∆−= +

+ (4.24)

Further time increments are taken until the velocity becomes negative, at which point

the final embedment depth (z) can be calculated by interpolating between the final two

embedment depth values:

( )

−−−=

++

1ii

i1iii vv

vzzzz (4.25)

A flow chart outlining the calculation procedure is presented in Figure 4.15.

4.4.2 Parameter Values

Accurate prediction of the embedment depth of dynamic anchors relies heavily upon the

determination of several parameters, namely, the bearing capacity factor, the shaft

adhesion factor and the strain rate parameter. The selection of values for these

parameters is discussed below.

It has been shown that for a circular foundation deeply embedded within saturated clay,

Nc = 9 (Skempton 1951 as cited in Skempton 1959). Consequently Richardson (2003)

adopted a value of Nc = 9 in determining the tip bearing resistance to dynamic anchor

penetration. However, as illustrated in Figure 4.16, the bearing capacity factor increases

with depth, up to embedments of four diameters, at which point the free surface no

longer influences the bearing mechanism. The increase in bearing capacity factor with

depth, for both circular and strip foundations has been formulated as (Skempton 1951 as

cited in Whitlow 2001):

+

+=D

z053.01

L

D2.0114.5Nc (4.26)

96

where D is the foundation diameter or width, L is the foundation length and z is the

embedment. Maximum values of the bearing capacity factor occur when z/D ≥ 4, with:

• Nc = 9 for circular or square footings (D/L = 1)

• Nc = 7.5 for strip footings (D/L = 0)

Since dynamically installed anchors typically embed up to 2 – 3 times the anchor length

(O’Loughlin et al. 2004b), the variation in bearing capacity factor over the first few

diameters of embedment is not expected to have a significant influence on the

calculated embedment depth, particularly as the surface soils are typically very weak.

Generally, the nose of a dynamically installed anchor is not simply circular but rather

elongated or pointed. Therefore bearing capacity factors derived from cone penetration

tests may be more appropriate for determining the anchor’s bearing resistance. Bearing

capacity factors derived both experimentally and theoretically for cone penetration tests,

however, cover a wide range of values, typically approximately 8 – 20 (Lunne et al.

1997). Based on appropriate bearing capacity factors for cone penetration tests,

O’Loughlin et al. (2004b) adopted an average bearing capacity factor of Nc = 12 for

calculating the penetration depth of dynamically installed anchors. In addition, the

bearing area of the anchor flukes is analogous to a strip footing. For a deeply embedded

strip footing, Nc = 7.5 (Skempton 1951 as cited in Whitlow 2001). Therefore bearing

capacity factors of Nc = 12 and Ncf = 7.5 have been adopted in the analysis for the

anchor nose and flukes respectively. For the hemispherically nosed anchors with

varying aspect ratios, it seems appropriate to adopt the bearing capacity factor for a ball

penetrometer. Chung (2005) reports bearing capacity factors for ball penetrometers

ranging from approximately 7 – 13. Consequently an average bearing capacity factor of

Nc = 10 has been adopted in the analysis for the model anchors with hemispherical

noses.

Typically, during installation, the frictional resistance generated along the wall of the

foundation is close to the remoulded shear strength of the clay. The ratio of the

frictional resistance to the undisturbed shear strength is defined as the adhesion factor

(α) and is often expressed as:

u

r,u

t s

s

S

1 =≅α (4.27)

97

where St is the soil sensitivity, su,r is the remoulded shear strength and su is the

undisturbed shear strength. In accounting for the frictional resistance during penetration

of cylindrical projectiles, True (1976) included a parameter to account for separation

between the anchor and the soil during dynamic penetration of the soil. However, there

is no experimental evidence justifying the existence of separation between projectiles

and the soil during installation. Consequently, it has been assumed in the analysis

adopted in this study that no separation occurs during penetration. Chen and Randolph

(2007) report installation friction ratios of α = 0.38 for suction caissons in kaolin clay.

This agrees well with typical sensitivities for kaolin clay of St = 2 – 2.5. Similarly,

adopting a tip bearing capacity factor of Nc = 12, a best fit value of α = 0.4 was reported

for dynamic anchor constant rate of penetration tests in the centrifuge (O’Loughlin et al.

2004b). Hence unless otherwise specified a shaft adhesion factor of α = 0.4 has been

adopted in the embedment depth analysis. In all calculations, the fluke adhesion factor

has been assumed to be equal to the shaft adhesion factor, i.e. αshaft = αfluke = 0.4.

The greatest uncertainty in the calculation of dynamic anchor embedment depths is the

determination of the strain rate parameter. Typically, the strain rate parameter has been

back-calculated from measured experimental data (Lisle 2001, Wemmie 2003,

Richardson 2003, O’Loughlin et al. 2004b). O’Loughlin et al. (2004b) reported strain

rate parameter values of 19 – 33 % (i.e. λ = 0.19 – 0.33) for dynamic anchor tests

conducted in the centrifuge in kaolin cay. Due to the degree of uncertainty surrounding

the strain rate effects in fine grained soils, particularly at the very high strain rates

encountered during dynamic anchor installation, the strain rate parameter values in this

study have again been back-calculated from the results of the experimental programme.

Further details are provided in Chapter 7.

4.5 HOLDING CAPACITY

In Section 2.3 two simplified analytical methods for determining the capacity of piles

were outlined. The relative infancy of the dynamic anchor concept has ensured that very

little capacity data exists for the validation of either method in relation to the dynamic

anchor capacity. This combined with the uncertainty surrounding the influence of the

dynamic anchor installation process on the anchor capacity and the added complexities

98

of the anchor geometry relative to standard piles suggest the use of a simple capacity

calculation technique. The API method is the simpler of the two methods, expressing

the bearing resistance in terms of standard bearing capacity factors and the shaft friction

as a proportion of the undrained shear strength. By contrast, the MTD method requires

the use of more sophisticated soil properties, thereby adding to the complexity of the

calculation. Hence the API method has been used to evaluate the vertical, monotonic

holding capacity of the model dynamic anchors.

4.5.1 Calculation Procedure

Based on the API method (see Section 2.3.1, API 2000), the capacity of a zero fluke

dynamic anchor under tension loading (Fv) can be expressed as:

srbsv FFFWF +++= (4.28)

where Fb is the bearing resistance at the anchor padeye, Fr is the reverse end bearing

resistance at the anchor tip and Fs is the frictional resistance (see Figure 4.17).

It should be noted that, as for the embedment depth analysis, calculation of the anchor

capacity assumes anchor verticality and partial closure of the cavity created by the

passage of the anchor through the soil. Consequently the bearing resistance at the

anchor padeye has been calculated with a factored bearing capacity factor to reflect the

degree of hole closure. The bearing resistance at the anchor padeye is defined as:

ppad,ucb AsfNF = (4.29)

where f is the degree of hole closure (i.e. f = 0 for fully open cavity and f = 1 for fully

closed cavity), su,pad is the undrained shear strength at the anchor padeye and Ap is the

projected area of the anchor. A nominal value of f = 0.1 has been adopted, reflecting 10

% hole closure. The value of f is not expected to have a significant influence on the

anchor capacity as the relatively small anchor padeye embedments result in the

mobilisation of low shear strengths and hence small padeye bearing resistances.

The reverse end bearing at the anchor tip is expressed as:

ptip,ucr AsNF = (4.30)

99

where su,tip is the undrained shear strength at the anchor tip. In addition the frictional

resistance is given by:

save,us AsF α= (4.31)

As for the embedment depth analysis in Section 4.4, for anchors with flukes, the

additional bearing and frictional resistances to vertical uplift loading need to be

considered (see Figure 4.18). The bearing resistance generated on the upper portion of

the anchor flukes can be expressed as:

pftf,ucfbf AsNF = (4.32)

where su,tf is the undrained shear strength at the top of the anchor flukes. Likewise the

reverse end bearing at the bottom of the anchor flukes is given by:

pfbf,ucfrf AsNF = (4.33)

where su,bf is the undrained shear strength at the bottom of the anchor flukes. Finally the

frictional contribution of the anchor flukes to the holding capacity of the anchor is

defined as:

sfsf,usf AsF α= (4.34)

where su,sf is the average undrained shear strength over the embedded length of the

flukes.

4.5.2 Parameter Values

The bearing capacity factor adopted for the anchor tip in the embedment analysis, Nc =

12, was derived from the results of cone penetration tests (see Section 4.4.2). Hence it

seems appropriate that the same bearing capacity factor be adopted in the holding

capacity analysis. However, Watson et al. (2000) and Chung (2005) present cone

extraction profiles which demonstrate a much more gradual development of the tip

extraction resistance compared with the tip resistance during penetration. This tends to

suggest a reduction in the mobilisation rates of the tip bearing resistance between cone

penetration and extraction. These findings support the observations of Lehane (1992)

who through a series of pile load tests showed a much softer pile response under tension

100

rather than compression. Therefore due to the similarities between dynamic anchors and

cone penetrometers it could be expected that the full bearing resistance at the anchor tip

may not be mobilised until the anchor has undergone significant vertical displacement.

This would likely manifest itself in non-simultaneous mobilisation of the anchor bearing

and frictional resistance, as discussed by Jeanjean et al. (2006) for suction caissons.

Since the API method is based on the simultaneous mobilisation of full bearing and

frictional resistance, the calculation procedure may result in a slight over prediction of

the anchor capacity. Hence it may be appropriate to use a reduced bearing capacity

factor to account for this difference in mobilisation rates. However, since the reverse

end bearing resistance typically comprises only 15 – 20 % of the total anchor uplift

resistance, a reduction in the tip bearing capacity factor from Nc = 12 to 9 will have a

relatively minor influence on the anchor capacity. Consequently, the calculation

procedure has been simplified by adopting a bearing capacity factor of Nc = 12.

Similarly, the fluke bearing capacity factor (Ncf = 7.5) and the bearing capacity factor

for the hemispherically shaped tip (Nc = 10) adopted in the holding capacity analysis

have been assumed to be the same as those adopted in the embedment analysis (see

Section 4.4.2).

Unlike the elongated tip, the dynamic anchor padeye is flat and circular, suggesting the

use of a bearing capacity factor for a deep circular foundation, Nc = 9 (Skempton 1951

as cited in Skempton 1959). However as discussed in Section 4.4.2 the bearing capacity

factor for circular foundations varies with depth, up to four times the anchor diameter.

With typical dynamic anchor tip embedments ranging from 2 – 3 times the anchor

length (O’Loughlin et al. 2004b) and corresponding padeye embedments of 1 – 2 times

the anchor length or 12.5 – 25 times the anchor diameter, it is unlikely that the soil

surface will influence the bearing mechanism at the anchor padeye until well after

realisation of the ultimate anchor capacity. Hence a bearing capacity factor of Nc = 9

has been adopted for the anchor padeye in the holding capacity analysis. Since the

anchors fitted with hemispherical tips also feature hemispherical padeye sections, the

same bearing capacity factor has been adopted for the padeye as the anchor tip, i.e. Nc =

10.

American Petroleum Institute guidelines (API 2000) define the shaft adhesion factor

during loading as:

101

For 1s

v

u ≤σ′

1s

5.05.0

v

u ≤

σ′=α

(4.35)

For 1s

v

u >σ′

1s

5.025.0

v

u ≤

σ′=α

(4.36)

where σv′ is the vertical effective stress.

4.5.3 Normalised Capacity

Anchor capacities measured during testing in the centrifuge were adjusted to account for

the submerged weight of the anchor (Ws) and then normalised by the average undrained

shear strength over the embedded anchor length (su,ave) and the anchor’s projected area

(Ap):

pave,u

svN As

WFF

−= (4.37)

where FN is the normalised anchor capacity. Normalisation in this manner allows direct

comparison of capacities, taking into account differences in anchor and soil properties

and the anchor’s embedment depth.

4.5.4 Anchor Efficiency

The anchor capacities measured in the experimental programme have also been

compared in terms of the anchor efficiency. The anchor efficiency (Ef) represents the

ratio of the holding capacity (FV) to the anchor’s dry weight (W):

W

FE v

f = (4.38)

4.6 CALCAREOUS SAND

Calcareous sands are defined as sands comprising calcium carbonate and they originate

from biological processes such as sedimentation of skeletal debris, coral reef formation

or chemical precipitation (Murff 1987). Unexpected difficulties have been encountered

102

with offshore foundations situated on high carbonate content soils (i.e. > 50 %). The

engineering properties of these materials are quite different to those of silica sands and

clays due to the presence of varying amounts of cementation and the high angularity of

the particles which results in high in situ void ratios. The high void ratios result in low

densities and low ratios of horizontal to vertical stress as well as high compressibility.

The highly variable nature of calcareous soils has led to uncertainty in pile capacity

predictions (Murff 1987, Randolph 1988). Despite this, conventional pile capacity

theory has been applied to predict the embedment depth and holding capacity of

dynamic anchors in reconstituted calcareous sediments.

4.6.1 Embedment Depth

4.6.1.1 Calculation Procedure

The embedment depth of dynamically installed anchors in calcareous sand has been

calculated using a similar method to that adopted for determining anchor embedment in

clay (see Section 4.4). The differential equation linking the forces acting on the anchor

to the acceleration is given by:

( ) dsbfs2

2

FFFRWdt

zdm −+−= (4.39)

Equation 4.39 is identical to Equation 4.14 for anchor embedment in clay; however the

differences in soil properties ensure that the bearing and frictional resistance terms are

calculated differently. In silica sands, the end bearing capacity is generally expressed in

terms of a bearing capacity factor (Nq) and the in situ overburden pressure (0vσ′ ). A

similar approach has been adopted for calcareous sand, with the bearing resistance

given by

p0vqb ANF σ′= (4.40)

The shaft friction resistance has also been linked to the overburden pressure and is given

by

save,0vCALCs AF σ′β= (4.41)

103

where βCALC represents the ratio of shaft friction to the effective overburden stress and

ave,0vσ′ is the average effective stress over the embedded shaft length.

The inertial drag resistance of the soil to the penetration of dynamically installed

anchors has been formulated using Equation 4.4.

Since no tests were conducted in calcareous sand using the four fluke model anchors, it

was not necessary to consider the additional resistance contributed by the flukes during

penetration.

The rate dependence of the strength of the calcareous sand has been formulated using

either Equation 4.20 or 4.21.

Once the forces resisting penetration were determined, the same time stepping approach

adopted for the normally consolidated clay was used to calculate the incremental

acceleration, given by

( )

m

FFFRWa disibifs

i

−+−= (4.42)

The incremental displacement and velocity were then calculated using Equations 4.23

and 4.24, with the time stepping approach continuing until a negative velocity was

obtained, in which case the final embedment was found by interpolating between the

last two embedment values using Equation 4.25.

4.6.1.2 Parameter Values

The determination of the values of Nq and βCALC is notoriously difficult in calcareous

sands. Experimental evidence shows that the value of Nq decreases significantly as the

stress level rises, due to decreasing peak friction angles with increasing stress and the

increased compressibility of the soil (Randolph 1988). At a given stress level the high

friction angles and high compressibility of calcareous sediments result in substantially

lower bearing capacities compared with silica sand (Randolph 1988). Poulos and Chua

(1985) reported bearing capacity values for calcareous sand that were approximately 40

% of the corresponding bearing capacities in silica sand (see Figure 4.19).

Consequently, an average value of Nq = 32 derived from CPTs conducted during the

experimental programme has been used in the embedment depth analysis.

104

It is known that as piles are driven deeper into silica sands, the ratio, βCALC, decreases

rapidly with distance from the pile tip due to a reduction in the friction angle at

increasing stress levels and the lower lateral effective stresses generated around the pile

due to the increasing compressibility of the soil (Randolph 1988). The compressibility

of calcareous soils is generally an order of magnitude greater than for silica sands at the

same stress level. Nauroy and Le Tirant (1983) showed that for model tests the net

change in lateral stress due to pile installation becomes negative in calcareous sands.

This reduction may be attributed to crushing and compaction of the sand due to

shearing, both ahead of the advancing pile tip, and also along the shaft of the pile as it

continues to penetrate the soil. The degree of cementation may also affect the skin

friction; however the cementation will be broken down locally as the pile tip advances

during installation. Abbs et al. (1988) presented a summary of βCALC values obtained

from field tests plotted against the length of the test section in calcareous sand (see

Figure 4.20). Note that to avoid confusion with the strain rate parameter for the power

rate law (see Section 2.2.3.1), βCALC has been used in place of β. For short piles (L ≤ 20

m), βCALC values of up to 0.4 are evident, whilst for longer piles Figure 4.20 shows that

values of up to approximately 0.05 are likely. In the dynamic anchor tests, the value of

βCALC has been determined from static penetration tests, with a bearing capacity factor

of Nq = 32, giving an average value of βCALC = 0.42. Considering the relatively short

dynamic anchor length (L = 15 m), this is relatively consistent with the βCALC values for

short piles reported by Abbs et al. (1988).

The strain rate parameter was back-calculated from the experimental data and is

discussed further in Section 7.4.2.1.

4.6.2 Holding Capacity

4.6.2.1 Calculation Procedure

The ultimate vertical holding capacity (Fv) of dynamically installed anchors was

determined as the sum of the submerged weight in soil (Ws) and the end bearing (Fb)

and shaft friction resistances (Fs):

sbsv FFWF ++= (4.43)

105

It should be noted that as the vertical anchor extraction in calcareous sand was

conducted under drained conditions, no reverse end bearing term at the anchor tip is

included in the capacity analysis. The bearing resistance at the anchor padeye is

expressed as:

ppad,0vqb AfNF σ′= (4.44)

where Nq is the bearing capacity factor of the anchor padeye and pad,0vσ′ is the vertical

effective stress at the anchor padeye. Note that full closure of the anchor’s entry

pathway has been assumed in calcareous sand, i.e. f = 1. The frictional resistance to

anchor pullout is then determined as:

save,0vCALCs AF σ′β= (4.45)

4.6.2.2 Parameter Values

The measured embedments during dynamic anchor tests in calcareous sand are

considerably lower than the corresponding embedments in clay (see Section 6.3.3).

Consequently, the anchor padeye is often close to the soil surface following installation

in calcareous sand. As such the bearing resistance of the anchor padeye is analogous to

the bearing resistance of a shallow embedded circular plate anchor (see Figure 4.21).

Rowe and Davis (1982) present bearing capacity factors for vertically loaded plate

anchors in sand, for embedment depths normalised by the anchor diameter (see Figure

4.22). At the friction angle of φ = 40° for the calcareous sand used in the test

programme (Table 3.3) it is therefore possible to use Figure 4.22 to determine a bearing

capacity factor for the anchor padeye during vertical loading. Rowe and Davis (1982)

consider bearing capacity factors of up to 7 for normalised embedments of 8 or less. No

similar studies are available for plate anchors in calcareous sands and as such the Rowe

and Davis (1982) results for silica sand have been used as a basis for the assessment of

the bearing capacity at the anchor padeye in calcareous sand.

The values of βCALC used in the holding capacity analysis have been back-calculated

from the holding capacities measured in the experimental program, assuming bearing

capacity factors as determined above.

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CHAPTER 5 - EXPERIMENTAL RESULTS FOR

DYNAMIC ANCHOR TESTING IN NORMALLY

CONSOLIDATED CLAY

5.1 INTRODUCTION

The key objective of the research programme was to establish a database of dynamic

anchor performance from centrifuge model tests, to investigate the relationship between

anchor impact velocity, embedment depth and holding capacity. Since dynamic anchors

have been proposed as an alternative deepwater anchoring solution, and deepwater

environments are typically characterised by soft clay deposits, this chapter presents the

results of the dynamic anchor centrifuge tests conducted in normally consolidated clay.

These tests accounted for over 90 % of the total dynamic anchor tests conducted in the

experimental programme and investigated the influence of anchor density, anchor

geometry, consolidation time, monotonic loading, sustained loading and cyclic loading

on the performance of dynamically installed anchors in clay. Tests were conducted in

both the beam and drum centrifuges. The beam centrifuge provided greater sample

depths, allowing heavier anchors and / or larger drop heights to be investigated. The

drum centrifuge on the other hand provided a sample plan area almost four times larger

than that in the beam centrifuge, allowing significantly more tests to be conducted in a

single sample, with the added benefit of in-flight changeover between tests thereby

avoiding the need for reconsolidation time. The results of the tests conducted in both the

beam and drum centrifuges have been considered separately and the test results have

been compared with the results of dynamic anchor field trials and previous laboratory

and centrifuge model tests.

When referring to individual tests the first letter of the test identifier indicates whether

the test was conducted in the beam (B) or drum (D) centrifuge, with the following

number referring to the sample number in that particular centrifuge. The subsequent

letter(s) specify the type of test.

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• D – dynamic anchor drop test, vertical monotonic extraction

• SUS – dynamic anchor drop test, vertical sustained loading

• CYC – dynamic anchor drop test, vertical one-way cyclic loading

The final number represents the number of that particular type of test in the sample. For

example ‘B5SUS3’ identifies the third sustained loading test conducted in beam

centrifuge sample number 5, whilst ‘D2D9’ represents the ninth vertical monotonic

extraction test in drum centrifuge sample number 2. The dynamic anchor installation

process is summarised in Sections 3.8.1.1 and 3.8.2.1 for the beam and drum centrifuges

respectively, whilst the vertical monotonic extraction procedure is detailed in Section

3.8.1.2 for the beam centrifuge and 3.8.2.2 for the drum centrifuge. Long-term sustained

loading and cyclic loading are described in Sections 3.8.1.3 and 3.8.1.4 respectively.

5.2 BEAM CENTRIFUGE

The experimental programme in the beam centrifuge comprised a number of tests aimed

at establishing the general relationships between impact velocity, embedment depth and

holding capacity as well as investigating the influence of the anchor tip geometry on

these relationships and evaluating the performance of dynamic anchors under cyclic and

sustained loading. The tests assessing the general performance of dynamic anchors were

conducted with ellipsoid nosed zero fluke model anchors (i.e. anchors E0-1, E0-2, IE0-1

and IE0-2), which have been detailed previously in Sections 3.6.1 and 3.6.4. Similarly,

the influence of the anchor tip shape was investigated using zero fluke model anchors

with ellipsoid, conical, ogive and flat noses (i.e. anchors E0-1, C0-1, O0-1 and F0-1; see

Sections 3.6.1 and 3.6.3). Finally, the cyclic and sustained loading tests were conducted

with a single ellipsoid nosed zero fluke model anchor (E0-2; see Section 3.6.1).

5.2.1 Strength Characterisation Tests

Profiles of undrained shear strength with depth were obtained for the beam centrifuge

samples using the T-bar penetrometer described in Section 3.5.1, with the undrained

shear strength expressed as:

109

barT

u N

qs

= (5.1)

where q is the average bearing pressure and NT-bar is a T-bar factor. The analytical value

of NT-bar depends on the roughness of the T-bar. Plasticity solutions give a value of

approximately 12 for a rough bar, and a value of 9 for a smooth bar. Stewart and

Randolph (1991) recommended a T-bar factor of 10.5, representing an average of the

rough and smooth cases. Consequently, the shear strengths have been calculated using

NT-bar = 10.5.

Figure 5.1 shows the undrained shear strength profile with depth for a typical T-bar

penetrometer test conducted in normally consolidated clay. The test indicates an

approximately linear increase in shear strength with depth, such that:

kzsu = (5.2)

where k is the shear strength gradient and z is the penetration depth. However,

centrifuge shear strength data tend to deviate slightly from a linear profile at greater

depths, due to the increase in radial acceleration with increasing radius and slight

underconsolidation of the body of the soil sample. Therefore the undrained shear

strength profile is often better described using a polynomial expression of the form:

bzazs 2u += (5.3)

where ‘a’ and ‘b’ are coefficients. Both linear and polynomial idealised shear strength

profiles are shown in Figure 5.1 and it is apparent that the polynomial formulation in

Equation 5.3 provides better agreement with the experimental data, particularly at

depths greater than 100 mm (20 m at prototype scale). Table 5.1 presents the

polynomial coefficient values for the average undrained shear strength profiles in each

of the beam centrifuge samples. The polynomial functions provided improved accuracy

in the calculation of undrained shear strengths at particular anchor embedment depths.

Also included in Table 5.1 are the gradients for the best fit linear profile over the first 20

m of penetration for each sample.

T-bar tests were conducted prior to and at the conclusion of dynamic anchor testing in

each sample. The average undrained shear strength profiles are shown in Figures 5.2 –

5.7. The measured profiles are typical for normally consolidated reconstituted kaolin,

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with approximate shear strength gradients of between 1 and 1.2 kPa/m and indicating a

slight increase in strength during the course of testing. Box 2 however, demonstrated a

lower shear strength gradient of approximately 0.8 kPa/m, possibly due to incomplete

consolidation of the sample. In addition, Box 6 demonstrated a higher shear strength

gradient of approximately 1.4 kPa/m, which can be attributed to the modified sample

preparation procedure adopted (see Section 3.4.2.1). Consequently the average shear

strength coefficients calculated at the bottom of Table 5.1 exclude the values

determined for Boxes 2 and 6. Figure 5.8 provides a comparison of the average

undrained shear strength profiles in each sample. It can be seen that apart from Boxes 2

and 6, the measured shear strengths are relatively consistent.

Sample a b k

(kPa/m2) (kPa/m) (kPa/m)

Box 1 0.012 0.973 1.17

Box 2 0.016 0.592 0.83

Box 3 0.018 0.797 1.09

Box 4 0.007 0.888 1.00

Box 5 0.013 0.822 1.03

Box 6 0.007 1.296 1.45

Average 0.013 0.870 1.07

Table 5.1 Polynomial and linear undrained shear strength coefficients

The shear strength profiles described by the coefficients presented in Table 5.1

represent the average shear strength profile for each sample. However the increase in

shear strength during the course of testing warrants the adoption of separate shear

strength profiles for each dynamic anchor test. Table 5.10 (see the Tables section)

provides values of the polynomial shear strength coefficients for individual dynamic

anchor tests derived from interpolation between T-bar tests conducted before and after

each test. These interpolated shear strength profiles have been used in the subsequent

analysis.

The undrained shear strength ratio, 0vu /s σ′ , was determined with the in situ vertical

effective stress calculated as:

zn0v γ ′=σ′ (5.4)

111

where n is the gravitational acceleration level, γ′ = 6.5 kN/m3 is the effective soil unit

weight (see Table 3.2) and z is the depth (at model scale). The average undrained shear

strength ratios in the beam centrifuge samples are presented in Table 5.2. The overall

average undrained shear strength ratio (excluding Boxes 2 and 6) compares favourably

with the value of 0.18 reported by Stewart (1992) for normally consolidated kaolin clay

(see Table 3.2).

Sample su / σ v0 k

(kPa/m)

Box 1 0.18 1.17

Box 2 0.13 0.83

Box 3 0.17 1.09

Box 4 0.15 1.00

Box 5 0.16 1.03

Box 6 0.22 1.45

Average 0.17 1.07

Table 5.2 Undrained shear strength ratio

Figure 5.9 shows an example of one of four cyclic T-bar tests conducted in Box 6 to

quantify the sensitivity of the clay (see Section 3.5.1). The development of sensitivity

with increasing number of cycles is shown in Figure 5.10. The steady state sensitivities

in Figure 5.10 indicate full remoulding of the soil after approximately 10 cycles. The

results of each of the four cyclic T-bar tests are relatively consistent and indicate a

sensitivity of approximately 2.5, which is in good agreement with sensitivity values for

normally consolidated kaolin clay of 2 – 2.8 reported by Watson et al. (2000). However,

the purpose of the modified sample preparation procedure outlined in Section 3.4.2.1

was to develop a clay sample with a higher than normal sensitivity; clearly it was not

successful in doing so. As a result of the addition of the dispersing agent and the lower

than normal moisture content, the exact soil properties of the sample are unclear.

Consequently the embedment and capacity results derived from dynamic anchor tests in

Box 6 have not been considered in the analysis. It should be noted that sensitivities

determined from cyclic T-bar tests are likely to under predict the actual soil sensitivity

as the undisturbed shear strength is mobilised ahead of the penetrometer with the soil

softening towards a partially remoulded strength behind the T-bar (Yafrate and DeJong

112

2005). As such cyclic T-bar tests are considered to provide a broad indication of the

sample sensitivity only.

5.2.2 Impact Velocity

The penetration depth achieved by dynamically installed anchors is dependent on the

velocity of the anchor at the point of impact with the seabed. The impact velocity is in

turn dependent on the drop height and the gravitational acceleration (see Section 4.3).

The velocities measured in the beam centrifuge tests are presented in Table 5.10.

A single PERP installation guide was used to measure the velocity in Boxes 1, 2 and 3.

As mentioned in Section 3.7.1, the single PERP velocity measurement system provides

a lower level of accuracy than the multiple PERP system adopted in Boxes 4, 5 and 6.

Figure 5.11 shows the variation in the measured velocity with drop height for the single

PERP tests. As expected the test results indicate an increase in velocity with increasing

drop height. Also included in Figure 5.11 are the results of similar centrifuge tests

conducted by Lisle (2001), Wemmie (2003) and Richardson (2003) using a single PERP

system. The current test data demonstrate good agreement with the results of the

previous centrifuge tests. It should be noted that the drop heights shown in Figure 5.11

are equivalent prototype drop heights, i.e. the drop height (at prototype scale) required

to achieve the same velocity as a dynamic anchor installed from a given drop height at

model scale in the centrifuge (see Section 4.3.2). Hence a model drop height of 300 mm

represents an equivalent prototype drop height of 51.5 m (assuming a sample height of

230 mm and an effective radius of 1.607 m). Both the model and corresponding

equivalent prototype drop heights are presented in Table 5.10.

A comparison of the velocities measured in the single and multiple PERP tests is

provided in Figure 5.12. The multiple PERP velocities are much more consistent and,

on average, approximately 30 % higher than the single PERP velocities over the range

of drop heights considered. In order to account for the apparent under estimation of

impact velocity in the single PERP tests, the measured single PERP velocities were

adjusted. The data were adjusted such that the best-fit line for the multiple PERP data

represented an approximate best-fit for the single PERP data. In order to achieve this, an

additional 6 m/s was added to each of the measured single PERP velocities (excluding

the situation of a zero drop height). It should be noted that for cases in which the drop

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height was zero (i.e. the anchor tip was positioned at the sample surface prior to

release), the impact velocity was assumed to be equal to zero. No adjustment was

necessary for the multiple PERP tests and the impact velocity (vi) was taken as the

measured velocity (vm). The adjusted velocities can be seen in Figure 5.13. The

velocities represented by the best-fit line through the centrifuge data in Figure 5.13 are

also presented in Table 5.3. In several tests, the logging software did not capture the

installation event and consequently no velocity measurement was obtained. For these

tests, the impact velocities at the corresponding drop height in Table 5.3 have been

adopted in Table 5.10 and the subsequent analysis.

Drop Height Average Impact

hd,m hd,eq Velocity

(mm) (m) (m/s)

0 0 0

50 9.4 11.7

100 18.4 16.6

150 27.2 20.3

200 35.6 23.4

250 43.7 26.2

300 51.5 28.7

Table 5.3 Variation in impact velocity with drop height – beam centrifuge

Figure 5.14 shows the velocity profile for a model anchor installed in the beam

centrifuge from a drop height of 200 mm above the surface. It is apparent that the

anchor velocity continues to increase after the point of impact. This is due to an

imbalance in the forces driving and resisting anchor penetration and highlights the fact

that the anchor impacted the sample at a sub-terminal velocity. By equating the

submerged weight and drag forces during free-fall through the water column, the

terminal velocity (vt) can be calculated according to the expression:

pD

st AC

W2v

ρ= (5.5)

where Ws is the submerged weight of the anchor in water, CD is the drag coefficient

determined in Section 4.2.2 and ρ = 1000 kg/m3 is the density of water. The terminal

velocities for the model anchors used in the beam centrifuge tests (see Section 3.6) are

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presented in Table 5.4. Restrictions in both drop height and sample depth, however,

limited the centrifuge tests to maximum velocities in the order of 30 m/s (see Table

5.10). These velocities are, on average, approximately 60 % lower than the terminal

velocities presented in Table 5.4 and approximately 40 % lower than impact velocities

recorded in field trials of nuclear waste disposal penetrometers (Freeman et al. 1984,

Freeman and Burdett 1986). It is therefore apparent that scope exists for substantial

increases in dynamic anchor impact velocity above those achievable in the beam

centrifuge. Given the dependence of embedment depth on impact velocity this also

suggests the potential for greater embedment depths and ultimately higher anchor

holding capacities.

Anchor CD vt

(m/s)

E0-1 0.24 86.0

E0-2 0.24 85.0

C0-1 0.22 90.6

O0-1 0.22 90.5

F0-1 0.88 45.9

IE0-1 0.24 84.3

IE0-2 0.24 86.0

Table 5.4 Model anchor terminal velocities

5.2.3 Embedment Depth

As the undrained shear strength of typical offshore clay deposits increases with depth

below the seabed, higher holding capacities can be mobilised by maximising the anchor

embedment depth. The embedment depth of dynamically installed anchors is dependent

on a number of factors, including impact velocity, anchor mass, anchor geometry and

soil strength characteristics. Anchor tip embedment depths measured in the beam

centrifuge tests ranged from 157 – 216 mm at model scale, representing 31.4 – 43.2 m

at prototype scale or 2.1 – 2.9 times the anchor length (see Table 5.10). These results are

in good agreement with torpedo anchor embedments of 2.4 times the anchor length

measured in field trials in normally consolidated clay (Medeiros 2001, 2002).

The anchor penetration depths were determined according to the method outlined in

Section 3.8.1.2. This method relies upon the measurement of the slack in the anchor

115

chain during extraction, prior to the onset of a tensile load. By examining the load

versus displacement response during extraction, the slack in the anchor chain can be

determined. Figure 5.15 shows a typical load displacement plot for a model dynamic

anchor test, illustrating the anchor chain slack length.

In certain tests, the penetration depth was either difficult to determine or misleading due

to twisting of the anchor chain (resulting in uncertainty over the point of load onset),

accidental premature installation of the anchor prior to the realisation of the target

acceleration level, or installation of the anchor in a previously disturbed test site. It

should be noted that although these embedment depths have been included in Table

5.10, they have not been considered in the analysis presented in this or following

chapters.

The embedment depths presented here and considered in the analysis refer to the

embedment of the anchor tip unless otherwise stated.

5.2.3.1 Influence of Impact Velocity

Figure 5.16 summarises the dependence of the dynamic anchor embedment depth on

impact velocity for the zero fluke ellipsoid nosed anchors in the beam centrifuge. The

data indicates an approximately linear increase in embedment depth with impact

velocity, such that from impact velocities of 0 – 30 m/s there is an approximate 30 %

increase in embedment. Despite very few data points at low velocities, Figure 5.16

suggests that the apparently linear relationship between impact velocity and embedment

depth is limited to a lower threshold impact velocity of approximately 10 m/s. These

observations are consistent with the findings of previous dynamic anchor centrifuge

studies by Lisle (2001), Wemmie (2003), Richardson (2003) and O’Loughlin et al.

(2004b). Interestingly, the relatively high embedment depths measured in the tests

installed from the sample surface, i.e. vi = 0 m/s, suggest a strong embedment depth

dependence on anchor mass.

Given the potential for higher dynamic anchor impact velocities (see Section 5.2.2)

there is also the potential for higher penetration depths. It should be noted, however,

that the samples in the beam centrifuge strongbox were approximately 230 mm deep

(including a 10 mm deep sand drainage layer), and as such tip penetrations were limited

to approximately 220 mm (44 m at prototype scale). Having said that, extrapolation of

116

the embedment data to impact velocities approaching terminal velocity (see Table 5.4)

indicate the potential for embedment depths in the order of 300 mm (60 m at prototype

scale) or 4 times the anchor length (see Figure 5.17). Such embedments are

considerably larger than those recorded in field trials of nuclear waste disposal

penetrometers (Freeman et al. 1984, Freeman and Burdett 1986), although the waste

disposal tests were conducted in sites with higher shear strengths (i.e. k = 1.5 kPa/m).

5.2.3.2 Influence of Anchor Geometry

O'Loughlin et al. (2004b) identified a significant discrepancy between the measured

penetration depths of two zero fluke model dynamic anchors with slightly different tip

shapes (Figure 5.18). The anchor with the ‘sharp’ tip exhibited penetration depths that

were on average over 20 % higher than the measured embedments for the ‘blunt’

anchor, suggesting a strong embedment depth dependency on anchor tip shape.

Consequently the tests in beam centrifuge Box 1 were used to investigate the influence

of tip shape on the penetration performance of dynamically installed anchors. Four

different tip shapes were assessed, a standard ellipsoid tip, a conical tip with a 15° cone

angle, a tangent ogive tip and a blunt or flat tip analogous to the head of a closed-ended

cylindrical pile (see Section 3.6.3). The ellipsoid, cone and ogive anchors were all

fabricated with approximately the same mass in order to eliminate the influence of the

anchor mass on the embedment depth. However, it was not possible to reduce the mass

of the flat nosed anchor further without exceeding safe wall thickness limits and as such

its final mass was slightly greater than the other three anchors (see Table 3.10).

Each of the four model anchors was installed three times from a drop height of 300 mm;

the measured embedment depths are shown in Figure 5.19 against the penetration

depths for the other ellipsoid nosed anchor tests conducted in the beam centrifuge. It can

be seen that the ellipsoid nosed anchor penetrations are consistent between individual

samples. It can also be seen that each of the other anchor tip shapes result in slightly

higher penetration depths. In fact the results indicate average prototype embedment

depths of 39.0 m, 42.7 m, 40.3 m and 42.3 m for the ellipsoid, cone, ogive and flat

nosed anchors respectively. Hence by selecting the conical anchor over the ellipsoid,

ogive and flat nosed anchors it was possible to achieve increases in embedment of 8.7

%, 5.6 % and 0.9 % respectively. Compared with a 30 % increase in embedment by

increasing the velocity from 0 – 30 m/s (see Section 5.2.3.1), it is therefore possible to

117

achieve a relatively high increase in embedment by selecting an appropriate anchor tip

shape. Interestingly, the flat nosed anchor provided similar embedment depths to the

conical anchor, although the differences in mass made it difficult to draw conclusions

about the influence of the tip geometry. However, by plotting the embedment depth as a

function of the kinetic energy at the point of impact, rather than the impact velocity, it

was possible to eliminate the effect of the anchor mass and thereby independently

evaluate the influence of the anchor tip shape. The kinetic energy (Ek) is dependent on

both the velocity of the anchor (v) and the anchor mass (m) and can be expressed as:

22

1k mvE = (5.6)

Figure 5.20 shows the variation in embedment depth with the kinetic energy at impact

for the four different anchor tip shapes. Similar to the impact velocity results in Figure

5.19, the ellipsoid nosed anchor recorded the lowest average embedment at an

equivalent kinetic energy, followed by the ogive, flat and conical anchors respectively.

It is apparent that at similar kinetic energies, the conical and flat nosed anchors provide

comparable embedment depths. This can be attributed to the fact that the bearing

capacity mechanism for a deep circular foundation is typically characterised by a central

soil wedge beneath the foundation, which remains in an elastic state of equilibrium and

acts as part of the foundation (Meyerhof 1951; see Figure 5.21). Hence during the

penetration of the flat nosed model anchor it is likely that a conical wedge of soil forms

beneath the circular anchor tip, with the wedge effectively acting as a conical tip. In this

regard it is not surprising that the flat nosed anchor and conical anchor achieved similar

embedment depths.

No four fluke anchor tests were conducted in the beam centrifuge experimental

programme. However, in order to assess the influence of the anchor flukes on

embedment, the results of the zero fluke anchor (0FA) tests have been compared with

the results of three (3FA) and four fluke anchor (4FA) tests conducted by Lisle (2001)

and Wemmie (2003) (see Figure 5.22). The results indicate an increase in embedment

with decreasing total surface area (i.e. number of flukes), with the 3FA embedding on

average approximately 9 % further than the 4FA and the 0FA approximately 20 %

further than the 3FA. This is not surprising considering that the higher surface area

afforded by the additional flukes will result in a higher frictional resistance to

penetration. Although this finding could be undermined somewhat by the higher mass

118

of the 0FAs, which in any case should promote an increase in embedment depth, it is

upheld by the observed increase in embedment of the 3FAs over the 4FAs, both of

which had the same mass (O’Loughlin et al. 2004b). Additionally, by plotting the

embedment against the kinetic energy at impact it is possible to eliminate the influence

of the anchor mass and thereby directly compare the influence of the anchor flukes on

the penetration depth (Figure 5.23). Just as for the impact velocity, the variation of

embedment with kinetic energy indicates an increase in embedment with decreasing

total anchor surface area.

5.2.3.3 Influence of Surface Water

Whilst the penetration results have not been considered directly in the analysis, several

tests conducted in Box 6 demonstrated interesting results. Typically, during the beam

centrifuge tests a nominal layer of surface water was maintained above the sample

surface in order to ensure complete saturation of the sample. For four tests conducted in

Box 6 (indicated by the superscript ‘w’ in Table 5.10), this surface water layer was

removed. The penetration depths recorded in these tests are compared in Figure 5.24

with the results of tests conducted in the same sample with the surface water layer

present. At corresponding impact velocities, the embedments measured in the tests in

which the surface water was removed are, on average, 20 % lower than those for the

tests in which the surface water was present.

Whilst it is acknowledged that during offshore installation of dynamic anchors, water

will always be present, these results highlight an important consideration which may

influence the short-term anchor capacity. The results tend to suggest that water may be

entrained in a boundary layer close to the anchor during penetration, thereby reducing

the effective stresses in the soil surrounding the anchor and allowing greater penetration

depths, but also resulting in lower short-term capacities prior to the dissipation of the

excess pore pressures generated in the boundary layer. Tika and Hutchinson (1999)

have commented on the reduction in strength observed in fast rate ring shear tests, in

which water was allowed to penetrate the shear zone. The short-term anchor capacity

and dissipation of excess pore pressures following dynamic anchor installation will be

discussed in greater detail in Section 5.3.6.

119

5.2.3.4 Verticality

Coriolis effects in the centrifuge mean that during installation, relative to the sample,

the model anchor will experience an apparent tangential component of acceleration,

unless otherwise restrained. Prior to impact with the sample surface, the anchor is

restrained by the rigid installation guide; however, once the anchor begins to penetrate

the deformable soil sample, the tangential acceleration component will tend to cause the

anchor to follow a curved trajectory through the sample. The only way to assess the

extent of this curved trajectory during penetration was to excavate the soil surrounding

the anchor following installation and to check the verticality of the anchor at its final

location. Three tests in two beam centrifuge samples were conducted in which the

embedded anchor was subsequently examined for verticality. Figure 5.25 shows a

photograph of an excavated beam centrifuge clay sample illustrating the inclination to

the vertical of a model dynamic anchor in one of these tests. Only a relatively minor

inclination (i.e. less than 3°) can be observed and hence the anchor is considered to

remain vertical during dynamic installation in the beam centrifuge. It was important,

however, to ensure that the tip of the installation guide remained as close as possible to

the sample surface to prevent rotation of the anchor prior to impact as an inclined

impact is likely to increase the inclination of the anchor during embedment.

5.2.4 Load Displacement Response

A typical load displacement plot following the onset of tensile load during the vertical

monotonic extraction of a dynamically installed anchor in the beam centrifuge is

presented in Figure 5.26. The response is characterised by a sharp increase in load

towards an initial maximum capacity (Peak 1) followed by a sudden drop in load and a

subsequent increase towards a secondary maximum capacity (Peak 2), generally of

lower magnitude than Peak 1. The initial maximum capacity at Peak 1 and rapid

softening is not wholly understood but appears to be due to high (and brittle) frictional

resistance, with the rise to Peak 2 indicating a more gradual mobilisation of bearing

resistance. Jeanjean et al. (2006) commented on the different mobilisation rates of

frictional and bearing resistance for suction caissons. Both the Peak 1 and Peak 2

capacities (Fv1 and Fv2), as well as the displacements required to mobilise each of these

capacities (z1 and z2), are presented in Table 5.10.

120

Previous dynamic anchor testing in the beam centrifuge reported by Lisle (2001),

Wemmie (2003), Richardson (2003) and O’Loughlin et al. (2004b) describe only the

overall maximum capacity, which generally corresponded to the Peak 1 capacity.

However, typical load displacement plots from Lisle (2001), Wemmie (2003) and

Richardson (2003) demonstrate the same Peak 1 and Peak 2 behaviour as shown in

Figure 5.26.

In Box 5 a single static installation, vertical monotonic extraction test (see Section

3.8.1.6) was conducted in order to assess the influence of the dynamic anchor

installation process on the observed load displacement behaviour during extraction. The

anchor was installed manually, via an adaptor fitted to the end of the T-bar shaft, at 1 g

with the centrifuge stationary. Following installation the adaptor was removed from the

sample leaving the anchor in place, the anchor chain was connected to the load cell and

the centrifuge ramped up to the test acceleration level of 200 g. The anchor was then

extracted vertically at a constant rate of 0.3 mm/s. The load displacement response

during the extraction of the model anchor is shown in Figure 5.27 and indicates the

same Peak 1 and Peak 2 behaviour. These observations suggest that the unusual load

displacement response is not attributable to the rate of installation of the model anchor.

The vast majority of tests conducted in the beam centrifuge utilised the standard

ellipsoidal shaped anchor tip described in Section 3.6.1. However, as discussed in

Section 5.2.3.2, the influence of the tip shape on the anchor performance was

investigated in Box 1. Figure 5.28 shows typical load displacement plots for each of the

model anchor nose shapes. It is apparent that, whilst the flat nosed anchor exhibits

similar load displacement behaviour up to Peak 1 and even in the subsequent rapid

softening, following this the flat nosed anchor capacity does not increase to a secondary

Peak 2 capacity but continues to decrease with increasing displacement. This behaviour

was observed in several tests with the flat nosed anchor and is unlike the load

displacement response observed for each of the other anchor tip shapes. This suggests

that the tip shape may influence the extraction behaviour of dynamically installed

anchors, possibly by altering the rate of mobilisation of the reverse end bearing

resistance.

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5.2.5 Vertical Monotonic Holding Capacity

Over the range of embedment depths in the beam centrifuge, the undrained vertical

monotonic holding capacity ranged from 41.2 to 95.4 N (1.6 – 3.8 MN at prototype

scale) for Peak 1 and 34.5 to 72.7 N (1.4 - 2.9 MN at prototype scale) for Peak 2.

Typically, the anchor capacity was determined after approximately 13 minutes (1 year

at prototype scale) of reconsolidation following installation, although accurate

reconsolidation periods were not recorded in a large number of tests. The Peak 1 and

Peak 2 capacities measured in the beam centrifuge tests are shown in Figures 5.29 and

5.30 respectively, compared with the results of previous 0FA beam centrifuge tests

reported by O’Loughlin et al. (2004b) and the results of torpedo anchor field trials

conducted in normally consolidated clay reported by Medeiros (2001). It can be seen

that the agreement between the Peak 1 capacities and the previous centrifuge data is

noticeably better than that for the Peak 2 capacities. This is not surprising considering

that the capacities reported by O’Loughlin et al. (2004b) correspond to the Peak 1

capacity. Both the Peak 1 and Peak 2 data, however, agree well with the torpedo anchor

field test data. Despite differences in anchor geometry and mass and variations in the

soil strength characteristics, the relative agreement between the measured field and

centrifuge capacities is encouraging and demonstrates the suitability of centrifuge

modelling for assessing the performance of dynamic anchors.

Both the Peak 1 and Peak 2 capacities measured in the beam centrifuge tests have been

normalised according to Equation 4.37 (Section 4.5.3). With the undrained shear

strength known to increase with depth, normalisation in this manner not only accounts

for variations in the shear strength profile but also variations in the anchor embedment

depth. The normalised Peak 1 and Peak 2 capacities are shown in Figures 5.31 and 5.32

respectively and are also presented in Table 5.10 (FN1 and FN2). For comparison, the

normalised capacities from the torpedo anchor field trials (Medeiros 2001) and the

previous 0FA centrifuge tests (O’Loughlin et al. 2004b) are also provided. It should be

noted that the normalised capacities from the field tests are only approximate as the

calculations were based on the limited anchor and soil property information available.

Figure 5.31, in particular, shows very good agreement between the normalised Peak 1

capacities and both the previous centrifuge data and the torpedo anchor field test data.

Having taken into account the dry weight of the anchor and differences in the undrained

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shear strength and embedment depth, the normalised centrifuge capacities compare

favourably with the results of the torpedo anchor field trials. Somewhat surprisingly

however, the normalised capacities presented in Figures 5.31 and 5.32 cover an

extremely wide range from approximately 40 – 70 for Peak 1 and 30 – 50 for Peak 2 at

embedment depths of approximately 2.3 – 2.9 times the anchor length. Despite slight

differences in the normalisation procedure significant scatter in the normalised capacity

of dynamic anchors at similar penetration depths was also reported by O’Loughlin et al.

(2004b).

Anchor efficiency is often used as an assessment of anchor performance (see Section

4.5.4). For the centrifuge tests reported here, Peak 1 efficiencies ranged from 1.4 – 3.2,

whilst Peak 2 efficiencies ranged from 1.2 – 2.4. In comparison, the efficiencies from

the torpedo anchor field trials ranged from approximately 3.2 – 3.5 (Medeiros 2001),

whilst the efficiencies for the previous 0FA centrifuge tests varied from 1.7 – 3.6

(O’Loughlin et al. 2004b). The torpedo anchor efficiencies appear slightly higher than

those in the centrifuge tests, although good agreement is achieved between the current

and previous centrifuge test data, particularly for Peak 1. Whilst these efficiencies are

significantly lower than those offered by conventional drag anchors (e.g. Vryhof 1999),

the measured anchor efficiencies are a function of the anchor capacity which varies with

embedment depth, with higher embedment depths yielding higher anchor efficiencies.

Hence given the potential for higher anchor embedment depths (see Section 5.2.3.1),

higher anchor efficiencies are also likely. That said, the concept of efficiency for these

anchors is not considered particularly useful, partly because fabrication and installation

costs are much lower than for a conventional drag anchor (so comparable efficiencies

do not reflect comparable cost) but also because the holding capacity is directly related

to the drop height and resulting embedment depth (O’Loughlin et al. 2004b).

5.2.5.1 Influence of Embedment Depth

Due to the increase in shear strength with depth observed in the beam centrifuge

samples (Section 5.2.1), it is expected that the anchor capacity will increase with

increasing embedment depth. The variation in vertical monotonic capacity with depth

for Peak 1 and Peak 2 is shown in Figures 5.29 and 5.30 respectively. It is apparent that

both the Peak 1 and Peak 2 capacities increase with embedment depth, due to the

mobilisation of higher shear strengths. However, care should be taken in this

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assessment, as although consolidation times of approximately 13 minutes (1 year at

prototype scale) were provided following installation in the majority of tests, accurate

consolidation times were not recorded for approximately half of the beam centrifuge

tests. The capacity of dynamically installed anchors is expected to increase with time

following installation due to the effects of consolidation. This is discussed in Section

5.3.6.

5.2.5.2 Influence of Anchor Geometry

The normalised Peak 1 and Peak 2 capacities for the different anchor tip shapes are

shown in Figures 5.33 and 5.34 respectively. Focusing on the Peak 1 capacities, it is

noticeable that, on average, the normalised capacity of the flat nosed anchor is lower

than the capacities of the three other nose types. This is somewhat surprising

considering the greater overall surface area of the flat nosed anchor; however, once

again, care should be taken in drawing conclusions from these results as no accurate

consolidation times were recorded for any of the tests with different anchor tip shapes.

Hence the differences in capacity may in fact be attributable to slight variations in

consolidation time (see Section 5.3.6). It should be noted that no Peak 2 capacities were

obtained for the flat nosed anchor tests.

Figure 5.35 compares the 0FA efficiencies from the current test series with the

efficiencies calculated from the capacities of 3 and 4FAs reported by Wemmie (2003).

It was expected that a decrease in the total anchor surface area (i.e. number of flukes)

should result in a decrease in the anchor capacity. Hence at similar penetration depths,

the 4FA should demonstrate the highest efficiency followed by the 3FA and the 0FA. It

can be seen that, on average, the 0FA efficiencies are lower than the efficiencies of both

the 3 and 4FAs, with the 0FA required to penetrate to a depth of approximately 200 mm

(40 m at prototype scale) to achieve a similar efficiency as the 3 and 4FAs at a depth of

150 mm (30 m at prototype scale). Somewhat surprisingly however, the 3FAs provide

similar, if not slightly higher efficiencies, at comparable embedment depths as the 4FAs

despite the 3FA having a lower total surface area.

5.2.6 Long-Term Sustained Loading

The design of offshore foundations may be governed by the capacity of the foundation

under long-term sustained loading. Five sustained loading tests were conducted in Box

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5 in order to assess the behaviour of dynamically installed anchors under sustained

loading conditions. Specifically, the effects of the sustained load magnitude and

duration were considered. The sustained loading tests were detailed in Section 3.8.1.3.

In each test the model anchor was installed from a drop height of 150 mm such that

similar embedment depths were achieved between tests. For the five sustained loading

tests, the variation in the measured embedment depth was approximately ± 3 % (see

Table 5.10). Following installation, the soil surrounding the anchor was allowed to

consolidate for 1 hour (4.5 years at prototype scale) prior to the application of the

sustained loading sequence (see Table 5.5). The sustained load magnitude in Table 5.5

has been specified as a proportion of the maximum Peak 1 capacity in a reference

vertical monotonic extraction test (B5D1), which was installed from the same drop

height and provided with the same consolidation period (see Section 3.8.1.3). If failure,

identified as excessive vertical displacement, was not observed during the sustained

loading sequence, the anchor was subsequently loaded monotonically to failure and

extracted under displacement control conditions at a rate of 0.3 mm/s. In tests B5SUS4

and B5SUS5, the model anchor was subjected to four consecutive sustained loading

stages of increasing load magnitude.

It should be noted that the results of test B5SUS1 have been excluded from the analysis

due to an error in the sustained loading sequence. The variations in load relative to the

Peak 1 capacity in B5D1 and displacement with time for each of the four successful

sustained loading tests are presented in Figures 5.36 – 5.39. It can be seen from these

figures that the sustained load actually fluctuated slightly with time, effectively

representing a very small amplitude cyclic loading sequence. This was attributed to the

resolution of the load cell, since sustained loads of less than 100 N were imposed on the

model anchors using the feedback from a load cell with a capacity of 1.7 kN. This was

not expected to have a significant influence on the test results. The point at which

failure occurred has been identified for each test. Figure 5.38 shows that during test

B5SUS4, the actuator control system overshot the desired sustained load. In the

transition from stage 1 to 2 the overshoot was approximately 14 %, whilst between

stages 2 and 3 the overshoot was approximately 9 %. The overshoot during the

transition from stage 2 to 3 was sufficient to cause instantaneous failure. Test B5SUS4

was subsequently repeated in test B5SUS5.

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Magnitude Duration

Test Stage Fsus/Fmon tsus,m tsus,p

(%) (s) (days)

B5SUS1 1 81 200 92.6

B5SUS2 1 81 200 92.6

B5SUS3 1 81 800 370.4

B5SUS4 1 50 200 92.6

2 70 200 92.6

3 90 200 92.6

4 110 200 92.6

B5SUS5 1 50 200 92.6

2 70 200 92.6

3 90 200 92.6

4 110 200 92.6

Table 5.5 Sustained loading sequences

5.2.6.1 Normalised Capacity Ratio

The influence of sustained loading on the ultimate anchor capacity was assessed via a

normalised capacity ratio (NCR), expressed as the ratio of the maximum normalised

capacity under sustained loading (FN,sus) to the normalised capacity in the reference

monotonic loading case (FN,mon).

mon,N

sus,N

F

FNCR = (5.7)

The normalised capacities have been calculated according to Equation 4.37 and are

presented in Table 5.10. The normalised capacity ratios for both the Peak 1 and Peak 2

capacities are presented in Table 5.6. Note that no Peak 2 capacity was observed in tests

B5SUS3 and B5SUS5. Table 5.6 shows that when both Peak 1 and Peak 2 capacities

were observed, the two normalised capacity ratios were similar. Hence the analysis

presented here considers only the Peak 1 capacities. Overall the NCR values indicate

that the imposed sustained loading sequences had minimal influence on the ultimate

anchor capacity.

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Test FN1 z1/D FN2 z2/D NCR1 NCR2

B5SUS2 63.0 1.67 40.7 1.88 1.03 1.06

B5SUS3 59.8 1.50 0.98

B5SUS4 57.4 1.37 36.9 1.70 0.94 0.96

B5SUS5 52.0 1.42 0.85

Table 5.6 Summary of normalised capacities from sustained loading tests

5.2.6.2 Influence of Load Magnitude

Sustained loading may lead to a reduction in the foundation capacity due to the adverse

effects of creep on the soil shear strength (Edil and Muchtar 1988). Evidence from

suction caisson tests in clay suggests that a threshold sustained loading level exists,

below which the sustained loading has very little influence on capacity. However, for

loads in excess of this threshold the caisson capacity may be significantly degraded.

Allersma et al. (2000) and Clukey et al. (2004) suggest threshold sustained loading

levels of approximately 80 - 85 % of the monotonic capacity. That said, an important

difference between suction caissons and dynamic anchors is that under sustained

loading, the suction caisson capacity may be reduced by the dissipation of negative

excess pore pressures at the bottom of the caisson and the corresponding reduction in

the reverse end bearing resistance.

The influence of the sustained load magnitude on the dynamic anchor capacity was

evaluated by comparing the results of tests B5SUS2, B5SUS4 and B5SUS5. In

B5SUS2, the model anchor was subjected to a 200 s duration sustained load with a

magnitude of approximately 80 % of the reference monotonic capacity. In contrast, the

initial stage of tests B5SUS4 and B5SUS5 were conducted with a 50 % load of similar

duration. Figure 5.40 shows the normalised load displacement response during the three

sustained loading tests, whilst Figure 5.41 shows the normalised displacements

measured during the sustained loading sequence. The normalised capacity ratio based

on the Peak 1 monotonic capacity is also shown in Figure 5.40. It can be seen that the

displacements under sustained loading develop in a similar manner in each test, with the

excellent agreement between tests B5SUS4 and B5SUS5 demonstrating good test

repeatability. It should be noted that due to the adjustment of the capacity by the

anchor’s submerged weight and the non-instantaneous mobilisation of the submerged

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weight upon the onset of a tensile load in the anchor chain, the initial normalised load is

negative and has not been shown in Figure 5.40.

Figure 5.41 indicates that the displacements developed under an 80 % sustained load are

approximately 40 % higher than the displacements under a 50 % sustained load of

similar duration. Consequently, the greater creep displacements under the higher

magnitude sustained load would be expected to result in a lower anchor capacity.

However, Table 5.6 shows that for B5SUS2, NCR = 1.03 indicating no apparent

reduction in capacity from the reference monotonic case. Tests B5SUS4 and B5SUS5

indicate lower NCR values of 0.94 and 0.85 respectively, although the model anchor in

these tests was subjected to subsequent 70 % and 90 % sustained loading stages. An

additional 110 % loading stage was planned (see Table 5.5), however, failure in each

case was observed at the 90 % loading level. This failure could potentially be attributed

to the accumulated creep displacements under each of the sustained loading stages;

however it should also be considered that the duration of these subsequent stages

provides additional time for consolidation of the clay ahead of the anchor, thereby

increasing the bearing resistance. It may also be the case that a threshold loading level

of between 80 and 90 % exists, such that by increasing the sustained load to 90 % of the

monotonic capacity the threshold is exceeded and subsequent failure is observed. A

threshold loading level of 80 – 90 % agrees with threshold levels reported for sustained

loading tests of suction caissons (Allersma et al. 2000, Clukey et al. 2004). Based on

the results of the centrifuge tests, there is no evidence to suggest that sustained loading

levels of up to 80 % of the reference monotonic capacity influence the dynamic anchor

holding capacity.

In order to assess the influence of sustained loading on the load displacement response

of dynamic anchors in the centrifuge (see Section 5.2.4), tests B5SUS2 and B5SUS3

were conducted with sustained loads of similar magnitude to the Peak 2 capacity in the

reference monotonic case (B5D1). It was thought that by applying a sustained load of

equal or greater magnitude than the Peak 2 capacity, the Peak 1 behaviour could be

eliminated by initiating failure at the lower capacity. It is evident from Figure 5.42

however, that the same load spike at Peak 1 was observed in both sustained loading

tests. Hence it can be concluded that sustained loading at a level equivalent to the Peak

2 capacity was not sufficient to induce failure at this lower capacity.

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5.2.6.3 Influence of Load Duration

In assessing the influence of the sustained load duration on the ultimate dynamic anchor

capacity, the effects of both creep and consolidation should be considered. As

mentioned previously, sustained loading may reduce the anchor capacity due to the

accumulation of creep displacements. Conversely, longer duration loading may lead to

further consolidation of the soil surrounding the anchor resulting in higher shear

strengths and therefore higher capacities.

The effect of sustained load duration on the ultimate anchor capacity was assessed in

tests B5SUS2 and B5SUS3, with a four fold difference in load duration at the same load

magnitude (see Table 5.5). The normalised load displacement response for both of these

tests is shown in Figure 5.42 with the normalised displacements under the sustained

loading sequences shown in Figure 5.43. It is evident that the normalised displacements

in each test are almost identical after 200 s, but the longer sustained load duration in

B5SUS3 results in total creep displacements after 800 s that are approximately 40 %

higher than those in B5SUS2 after 200 s. These higher creep displacements are likely to

result in a reduction in the anchor capacity, although, considering the additional

consolidation time, it is also likely that the shear strength will increase over the course

of the 800 s test, leading to an increase in the anchor capacity and thereby offsetting the

decrease in capacity due to creep.

Failure was not observed during the sustained loading sequence in either test and the

anchor was subsequently loaded monotonically to failure. The NCR values in Table 5.6

indicate a slight decrease in anchor capacity with increasing load duration from 103 %

of the monotonic capacity after 200 s to 98 % after 800 s. Hence whilst an increase in

the load duration appears to result in a slight decrease in anchor capacity, the difference

in capacity is not large enough for this to be considered conclusive.

5.2.7 Cyclic Loading

Offshore structures are continuously subjected to cyclic loads in the form of wind,

waves and currents. These loads are subsequently transmitted to the foundations and

may lead to failure of the anchoring system under extreme storm conditions. Seven

cyclic loading tests were conducted in Box 5 with the aim of assessing the behaviour of

dynamically installed anchors under cyclic loading conditions. In particular, the

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influence of the cyclic load amplitude, cyclic load magnitude and number of cycles

were evaluated. The cyclic loading tests were detailed in Section 3.8.1.4.

In each test the zero fluke model anchor was installed from a drop height of 150 mm

such that similar embedment depths were achieved between tests. Across the seven

cyclic loading tests, the variation in the measured embedment depth was approximately

± 2 % (see Table 5.10). Following installation, the soil surrounding the anchor was

allowed to consolidate for 1 hour (4.5 years at prototype scale) prior to the application

of the cyclic loading sequence (see Table 5.7). The minimum and maximum cyclic load

magnitude values in Table 5.7 have been specified as a proportion of the maximum

Peak 1 capacity in the reference vertical monotonic extraction test (B5D1). If failure

was not observed during the cyclic loading sequence, the anchor was subsequently

loaded monotonically to failure under displacement control conditions at a rate of 0.3

mm/s.

Frequency Magnitude Duration

Test fr,m fr,p Fmin/Fmon Fmax/Fmon tcyc,m tcyc,p Cycles

(Hz) (mHz) (%) (%) (s) (days)

B5CYC1 1.5 0.0375 75 85 200 92.6 300

B5CYC2 0.5 0.0125 65 75 200 92.6 100

B5CYC3 0.3 0.0075 50 80 200 92.6 60

B5CYC4 0.3 0.0075 50 80 800 370.4 240

B5CYC5 0.3 0.0075 50 80 800 370.4 240

B5CYC6 0.5 0.0125 50 80 200 92.6 100

B5CYC7 0.3 0.0075 70 80 200 92.6 60

Table 5.7 Cyclic loading sequences

It should be noted that the results of test B5CYC1 have been excluded from the analysis

due to variability in the minimum and maximum cyclic loads achieved during the

course of the cyclic loading sequence. This was a direct result of the cyclic loading

frequency exceeding the capabilities of the actuator, with the load limits varying as the

anchor response stiffened. Failure was observed in test B5CYC1 after approximately 30

sec of cyclic loading. In addition, the results of test B5CYC4 are not considered in the

analysis due to an error in the cyclic loading sequence; the test was subsequently

repeated in B5CYC5. The results of test B5CYC6 have also been excluded from the

analysis as failure was observed upon initiation of the cyclic loading sequence. The

130

variations in the load relative to the monotonic capacity and displacement with time for

each of the four successful cyclic loading tests, as well as tests B5CYC1 and B5CYC6

are presented in Figures 5.44 – 5.49. The point at which failure occurred has been

identified in each test.

5.2.7.1 Normalised Capacity Ratio

The influence of cyclic loading on the ultimate anchor capacity was assessed using a

normalised capacity ratio (NCR), similar to that adopted in the sustained loading tests

(see Section 5.2.6.1), representing the ratio of the maximum normalised capacity under

cyclic loading (FN,cyc) to the normalised capacity in the reference monotonic loading

case (FN,mon).

mon,N

cyc,N

F

FNCR = (5.8)

The normalised capacities have been calculated according to Equation 4.37 and are

presented in Table 5.10. The normalised capacity ratios for both the Peak 1 and Peak 2

capacities are presented in Table 5.8. Note that no Peak 2 capacity was observed for test

B5CYC5. Table 5.8 shows that in tests B5CYC2 and B5CYC3, the Peak 1 and Peak 2

normalised capacity ratios were noticeably different. By contrast, the normalised

capacity ratios for test B5CYC7 were identical. Given this discrepancy, and to ensure

consistency with the sustained loading tests, only the Peak 1 capacities have been

considered in the analysis. It is interesting to note that the normalised capacity ratios

indicate a slight increase in capacity following cyclic loading in all but test B5CYC7.

Test FN1 z1/D FN2 z2/D NCR1 NCR2

B5CYC2 66.9 1.52 45.8 1.88 1.09 1.20

B5CYC3 64.1 1.27 42.5 1.43 1.05 1.11

B5CYC5 62.3 1.28 1.02

B5CYC7 59.9 1.43 37.5 1.63 0.98 0.98

Table 5.8 Summary of normalised capacities from cyclic loading tests

5.2.7.2 Influence of Mean Load / Cyclic Load Amplitude

The anchor capacity under cyclic loading may be affected by both the mean load and

the cyclic load amplitude. The mean load refers to the average load imposed on the

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anchor during the cyclic loading sequence, whilst the cyclic load amplitude is defined as

the maximum variation from this average load (see Figure 5.50).

From the limited number of successful cyclic loading tests, it is not possible to separate

the individual effects of mean load and cyclic load amplitude. However, tests B5CYC3

and B5CYC7 provide an indication of their combined influence on the dynamic anchor

holding capacity. In B5CYC3, the model anchor was subjected to a cyclic loading

sequence with an average magnitude of 65 % of the reference monotonic capacity and a

cyclic load amplitude of 15 % of the reference monotonic capacity. By contrast, in

B5CYC7, the anchor was subjected to cyclic loading with an average of 75 % of the

monotonic capacity and an amplitude of only 5 % of the monotonic capacity. Figure

5.51 shows the normalised load displacement response for both tests. It can be seen that

despite a lower cyclic load amplitude, test B5CYC7 mobilises a lower capacity than

B5CYC3. This is likely to be due to the higher average load experienced by the anchor

during test B5CYC7. NCR values of 1.05 and 0.98 for tests B5CYC3 and B5CYC7

respectively (see Table 5.8), suggest that an increase in the mean load has a greater

influence on the anchor capacity than an increase in the cyclic load amplitude.

However, the difference in capacity is not large enough for this to be considered

conclusive.

Figure 5.52 shows the normalised displacements accumulated under the cyclic loading

sequences in B5CYC3 and B5CYC7. It is evident that the displacements in each test

develop similarly, with an increase in stiffness with continued cyclic loading.

Interestingly, this trend is similar to that observed in the sustained loading tests

discussed in Section 5.2.6 (see Figure 5.53). The average displacement at the end of the

cyclic loading sequence in B5CYC3 is only 13.8 % higher than the average

displacement at the end of the cyclic loading sequence in B5CYC7. This suggests that

the difference in capacity is not likely to be due to discrepancies in the accumulated

displacements, but rather differences in the excess pore pressures generated during the

cyclic loading sequence. The higher load magnitude in test B5CYC7 will result in the

development of higher excess pore pressures leading to lower effective stresses and

ultimately lower anchor capacities.

In a similar manner as the sustained loading tests, the influence of cyclic loading on the

dynamic anchor load displacement response (Section 5.2.4) was considered. In test

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B5CYC7, an average cyclic load approximately equal to the Peak 2 capacity in the

reference monotonic case was applied to the model anchor. It was thought that by

applying cyclic loading at a magnitude equal to or greater than the Peak 2 capacity,

failure could be initiated at this lower capacity, thereby eliminating the somewhat

unusual Peak 1 behaviour observed. However, as Figure 5.54 shows, the load

displacement response in test B5CYC7 is typical of that observed in the beam

centrifuge tests. Hence it is apparent that cyclic loading at a level equivalent to the Peak

2 capacity was not sufficient to induce failure at this capacity.

5.2.7.3 Influence of Number of Cycles

The number of cycles or the duration of a cyclic loading sequence will influence the

dynamic anchor capacity due to consolidation and excess pore pressure development as

well as the accumulation of cyclic displacements. Excess pore pressures and

displacements generated during the cyclic loading of the model anchors will

detrimentally affect the anchor holding capacity. By contrast, the increased duration of

loading provides additional time for the excess pore pressures generated during dynamic

anchor installation to be dissipated, resulting in the mobilisation of higher shear

strengths and therefore higher anchor capacities. These opposing effects should be

considered when examining the influence of the number of cycles on the anchor holding

capacity.

Cyclic loading tests B5CYC3 and B5CYC5 have been used to assess the influence of

the number cycles on the dynamic anchor holding capacity. Test B5CYC3 was

conducted between load limits of 50 and 80 % of the reference monotonic holding

capacity at a frequency of 0.3 Hz for 60 cycles or 200 sec duration. Test B5CYC5 was

conducted at the same frequency and with the same load limits but with four times as

many cycles. The normalised load displacement response for both of these tests is

presented in Figure 5.55 with the normalised displacements under the cyclic loading

sequences shown in Figure 5.56. It is evident from Figure 5.55 and Table 5.8 that

similar maximum capacities are obtained in both tests. Similarly, comparison of the

normalised displacements in Figure 5.56 shows almost identical development of anchor

displacements under the cyclic loading sequence. However, the longer duration of the

cyclic loading in test B5CYC5 results in average accumulated displacements that are

approximately 31 % higher than the average displacements accumulated under the

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shorter duration cyclic loading sequence in B5CYC3. The higher accumulated

displacements are likely to result in a reduction in the anchor capacity. However, the

increase in capacity due to the additional consolidation time provided by the longer

duration test may offset these negative effects.

Failure was not observed during the cyclic loading sequence in either test and the

anchor was subsequently loaded monotonically to failure. The NCR values in Table 5.8

indicate that neither cyclic loading sequence has a significant effect on the ultimate

anchor capacity with capacities of 105 % and 102 % of the monotonic capacity for tests

B5CYC3 and B5CYC5 respectively. Hence, whilst increasing the number of cycles may

decrease the anchor capacity, the influence on the ultimate anchor capacity over the

range of cycles considered was negligible.

5.2.8 Static Push Tests

5.2.8.1 Static Installation

The static penetration resistance of the model dynamic anchors was assessed via static

installation tests (see Section 3.8.1.5) in Box 1. Tests were conducted with each of the

four different anchor tip shapes (see Sections 3.6.1 and 3.6.3). The model anchors were

installed at a rate of 1 mm/s to depths of approximately 180 mm (36 m at prototype

scale). The average static resistance profiles with depth for each of the anchor tip shapes

are presented in Figure 5.57. Each of the model anchors exhibited static resistance

profiles that increase approximately linearly with depth, with a change of gradient at

approximately 70 mm (14 m at prototype scale) embedment, corresponding to the point

at which the model anchor becomes completely embedded within the sample. The

ellipsoid nosed anchors provided the highest static resistance, whilst somewhat

surprisingly the flat nosed anchor recorded the lowest resistance, with a maximum

penetration resistance almost 50 % lower than that for the ellipsoid anchor. These

observations support the findings of the dynamic anchor tests discussed in Section

5.2.3.2, in which the ellipsoid anchor recorded the lowest embedments and the flat

nosed anchor the highest embedments (comparable to the conical anchor).

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5.2.8.2 Monotonic Extraction Following Static Installation

The dynamic anchor load displacement response following static installation was

assessed in a single test conducted in Box 5 in which the model anchor was installed

manually at 1 g via an adaptor fitted to the end of the T-bar shaft (see Section 3.8.1.6).

Following installation the anchor was extracted monotonically via the anchor chain

upon achievement of the target centrifuge acceleration level. The test was aimed at

evaluating the influence of the installation method on the dynamic anchor load

displacement response, considering the unusual behaviour described in Section 5.2.4.

The results of this test have been discussed previously in Section 5.2.4, with the

extraction load displacement response presented in Figure 5.27. It was concluded that

the dynamic anchor load displacement response was not attributable to the dynamic

installation process.

5.2.9 Summary

A total of 81 dynamic anchor drop tests were conducted in 6 beam centrifuge clay

samples during the experimental programme. These tests were aimed at assessing the

performance of zero fluke dynamic anchors in normally consolidated clay, both in terms

of embedment depth and holding capacity. In general the sample strength characteristics

were typical of normally consolidated kaolin clay samples in the beam centrifuge with

an average shear strength gradient of approximately 1 kPa/m, increasing to 1.2 kPa/m

during the course of testing.

Impact velocities of up to 30 m/s were recorded in the dynamic anchor tests for drop

heights ranging from 0 – 300 mm. The multiple PERP velocity system adopted in later

tests was successful in improving the accuracy of the impact velocity measurements

from the original single PERP system. The dependence of impact velocity on drop

height was clearly demonstrated and is in good agreement with the results of previous

dynamic anchor centrifuge tests.

Anchor tip embedments of 2.1 – 2.9 times the anchor length were recorded in the

experimental programme. The embedments are in agreement with the results of torpedo

anchor field trials conducted in normally consolidated clay. The test results indicate an

approximately linear increase in embedment with impact velocity for velocities greater

than 10 m/s. In addition, the anchor tip shape was shown to influence the anchor

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embedment depth by as much as 9 %. It was interesting to note, however, that after

accounting for the effects of anchor mass, the flat nosed anchor proved comparable to

the anchor with the conical nose in terms of embedment efficiency. Although no three

or four fluke anchor tests were conducted in the beam centrifuge test programme,

comparison of the results of the zero fluke anchor tests with the results of three and four

fluke anchor tests in previous studies confirmed the assumption that an increase in total

anchor surface area (number of flukes) results in a decrease in embedment at a given

impact velocity. Excavation of the soil surrounding model anchors indicated that the

model anchors remained relatively vertical during installation.

The majority of the dynamic anchor tests conducted in the beam centrifuge exhibited

unusual load displacement behaviour, characterised by an initial maximum capacity,

followed by rapid softening and the realisation of a secondary maximum capacity. It is

thought that this behaviour may be attributable to the non-simultaneous mobilisation of

the end bearing and frictional resistance. Extraction of a dynamic anchor installed

statically at 1 g indicated that the dual capacity behaviour was not a result of the

dynamic anchor installation process. In addition, cyclic and sustained loading were not

sufficient to induce failure at the secondary capacity level.

Vertical monotonic holding capacities representing 1.4 – 3.2 times the anchor dry

weight were recorded for Peak 1, with Peak 2 capacities representing 1.2 – 2.4 times the

anchor dry weight. Due to the mobilisation of higher shear strengths at greater depths,

the vertical anchor capacity was found to increase with penetration depth. Sustained

loading tests suggest the existence of a threshold loading level of approximately 80 – 90

% of the monotonic capacity, below which continued sustained loading had little

influence on the anchor capacity. At higher sustained loads, the anchor capacity may be

negatively impacted by as much as 15 %. After accounting for the effects of additional

consolidation, an increase in the sustained loading duration resulted in a reduction in the

anchor capacity due to the adverse effects of creep. Ultimately, however, the imposed

sustained loading sequences had minimal influence on the dynamic anchor capacity.

The results of the cyclic loading tests conducted in the beam centrifuge tend to suggest

that the mean load rather than the cyclic load amplitude has a greater influence on the

dynamic anchor holding capacity. It was difficult, however, to separate the individual

influences of the mean load and cyclic amplitude in the limited number of cyclic

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loading tests conducted. In addition, just as for the sustained loading tests, by increasing

the cyclic loading duration (number of cycles) the anchor capacity was reduced. Once

again, however, the overall impact of cyclic loading on the anchor capacity was

minimal.

5.3 DRUM CENTRIFUGE

The drum centrifuge tests focused primarily on evaluating the effects of soil setup on

the dynamic anchor holding capacity but were also used to investigate the influence of

the anchor aspect ratio and density on the performance of dynamically installed anchors

in normally consolidated clay. The setup tests utilised both zero fluke anchors (i.e.

anchors E0-3, E0-4 and E0-5) and four fluke anchors (i.e. anchors E4-1, E4-2, E4-3 and

E4-4), the details of which have been provided previously in Sections 3.6.1 and 3.6.2.

The parametric study investigating the influence of dynamic anchor aspect ratio and

density was conducted using a series of twenty model anchors with aspect ratios ranging

from 1 – 14 and diameters of 6, 9 and 12 mm (i.e. anchors H0-1 to H0-20; see Section

3.6.5).

The results of the tests conducted in Drum 1 have previously been published by

Cunningham (2005) and Richardson et al. (2006), whilst the results of the tests in Drum

2 have been published by Richardson et al. (2008).

5.3.1 Strength Characterisation Tests

Profiles of undrained shear strength with depth were obtained for the drum centrifuge

samples using the T-bar penetrometer described in Section 3.5.1. The shear strength was

determined from the average bearing pressure according to Equation 5.1, with a T-bar

factor of 10.5 (see Section 5.2.1).

A total of thirteen T-bar penetrometer tests were conducted in each of the drum

centrifuge samples. In Drum 1, all of the T-bar tests were affected by high unbalance

between the drum centrifuge channel and the tool table actuator. High levels of

unbalance cause vibration of the channel relative to the actuator resulting in vibration of

the T-bar relative to the soil during penetration. The vibration of the T-bar causes

softening of the soil ahead of the advancing penetrometer, leading to a reduction in the

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local shear strength. Figure 5.58 presents the shear strength profiles obtained from

several tests in Drum 1 at various unbalance levels. It is evident that, as the unbalance

increases, the strength derived from the T-bar measurements decreases, with reductions

in the maximum shear strength of approximately 60 % and 73 % when the unbalance is

increased from 0.43 g to 0.57 g and 0.72 g respectively. Unfortunately it was not

possible to improve the unbalance in Drum 1 and as such no usable shear strength

profiles were obtained from the T-bar penetrometer tests.

Similar observations were made in Drum 2. A single test was conducted at a high

unbalance level of 0.6 g, with all but one of the remaining T-bar penetrometer tests

conducted at unbalance levels between 0.35 and 0.4 g. The other test was conducted

immediately upon conclusion of the dynamic anchor test programme with the centrifuge

stationary, thereby eliminating any unbalance effects between the channel and tool

table. Figure 5.59 shows the undrained shear strength profile derived from this test

compared with the average shear strength profile for the tests conducted at unbalance

levels between 0.35 and 0.4 g and the profile obtained in the high unbalance test. Once

again a substantial decrease in shear strength was observed with increasing centrifuge

vibration. Given that the shear strength in the zero unbalance test was, on average,

approximately 20 % higher than that in the moderate unbalance level tests (0.35 – 0.4

g), only the shear strength profile in the 1 g test has been adopted in the analysis. Note

that in the beam centrifuge, the actuator was mounted on top of the sample strongbox;

hence unbalance effects do not need to be considered.

The zero unbalance T-bar test represented an average shear strength gradient of 1.03

kPa/m (see Figure 5.60) and an undrained shear strength ratio of su/σ΄v0 = 0.16 (with γ' =

6.5 kN/m3), both of which are at the lower end of typical in situ values for normally

consolidated clay deposits. As for the beam centrifuge tests, the undrained shear

strength profile was described using a polynomial expression of the form presented in

Equation 5.3, with coefficient values of a = 0.0037 kPa/m2 and b = 0.9590 kPa/m (see

Figure 5.60). The shear strength coefficients for the zero unbalance test have been

adopted for each of the individual dynamic anchor tests in Drum 2 (see Table 5.11).

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5.3.2 Impact Velocity

For each of the dynamic anchor tests conducted in the drum centrifuge, the velocity was

measured using a multiple PERP system (see Section 3.7.1). Evidence from the beam

centrifuge tests indicated that such a method provides improved accuracy over the

single PERP system (see Section 5.2.2). The velocities measured in the drum centrifuge

tests are presented in Table 5.11 and vary from approximately 0 – 20 m/s for drop

heights of 0 – 250 mm, representing equivalent prototype drop heights of up to 29.2 m.

Note that as the acceleration fields in the beam and drum centrifuges are different, the

equivalent prototype drop heights in the drum centrifuge do not correspond to

equivalent prototype drop heights in the beam centrifuge (see Section 4.3.2).

The variations in impact velocity with equivalent prototype drop height for the 0 and

4FA tests in the drum centrifuge are presented in Figures 5.61 and 5.62 respectively.

Similarly, the impact velocities for the hemispherically tipped anchors with L/D < 7 and

L/D > 7 (see Section 3.6.5) are presented in Figures 5.63 and 5.64 respectively. Figure

5.65 shows the best-fit lines through the experimental data for the 0FAs and the

hemispherically tipped anchors. It is evident that whilst the impact velocity in each case

increases with drop height, the rate of increase in impact velocity is somewhat

dependent on the anchor type. This observation suggests differences in the energy losses

experienced by the different model anchor types during installation. The most likely

source of these energy losses during dynamic anchor installation in the centrifuge is

friction between the anchor and the installation guide. Therefore the greater the surface

area of the anchor in contact with the installation guide, the higher the potential for

frictional energy losses and hence the greater the likelihood of lower impact velocities.

As expected, Figure 5.65 shows that the anchors with the lowest surface area (i.e. L/D <

7) exhibited the highest impact velocities for a given drop height. By contrast the 0FAs,

which on average have the largest surface area, demonstrated the lowest impact

velocities. It should be noted that the velocities of the 4FAs have not been included in

Figure 5.65 as a different guide was used during installation.

The velocities representing the best-fit line through the experimental data for each of the

four different anchor types are presented in Table 5.9. For the tests in which the logging

139

software failed to record the installation event, the average best-fit velocity for the

corresponding drop height in Table 5.9 has been adopted in the analysis.

Drop Height Average Impact Velocity

hd,m hd,eq 0FA 4FA L/D > 7 L/D < 7

(mm) (m) (m/s) (m/s) (m/s) (m/s)

0 0 0 0 0 0

50 7.7 8.9 9.0 10.5 10.1

100 14.5 11.3 11.9 14.1 12.9

150 20.4 12.8 13.8 16.5 14.7

200 25.3 13.9 15.1 18.2 16.0

250 29.2 14.6 16.1 19.4 16.9

Table 5.9 Variation in impact velocity with drop height – drum centrifuge

The average maximum impact velocity achieved in the drum centrifuge tests was 19.4

m/s, which is approximately 32 % lower than the average maximum impact velocity of

28.7 m/s measured in the beam centrifuge (see Table 5.3). This is largely due to

differences in the respective acceleration fields of the two centrifuges, but can also be

attributed to the drop height being restricted to 250 mm in the drum centrifuge. The

maximum velocities in Table 5.9 are also over 50 % lower than impact velocities of

approximately 45 – 55 m/s achieved in high level radioactive waste disposal field trials

(Freeman et al. 1984, Freeman and Burdett 1986). However, the drum centrifuge

velocities agree relatively well with torpedo anchor velocities of 10 – 22 m/s reported

by Medeiros (2001). The restrictions on drop height in the drum centrifuge limit the

impact velocities obtainable. However, just as for the beam centrifuge tests, there is the

potential for dynamic anchors to achieve much higher impact velocities and thereby

penetrate to much greater embedment depths than those measured in the current

experimental programme.

5.3.3 Embedment Depth

Embedment depths measured in the drum centrifuge tests ranged from 39 – 128 mm,

representing 7.8 – 25.6 m at prototype scale. Considering the different anchor lengths,

the normalised embedments ranged from approximately 0.9 – 7.7 times the anchor

length. The tip embedments measured in the drum centrifuge tests are presented in

Table 5.11.

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The anchor penetration depths were determined in accordance with the method outlined

in Section 3.8.1.2. In a number of tests, the penetration depth was either difficult to

determine or misleading. This includes a number of tests that were inadvertently

conducted in previously disturbed test sites. These tests have been labelled accordingly

in Table 5.11 and are not included in the analysis.

5.3.3.1 Influence of Impact Velocity

The dependence of embedment depth on impact velocity in the drum centrifuge, for the

0FAs, 4FAs and a selection of anchors with various aspect ratios is presented in Figures

5.66 – 5.68. It is evident, particularly in the 0FA tests, that the embedment depth varies

with impact velocity in a manner similar to that observed in the beam centrifuge tests.

The results tend to suggest that for velocities greater than approximately 5 m/s, the

embedment depth increases approximately linearly with impact velocity. It should be

noted that while the results from only a small selection of anchors with different aspect

ratios have been presented, an approximately linear increase in embedment with impact

velocity was observed for each of the other anchors in the experimental programme.

The trend of increasing embedment with impact velocity is also consistent with the

findings of previous dynamic anchor centrifuge studies reported by Lisle (2001),

Wemmie (2003), Richardson (2003) and O’Loughlin et al. (2004b).

The experimental data suggest that by maximising the anchor impact velocity, the

embedment depth may be increased significantly. Figure 5.69 shows the results of the

0FA drum centrifuge tests relative to the results of field trials of nuclear waste disposal

penetrometers reported by Freeman et al. (1984) and Freeman and Burdett (1986). It is

apparent that the penetration depths achieved in the centrifuge tests are much lower than

those in the field trials, despite the higher shear strength gradients at the penetrometer

test sites and comparable projectile densities and aspect ratios. However, the centrifuge

data relate to impact velocities that are approximately 25 % of those in the waste

disposal trials. Consequently linear extrapolation of the centrifuge data to the terminal

velocities presented in Table 5.4 suggests similar embedment depths to the waste

disposal penetrometers at comparable impact velocities and likely zero fluke dynamic

anchor embedments of approximately 200 mm (40 m at prototype scale) at velocities

approaching 80 m/s. It should be noted, however, that the samples in the drum

centrifuge were approximately 165 mm deep (including a 10 mm deep sand drainage

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layer) and as such tip penetrations greater than 155 mm (31 m at prototype scale) were

not possible.

5.3.3.2 Influence of Anchor Aspect Ratio

The anchor geometry has been identified as a key parameter influencing the penetration

depth of dynamically installed anchors. A major component of the anchor geometry is

the aspect ratio or length to diameter ratio (L/D). An increase in aspect ratio represents

an increase in the anchor surface area, which is likely to result in the generation of a

higher frictional resistance to penetration and subsequently lower embedment depths.

Several anchors were fabricated with similar masses but different aspect ratios in order

to investigate the influence of aspect ratio on dynamic anchor performance (see Section

3.6.5):

1. Anchor H0-5 (L/D = 4) and H0-13 (L/D = 12)

2. Anchor H0-15 (L/D = 1) and H0-18 (L/D = 3)

The relative penetration depths for the two pairs of anchors are presented in Figures

5.70 and 5.71. For comparison purposes, both the tip and padeye embedments have

been shown. In both cases, the anchor with the lower aspect ratio demonstrated higher

embedment depths across the range of impact velocities considered. For a three fold

increase in aspect ratio, a decrease in tip embedment of approximately 13 – 17 % was

measured.

5.3.3.3 Influence of Anchor Density

Considering the submerged weight is the driving force responsible for the penetration of

dynamic anchors into the seabed, an increase in the anchor density should result in a

corresponding increase in penetration. The influence of anchor density on the dynamic

anchor embedment depth was evaluated by comparing the embedments of several

groups of anchors with the same geometry but different mass (see Sections 3.6.1 and

3.6.5). These included:

1. Anchor E0-3 (m = 8.2 g), E0-4 (m = 6.2 g) and E0-5 (m = 5.4 g)

2. Anchor H0-5 (m = 4.7 g) and H0-7 (m = 1.4 g)

3. Anchor H0-6 (m = 7.4 g) and H0-8 (m = 2.3 g)

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It should be noted that these anchors represent only a selection of the anchors available

for assessing the influence of the anchor density on penetration depth. The relative

penetration depths for the three groups of anchors are presented in Figures 5.66, 5.72

and 5.73 respectively. As expected, in each case an increase in density resulted in an

increase in penetration depth. Even a relatively small, 15 % increase in density (i.e.

anchor E0-5 to E0-4) resulted in an approximate 16 % increase in embedment. A greater

than three fold increase in density resulted in an increase in embedment of over 100 %.

5.3.3.4 Combined Influence of Aspect Ratio and Mass

Typically an increase in aspect ratio leads to both an increase in projectile mass and

shaft surface area. Section 5.3.3.2 showed that an increase in aspect ratio at a constant

mass lead to a reduction in the embedment depth. Conversely, Section 5.3.3.3 showed

an increase in embedment depth when the density was increased at a constant aspect

ratio. Anchors H0-1, H0-4 and H0-6 were each fabricated from brass with the anchor

mass increasing naturally with aspect ratio, from 0.9 grams at L/D = 1 to 7.4 grams for

L/D = 6. The combined effects of increasing the aspect ratio and projectile mass are

shown in Figure 5.74. It can be seen that the natural progression of mass with aspect

ratio results in increased tip embedments, with the mass effects dominating the

additional resistance created by the increased projectile surface area. Consequently for a

given material density, maximising the aspect ratio, and therefore mass, will maximise

the anchor embedment depth.

5.3.4 Load-Displacement Response

Figure 5.75 presents the load displacement response for four individual tests conducted

with anchor E4-3 (see Section 3.6.2) following various periods of consolidation prior to

extraction. It is apparent that the Peak 1 capacities in each case develop similarly, with

the Peak 1 magnitude and the displacement required to mobilise this capacity increasing

with consolidation time. Figure 5.75 also shows that the Peak 2 capacity, particularly in

the two tests with the lowest consolidation times, occurs after approximately the same

displacement despite different load magnitudes. The combined result of these two

effects is the merging of the Peak 1 and Peak 2 capacities into a single maximum

capacity with increasing consolidation time. In addition the post-peak softening

observed after longer consolidation times was much more gradual than was observed in

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the short consolidation time tests. These observations reinforce the assertion that the

observed Peak 1 and Peak 2 load displacement behaviour can be attributed to

differences in the mobilisation rates of the frictional and end bearing resistances (see

Section 5.2.4). Hence with increasing consolidation time the displacement required to

mobilise the high frictional resistance responsible for Peak 1 increases to the point

where it coincides with the displacement required to mobilise the maximum bearing

resistance, resulting in a single maximum capacity.

Figure 5.76 demonstrates the influence of the aspect ratio on the dynamic anchor load

displacement response. Despite low data logging rates, it is evident that at low aspect

ratios a single maximum capacity develops, whilst at larger aspect ratios dual maximum

capacities are observed. The results in Figure 5.76 tend to suggest a transition between

single and multiple maximum capacity behaviour at an aspect ratio of approximately 6 -

8. In Section 5.2.4 it was suggested that the initial Peak 1 capacity and subsequent rapid

softening were due to high (and brittle) frictional resistance. Consequently, at low

aspect ratios, the anchor surface area may not be sufficient to develop a significant level

of frictional resistance and hence the more gradual development of the bearing

resistance dominates the load displacement response, resulting in a single maximum

capacity value. At higher aspect ratios, however, the anchor surface area is considerably

larger and as such a substantial increase in the frictional resistance develops, with this

frictional resistance dominating the end bearing effects and resulting in two separate

capacity values. It should be noted that all of the dynamic anchor aspect ratio tests were

conducted following approximately 800 s of consolidation (1 year at prototype scale)

and as such consolidation effects were not considered.

5.3.5 Vertical Monotonic Holding Capacity

Vertical monotonic holding capacities in the drum centrifuge ranged from 2.0 – 93.2 N

(0.1 – 3.7 MN at prototype scale) for Peak 1 and 4.0 – 56.4 N (0.2 – 2.3 MN at

prototype scale) for Peak 2, bearing in mind that Peak 2 capacities were not observed in

all tests. The Peak 1 and Peak 2 capacities are presented in Table 5.11 and represent

efficiencies of approximately 1 - 4 times the dry weight. Whilst these efficiencies are

somewhat lower than those offered by conventional drag anchors (Vryhof 1999), they

are comparable with the results of the beam centrifuge tests (see Section 5.2.5), previous

144

centrifuge tests (O’Loughlin et al. 2004b) and torpedo anchor field trials (Medeiros

2001). It should be noted that the results of several tests have been excluded from the

analysis either due to disturbance of the sample or problems with the data acquisition

system. These tests have been labelled accordingly in Table 5.11.

5.3.5.1 Influence of Embedment Depth

The beam centrifuge tests indicated an increase in the vertical monotonic holding

capacity with depth due to the mobilisation of higher shear strengths. The dependence

of holding capacity on embedment depth for the 0FAs in the drum centrifuge tests is

shown in Figures 5.77 and 5.78 for Peak 1 and Peak 2 respectively. Only the results of

tests with similar reconsolidation times have been considered. As for the beam

centrifuge tests, the results demonstrate an increase in holding capacity with increasing

embedment depth for both the Peak 1 and Peak 2 capacities. Hence in order to maximise

the anchor holding capacity it is necessary to maximise the embedment depth.

5.3.5.2 Influence of Anchor Aspect Ratio

The influence of aspect ratio on the dynamic anchor holding capacity was assessed by

considering the holding capacities of the two anchor pairs identified in Section 5.3.3.2,

i.e. anchors H0-5 and H0-13, and anchors H0-15 and H0-18. Since Peak 2 capacities

were not recorded for all of these tests only the Peak 1 capacities have been considered.

Figures 5.79 and 5.80 show the variation in holding capacity with embedment for the

two pairs of anchors. A higher aspect ratio provides a greater anchor surface area and is

therefore likely to result in higher anchor capacities due to the increased frictional

resistance generated along the anchor shaft. However, for a given tip penetration, higher

aspect ratios also mean lower padeye embedment depths, resulting in the mobilisation

of lower shear strengths at the anchor padeye and a possible change in the bearing

mechanism from a flow-round type mechanism for low aspect ratios to a shear failure

mechanism to the surface at higher aspect ratios. Given that the bearing capacity factor

increases with depth up to z/D = 4 (see Section 4.4.2), padeye embedments less than 4

anchor diameters may result in significant reductions in the padeye bearing resistance.

Hence when considering the influence of aspect ratio on the dynamic anchor holding

capacity, the effects of both the increased frictional resistance and reduced padeye

bearing resistance should be considered.

145

This is apparent in Figure 5.79, where the capacity for L/D = 12 is lower than that for

L/D = 4, at low padeye embedments. At slightly higher padeye embedments, the

capacity of the higher aspect ratio anchor exceeds that of the lower aspect ratio anchor.

With an anchor diameter of 6 mm, padeye embedments less than 24 mm would likely

result in significant reductions in the padeye bearing resistance. In the case of L/D = 12,

the maximum padeye embedment is 15 mm (2.5D) and hence the anchor capacity may

be significantly influenced by the reduction in capacity at the anchor padeye. In Figure

5.80 the anchor with the lower aspect ratio provides a higher holding capacity. In this

case the anchor diameter is 9 mm and as such padeye embedments less than 36 mm may

result in significant reductions in the padeye bearing resistance. The maximum padeye

embedment for L/D = 3 is 25 mm which is still well within this zone of influence.

Hence the reduction in bearing resistance at the anchor padeye may have offset the

increased frictional resistance to result in a lower overall capacity.

5.3.6 Setup and Consolidation

A number of tests in Drum 2 were conducted with the aim of assessing the influence of

setup on the dynamic anchor holding capacity. Setup refers to the gradual recovery of

the shear strength of the soil in the vicinity of the anchor following disturbance and

remoulding during installation. During installation, significant excess pore pressures are

generated in the soil surrounding the anchor, resulting in low effective stresses and

consequently low short-term frictional resistance. With time, the excess pore pressures

dissipate and the shear strength of the soil increases due to the combined effects of

thixotropy and consolidation. In soils in which the effective stresses are increasing,

separating the effects of thixotropy and consolidation is difficult. However, Skempton

and Northey (1952) showed that thixotropic effects in kaolin clay are negligible and as

such, the effects of thixotropy in this study have been ignored.

Field measurements of excess pore pressure distributions around driven piles show that

the major pore pressure gradients are radial (Bjerrum and Johannessen 1961, Koizumi

and Ito 1967, Lo and Stermac 1965 as cited by Randolph and Wroth 1979). Hence

consolidation of the soil surrounding dynamic anchors, following installation, is

assumed to proceed with the radial dissipation of excess pore pressures. As the soil

consolidates, the water content decreases and an increase in mean effective stress is

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observed resulting in higher shear strengths and consequently higher anchor capacities.

Soderberg (1962) indicates that the timescale of this increase in capacity is proportional

to the square of the foundation diameter and inversely proportional to the coefficient of

consolidation. Since the major excess pore pressure gradients during consolidation are

assumed to be radial rather than vertical, the horizontal coefficient of consolidation (ch)

rather than the vertical coefficient of consolidation (cv) becomes the relevant

consolidation parameter. The Rowe cell test discussed in Section 3.4.1.1 resulted in cv

values in the range 1 – 6 m2/yr at vertical effective stresses of up to 500 kPa. Based on

the results of this test and the results of piezocone dissipation tests reported by

Randolph and Hope (2004) which showed that ch = 2.2cv, ch is assumed to vary from 3.6

– 7.3 m2/yr over the range of dynamic anchor embedments considered. The average

vertical effective stress at the mid-depth of the anchors following installation was

approximately 80 kPa and as such a value of ch = 5.5 m2/yr has been adopted in

normalising the consolidation times.

Two 0FAs (E0-3 and E0-4) and two 4FAs (E4-2 and E4-3) were specifically designed

with masses that would achieve similar penetration depths from different drop heights

(see Table 3.6 and Table 3.8). The lighter of the two anchors was dynamically installed

from a drop height of 200 mm, whilst the heavier anchor was installed quasi-statically

by release from the sample surface. This resulted in an average tip embedment depth of

106 mm (21.2 m at prototype scale) and allowed the effects of quasi-static and dynamic

installation on the time-dependent capacity of dynamic anchors to be compared

objectively. Following installation, reconsolidation periods of 40 seconds to 50 hours

(18 days to 228 years at prototype scale) were permitted prior to vertical monotonic

extraction.

Figure 5.81 presents the variation in Peak 1 capacities with consolidation time for each

of the four model anchors. Note that the analysis focuses on the Peak 1 capacities,

although the Peak 2 capacities exhibit a similar increase in capacity with time. In order

to correct for variations in anchor mass and embedment depth between tests, the Peak 1

capacities have been normalised according to Equation 4.37. These normalised

capacities are given in Table 5.11 and are plotted in Figure 5.82 against the non-

dimensional time factor, T = cht/d2. For anchors E0-3, E0-4 and E4-3, the final anchor

test was carried out about 15 hours after installation (T ~ 260, or prototype time of ~70

147

years), while for anchor E4-2 the final test was after 49 hours. In order to compare all

four tests on an equal basis, the ‘maximum’ anchor capacity has been taken as the value

after 15 hours, with the value for anchor E4-2 estimated as FN = 120, by interpolation

from Figure 5.82. The normalised capacity ratios (i.e. the ratio of the normalised

capacity to the ‘maximum’ normalised capacity, FN/FN,max) for each anchor are

presented in Figure 5.83. It is apparent that the anchor capacity increases significantly

with consolidation time.

5.3.6.1 Short-Term Anchor Capacity

A value of T = 0.001 was assumed to represent the anchor capacity immediately after

installation as it corresponds to a prototype consolidation period of 2.3 hours for a

prototype anchor diameter of 1.2 m and ch = 5.5 m2/yr. However, the shortest

consolidation period achievable in the test programme was approximately 40 sec, which

corresponds to 18 days at prototype scale and T ~ 0.2. Hence the initial short-term

anchor capacity was estimated by extrapolating the normalised capacity data using a

curve fitting function expressed as:

( ) 2p0

21

max,N

N ATT1

AA

F

F ++

−= (5.9)

Where A1 represents the initial normalised capacity ratio, A2 represents the final

normalised capacity ratio, T0 is the value of T at the mid point between A1 and A2 and p

is a fitting parameter governing the slope of the curve. Anchors E0-3 and E4-2 (solid

symbols) were installed quasi-statically by release from the sample surface, whilst

anchors E0-4 and E4-3 (open symbols) were dynamically installed from a drop height

of 200 mm. It is apparent in Figure 5.83 that the normalised capacity ratios diverge for

the two different installation methods for T < 0.5. Consequently, separate fitting

functions were applied to the experimental data for each drop height. The best-fit

parameters for the quasi-static installation tests were A1 = 0.35, A2 = 1.13, T0 = 15.7 and

p = 0.48, whilst for the dynamic installation tests A1 = 0.04, A2 = 1.10, T0 = 3.1 and p =

0.48.

The extrapolated data suggest that the short-term dynamic anchor capacity is dependent

on the anchor velocity at impact with the seabed, with quasi-static installation resulting

in a short-term capacity of approximately 35 % of the maximum anchor capacity

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compared with 6 % for dynamic installation. This can be interpreted as resulting from

lower effective stresses around the dynamically installed anchor, possibly due to

entrainment of water in a boundary layer close to the anchor. Tika and Hutchinson

(1999) have commented on the reduction in strength observed in fast rate ring shear

tests, in which water is allowed to penetrate the shear zone. The results of several beam

centrifuge tests seem to support this assertion with the presence of surface water

resulting in greater dynamic anchor penetration depths (see Section 5.2.3.3).

Alternatively Vardoulakis (2002) suggested that strength softening at high strain rates

may in fact be due to thermal softening through the dissipation of mechanical energy

resulting in vaporisation of the pore water within the shear zone and consequently

higher pore pressures.

Pile installation is considered a quasi-static event since it occurs at relatively low

penetration velocities when compared to dynamic anchor impact velocities of 15 m/s in

the centrifuge tests and 25 – 30 m/s expected in the field. Typical short-term pile

capacities in clay range from approximately 25 – 45 % of the maximum pile capacity

(Esrig et al. 1977, Bogard and Matlock 1990), although Seed and Reese (1957) (as cited

in Fleming et al. 1985) reported short-term capacities of only approximately 10 % of the

long-term pile capacity. For UWA kaolin, Chen and Randolph (2007) reported typical

suction caisson installation friction ratios of 0.38, which assuming the short-term

capacity is governed solely by the remoulded shear strength during caisson installation

suggests a capacity immediately after installation of 38 % of the long-term capacity.

Similarly, laboratory tests of torpedo anchors quasi-statically installed in clay

demonstrated capacities immediately after installation of approximately 30 % of the

ultimate anchor capacity (Audibert et al. 2006). By comparison, the extrapolated quasi-

static short-term anchor capacity (FN,0/FN,max = 35 %) reported here is relatively

consistent with the short-term capacities for quasi-statically installed piles, suction

caissons and torpedo anchors.

5.3.6.2 Capacity Increase with Time

The degree of consolidation can be assessed by examining the relative increase in

anchor capacity with time from tests conducted at various time intervals following

installation. The relative increase in anchor capacity was determined through

consideration of the normalized capacity (FN) relative to the immediate capacity (FN,0)

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and the ultimate long-term capacity (FN,max), and assumed linked to the degree of

consolidation by:

max0,Nmax,N

0,NN

u

u1

FF

FF

∆∆−≈

−−

(5.10)

where ∆u is the excess pore pressure adjacent to the anchor and ∆umax is the maximum

value of ∆u immediately after installation of the anchor. The assumption that the regain

in anchor capacity is proportional to the degree of consolidation may not necessarily be

valid due to stress relaxation effects and changes in radial effective stress during loading

(Randolph 2003). However, Equation 5.10 is considered to be a reasonable approach,

and has been used effectively for suction caissons (Jeanjean 2006). Figure 5.84 shows

the degree of consolidation with time after installation. In general, it can be seen that

consolidation proceeds slightly faster for the dynamically installed anchors (E0-4 and

E4-3).

Also shown in Figure 5.84 are the results of the torpedo anchor laboratory tests reported

by Audibert et al. (2006). Whilst the rate of increase in consolidation and therefore

anchor capacity appears slightly steeper for the torpedo anchor data, there is generally

relatively good agreement with the centrifuge test results. It should be noted that the

tests by Audibert et al. (2006) were conducted in kaolin clay, although the coefficient of

consolidation has not been reported. Consequently, the non-dimensional time factor (T)

for the data presented in Figure 5.84 has been calculated assuming ch = 5.5 m2/yr, as has

been adopted in the centrifuge tests. Given the lower effective stress level of the torpedo

anchor tests, the data should possibly be shifted towards lower values of T, reflecting a

lower ch (see Figure 3.9).

5.3.6.3 t50 and t90

The time required for a dynamically installed anchor to attain its operational capacity

can be evaluated by considering the times for 50 % (t50) and 90 % (t90) consolidation.

The consolidation data for dynamic anchors presented in Figure 5.84 suggests t50 values

of approximately 35 – 350 days for a prototype dynamic anchor with a diameter of 1.2

m and typical values of ch = 3 – 30 m2/yr. Likewise the data indicate t90 values of

approximately 2.4 – 24 years.

150

The consolidation times for high values of the coefficient of consolidation agree with

periods of 1 – 2 years for relatively large offshore piles to achieve their full capacity

(Mirza 1999). However, the dynamic anchor values are much greater than 90 %

consolidation times for suction caissons of around 90 days or less (Jeanjean 2006).

Randolph (2003) showed that dissipation times for open ended piles and suction

caissons are one to two orders of magnitude shorter than for closed ended piles of the

same diameter, since the key dimension is the ‘equivalent diameter’. It is not surprising

therefore that solid dynamic anchors record much larger consolidation times than thin

walled suction caissons. From a practical perspective, however, it is not feasible for an

anchoring system to require several years of consolidation prior to achieving its design

capacity. It is therefore apparent that dynamic anchors should be installed in soils in

which consolidation proceeds sufficiently quickly so as to ensure excessive

consolidation times are avoided. Alternatively, the anchoring system should be designed

such that the anchor is only required to develop a relatively small proportion of its

ultimate capacity prior to loading.

5.3.7 Summary

A total of 138 dynamic anchor drop tests were conducted in the 2 drum centrifuge clay

samples. The tests focused on assessing the influence of the anchor geometry on the

embedment depth and holding capacity performance of dynamically installed anchors

and the effects of consolidation following installation on the dynamic anchor holding

capacity. Unfortunately no usable shear strength information was obtained from Drum 1

due to severe unbalance effects between the drum centrifuge channel and tool table

actuator. In Drum 2, a T-bar test conducted at 1 g indicated a shear strength gradient of

approximately 1.03 kPa/m and an average undrained shear strength ratio of 0.16, both of

which are slightly lower than is typically expected for normally consolidated kaolin clay

samples in the centrifuge.

Impact velocities of up to 20 m/s were recorded using the multiple PERP velocity

measurement system, for dynamic anchor drop heights ranging from 0 – 250 mm. Just

as for the beam centrifuge tests, the impact velocity was found to be heavily dependent

on the drop height. Differences in the frictional losses between the model anchor and

151

installation guide resulted in slight variations in the impact velocity drop height

relationship for the different anchor types.

Considering the range of lengths of the model anchors tested in the drum centrifuge,

normalised tip embedments of 0.9 – 7.7 times the anchor length were observed. In

accordance with the results of the beam centrifuge tests and the results of previous

dynamic anchor centrifuge studies, the data for each individual anchor indicated an

approximately linear increase in embedment with impact velocity. Given this

dependence of embedment depth on impact velocity and the potential for higher anchor

impact velocities, the potential exists for dynamic anchors to achieve much higher

embedment depths than have been measured in the centrifuge tests. Additionally, as

expected, an increase in aspect ratio at a constant mass lead to a reduction in anchor

penetration, and an increase in density at a constant aspect ratio resulted in an increase

in embedment. However, when the density was held constant, so that the mass increased

linearly with aspect ratio, higher penetrations were observed, suggesting that the mass

tends to dominate the influence of the additional frictional resistance provided by the

increased surface area at higher anchor aspect ratios.

Interestingly, the load displacement response observed during the vertical monotonic

extraction of dynamic anchors in the centrifuge was found to be dependent on the

consolidation time provided prior to extraction. Higher consolidation times resulted in

the merging of the Peak 1 and Peak 2 capacities into a single maximum capacity,

suggesting that the dynamic anchor load displacement behaviour can be explained in

terms of the different mobilisation rates of the frictional and end bearing uplift

resistance components. The anchor aspect ratio was also found to influence the load

displacement response, with low aspect ratios resulting in a single maximum capacity

and higher aspect ratios demonstrating the typical dual capacity behaviour. The

transition between these effects was found to occur at aspect ratios of between 6 and 8.

The Peak 1 and Peak 2 holding capacities measured in the drum centrifuge tests

represented efficiencies of 1 – 4 times the anchor dry weight. Predictably, the capacity

of each of the model anchors increased with increasing penetration depth. An increase

in the anchor aspect ratio may lead to an increase in holding capacity due to the

increased frictional resistance over the larger anchor surface area. However, it may also

lead to a reduction in capacity due to the decreased bearing resistance at the anchor

152

padeye. Generally in the drum centrifuge tests, a lower aspect ratio resulted in higher

holding capacities at comparable tip embedment depths.

The results of the tests investigating the influence of post-installation consolidation time

on the dynamic anchor holding capacity indicated that the short-term capacity

immediately after installation was dependent on the rate at which the anchor was

installed. Model anchors quasi-statically installed from the sample surface were found

to provide short-term capacities, relative to the ultimate capacity, which were

comparable to the results of load tests on piles and laboratory tests of torpedo anchors.

In addition, it was found that the regain in anchor capacity following installation could

be linked to the degree of consolidation. Although recorded consolidation times were

significantly lower than have been reported for open-ended piles and thin-walled

suction caissons, consolidation times to attain the maximum dynamic anchor holding

capacity of 1 – 2 years were achieved.

5.4 CONCLUSIONS

Tables 5.10 and 5.11 present the results of over 200 individual centrifuge model tests

forming the dynamic anchor experimental database on which this research is based. The

tests have addressed issues concerning the relationship between impact velocity,

embedment depth and holding capacity and the influences of factors such as the soil

strength characteristics, anchor geometry and loading conditions on these relationships.

The conclusions for this portion of the experimental programme are summarised below:

1. Undrained shear strength measurements from T-bar penetrometer tests in the

drum centrifuge are highly sensitive to vibrations caused by unbalance between

the centrifuge channel and tool table actuator.

2. Due to drop height and sample depth restrictions, dynamic anchor impact

velocities were limited to approximately 30 m/s in the beam centrifuge and 20

m/s in the drum centrifuge. Drag coefficients for zero fluke anchors suggest that

significantly higher impact velocities are possible.

3. For all of the anchors tested, the embedment depth was shown to increase

approximately linearly with impact velocity. This linear relationship was limited

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to lower threshold velocities of approximately 5 – 10 m/s and is consistent with

behaviour observed in previous dynamic anchor centrifuge tests.

4. Tip embedment depths of up to 3 times the anchor length were recorded for

typical dynamic anchor geometries, representing approximately 45 m at

prototype scale. Embedments of up to almost 8 times the anchor length were

measured for anchors with lower aspect ratios. Given the dependence of

embedment depth on impact velocity, considerably higher embedment depths

are possible by increasing the impact velocity to terminal values in water.

5. The load displacement response of dynamic anchors during vertical monotonic

extraction in the centrifuge was typically characterised by a sharp increase in

load towards an initial maximum capacity followed by a sudden drop in load and

a subsequent increase towards a secondary maximum capacity, generally of

lower magnitude than the initial maximum. The apparent merging of these two

maximum capacities following longer consolidation times and the absence of the

initial maximum capacity for low anchor aspect ratios, support the assumption

that this dual maximum capacity behaviour can be attributed to differential

mobilisation rates of the shaft friction and end bearing resistances during uplift.

6. Vertical monotonic holding capacities of up to 4 times the anchor’s dry weight

were measured. The holding capacity was also found to be dependent on the

penetration depth, with higher shear strengths mobilised at greater embedment

depths. Considering the potential increases in embedment, higher dynamic

anchor holding capacities are also possible.

7. Variations in the anchor tip shape were found to influence the penetration depth

and holding capacity. Reductions in the total anchor surface area, through a

reduction in the number of flukes, resulted in higher penetrations, but also lower

capacities at comparable embedment depths. Higher anchor aspect ratios were

found to result in lower embedment depths; however when the density was held

constant and the mass allowed to increase linearly with aspect ratio, the increase

in embedment due to the increase in anchor mass was greater than the reduction

in embedment due to the increased frictional resistance such that the overall

effect was an increase in penetration depth.

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8. Long-term sustained loading was found to have minimal influence on the

dynamic anchor holding capacity. A threshold sustained loading level of

between 80 and 90 % of the reference monotonic capacity was observed, below

which the sustained loading was not sufficient to cause failure. An increase in

the sustained loading duration was found to result in a slight reduction in anchor

capacity.

9. Cyclic loading was also found to have minimal influence on the dynamic anchor

holding capacity. However, the average load was found to have a greater

influence on the anchor capacity than the cyclic load amplitude. An increase in

the load duration (number of cycles) resulted in a slight reduction in the anchor

capacity.

10. The dynamic anchor capacity increased with time following installation due to

setup effects. The short-term anchor capacity was found to be dependent on the

rate of anchor installation. The degree of consolidation was assessed by

examining the relative time-scale of the increase in anchor capacity. The tests

indicated that consolidation times for the realisation of 90 % of the ultimate

anchor capacity of approximately 2 years are possible.

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CHAPTER 6 - EXPERIMENTAL RESULTS FOR

DYNAMIC ANCHOR TESTING IN SILICA AND

CALCAREOUS SAND

6.1 INTRODUCTION

Chapter 5 presented the experimental data from the dynamic anchor tests in normally

consolidated clay. However, substantial oil and gas deposits exist in areas of the world

where the seabed is characterised by silica or calcareous sand sediments. This chapter

presents the experimental results of dynamic anchor tests conducted in the beam

centrifuge in both silica and calcareous sand samples. Evaluation of the behaviour of

dynamically installed anchors in various seabed soil conditions is a significant aspect of

the research project and an important consideration in the commercial application of this

technology.

6.2 SILICA SAND

A single silica sand sample was prepared for the dynamic anchor beam centrifuge tests,

according to the procedure outlined in Section 3.4.2.3. Due to grain size effects in the

centrifuge, the sample was prepared from silica flour, the geotechnical properties of

which have been presented in Table 3.4. In the silica sand sample (Box 10) a total of

two anchor drop tests were conducted to assess both the penetration and holding

capacity performance of dynamically installed anchors in silica sand. The results of the

two anchor drop tests are presented in Table 6.1.

The extremely low penetration depths prevented capacity measurements from being

obtained and consequently the planned test programme was abandoned. The test results

are discussed in more detail below.

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Drop Height Velocity Embedment

Test Anchor hd,m hd,eq vm vi ze,m ze,p ze/L

(mm) (m) (m/s) (m/s) (mm) (m)

B10D1 E0-1 300 51.5 28.7 25 5.0 0.33

B10D2 O0-1 300 51.5 28.7 27 5.4 0.36

Table 6.1 Silica sand test summary

6.2.1 Strength Characterisation Tests

Profiles of cone tip resistance with depth were obtained for the silica sand sample using

the cone penetrometer described in Section 3.5.2.2. A total of four cone penetration tests

(CPTs) were conducted prior to the commencement of model anchor testing. The cone

tip resistance profiles are shown in Figure 6.1. The cone tip resistance profiles indicate

an approximately linear increase in strength with depth over the first 60 – 80 mm of

penetration, with a significant increase in strength with depth thereafter, possibly due to

the proximity of the bottom of the centrifuge strongbox.

The four individual CPTs are relatively consistent, particularly over the first 60 mm of

penetration, diverging slightly at higher penetration depths. The agreement between the

individual tests indicates the relative uniformity of the sample. The maximum tip

resistance measured was approximately 70 MPa, but the gradient over the upper 15 m

was approximately 1.1 MPa/m.

6.2.2 Impact Velocity

Due to a problem with the logging software, no velocity data was obtained for either of

the two anchor drop tests (see Table 6.1). The tests were both conducted from a model

drop height of 300 mm (i.e. an equivalent prototype drop height of 51.5 m) and

therefore an assumed impact velocity of 28.7 m/s has been adopted, based on the results

of model dynamic anchor tests in normally consolidated clay (see Table 5.3).

6.2.3 Embedment Depth

Tip embedment depths of 25 and 27 mm (i.e. 5.0 and 5.4 m at prototype scale) were

recorded in the two anchor drop tests, representing 0.33 – 0.36 times the anchor length

(Table 6.1). The lack of penetration of the model anchor prevented the actuator from

157

being moved horizontally the required 43 mm (see Section 3.8.1.2) to enable vertical

extraction of the anchor. Consequently, no vertical extraction test was performed in

either case and the anchor embedment was obtained via direct measurement of the

length of anchor protruding from the sample surface (see Figure 6.2).

Figure 6.3 shows a comparison of the embedment depths achieved in silica sand and

normally consolidated clay. It is apparent that the penetration depths in silica sand are

considerably lower than those achieved with the same anchors at similar impact

velocities in normally consolidated clay. In fact, the measured tip embedments in silica

sand are, on average, only 13.5 % of the embedment depths recorded in the normally

consolidated clay tests. This can be largely attributed to the strength of the silica sand

sample. The high cone tip resistance measured in the CPTs discussed in Section 6.2.1

indicates a relatively large anchor tip bearing resistance to penetration which is likely to

lead to lower anchor embedments.

The low embedment depths may also be partially explained by the undrained conditions

encountered during dynamic anchor installation. Dilatant materials, such as silica flour,

become stronger when they are sheared at a constant volume (i.e. under undrained

conditions). At a constant volume, the soil is not free to dilate and hence negative

excess pore pressures are generated resulting in higher effective stresses and an increase

in the penetration bearing resistance.

As a result of the dilatant nature of silica flour and the relatively high cone tip

resistances encountered, dynamically installed anchors are not likely to achieve

sufficient embedment depths in silica sand to provide an adequate holding capacity.

Hence they are not deemed suitable for use in silica sand sediments.

6.3 CALCAREOUS SAND

The performance of dynamically installed anchors in calcareous sand was investigated

in the beam centrifuge using reconstituted uncemented calcareous sand recovered from

the seabed in the vicinity of the North Rankin platform off the North West coast of

Western Australia. A total of three calcareous sand samples were prepared, although as

mentioned in Section 3.4.2.2, Box 8 was unsuccessfully reconstituted from the sample

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in Box 7 and has subsequently been excluded from the analysis. The results of the

anchor drop tests conducted in Boxes 7 and 9 are presented in Table 6.2 (see Tables

section). The results of the centrifuge tests in calcareous sand have previously been

reported by Richardson et al. (2005).

6.3.1 Strength Characterisation Tests

Profiles of cone tip resistance with depth were obtained with the cone penetrometer

described in Section 3.5.2.1. The average tip resistance profiles for each sample are

presented in Figure 6.4. Apart from the upper 20 – 40 mm, average cone resistance

profiles in Boxes 7 and 9 (before dynamic anchor testing) indicate a relatively uniform

increase in tip resistance with sample depth.

Box 8 was prepared by reconstituting the sample in Box 7 (see Section 3.4.2.2). The

average cone resistance profile for Box 8 indicates relatively high tip resistances within

the upper 40 mm of the sample compared with Boxes 7 and 9. At greater depths the

measured tip resistance remains relatively constant with depth. This suggests some form

of segregation or non-uniformity within the sample and implies that the reconstitution

method adopted was not effective in producing a sample consistent with those in Boxes

7 and 9. Consequently, the model anchor test results in Box 8 have been excluded from

the analysis.

In Box 9, CPTs were conducted both prior to and at the conclusion of the dynamic

anchor test programme. Figure 6.4 indicates an increase in tip resistance during the

course of testing, with the CPTs conducted after the dynamic anchor test programme

recording higher tip resistances than those conducted before the dynamic anchor tests.

This may be attributed to the sample ‘settling’ to a certain degree due to ramping up and

down of the centrifuge, leading to a maximum density and strength condition after

several ramp up/down cycles.

6.3.2 Impact Velocity

A single PERP installation guide (see Section 3.7.1) was used in the measurement of the

anchor velocities in the calcareous sand tests. These velocities are presented in Table

6.2 and in Figure 6.5 against the equivalent prototype drop height (see Section 4.3.2).

Also included in Figure 6.5 are the velocities measured in the normally consolidated

159

clay tests. As the velocity is independent of the soil properties it is not surprising that

the single PERP velocities measured in the calcareous sand tests agree well with the

single PERP velocities determined for model anchor tests in normally consolidated clay.

However, as mentioned in Section 5.2.2, the single PERP velocities under predict the

expected impact velocity and as such the measured velocities need to be adjusted. The

measured velocities have been adjusted in a similar manner as the single PERP

velocities in the normally consolidated clay tests, with the multiple PERP data

representing an approximate best fit of the single PERP velocities. The adjusted impact

velocities are shown in both Table 6.2 and Figure 6.6.

For the tests in Table 6.2 in which no velocity was measured, the average impact

velocity for the corresponding drop height in Table 5.3 has been adopted. For model

drop heights ranging from 0 to 300 mm, representing equivalent prototype drop heights

of 0 to 51.5 m, impact velocities of up to approximately 30 m/s were determined.

6.3.3 Embedment Depth

The tip embedment depths measured in the calcareous sand tests are presented in Table

6.2. The variation in penetration depth with impact velocity is shown in Figure 6.7.

Over the range of impact velocities considered, tip embedments ranging from

approximately 50 – 110 mm (10 – 22 m prototype) were observed, corresponding to

approximately 0.7 – 1.5 times the anchor length. Medeiros (2001, 2002) report average

tip penetrations for torpedo anchors in uncemented calcareous sand of 15 m,

corresponding to 1.25 times the anchor length and hence indicating good agreement

with the centrifuge test data. The test results in Figure 6.7 indicate a similar trend of

increasing embedment with impact velocity as observed in the normally consolidated

clay tests (see Section 5.2.3.1). Hence, given the potential for dynamic anchor terminal

velocities of approximately 80 m/s (see Section 5.2.2), embedment depths in the order

of 180 mm (36 m at prototype scale) are possible (see Figure 6.8).

It is evident that, at similar impact velocities, the tip embedments in calcareous sand are,

on average, approximately 50 % of the embedment depths measured in normally

consolidated clay and over three times larger than those measured in silica sand. In

calcareous sands, which are characterised by high friction angles and high

compressibility, the end bearing resistance has been shown to be significantly lower at a

160

given stress level than for silica sands (Poulos and Chua 1985). The difference in

bearing resistance is also apparent when comparing the cone tip resistance profiles in

the CPTs conducted in both silica and calcareous sand (Figures 6.1 and 6.4). The silica

sand sample exhibited cone tip resistances that were at least an order of magnitude

greater than those measured in the calcareous sand tests. Hence the lower bearing

resistance should be reflected in higher calcareous sand dynamic anchor embedment

depths.

It is also known that for piles in calcareous sands, very low shaft friction resistances are

common (Randolph 1988). It is generally accepted that these low values of shaft friction

are due to low normal effective stresses acting on the pile shaft as a result of the high

compressibility of the soil. The high soil compressibility may be attributed to crushing

of the highly angular and brittle soil particles during anchor penetration. Hence in

addition to lower end bearing resistances, when compared with silica sands, calcareous

sands also exhibit lower shaft friction resistances, ultimately resulting in higher

embedment depths.

Calcareous sands are also characterised by varying degrees of cementation. This

cementation may enhance the soil strength, although the penetration of the anchor may

also break down the cementation resulting in lower penetration resistances and therefore

higher embedments than in uncemented calcareous sand of identical cone resistance.

6.3.4 Load-Displacement Response

A typical load versus displacement plot during the vertical extraction of a model

dynamic anchor in the beam centrifuge in calcareous sand is presented in Figure 6.9.

Unlike the load displacement response observed during extraction of the model anchors

in normally consolidated clay (see Section 5.2.4), only a single maximum capacity is

recorded. No load spike at Peak 1 is encountered or any subsequent rapid softening;

rather the load steadily builds to a relatively smooth maximum before reducing

gradually with increased vertical displacement. Hence Table 6.2 includes only a single

maximum capacity value and a single displacement value required to mobilise this

capacity.

161

6.3.5 Holding Capacity

The maximum vertical holding capacities measured in the dynamic anchor tests in

calcareous sand ranged from approximately 30 – 55 N (i.e. 1.2 – 2.2 MN at prototype

scale) representing approximately 1 – 2 times the anchor’s dry weight. The dependence

of the ultimate vertical capacity on the embedment depth is shown in Figure 6.10. For

comparison, Figure 6.10 also shows both the Peak 1 and Peak 2 holding capacities

measured in the normally consolidated clay tests. Evidently, the shallower embedment

depths in calcareous sand result in capacities that are generally lower than the Peak 1

capacities in normally consolidated clay. However, it is apparent that the capacities in

calcareous sand are on average approximately 70 – 80 % of the Peak 2 capacities

measured in normally consolidated clay, despite the obvious differences in penetration.

Unfortunately, no field capacity data exists to verify these capacities.

6.3.6 Static Push Tests

Two static installation tests were conducted in Box 9 in order to assess the static

resistance to dynamic anchor penetration. Figure 6.11 shows the variation in static

resistance with penetration depth in both of the static penetration tests. It can be seen

that the static resistance force increases approximately linearly with depth, with good

agreement between the tests over the first 50 mm (10 m at prototype scale) of

penetration. At depths greater than 50 mm, the static resistances diverge slightly,

possibly due to local non-uniformities in the sample, reaching maximum resistances of

approximately 175 N and 225 N (7 MN and 9 MN at prototype scale) at the maximum

penetration depth of approximately 175 mm (35 m at prototype scale).

6.4 CONCLUSIONS

The results of the centrifuge tests in silica and calcareous sands formed a small but

important component of the dynamic anchor centrifuge test database. As in the tests in

normally consolidated clay presented in Chapter 5, these tests assessed the relationship

between impact velocity, embedment depth and holding capacity, but in soils with

vastly different properties. The conclusions derived from the dynamically installed

anchor tests in silica and calcareous sand are summarised below:

162

1. Dynamic anchors are not suitable for use in silica sand sediments. High cone tip

resistances and the dilatant nature of the soil resulted in extremely low

embedment depths which were not sufficient to develop adequate holding

capacities.

2. Dynamic anchors were found to be suitable for use in calcareous sediments. For

impact velocities of up to 30 m/s, tip embedments of up to 1.5 times the anchor

length were recorded. These embedments were significantly lower than the

corresponding embedments in normally consolidated clay, but over three times

larger than those in silica sand. The measured embedment depths span the value

reported from torpedo anchor field trials in uncemented calcareous sand

conducted in Brazilian waters.

3. The embedment depth in calcareous sand increased approximately linearly with

impact velocity in a similar manner to the normally consolidated clay tests.

Given the potential for higher dynamic anchor impact velocities, embedment

depths in the order of 2.4 times the anchor length are considered possible.

4. In calcareous sand, the load displacement response was characterised by only a

single maximum capacity. The dual capacity and rapid softening behaviour

observed in the normally consolidated clay tests was not evident in calcareous

sand.

5. The dynamic anchor holding capacity in calcareous sand was found to be

dependent on the embedment depth, with anchor capacities of 1 – 2 times the

anchor dry weight measured. Considering the potential for higher embedment

depths due to the maximisation of the impact velocity, considerably higher

holding capacities than were measured in the centrifuge tests are possible.

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CHAPTER 7 - COMPARISON OF EXPERIMENTAL

AND THEORETICAL RESULTS

7.1 INTRODUCTION

In Chapter 4, analytical methods were introduced for evaluating the performance of

dynamically installed anchors, in terms of their impact velocity, embedment depth and

holding capacity. Subsequently Chapters 5 and 6 presented the results of the dynamic

anchor centrifuge tests forming the experimental database for the validation of these

analytical methods. This chapter summarises the comparison between the analytical

methods in Chapter 4 and the test results detailed in Chapters 5 and 6. In particular the

chapter focuses on evaluating the accuracy of the analytical embedment and holding

capacity solutions in both normally consolidated clay and calcareous sand. Successful

calibration of the analytical design models against the centrifuge database resulted in the

development of design charts summarising the potential performance of both zero and

four fluke dynamic anchors at prototype scale. The chapter concludes with a design

example demonstrating the use of the design charts.

7.2 CLAY - BEAM CENTRIFUGE

7.2.1 Impact Velocity

Figure 7.1 shows the comparison between the impact velocities reported in the beam

centrifuge tests in Section 5.2.2 and the theoretical impact velocities described in

Section 4.3.2, accounting for the non-uniform acceleration field in the centrifuge. The

theoretical velocities over predict the measured impact velocities by approximately 12

% over the range of drop heights considered. This can be attributed to frictional energy

losses between the anchor and guide during installation. Similar observations have been

made in previous dynamic anchor centrifuge tests reported by Lisle (2001), Wemmie

(2003), Richardson (2003) and O’Loughlin et al. (2004b).

164

7.2.2 Embedment Depth

The theoretical embedment depth following dynamic anchor installation in normally

consolidated clay in the beam centrifuge was determined according to the method

detailed in Section 4.4.1. For a specific impact velocity and a given set of anchor and

soil properties, this method produced a profile showing the variation in anchor velocity

with depth below the sample surface. The final embedment depth was assessed by

determining the depth at which the anchor velocity became zero. Figure 7.2 shows

example velocity profiles for a model zero fluke anchor (0FA; L/D = 12.5, m = 15

grams, Nc = 12, α = 0.4, CD = 0.24) impacting the sample (su = 1 kPa/m) at velocities of

0, 10, 20 and 30 m/s. Interestingly, in each case the anchor velocity increased during the

early stages of penetration.

7.2.2.1 Back-Calculated Strain Rate Parameter

Uncertainty surrounding strain rate effects during dynamic anchor penetration in fine

grained soils required the strain rate parameter (λ or β) in Equations 4.20 and 4.21 to be

back-calculated from the experimental data. The value of the strain rate parameter was

varied until the embedment depth measured in the beam centrifuge tests matched the

calculated embedment depth, assuming Nc = 12 and α = 0.4 (see Section 4.4.2). The

strain rate parameter values back-calculated from the 0FA embedment data for both the

semi-logarithmic and power rate laws are shown in Figure 7.3. It is evident that for both

rate laws, the back-calculated strain rate parameter values increase with increasing

impact velocity. However, if the strain rate parameter increases with impact velocity,

the embedment depth dependence on velocity is effectively considered twice. Hence the

embedment depth calculations should be performed with a constant strain rate

parameter. Whilst True (1976) and Biscontin and Pestana (2001) reported increases in

the strain rate parameter with increasing strain rate (see Section 2.2.3.1), the apparent

dependence of the strain rate parameter on impact velocity suggests that neither the

semi-logarithmic nor power rate law adequately reflect the soil response during

dynamic anchor installation. The inability of the embedment prediction method to fully

capture the soil behaviour may also be attributed to differences in the flow mechanism

or shear band thickness during penetration, or even changes in the inertial resistance at

high strain rates.

165

The values of λ in Figure 7.3a suggest increases in the undrained shear strength of

approximately 30 – 80 % per log cycle increase in strain rate (v/D). By comparison,

Sheahan et al. (1996) reported λ values of up to 17 % for triaxial compression tests at

strain rates of 0.0014 – 670 %/hr, while Biscontin and Pestana (2001) reported values of

1 – 60 % for vane shear tests conducted at rates of 0.06 – 3000 °/min. Similarly, typical

λ values for field and centrifuge penetrometer tests range from approximately 12 – 20 %

for installation rates of up to 200 mm/s (Boylan et al. 2007, Lehane et al. 2008). On

average, the semi-logarithmic strain rate parameter values determined from the dynamic

anchor tests are considerably higher than those reported in the laboratory and field tests.

This discrepancy may be attributed to the limitations of the semi-logarithmic law,

particularly when considering strain rates which cover several orders of magnitude. For

instance, in the centrifuge, a 6 mm diameter anchor impacting the sample at 30 m/s will

result in strain rates of v/D = 5000 s-1, which are 25000 times larger than the reference

strain rate (v/D = 0.2 s-1, 5 mm diameter T-bar installed at 1 mm/s). By comparison, the

laboratory and field tests mentioned above were typically conducted at strain rates

covering a much smaller range of values.

The limitations of the semi-logarithmic method can be seen by comparing the

normalised shear strength (su/su,ref) due to strain rate effects for both the semi-

logarithmic and power rate laws (see Figure 7.4). At low strain rates, good agreement is

obtained between the semi-logarithmic law with λ ≈ 0.2 and the power law with β = 0.1.

However at a normalised strain rate of γ& / γ& ref = 25000 (i.e. 5000/0.2), a value of λ = 0.4

is required to achieve the same normalised shear strength as the power law with β = 0.1.

Therefore the λ values of 0.3 – 0.8 back-calculated from the experimental data represent

some form of ‘secant’ fit to a power law model. Hence for strain rates covering several

orders of magnitude, the power law rate function is likely to provide improved accuracy

over the semi-logarithmic model. Given the limitations of the logarithmic model and the

apparent improvements afforded by the power law model, the predicted embedments

presented in Section 7.2.2.2 have been evaluated using the power law rate model with

an average value of β = 0.12.

The λ values in Figure 7.3a are also somewhat higher than values of 3 – 36 % reported

by Lisle (2001), Wemmie (2003), Richardson (2003) and O’Loughlin et al. (2004b) for

previous dynamic anchor centrifuge tests. These differences can be attributed to

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improvements made to the embedment prediction model, including the use of a strain

rate rather than velocity rate dependence formulation and accounting for the variation in

the anchor weight as the anchor moves through the gravitational acceleration field. In

addition, the current calculations have been made using multiple PERP or adjusted

single PERP velocities (see Section 5.2.2), which are higher and more accurate than the

single PERP velocities utilised in these previous studies.

7.2.2.2 Predicted Embedment Depth

The theoretical embedment depth of the 0FAs in the beam centrifuge was calculated

using the power law rate model given in Equation 4.21, with an average value of β =

0.12. The calculations were based on an ellipsoid nosed anchor (see Table 3.5 for

anchor dimensions) with an average mass of 14.5 grams and a normally consolidated

clay sample with an average shear strength gradient of approximately 1.07 kPa/m (see

Table 5.1). Note that the calculations were actually performed using the average

polynomial shear strength profile given by Equation 5.3, with a = 0.013 kPa/m2 and b =

0.870 kPa/m, which correspond to the average linear shear strength gradient of 1.07

kPa/m (see Table 5.1). Figure 7.5 shows the measured and predicted embedment depths

for impact velocities of up to 35 m/s. For comparison, the embedment depths calculated

assuming average lower and upper bound values of β = 0.08 and 0.14 respectively, have

also been shown. It is apparent that whilst β = 0.12 provides relatively good agreement

with the experimental data for impact velocities between 15 and 30 m/s, at lower impact

velocities the embedment depth is underestimated by as much as 24 %. This

underestimation at low impact velocities highlights the limitations of the model in

predicting embedments over a wide range of potential strain rates. However, it is

difficult to make conclusive statements regarding the accuracy of these predictions

given the lack of centrifuge test data at velocities below 15 m/s. That said, field

installations of dynamic anchors will typically occur at velocities greater than 15 m/s, as

maximisation of the impact velocity has been shown to lead to higher embedment

depths and therefore higher holding capacities. Hence, the need for accurate embedment

predictions at lower impact velocities is not as critical as at moderate to high impact

velocities.

The experimental data presented in Section 5.2.3.1 demonstrated that the dynamic

anchor embedment depth depended on the velocity of the anchor at the point of impact

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with the sample surface. Hence, given the potential for 0FAs to achieve theoretical

terminal velocities in the order of 80 m/s (see Section 5.2.2), extrapolation of the

experimental data suggested embedment depths in the order of 300 mm (60 m at

prototype scale). Figure 7.6 shows that by extending the embedment predictions to

similar impact velocities, potential embedment depths of approximately 360 mm (72 m

at prototype scale) are possible, assuming β = 0.12. Therefore following optimisation of

the impact velocity, dynamic anchors appear capable of achieving normalised

embedments of up to 4.8 times the anchor length.

It should be noted that as the strain rates encountered during dynamic anchor

installation in the centrifuge are n times larger than those encountered at prototype

scale, the penetration strain rate effects in the field will be less than those experienced in

the centrifuge (assuming a constant strain rate parameter). Consequently, higher

penetration depths should be expected in the field when compared with the centrifuge

test data.

7.2.2.3 Sensitivity Analysis

The influence of the tip bearing capacity factor, shaft adhesion factor, shear strength

gradient and drag coefficient on the calculated embedment depth were assessed via

sensitivity analysis. The calculations in Section 7.2.2.2 were based on the following

assumptions:

• Nc = 12

• α = 0.4

• k = 1.07 kPa/m (a = 0.013 kPa/m2, b = 0.870 kPa/m)

• CD = 0.24

For the sensitivity analysis, values of Nc were assumed to range from 8 – 20 based on

the results of cone penetration tests (Lunne et al. 1997). In addition, the shaft adhesion

factor was varied from 0 (no shaft friction) to 1 (undisturbed shear strength mobilised

along anchor shaft), whilst typical shear strength gradients for normally consolidated

clay in the centrifuge range from 1 to 1.5 kPa/m. The drag coefficient was assumed to

vary from 0 (no inertial drag resistance) to 0.7 (drag coefficient of cylindrical projectiles

reported by True 1976). A summary of the embedment depth sensitivities is provided in

Table 7.1 and Figures 7.7 – 7.10.

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Parameter Value Average Change in Embedment (%)

Tip bearing capacity factor, Nc 8 13.0

20 -18.1

Shaft adhesion factor, α 0 43.1

1 -21.2

Shear strength gradient, k (kPa/m) 1 5.8

1.5 -18.3

Drag coefficient, CD 0 1.7

0.7 -2.9

Table 7.1 Summary of the beam centrifuge embedment depth sensitivity analysis

It can be seen that the theoretical embedment depth is relatively sensitive to variations

in the tip bearing capacity factor, shaft adhesion factor and shear strength gradient. This

is not surprising considering that the bearing and shaft friction resistances comprise a

relatively large proportion of the total penetration resistance force and that these are

largely dependent on the shear strength of the target material. However, the insensitivity

of the penetration calculations to the anchor drag coefficient tends to support the

assumption that inertial drag effects comprise only a relatively small proportion of the

total dynamic anchor penetration resistance (see Section 4.2.3).

7.2.3 Holding Capacity

The theoretical vertical monotonic holding capacity following dynamic anchor

installation in normally consolidated clay in the beam centrifuge was determined

according to the American Petroleum Institute (API) method summarised in Section

4.5.1.

7.2.3.1 Predicted Vertical Monotonic Holding Capacity

The vertical monotonic holding capacity of the ellipsoid nosed 0FAs in the beam

centrifuge was calculated assuming Nc = 12 at the anchor tip, Nc = 9 at the anchor

padeye (see Section 4.5.2) and f = 0.1 (see Section 4.5.1). As for the embedment depth

calculations an average anchor mass of 14.5 grams and an average shear strength

gradient of 1.07 kPa/m were adopted. Note that the calculations were actually

performed using the average polynomial shear strength profile given by Equation 5.3,

with a = 0.013 kPa/m2 and b = 0.870 kPa/m, which correspond to the average linear

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shear strength gradient of 1.07 kPa/m (see Table 5.1). The shaft adhesion factor was

determined according to Equations 4.35 and 4.36, resulting in α = 1. Given the dual

maximum capacity behaviour observed in the beam centrifuge tests (see Section 5.2.4),

the measured Peak 1 and Peak 2 capacities have been compared with the theoretical

holding capacities in Figures 7.11 and 7.12 respectively. It is apparent that the predicted

capacity, assuming α = 1, provides reasonable agreement with the Peak 1 data, but

noticeably over predicts the Peak 2 holding capacities. Better agreement with the

experimental data is obtained with α = 0.8 and 0.5 for the Peak 1 and Peak 2 holding

capacities respectively (see Figures 7.11 and 7.12). A shaft adhesion factor of 0.8 agrees

with the findings of dynamic anchor centrifuge model tests reported by O’Loughlin et

al. (2004b).

Despite the satisfactory agreement obtained between the measured and predicted

capacities, a significant degree of variability exists amongst the measured capacities. It

is likely that these discrepancies can be attributed to variations in the consolidation time

permitted following installation, differences in the anchor mass or slight variations in

the undrained shear strength between samples. Section 5.3.6 showed that the anchor

capacity increases with consolidation time following installation, due to setup. Whilst

every effort was made to ensure similar consolidation times in each of the beam

centrifuge tests (i.e. approximately 13 min or 1 year at prototype scale), accurate times

were not recorded in a large number of cases. In addition, whilst the average shear

strength gradients in each of the beam centrifuge samples were similar, slight variations

between samples and even variations within individual samples between tests conducted

at the beginning and at the end of the test programme may have introduced

inconsistencies in the measured capacity data. Taking into account these potential

differences, the API framework is seen to provide a satisfactory method for predicting

the range of dynamic anchor holding capacities measured in the beam centrifuge tests.

In Section 5.2.5.1, the anchor capacities measured in the beam centrifuge tests were

found to increase with increasing embedment depth, due to the mobilisation of higher

undrained shear strengths. The predicted capacities shown in Figures 7.11 and 7.12

support these observations, indicating that in soils where the shear strength increases

with depth, the anchor capacity also increases with increasing penetration depth. This

highlights the importance of accurately predicting the dynamic anchor embedment

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depth in order to be able to accurately predict the subsequent holding capacity. Given

the potential for the zero fluke dynamic anchors to achieve penetration depths in the

order of 360 mm (72 m at prototype scale; see Section 7.2.2.2), extending the holding

capacity predictions to similar depths indicates potential vertical monotonic holding

capacities in the order of 135 – 200 N (5.4 – 8.0 MN at prototype scale) for shaft

adhesion factors ranging from α = 0.5 – 1 (see Figure 7.13). These capacities represent

efficiencies of approximately 4.7 – 7.0 times the anchor dry weight.

7.2.3.2 Sensitivity Analysis

Just as for the embedment depth predictions, sensitivity analyses were also performed

on the predicted holding capacity. The calculations in Section 7.2.3.1 assumed:

• Nc = 12 at the anchor tip

• Nc = 9 at the padeye

• f = 0.1

• α = 0.8

• k = 1.07 kPa/m (a = 0.013 kPa/m2, b = 0.870 kPa/m)

For the sensitivity analysis, the bearing capacity factor at the anchor tip was assumed to

range from 8 – 20. The influence of the padeye bearing capacity factor was found to

depend on the degree of hole closure. Therefore the effects of both the padeye bearing

capacity factor and degree of hole closure were combined, with the limiting cases

defined as either no hole closure (f = 0) in which case no padeye bearing resistance is

generated, i.e. f.Nc = 0 and full hole closure (f = 1), in which case the maximum bearing

capacity factor for a circular foundation is assumed, i.e. f.Nc = 9. Similar to Section

7.2.2.3, the shaft adhesion factor was assumed to vary from 0 to 1 and the shear strength

gradient from 1 to 1.5 kPa/m. A summary of the holding capacity sensitivities is

provided in Table 7.2 and Figures 7.14 – 7.17. Note that for comparison, Figures 7.14 –

7.17 include the Peak 1 capacities from the 0FA centrifuge tests.

It is apparent that the theoretical holding capacity is relatively sensitive to variations in

the tip bearing capacity factor, shaft adhesion factor and shear strength gradient.

However, as a result of relatively low padeye embedment depths, the holding capacity is

insensitive to variations in the padeye bearing resistance.

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Parameter Value Average Change in Capacity (%)

Tip bearing capacity factor, Nc 8 -6.2

20 12.5

Padeye bearing resistance, f.Nc 0 -0.6

9 5.4

Shaft adhesion factor, α 0 -33.9

1 8.5

Shear strength gradient, k (kPa/m) 1 -11.3

1.5 9.7

Table 7.2 Summary of beam centrifuge holding capacity sensitivity analysis

One of the key arguments proposed for dynamic anchors is that their performance is less

dependent on accurate assessment of the seabed shear strength profile, since lower shear

strengths permit greater penetrations, and vice versa. Hence, given the holding capacity

dependence on embedment depth, the capacity is effectively a function of the energy of

the anchor at impact (i.e. impact velocity and mass). Section 7.2.2.3 demonstrated that

the predicted embedment depth was relatively sensitive to variations in the undrained

shear strength gradient, with Table 7.2 showing a similar sensitivity for the predicted

holding capacity. These relative sensitivities have been combined in Figure 7.18, with

the holding capacity plotted against impact velocity for the limiting undrained shear

strength gradients of 1 and 1.5 kPa/m. It is evident that the predicted holding capacity is

relatively insensitive to variations in the shear strength gradient, particularly at low

impact velocities; although at higher impact velocities an increase in the undrained

shear strength gradient provided higher holding capacities.

7.2.4 Summary

Due to frictional effects, the theoretical impact velocity in the beam centrifuge over

predicted the measured impact velocities by approximately 12 %, over the range of drop

heights considered.

Back-calculated values of the strain rate parameter increased with impact velocity,

indicating potential limitations of the embedment depth prediction method and in

particular the semi-logarithmic and power law rate functions. Theoretical embedment

depths calculated using the power law rate model, assuming a constant strain rate

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parameter, provided adequate agreement with the measured centrifuge data at velocities

above 15 m/s. However, for impact velocities below 15 m/s, the embedment depth was

under estimated by as much as 24 %. Given the dependence of penetration depth on

impact velocity, the calculations indicated that embedments of up to 4.8 times the

anchor length were possible at 0FA terminal velocities approaching 80 m/s. The

theoretical embedment depth was found to be sensitive to variations in the bearing

capacity factor, shaft adhesion factor and undrained shear strength gradient.

The API method with α = 0.8 and 0.5 provided reasonable predictions of the measured

Peak 1 and Peak 2 capacities respectively. The calculations supported the experimental

observations of an increase in holding capacity with embedment depth. Given the

potential for 0FA embedment depths of up to 4.8 times the anchor length, the

calculations suggested that capacities approaching 7.0 times the anchor dry weight were

possible. The theoretical holding capacity was found to be sensitive to the selection of

the tip bearing capacity factor, shaft adhesion factor and variations in the undrained

shear strength gradient. However, the shear strength gradient influences both the

embedment depth and holding capacity, with lower shear strengths resulting in lower

capacities but higher embedments and vice versa. The resulting relative insensitivity of

the anchor performance to accurate assessment of the undrained shear strength profile

represents a key advantage of dynamically installed anchors.

7.3 CLAY - DRUM CENTRIFUGE

7.3.1 Impact Velocity

The impact velocities measured in the drum centrifuge tests for the 0FAs, four fluke

anchors (4FAs) and hemispherically tipped anchors with L/D < 7 and L/D > 7 are

presented in Figure 7.19 compared with the theoretical impact velocity determined

according to the method outlined in Section 4.3.2. As in the beam centrifuge tests, it is

apparent that the theoretical impact velocity over predicts the measured velocities.

Again, this can be attributed to friction developed between the anchor and the

installation guide. As mentioned in Section 5.3.2, the various anchor types generated

different levels of friction depending on the anchor geometry and the installation guide

used, resulting in differences in the accuracy of the impact velocity calculations.

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However, on average, the theoretical impact velocity over predicted the measured

velocity by approximately 36 %.

7.3.2 Embedment Depth

The theoretical embedment depths in the drum centrifuge were calculated using the

method outlined in Section 4.4.1.

7.3.2.1 Back-Calculated Strain Rate Parameter

Once again, the strain rate parameter values were back-calculated from the measured

embedment depth data. Since no accurate shear strength information was available for

Drum 1, strain rate parameter values have only been calculated based on the results of

tests conducted in Drum 2. For the 0FA tests, the strain rate parameter was calculated

assuming Nc = 12 and α = 0.4 (see Section 4.4.2). The strain rate parameter values back-

calculated from the 0FA embedment data for both the semi-logarithmic and power rate

laws are shown in Figure 7.20. As in the beam centrifuge tests (see Section 7.2.2.1), the

strain rate parameter values for both rate laws increased with increasing impact velocity.

These results once again highlight the limitations of the rate laws in describing the soil

response during dynamic anchor installation. Somewhat surprisingly however, the λ

values of 0.15 – 0.3, are lower than values of 0.3 – 0.8 reported in the beam centrifuge

tests (see Section 7.2.2.1), although good agreement is obtained with back-calculated λ

values of 0.03 – 0.36 from previous dynamic anchor centrifuge tests reported by Lisle

(2001), Wemmie (2003), Richardson (2003) and O’Loughlin et al. (2004b). This

discrepancy may be partially attributed to the lower impact velocities in the drum

centrifuge. In the 0FA tests in the drum centrifuge, a maximum impact velocity of

approximately 15 m/s corresponded to λ = 0.3. At a similar impact velocity, the beam

centrifuge tests indicated an average value of λ = 0.4, which considering the variability

of the back-calculated strain rate parameter values is relatively comparable. Given the

advantages of the power law model (see Section 7.2.2.1), the predicted embedment

depths for the 0FAs in Section 7.3.2.2 have been calculated assuming an overall average

strain rate parameter value of β = 0.06.

For the 4FA tests, the strain rate parameter was calculated assuming Nc = 12, Ncf = 7.5

and α = 0.4 (see Section 4.4.2). Figure 7.21 shows the back-calculated strain rate

parameter values for both the semi-logarithmic and power rate laws. Note that only a

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limited number of 4FA tests were conducted in the drum centrifuge, many of which

were conducted at impact velocities of 0 m/s. However, the overall best-fit to the 4FA

data indicates an apparent increase in the strain rate parameter with increasing impact

velocity. In addition, the λ values in Figure 7.21a are consistent with the values of λ

determined for the 0FA tests. The 4FA embedment calculations presented in Section

7.3.2.2 are based on the power rate law with an average value of β = 0.08.

Strain rate parameters were also calculated for the tests conducted in Drum 2 with

anchors H0-3, H0-5, H0-9 and H0-13 (see Section 3.6.5), assuming Nc = 10 and α = 0.4

(see Section 4.4.2). The mass and aspect ratio of each of these anchors is summarised in

Table 7.3 and the back-calculated strain rate parameters from these tests are presented in

Figure 7.22. For all but anchor H0-5, the strain rate parameter appeared to increase with

impact velocity, although only a limited number of tests were conducted with each

anchor. Interestingly, the magnitude of the back-calculated strain rate parameter seemed

to vary with the anchor type (aspect ratio). This goes further to suggest that the

embedment depth prediction model does not completely reflect the soil behaviour

during dynamic anchor penetration. That said, the embedment predictions presented in

Section 7.3.2.2 are based on the power law rate model using individual average strain

parameters for each anchor type (see Table 7.3). The average β value of 0.07 compares

favourably with the average values from the 0 and 4FA tests. Hence the overall average

β value for the drum centrifuge tests was also 0.07.

Anchor L/D Mass Average β

(g)

H0-3 2 2.0 0.09

H0-5 4 4.7 0.11

H0-9 6 1.9 0.03

H0-13 12 4.7 0.06

Average 0.07

Table 7.3 Power law strain rate parameters for hemispherically tipped anchors

7.3.2.2 Predicted Embedment Depth

The theoretical embedment depths for the 0FAs in the drum centrifuge were calculated

using the power law rate model with β = 0.06. Figure 7.23 shows the measured and

predicted embedment depths for anchor E0-3. For comparison, the embedment depths

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calculated assuming the overall average strain rate parameter value of β = 0.07 have

also been shown. Similar predictions for anchors E0-4 and E0-5 are provided in Figures

7.24 and 7.25 respectively. It is apparent that the embedment depths calculated using

both the average 0FA strain rate parameter (β = 0.06) and the overall drum centrifuge

average strain rate parameter (β = 0.07) provide reasonable agreement with

experimental data for each individual anchor. Despite this, at low impact velocities, the

embedments for anchors E0-3 and E0-5 are slightly under estimated.

For the 4FAs, the theoretical embedment depths were calculated assuming β = 0.08 as

discussed in Section 7.3.2.1. Figure 7.26 shows the measured and predicted embedment

depths for anchor E4-2. For comparison, the embedment depths calculated assuming the

overall average strain rate parameter value of β = 0.07 have also been provided. Similar

predictions for anchor E4-3 are provided in Figure 7.27. The theoretical embedment

depths calculated assuming both strain rate parameter values provide good agreement

with the experimental data for each anchor, despite a relatively small number of tests.

Figures 7.28, 7.29, 7.30 and 7.31 show the measured and theoretical embedment depths

for anchors H0-3, H0-5, H0-9 and H0-13 respectively. The embedment depths have

been calculated assuming the average strain rate parameter values given in Table 7.3.

For comparison, the embedment depths calculated assuming the overall average strain

rate parameter value of β = 0.07 have also been shown. As expected, the anchor specific

strain rate parameters provided the best agreement with the experimental data, although

for all but anchor H0-13, the embedment depths calculated using the overall average

strain rate parameter varied noticeably from the centrifuge test data. It should be noted

that anchor H0-13 had an aspect ratio of 12, which is very close to the aspect ratio of the

0 and 4FAs (i.e. L/D = 12.5), suggesting that the strain rate parameter may also depend

on the anchor aspect ratio. Such an observation indicates another potential limitation of

the embedment prediction model.

Since the calculation procedure adopted for the drum centrifuge tests was similar to that

used for the beam centrifuge, further sensitivity analyses were not undertaken.

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7.3.3 Holding Capacity

The theoretical vertical monotonic holding capacities for the model anchors in the drum

centrifuge were determined using the API method outlined in Section 4.5.1.

7.3.3.1 Predicted Vertical Monotonic Holding Capacity

The holding capacities of the 0FAs in the drum centrifuge were calculated assuming Nc

= 12 for the anchor tip, Nc = 9 at the anchor padeye (see Section 4.5.2) and f = 0.1 (see

Section 4.5.1). The shaft adhesion factor was calculated according to Equations 4.35

and 4.36 resulting in α = 1. Figure 7.32 shows the comparison between the theoretical

capacity and the measured Peak 1 and Peak 2 holding capacities for anchor E0-3 in the

drum centrifuge. Figures 7.33 and 7.34 show similar comparisons for anchors E0-4 and

E0-5 respectively. It is apparent that for both anchors E0-3 and E0-4, the Peak 1

capacities in particular, vary significantly at comparable embedment depths. This can be

attributed to setup effects, with longer consolidation times resulting in higher anchor

capacities (see Section 5.3.6). The predicted capacity with α = 0.8 provided reasonable

estimates of the Peak 1 capacities for anchors E0-3 and E0-4 following consolidation

periods of approximately 14 min (1.1 years at prototype scale). However, for tests

conducted with longer consolidation times (i.e. up to approximately 15 hours or 68

years at prototype scale), the theoretical capacity under predicted the measured capacity

by approximately 40 %. The increase in capacity due to consolidation is discussed

further in Section 7.3.3.2. For anchor E0-5, with an average consolidation time of

approximately 16 min (1.2 years at prototype scale), α = 0.6 provided good agreement

with the measured Peak 1 capacities. The theoretical capacity assuming α = 0.5 – 0.6

provided good agreement with the Peak 2 capacity data for each of the model anchors

across the range of consolidation times considered. These adhesion factor values are

consistent with α = 0.8 and 0.5 for the Peak 1 and Peak 2 capacities in the beam

centrifuge tests (see Section 7.2.3.1).

For the 4FAs, the theoretical holding capacity was calculated assuming Nc = 12 at the

anchor tip, Nc = 9 at the anchor padeye, Ncf = 7.5 for the anchor flukes (see Section

4.5.2) and f = 0.1. It should be noted that complete closure of the entry pathway behind

the anchor flukes was assumed. The shaft adhesion factor was calculated according to

Equations 4.35 and 4.36 resulting in α = 1. Note also that the same adhesion factor was

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assumed for both the anchor shaft and flukes. Figures 7.35 and 7.36 show the measured

and theoretical holding capacities for anchors E4-2 and E4-3 respectively. Just as in the

0FA tests, the measured holding capacities varied with consolidation time at comparable

embedment depths. The theoretical capacity assuming α = 1 provided good agreement

with the measured Peak 1 capacity data for anchor E4-2 following approximately 5 min

(0.4 years at prototype scale) of consolidation. However, following approximately 49

hours (224 years at prototype scale) of consolidation the holding capacity was under

predicted by approximately 30 %. For anchor E4-3, the theoretical capacity assuming α

= 0.7 provided good agreement with the Peak 1 capacity following approximately 7 min

(0.5 years at prototype scale) of consolidation, although the capacity following 15 hours

(68 years at prototype scale) of consolidation was under predicted by approximately 40

% with the same adhesion factor. The influence of consolidation is considered further in

Section 7.3.3.2. Shaft adhesion factors of α = 0.7 and α = 0.4 provided the best

agreement with the Peak 2 capacity data for anchors E4-2 and E4-3 respectively.

The theoretical holding capacities of the model anchors with different aspect ratios were

evaluated assuming Nc = 10 at both the anchor tip and padeye (hemispherical ends; see

Section 4.5.2), α = 1 and f = 0.1. Figures 7.37, 7.38, 7.39 and 7.40 show the measured

and theoretical holding capacities for anchors H0-3, H0-5, H0-9 and H0-13 respectively.

It should be noted that due to the lack of shear strength data from Drum 1, only the test

results from Drum 2 have been considered. In addition, only anchor H0-13 exhibited

Peak 2 capacities. Each of the anchors was extracted following approximately 14 min

(1.1 years at prototype scale) of consolidation. For anchors H0-3 and H0-5, the

theoretical capacities assuming α = 0.8 provide good agreement with the measured

capacities, with α = 0.7 providing a better fit to the experimental data for anchor H0-13.

These shaft adhesion factors are consistent with the values determined for the 0 and

4FAs. Somewhat surprisingly however, α = 0.4 was required to match the measured

capacities for anchor H0-9.

As the same method was used to predict the dynamic anchor capacity in both the beam

and drum centrifuge tests, it was not considered necessary to reconsider the sensitivity

of the calculation procedure to changes in the various parameter values.

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7.3.3.2 Consolidation Solutions

Section 5.3.6 showed that the dynamic anchor capacity increases with time following

installation in fine grained soils due to setup. Since thixotropic effects in kaolin clay are

considered negligible (Skempton and Northey 1952), the time dependent increase in

anchor capacity was attributed to consolidation of the soil in the vicinity of the anchor.

Randolph and Wroth (1979) presented a closed form solution for the radial

consolidation of soil around a driven pile, leading to the development of a realistic

method for modelling the dissipation of excess pore pressures following pile installation

(Cavity Expansion Method; see Section 2.3.3). The method assumes that the initial pore

pressure distribution is a function of the rigidity index, Ir = G/su of the soil, with typical

values of Ir ranging from 50 – 500 (Randolph 2003). The change in the degree of

consolidation with non-dimensional time (T) for anchors E0-3, E0-4, E4-2 and E4-3 in

the drum centrifuge (see Section 5.3.6.2) is shown in Figure 7.41 along with the degree

of consolidation predicted by the Cavity Expansion Method (CEM) for Ir = 50 and 500.

For comparison, the results of torpedo anchor laboratory tests reported by Audibert et

al. (2006) have also been shown. It can be seen that the theoretical solution for the

upper bound value of Ir = 500 provides a relatively accurate representation of the

measured increase in capacity for the anchors which were installed dynamically

(anchors E0-4 and E4-3), but overestimates the anchor capacity regain for the quasi-

statically installed anchors (anchors E0-3 and E4-2). For T > 10, Ir = 500 agrees well

with the torpedo anchor data, whilst for T ≤ 10 a lower degree of consolidation is

observed. The extent of the conformity between the analytical solution and the

experimental data, particularly for the dynamic installation tests, suggests that cavity

expansion techniques may be appropriate for determining the consolidation behaviour

and therefore capacity regain with time following dynamic anchor installation.

Kehoe (1989), as reported by Bullock et al. (2005), indicated that setup following pile

driving is dominated by the regain in shaft frictional resistance. Hence it was assumed

that the time dependent regain in dynamic anchor capacity was due entirely to the

recovery of shaft and fluke friction and that any time changes in bearing resistance were

assumed to have negligible impact on setup. Section 7.3.3.1 demonstrated that the API

method (see Section 4.5.1) provided reasonable predictions of the Peak 1 anchor

capacity for consolidation times of up to approximately 1 year at prototype scale, with

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adhesion factor values of up to α = 1. However, for consolidation times greater than 1

year, the capacity predictions assuming α = 1 significantly under predicted the measured

capacity for both the 0 and 4FAs. Assuming Nc = 12 for the anchor tip, Nc = 9 for the

anchor padeye and Ncf = 7.5 for the anchor flukes, adhesion factor values required to

achieve the measured holding capacities were back-calculated for the various time

intervals following installation (see Figure 7.42). An expected increase in α with

increasing consolidation time was observed, reflecting the increase in soil shear strength

with dissipation of the excess pore pressures. A value of α = 1 indicates that the shear

strength mobilised along the anchor shaft and flukes during vertical extraction is

equivalent to the undisturbed soil shear strength. However, as can be seen in Figure

7.42, for T > 4, i.e. after approximately 1 year of consolidation (assuming ch = 5.5 m2/yr

and D = 1.2 m), back-calculated values of α exceed 1, indicating an increase in the shear

strength above the intact strength. The assumption of constant bearing factors for the

anchor tip and edges of the flukes contributes to the high long-term α values shown in

Figure 7.42. There is little data in the literature as guidance for estimating any increase

in the bearing resistance, but if it were assumed that the bearing resistance increased by

50 % in the long-term the final α values would be reduced by ~15 %, from around 2

down to ~1.7. This is still significantly greater than unity.

With the adhesion factor limited to α = 1, according to API guidelines (see Section 4.5),

shear strength gradients of up to 1.7 kPa/m were required for agreement between the

measured and predicted capacities. This is considerably higher than the shear strength

gradient of 1.03 kPa/m measured in the T-bar penetrometer test (see Section 5.3.1) and

higher than typical shear strength gradients for normally consolidated kaolin clay in the

centrifuge of 1 – 1.5 kPa/m. Whilst the results may be complicated somewhat by the

unusual load displacement response observed during extraction (see Section 5.3.4), the

results tend to suggest that following long periods of post-installation consolidation,

undrained shear strengths higher than the initial undisturbed shear strength can be

mobilised by dynamic anchors to resist uplift loading. It should be noted that this

analysis has focused on the Peak 1 capacity, although back-calculated adhesion factor

values for Peak 2 would be some 25 to 50 % lower than those determined for Peak 1.

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Based on the information in Figure 7.42 it was possible to develop an alternative

expression for the adhesion factor to account for the apparent increase in shear strength

with increasing consolidation time. The expression was obtained by fitting a curve to

the back-calculated α data, of the form:

( ) 2p0

21

TT1α+

+α−α=α (7.1)

where α1 represents the initial adhesion factor, α2 represents the final adhesion factor, T0

is the value of T at the mid point between α1 and α2 and p is a fitting parameter

governing the slope of the curve. It should be noted that due to the difficulty associated

with determining an appropriate cut-off velocity between quasi-static and dynamic

installation, a single curve has been fitted to the adhesion factor data in Figure 7.42

despite an apparent divergence between the values of α for quasi-static and dynamic

installation for T < 1. The best-fit parameters for the experimental data were α1 = 0.04,

α2 = 2.2, T0 = 9.5 and p = 0.42. Figure 7.43 shows the measured Peak 1 capacity data

for anchor E0-3 compared with the predicted capacities for revised adhesion factor

values of α = 0.4 and α = 1.8, representing the values following the minimum and

maximum consolidation times respectively. It can be seen that the modified adhesion

factors provide reasonable agreement with both the minimum and maximum holding

capacities for anchor E0-3.

7.3.4 Summary

On average, the theoretical impact velocity in the drum centrifuge over predicted the

impact velocities of the various model anchors by 36 %. The discrepancy between the

measured and theoretical impact velocity was attributed to friction, with differences in

the anchor geometry and installation guide leading to slight variations in the accuracy of

the calculations for the different anchor types.

Back-calculated strain rate parameter values were found to increase with impact

velocity, reinforcing the potential limitations of the semi-logarithmic and power rate

laws identified in the beam centrifuge analysis. Strain rate parameter values from the

drum centrifuge were generally lower than the values determined in the beam centrifuge

and provided reasonable agreement with the results of previous dynamic anchor

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centrifuge tests. The 0 and 4FA theoretical embedment depths calculated using the

power law rate model, with an average strain rate parameter provided reasonable

agreement with the experimental data, although the embedment depths at low impact

velocities were slightly under predicted. For the anchors with varying aspect ratios,

anchor specific strain rate parameter values provided better agreement with the

centrifuge data, indicating further potential inadequacies in the embedment prediction

method.

Theoretical holding capacities calculated according to the API method with adhesion

factor values between 0.8 and 1 provided reasonable predictions of the dynamic anchor

holding capacity for post-installation consolidation times of up to approximately 1 year

at prototype scale. Agreement between the measured and theoretical holding capacities

following longer periods of consolidation required adhesion factor values considerably

higher than α = 1, suggesting the mobilisation of shear strengths higher than the

undisturbed strength. Cavity expansion solutions for radial consolidation around solid

driven piles provided a reasonable approximation of the dynamic anchor post-

installation consolidation behaviour.

7.4 CALCAREOUS SAND – BEAM CENTRIFUGE

7.4.1 Impact Velocity

The dynamic anchor impact velocity is independent of the soil properties, hence the

theoretical impact velocity for the calcareous sand tests was identical to the velocity for

the normally consolidated clay tests in the beam centrifuge (see Sections 4.3.2 and

7.2.1). Figure 7.44 shows the comparison between the predicted and adjusted impact

velocities for the 0FA tests in calcareous sand. Friction between the anchor and the

guide during installation resulted in the theoretical impact velocity over predicting the

measured velocities by approximately 17 %. This is consistent with the degree of

accuracy obtained in the normally consolidated clay tests in the beam centrifuge.

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7.4.2 Embedment Depth

The theoretical embedment depth following dynamic anchor installation in calcareous

sand in the beam centrifuge was determined according to the method outlined in Section

4.6.1.

7.4.2.1 Back-Calculated Strain Rate Parameter

The strain rate parameter (λ or β) in Equations 4.20 and 4.21 was back-calculated from

the measured experimental data assuming Nq = 32, from cone penetration tests (CPTs)

conducted during the experimental programme (see Section 4.6.1.2), and βCALC = 0.42

from static penetration tests (see Section 6.3.6). The in situ vertical effective stress was

calculated assuming an average effective soil unit weight of 5.2 kN/m3 (Richardson et

al. 2005). Figure 7.45 shows the strain rate parameter values back-calculated from the

experimental data for both the semi-logarithmic and power rate laws. The strain rate

parameter values appear to increase with increasing impact velocity, although a

significant degree of variability exists, with several tests indicating a negative strain rate

parameter, i.e. a reduction in strength with increasing strain rate, which is physically

unlikely. The values of λ in Figure 7.45a indicate increases in the undrained shear

strength of up to approximately 25 % per log cycle increase in strain rate. This is

comparable to the average value of λ = 0.26 back-calculated from dynamic anchor

centrifuge tests in normally consolidated clay reported by O’Loughlin et al. (2004b).

However, the average value of λ = 0.09 for the calcareous sand tests, suggests lower

strain rate effects than in normally consolidated clay. In fact, Figure 7.45 indicates

negligible strain rate effects at low impact velocities. This is consistent with the reported

findings of CPTs conducted at rates of 0.2 – 1 mm/s in slightly cemented calcareous

sand (Joer et al. 1998). However, Figure 7.45 also indicates considerably higher strain

rate effects at higher impact velocities. This behaviour could possibly be attributed to

more complex phenomena than purely viscous effects, such as dilation, or it could also

reflect the limitations of the rate models in analysing the behaviour of dynamic anchors

during penetration of calcareous sediments. The strain rate parameter values in Figure

7.45a are also somewhat higher than the values reported by Richardson et al. (2005)

based on analysis of the same test data. The discrepancy can be attributed to

improvements in the embedment depth prediction model and the use of adjusted single

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PERP impact velocities (see Section 6.3.2) as opposed to the non-adjusted velocities

reported by Richardson et al. (2005).

Considering the advantages of the power law rate model over the semi-logarithmic

model, and to ensure consistency with the normally consolidated clay tests, the

embedment depths in Section 7.4.2.2 have been calculated using the power law rate

model with an average strain rate parameter of β = 0.03.

7.4.2.2 Predicted Embedment Depth

The theoretical embedment depth for the 0FAs in calcareous sand was calculated

assuming β = 0.03 as described in Section 7.4.2.1. Since several different 0FAs were

used in the calcareous sand tests, the calculations were based on an anchor with an

average mass of 14.7 grams. Figure 7.46 shows the measured and theoretical

embedment depths for the 0FA calcareous sand tests. Whilst the calculations under

estimate the embedment depth at vi = 0 m/s by approximately 20 %, in general, the

theoretical embedment depths provide good agreement with the experimental data.

However, due to the variability of the measured embedment depths, the embedment

predictions in calcareous sand were not as accurate as those in normally consolidated

clay.

Terminal velocities of approximately 80 m/s were determined for the 0FAs (see Section

5.2.2); however, sample depth and drop height restrictions in the centrifuge limited the

impact velocity to approximately 30 m/s. Therefore, given the dependence of the

embedment depth on impact velocity, considerably higher embedments are likely

following maximisation of the anchor impact velocity. Extending the embedment depth

predictions to impact velocities of 80 m/s indicates potential embedment depths of up to

3.1 times the anchor length in calcareous sand (see Figure 7.47).

7.4.2.3 Sensitivity Analysis

The influence of the tip bearing capacity factor, adhesion factor and effective soil unit

weight on the calculated embedment depth in calcareous sand was assessed via

sensitivity analysis. The calculations in Section 7.4.2.2 were based on the following

assumptions:

• Nq = 32

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• βCALC = 0.42

• γ΄ = 5.2 kN/m3

For the sensitivity analysis, values of Nq were assumed to range from 20 – 50 based on

the variation in the back-calculated bearing capacity factor during the CPTs.

Determination of appropriate bearing capacity factors in calcareous sand is notoriously

difficult, given that Nq decreases significantly as the stress level increases, due to

decreasing peak friction angles and the increased compressibility of the soil (Randolph

1988). The adhesion factor (βCALC) was assumed to vary from 0 – 0.5, based on values

reported by Abbs et al. (1988) for piles in calcareous sand. According to the soil

properties in Table 3.3, minimum and maximum values of the effective soil unit weight

were 4.3 kN/m3 and 6.8 kN/m3 respectively. A summary of the embedment depth

sensitivities is provided in Table 7.4 and Figures 7.48 – 7.50.

Parameter Value Average Change in Embedment (%)

Tip bearing capacity factor, Nq 20 33.8

50 -26.4

Adhesion factor, βCALC 0 6.0

0.5 -0.9

Effective unit weight, γ΄ (kN/m3) 4.3 14.9

6.8 -17.7

Table 7.4 Summary of calcareous sand embedment depth sensitivity analysis

The results suggest that the theoretical embedment depth in calcareous sand is relatively

sensitive to variations in the tip bearing capacity factor and the effective unit weight of

the soil. However, the calculated embedment is also relatively insensitive to variations

in the adhesion factor, suggesting that the shaft friction comprises a relatively small

proportion of the total penetration resistance.

7.4.3 Holding Capacity

The holding capacity of the dynamic anchors installed in calcareous sand was calculated

according to the method described in Section 4.6.2.

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7.4.3.1 Predicted Vertical Monotonic Holding Capacity

The vertical monotonic holding capacity of the 0FAs in calcareous sand was evaluated

assuming a bearing capacity factor at the anchor padeye given by the bearing capacity

factors of flat plates in silica sand (see Section 4.6.2.2). For a friction angle of 40° (see

Table 3.3), the padeye bearing capacity factors taken from Figure 4.21 ranged from 2.0

– 5.3 for the range of measured embedment depths. Using these bearing capacity

factors, the adhesion factor was back-calculated by varying βCALC until the theoretical

capacity matched the capacity measured in the centrifuge tests. Note that no reverse end

bearing resistance was considered as the extraction was assumed to take place under

drained conditions. Interestingly, an average back-calculated value of βCALC = 0.42 was

determined from the measured capacity data. Encouragingly, this was identical to the

value of βCALC obtained from the static penetration tests adopted in the embedment

analysis (see Section 7.4.2.1). The theoretical holding capacity calculated assuming an

average bearing capacity factor of Nq = 3.3 and βCALC = 0.42 is presented in Figure 7.51

together with the holding capacities measured in the centrifuge tests. It is apparent that

the predicted capacity provides good agreement with the experimental capacity data.

Embedment depth predictions in Section 7.4.2.2 indicated potential embedment depths

for 0FAs in calcareous sand of approximately 230 mm (46 m at prototype scale). Given

the increase in capacity with embedment depth, theoretical holding capacities of up to

approximately 140 N (5.6 MN at prototype scale) have been calculated, representing

efficiencies of approximately 5 times the anchor dry weight (see Figure 7.51). These

efficiencies are comparable to the lower end extrapolated efficiencies determined for the

0FAs in normally consolidated clay (see Section 7.2.3.1) and highlight the potential for

the use of dynamic anchors in calcareous sediments.

7.4.3.2 Sensitivity Analysis

Just as for the embedment depth predictions, sensitivity analyses were also performed

on the theoretical holding capacity. The calculations in Section 7.4.3.1 were based on

the following assumptions:

• Nq = 3.3

• f = 1

• βCALC = 0.42

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• γ΄ = 5.2 kN/m3

For the sensitivity analysis, the bearing capacity factor at the anchor padeye was

assumed to range from 2.0 – 5.3 based on the bearing capacity factors for flat plate

anchors in silica sand. Full hole closure was assumed in the calculations, although

potential values of f range from 0 to 1. The combined effects of the degree of hole

closure and the padeye bearing capacity factor gave limiting cases of the padeye bearing

resistance of f.Nq = 0 (assuming no hole closure) and f.Nq = 5.3 (full hole closure with

the maximum bearing capacity factor). As mentioned in Section 7.4.2.3, the adhesion

factor was assumed to range from 0 – 0.5, whilst the effective unit weight of the soil

varied from 4.3 – 6.8 kN/m3. A summary of the holding capacity sensitivities is

provided in Table 7.5 and Figures 7.52 – 7.54.

Parameter Value Average Change in Capacity (%)

Padeye bearing resistance, f.Nq 0 -6.6

5.3 4.0

Adhesion factor, β 0 -53.0

0.5 10.1

Effective unit weight, γ΄ (kN/m3) 4.3 -9.9

6.8 17.6

Table 7.5 Summary of calcareous sand holding capacity sensitivity analysis

It can be seen that the theoretical holding capacity in calcareous sand is sensitive to

variations in both the adhesion factor and effective soil unit weight. However, the

calculations are also relatively insensitive to variations in the padeye bearing resistance,

largely as a result of the low padeye embedments encountered in calcareous sand. In the

normally consolidated clay tests, it was shown that the overall holding capacity

performance of dynamic anchors was relatively insensitive to variations in the

undrained shear strength profile since lower shear strengths permitted greater

penetrations, and vice versa. Similarly in calcareous sand, both the embedment depth

and holding capacity predictions are relatively sensitive to variations in the effective soil

unit weight. Combining these relative sensitivities by plotting the holding capacity

against impact velocity for the limiting effective soil unit weights of 4.3 and 6.8 kN/m3

allows the overall sensitivity of dynamically installed anchors to the effective soil unit

weight to be evaluated (see Figure 7.55). It is evident that the predicted holding capacity

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is relatively insensitive to variations in the effective unit weight, hence dynamic anchors

provide a significant advantage over other conventional anchoring systems in that

accurate assessment of the seabed strength properties is not required prior to

installation.

7.4.4 Summary

The theoretical impact velocity for the calcareous sand tests over predicted the

measured impact velocities by approximately 17 %. The accuracy of the theoretical

velocity was comparable to that determined in the normally consolidated clay tests in

the beam centrifuge.

Despite a significant degree of variability, back-calculated values of the strain rate

parameter appeared to increase with impact velocity. In general, the magnitude of the

strain rate effects was lower than observed in normally consolidated clay. At low strain

rates, the rate effects were found to be negligible, although at higher strain rates, back-

calculated values of the strain rate parameter were, in some instances, similar to those

reported in previous dynamic anchor studies. These findings highlight the limitations of

the semi-logarithmic and power rate laws in assessing the embedment depth of dynamic

anchors, with the variability and high magnitude of the strain rate parameter at high

strain rates potentially reflecting more complicated phenomena than purely viscous

effects. Despite this, theoretical embedment depths calculated using the power rate law

with an average strain rate parameter value provided good estimates of the measured

centrifuge embedment data in calcareous sand. The calculations indicated that following

maximisation of the dynamic anchor impact velocity, embedment depths of up to 3.1

times the anchor length are possible, compared with 4.8 times the anchor length in

normally consolidated clay.

Adhesion factor values back-calculated from the holding capacity data indicated an

average value which coincided with the adhesion factor adopted in the embedment

analysis. The theoretical holding capacity provided good agreement with the capacities

measured in the centrifuge tests. Given potential embedment depths of up to 3.1 times

the anchor length at terminal velocities approaching 80 m/s, the theoretical holding

capacity calculations indicated possible vertical monotonic holding capacities of up to 5

times the anchor weight, compared with 4.7 – 7.0 in normally consolidated clay. The

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holding capacity performance of dynamically installed anchors was found to be

relatively insensitive to variations in the effective unit weight of the target material,

thereby providing dynamic anchors with a significant advantage over conventional

anchoring systems.

7.5 DYNAMIC ANCHOR DESIGN CHARTS

Two major research objectives were outlined in Section 1.5. The first of these objectives

was the establishment of an extensive centrifuge database to investigate the

geotechnical performance of dynamically installed anchors (see Chapters 5 and 6). The

second objective focused on the development of analytical design tools for predicting

the penetration and holding capacity behaviour of dynamic anchors. The earlier sections

of this chapter summarised the comparison of the individual embedment and capacity

prediction models with the experimental data and indicated that reasonable predictions

of both the penetration depth and holding capacity could be made using these methods.

However, from a practical perspective, and to improve the usability of these techniques,

the analyses have been combined in the form of dynamic anchor design charts for 0 and

4FAs in both normally consolidated clay and calcareous sand. Note that these design

charts have been presented in prototype units only, despite the analytical methods used

being calibrated from centrifuge model test data.

7.5.1 0FA – Normally Consolidated Clay

The embedment depth and holding capacity design charts for the standard 0FA (see

Table 3.5 and Figure 3.15) in normally consolidated clay are presented in Figures 7.56

and 7.57. The results have been presented for 50, 75, 100 and 125 tonne anchor masses

between shear strength gradient limits of 1 – 1.5 kPa/m. Figure 7.58 shows the variation

in capacity of a 100 tonne 0FA for limiting coefficient of consolidation values of ch = 3

– 30 m2/yr at a shear strength gradient of 1 kPa/m. The calculations were based on the

following assumptions:

• Nc = 12 at the anchor tip and Nc = 9 at the anchor padeye

• α = 0.4 during installation

• During extraction α given by Equation 7.1

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• Figures 7.56 and 7.57 based on 1 year of consolidation with ch = 5.5 m2/yr

• CD = 0.24

• Power rate law with β = 0.09 (average of beam, β = 0.12 and drum, β = 0.06)

• 10 % closure of entry pathway, i.e. f = 0.1

• Vertical monotonic loading – undrained conditions

7.5.2 4FA – Normally Consolidated Clay

The embedment depth and holding capacity design charts for the standard 4FA (see

Table 3.7 and Figure 3.18) in normally consolidated clay are presented in Figures 7.59

and 7.60. The results have been presented for 50, 75, 100 and 125 tonne anchor masses

between shear strength gradient limits of 1 – 1.5 kPa/m. Figure 7.61 shows the variation

in capacity of a 100 tonne 4FA for limiting coefficient of consolidation values of ch = 3

– 30 m2/yr at a shear strength gradient of 1 kPa/m. The calculations were based on the

following assumptions:

• Nc = 12 at the anchor tip, Nc = 9 at the anchor padeye and Ncf = 7.5 for the

anchor flukes

• α = 0.4 during installation

• During extraction α given by Equation 7.1

• Figures 7.59 and 7.60 based on 1 year of consolidation with ch = 5.5 m2/yr

• CD = 0.63

• Power rate law with β = 0.08

• 10 % closure of entry pathway behind anchor shaft (i.e. f = 0.1), full closure

behind anchor flukes

• Vertical monotonic loading – undrained conditions

7.5.3 0FA – Calcareous Sand

The embedment depth and holding capacity design charts for the standard 0FA (see

Table 3.5 and Figure 3.15) in calcareous sand are presented in Figures 7.62 and 7.63.

The results have been presented for 50, 75, 100 and 125 tonne anchor masses between

effective soil unit weight limits of 4.3 – 6.8 kN/m3. The calculations were based on the

following assumptions:

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• Nq = 32 at the anchor tip and Nq = 3.3 at the anchor padeye

• βCALC = 0.42 during both installation and extraction

• CD = 0.24

• Power rate law with β = 0.03

• Full closure of entry pathway, i.e. f = 1

• Vertical monotonic loading – drained conditions

7.5.4 Design Example

As an example, the design charts have been used in the analysis of a hypothetical design

problem. The site proposed for the anchoring of a MODU is characterised by soft

normally consolidated clay with a shear strength gradient of 1 kPa/m and coefficient of

consolidation of ch = 5.5 m2/yr. If an uplift capacity of 3.0 MN is required following 1

year of consolidation, what dynamic anchor options are available? See Figure 7.64.

0FA 4FA

m vi,min m vi,min

(tonnes) (m/s) (tonnes) (m/s)

50 70 50 48

75 44 75 26

100 28 100 12

125 14 125 0

Table 7.6 Design example – dynamic anchor options Stage I

If strong lateral ocean currents restrict the drop height such that a maximum impact

velocity of only 40 m/s is possible, what options remain available?

0FA 4FA

m vi,min m vi,min

(tonnes) (m/s) (tonnes) (m/s)

100 28 75 26

125 14 100 12

125 0

Table 7.7 Design example – dynamic anchor options Stage II

How far will the anchor penetrate at these velocities? See Figure 7.65.

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0FA 4FA

m vi,min ze,min m vi,min ze,min

(tonnes) (m/s) (m) (tonnes) (m/s) (m)

100 28 46 75 26 27

125 14 42 100 12 25

125 0 26

Table 7.8 Design example – dynamic anchor options Stage III

If the 100 tonne 0FA was the selected option and it was decided that an impact velocity

of 30 m/s would be targeted, what is the ultimate anchor capacity and how long would it

take to achieve 50 % and 90 % of this capacity, considering subsequent soil analysis

actually indicated ch = 3 m2/yr.

According to Figure 7.66, the ultimate anchor capacity is approximately 5 MN, t50 = 0.3

years and t90 = 60 years.

7.6 CONCLUSIONS

This chapter has presented the comparison of analytical impact velocity, embedment

depth and holding capacity design methods with the results of centrifuge model tests for

the validation of these techniques and the development of dynamic anchor design tools.

In general, the techniques adopted proved successful in predicting the performance of

dynamically installed anchors in both normally consolidated clay and calcareous sand

soil conditions. The main findings are summarised below:

1. On average, the theoretical impact velocity over predicted the measured impact

velocity by approximately 15 % in the beam centrifuge and 36 % in the drum

centrifuge. The over prediction was attributed to friction between the anchor and

the installation guide.

2. Back-calculated strain rate parameter values increased with increasing impact

velocity in both the normally consolidated clay and calcareous sand samples,

indicating potential limitations of the semi-logarithmic and power rate functions

in assessing dynamic anchor embedment depths. The power law model, with a

constant strain rate parameter, was expected to provide improved accuracy over

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the semi-logarithmic formulation, particularly over a wide range of strain rates.

The strain rate parameter values determined from the drum centrifuge tests were

typically lower than those from the beam centrifuge tests. Strain rate effects in

calcareous sand were found to be negligible at low impact velocities.

3. In normally consolidated clay, the embedment depth predicted using the power

law model with an average strain rate parameter value provided reasonable

agreement with the zero and four fluke anchor data in both the beam and drum

centrifuges, although the embedment depth at low impact velocities was under

estimated by as much as 24 %. For the anchors with lower aspect ratios, anchor

specific strain rate parameters provided improved agreement. The embedment

depth predicted using the average back-calculated strain rate parameter for

calcareous sand compared favourably with the experimental data.

4. The simplified API pile capacity method was found to provide reasonable

predictions of the vertical monotonic holding capacity of dynamic anchors in

normally consolidated clay for post-installation consolidation times of up to 1

year. For longer consolidation times an apparent increase in the soil shear

strength above the undisturbed strength was required for agreement between the

measured and theoretical capacities. A modified adhesion factor was adopted to

reflect the increase in frictional resistance with time after installation. Cavity

expansion solutions for the radial consolidation of soil around a driven pile

provided a reasonable approximation of the consolidation behaviour of dynamic

anchors following installation. The theoretical capacity calculated in calcareous

sand provided good agreement with the measured capacity data.

5. Given the potential for dynamic anchors to attain higher impact velocities than

were achievable in the centrifuge, the theoretical calculations indicate potential

embedment depths of up to 4.8 times the anchor length in normally consolidated

clay and 3.1 times the anchor length in calcareous sand. These embedments

correspond to vertical monotonic holding capacities of up to 7 and 5 times the

dry weight of the anchor in normally consolidated clay and calcareous sand

respectively.

6. Dynamic anchor embedment depths and holding capacities are both relatively

sensitive to variations in the soil strength characteristics. However, the

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dependence of the capacity on embedment depth effectively results in an overall

insensitivity of the holding capacity performance to the soil strength. Lower

strengths result in lower capacities, but also higher embedments and vice versa.

Advantageously dynamic anchors therefore do not require precise knowledge of

the strength characteristics of the seabed material prior to installation.

7. Ultimately, both the embedment and holding capacity methods adopted were

found to provide acceptable predictions of the geotechnical behaviour of zero

and four fluke dynamic anchors. The successful calibration of these methods

against the centrifuge database resulted in the subsequent production of dynamic

anchor design charts for both normally consolidated clay and calcareous sand

soil conditions.

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CHAPTER 8 - CONCLUSIONS AND FURTHER

RESEARCH

8.1 INTRODUCTION

Dynamically installed anchors have been proposed as a cost-effective alternative to

conventional anchoring systems for offshore structures in deepwater environments. This

dissertation has focused on investigating the geotechnical performance of dynamic

anchors through the calibration of analytical techniques against an extensive centrifuge

test database. The penetration and holding capacity performance of dynamic anchors

was evaluated experimentally in normally consolidated clay and silica and calcareous

sand samples, under monotonic, sustained and cyclic loading conditions. The centrifuge

test data were compared with the results of analytical embedment and capacity

prediction methods for the development of robust and versatile dynamic anchor design

tools. This chapter presents the major research findings, the implications of these

findings for the offshore industry and recommendations for further research.

8.2 MAIN FINDINGS

8.2.1 Experimental Modelling in Normally Consolidated Clay

The installation and subsequent loading of model dynamic anchors in normally

consolidated clay was successfully carried out in both the beam and drum centrifuges.

For impact velocities exceeding a lower threshold of 5 – 10 m/s the dynamic anchor

embedment depth was found to increase approximately linearly with impact velocity.

Relatively high embedment depths at velocities below this threshold indicated a strong

embedment depth dependence on the anchor mass with the anchor continuing to

accelerate initially within the soft upper sediments. Penetration depths measured in the

centrifuge tests were also found to depend on the anchor geometry, including the tip

shape, aspect ratio and fluke configuration.

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The load displacement response of the model dynamic anchors during vertical

monotonic extraction in the centrifuge was typically characterised by a sharp increase in

load to an initial maximum capacity followed by a sudden drop in load and a subsequent

increase to a secondary maximum. This behaviour appears to be a result of non-

simultaneous mobilisation of the bearing and frictional resistance during extraction,

with the initial maximum capacity and rapid softening attributed to high (and brittle)

frictional resistance and the secondary peak indicating a more gradual mobilisation of

the bearing resistance. This is supported by experimental data indicating a merging of

the two capacities following longer consolidation times and the absence of the initial

maximum capacity at low anchor aspect ratios. It was shown that the dual capacity

behaviour was not caused by the dynamic anchor installation process.

With the soil shear strength increasing with depth, dynamic anchor capacities under

vertical monotonic loading were found to depend markedly on the penetration depth of

the anchor. Holding capacities were also found to vary with time following installation

due to consolidation effects. Short-term anchor capacities immediately following

installation depended on the impact velocity and the degree of consolidation was

quantified through analysis of the relative time-scale of the regain in anchor capacity.

Cyclic and long-term sustained loading of dynamically installed anchors in the

centrifuge had minimal influence on the ultimate anchor holding capacity. However,

sustained loading indicated a potential threshold loading level of between 80 and 90 %

of the reference monotonic capacity above which sustained loading may lead to a

reduction in the anchor capacity. Under cyclic loading, the influence of the mean load

on the anchor capacity appeared to override the effect of the cyclic load amplitude.

Increases in the duration of loading under both cyclic and sustained loading conditions

led to a slight reduction in anchor capacity.

8.2.2 Experimental Modelling in Silica and Calcareous Sand

Centrifuge testing of model dynamic anchors indicated that they were not suitable for

use in silica sand. This was attributed to the failure of the anchors to embed beyond 40

% of the anchor length, preventing the generation of capacities considered sufficient for

offshore applications.

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Similar tests in uncemented calcareous sand demonstrated the potential of dynamic

anchors for use in carbonate soils. Despite penetration depths considerably lower than

those in normally consolidated clay, the embedment depths were sufficient for the

model dynamic anchors to achieve vertical monotonic holding capacities of up to 70 %

of the average capacity measured in the normally consolidated clay tests. The test

results also indicated an approximately linear increase in embedment with impact

velocity and an increase in holding capacity with embedment depth. Given the potential

for higher impact velocities, higher embedment depths, and consequently higher holding

capacities, are likely.

8.2.3 Analytical Methods and Design Tools

An analytical prediction method for the embedment depth was developed, based on

conventional bearing and frictional resistance theory but incorporating allowances for

viscous enhanced shearing resistance and inertial drag resistance. Strain rate parameters

back-calculated from the experimental data increased with impact velocity, suggesting

that the semi-logarithmic and power law functions used in quantifying the viscous strain

rate effects were not capable of fully capturing the soil response during dynamic anchor

installation. The power law, with a constant strain rate parameter was found to provide

improved accuracy over the semi-logarithmic law, particularly over strain rates covering

several orders of magnitude. In normally consolidated clay, the back-calculated strain

rate parameter values, particularly at low impact velocities, were in general agreement

with values reported in previous dynamic anchor centrifuge tests. In calcareous sand,

strain rate effects at low impact velocities were negligible. Embedment depths predicted

using the power law model with an average strain rate parameter were found to provide

good agreement with the zero and four fluke anchor data, although the calculations

tended to under estimate the embedment at low impact velocities. The calculations also

indicate the potential for considerably higher embedment depths at higher impact

velocities.

An existing simplified pile capacity technique was successfully implemented to predict

the vertical monotonic holding capacity of dynamically installed anchors in normally

consolidated clay for prototype consolidation times of up to approximately 1 year. For

longer consolidation times a modified adhesion factor, based on back-calculated values

198

from the centrifuge tests, was adopted to account for the apparent increase in shaft

friction above the original shear strength of the soil. A similar pile capacity method was

found to provide accurate predictions of the holding capacity of dynamic anchors in

calcareous sand.

The successful calibration of the embedment depth and holding capacity prediction

methods against the experimental data in both normally consolidated clay and

calcareous sand highlighted the suitability of these methods as dynamic anchor design

tools. Combining the individual embedment and capacity models enabled the

development of dynamic anchor design charts relating the impact velocity to the

penetration depth and holding capacity for zero and four fluke dynamic anchors. The

design charts are intended to be indicative of the potential anchor performance, at

prototype scale, in order to increase the understanding of the geotechnical behaviour of

dynamically installed anchors and thereby improve industry confidence in the concept.

8.3 APPLICATION TO INDUSTRY

With installation and procurement costs for conventional foundation technologies

increasing rapidly with water depth, dynamically installed anchors represent a

financially attractive development for the offshore oil and gas industry. Despite this

their use is scarce. Improved industry confidence in the geotechnical performance and

reliability of dynamic anchors is required before widespread implementation can be

achieved. From a practical point of view, this section details likely performance data for

typical dynamic anchors with the aim of highlighting aspects of the study relevant to the

industry.

Dynamic anchor impact velocities in the centrifuge were limited to approximately 30

m/s. However, terminal velocity calculations indicate potential impact velocities in the

field of up to 80 m/s for zero fluke anchors and 40 m/s for four fluke anchors. Given the

embedment depth dependence on impact velocity, a typical 15 m long, 1.2 m diameter,

100 tonne dynamic anchor would therefore be likely to achieve embedment depths in

normally consolidated clay of up to 90 m and 57 m in the zero and four fluke

configurations respectively. Further optimisation of the anchor geometry has the

199

potential of delivering additional increases in impact velocity, which in turn should

translate to higher penetration depths in the field.

Following installation, the short-term anchor capacity in normally consolidated clay is

expected to range from approximately 5 – 35 % of the ultimate long-term capacity,

indicating setup factors of approximately 3 – 20. For long-term capacities of up to 7 MN

(assuming a shear strength gradient of 1 kPa/m), these suggest vertical monotonic

holding capacities immediately after installation of up to approximately 2.5 MN.

Assuming typical values of ch = 3 – 30 m2/yr, the increase in anchor capacity with time

is reflected in consolidation times of 35 – 350 days for 50 % consolidation and 2.4 – 24

years for 90 % consolidation. Cyclic and sustained loading of dynamically installed

anchors is not expected to reduce the anchor capacity by more than 15 %. Given the

dependence of holding capacity on embedment depth, optimisation of the anchor impact

velocity will also translate into higher anchor capacities.

In uncemented calcareous sand, a typical zero fluke dynamic anchor, impacting the

seabed at a velocity of up to 80 m/s, will penetrate to a maximum embedment depth of

approximately 45 m. At this depth, the anchor is expected to achieve a vertical

monotonic holding capacity of up to 4.5 MN. Just as in normally consolidated clay,

optimisation of the anchor geometry has the potential of further increasing the

embedment depth and holding capacity of dynamic anchors in calcareous sand.

8.4 RECOMMENDATIONS FOR FURTHER RESEARCH

A degree of uncertainty remains regarding strain rate and inertia effects during dynamic

anchor installation. Direct measurement of the anchor velocity and displacement during

installation would assist in quantifying these effects and thereby aid in the calibration of

the embedment prediction model. Additional experimental data are required to

investigate the influence of the anchor geometry on the penetration performance of

dynamic anchors, in order to facilitate verification of the embedment model for different

anchor types.

A limited number of cyclic and sustained loading tests were undertaken in this study. It

is recommended that further experimental modelling should focus on increasing the

200

understanding of the behaviour of dynamic anchors under cyclic and sustained loading

conditions. Specifically this should be aimed at addressing the influence of the load

frequency, magnitude and amplitude on the holding capacity of the anchor. In addition,

dynamic anchors installed in offshore environments are subjected to inclined rather than

purely vertical loads. Hence any testing undertaken should also investigate the ability of

dynamic anchors to withstand monotonic, sustained or cyclic loads with inclined

orientations.

The test programme described in this research evaluated the performance of

dynamically installed anchors in normally consolidated clay, silica sand and calcareous

sand samples. However, offshore sites are often also characterised by higher sensitivity

or overconsolidated clays or layered soil stratigraphies. Therefore experimental testing

should be undertaken to assess the behaviour of dynamic anchors under a range of soil

conditions.

Field tests, even at a reduced scale, would prove invaluable in evaluating the

embedment depth and holding capacity of dynamic anchors. Not only would field

testing provide information for verification of the experimental results obtained in the

centrifuge model tests, but it would also allow further calibration of the design models

without the added complexities of centrifuge modelling. Given the relative infancy of

the concept, field testing is considered an essential component of any further research

on dynamically installed anchors.

201

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215

TABLES

Anc

hor

Mat

eria

l L/

D

Leng

th

Dia

met

er

Tip

Len

gth

Pad

eye

Leng

th

Mas

s P

roje

cted

Are

a S

haft

Are

a

Lm

Lp

Dm

Dp

Ltip

,m

Ltip

,p

Lpa

d,m

Lpa

d,p

mm

mp

Ap,

m

Ap,

p A

s,m

As,

p

(mm

) (m

) (m

m)

(m)

(mm

) (m

) (m

m)

(m)

(g)

(x 1

03 kg)

(m

m2 )

(m2 )

(mm

2 ) (m

2 ) H

0-1

bras

s 1

6 1.

2 6

1.2

3 0.

6 3

0.6

0.9

7.2

28.3

1.

13

0 0

H0-

2 br

ass

1.5

9 1.

8 6

1.2

3 0.

6 3

0.6

1.8

14.4

28

.3

1.13

56

.5

2.26

H0-

3 br

ass

2 12

2.

4 6

1.2

3 0.

6 3

0.6

2.0

16.0

28

.3

1.13

11

3.1

4.52

H0-

4 br

ass

3 18

3.

6 6

1.2

3 0.

6 3

0.6

3.0

24.0

28

.3

1.13

22

6.2

9.05

H0-

5 br

ass

4 24

4.

8 6

1.2

3 0.

6 3

0.6

4.7

37.6

28

.3

1.13

33

9.3

13.5

7

H0-

6 br

ass

6 36

7.

2 6

1.2

3 0.

6 3

0.6

7.4

59.2

28

.3

1.13

56

5.5

22.6

2

H0-

7 al

umin

ium

4

24

4.8

6 1.

2 3

0.6

3 0.

6 1.

4 11

.2

28.3

1.

13

339.

3 13

.57

H0-

8 al

umin

ium

6

36

7.2

6 1.

2 3

0.6

3 0.

6 2.

3 18

.4

28.3

1.

13

565.

5 22

.62

H0-

9 al

umin

ium

6

36

7.2

6 1.

2 3

0.6

3 0.

6 1.

9 15

.2

28.3

1.

13

565.

5 22

.62

H0-

10

alum

iniu

m

8 48

9.

6 6

1.2

3 0.

6 3

0.6

3.2

25.6

28

.3

1.13

79

1.7

31.6

7

H0-

11

alum

iniu

m

10

60

12

6 1.

2 3

0.6

3 0.

6 4.

2 33

.6

28.3

1.

13

1017

.9

40.7

2

H0-

12

alum

iniu

m

12

72

14.4

6

1.2

3 0.

6 3

0.6

5.0

40.0

28

.3

1.13

12

44.1

49

.76

H0-

13

alum

iniu

m

12

72

14.4

6

1.2

3 0.

6 3

0.6

4.7

37.6

28

.3

1.13

12

44.1

49

.76

H0-

14

alum

iniu

m

14

84

16.8

6

1.2

3 0.

6 3

0.6

6.0

48.0

28

.3

1.13

14

70.3

58

.81

H

0-15

br

ass

1 9

1.8

9 1.

8 4.

5 0.

9 4.

5 0.

9 3.

0 24

.0

63.6

2.

54

0 0

H0-

16

bras

s 2

18

3.6

9 1.

8 4.

5 0.

9 4.

5 0.

9 7.

1 56

.8

63.6

2.

54

254.

5 10

.18

H0-

17

bras

s 3

27

5.4

9 1.

8 4.

5 0.

9 4.

5 0.

9 11

.4

91.2

63

.6

2.54

50

8.9

20.3

6

H0-

18

alum

iniu

m

3 27

5.

4 9

1.8

4.5

0.9

4.5

0.9

3.0

24.0

63

.6

2.54

50

8.9

20.3

6

H0-

19

bras

s 1

12

2.4

12

2.4

6 1.

2 6

1.2

7.2

57.6

11

3.1

4.52

0

0

H0-

20

alum

iniu

m

2 24

4.

8 12

2.

4 6

1.2

6 1.

2 18

.0

144.

0 11

3.1

4.52

45

2.4

18.1

0

Tab

le 3

.13

Pro

pert

ies

of m

odel

anc

hors

with

diff

eren

t asp

ect r

atio

s u

= a

z2 + b

z D

rop

Hei

ght

Vel

ocity

E

mbe

dmen

t R

econ

. tim

e, t

Cap

acity

1 D

isp.

1

Cap

acity

2 D

isp.

2

Nor

m. C

apac

ity

Sam

ple

Tes

t A

ncho

r a

b h d

,m

h d,e

q v m

v i

z e

,m

z e,p

z e/L

M

odel

P

roto

type

Fv1

,m F

v1,p

z 1,m

z 1

,p

Fv2

,m

Fv2

,p

z 2,m

z 2

,p

FN

1 F

N2

(k

Pa/

m2 ) (

kPa/

m)

(mm

) (m

) (m

/s) (

m/s

) (m

m)

(m)

(h

h:m

m:s

s) (

yy:d

dd)

(N)

(MN

) (m

m)

(m)

(N)

(MN

) (m

m)

(m)

Box

1

B1D

1 E

0-1

0.01

80

0.86

77

300

51.5

24

.1

30.1

19

2 38

.4

2.6

91.1

3.

6 5.

1 1.

0 69

.9

2.8

9.9

2.0

56.0

38

.4

B

1D2

E0-

1 0.

0180

0.

8677

30

0 51

.5

24.8

30

.8

195

39.0

2.

6

84

.1

3.4

4.7

0.9

64.3

2.

6 8.

7 1.

7 48

.8

32.8

B1D

3 E

0-1

0.01

80

0.86

77

300

51.5

24

.6

30.6

19

8 39

.6

2.6

95.4

3.

8 4.

5 0.

9 72

.3

2.9

8.8

1.8

56.4

38

.2

B

1D4

C0-

1 0.

0083

0.

9950

30

0 51

.5

23.4

29

.4

216

43.2

2.

9

80

.2

3.2

6.2

1.2

65.1

2.

6 8.

0 1.

6 45

.7

33.2

B1D

5 C

0-1

0.00

83

0.99

50

300

51.5

23

.8

29.8

21

6 43

.2

2.9

85.0

3.

4 4.

8 1.

0 61

.4

2.5

6.6

1.3

49.7

30

.2

B

1D6

C0-

1 0.

0091

1.

0754

30

0 51

.5

23.7

29

.7

208

41.6

2.

8

82

.5

3.3

4.1

0.8

60.5

2.

4 8.

7 1.

7 46

.7

28.9

B1D

7 O

0-1

0.00

87

1.03

52

300

51.5

23

.1

29.1

20

3 40

.6

2.7

82.6

3.

3 4.

6 0.

9 62

.4

2.5

9.6

1.9

50.8

33

.1

B

1D8

O0-

1 0.

0087

1.

0352

30

0 51

.5

22.6

28

.6

202

40.4

2.

7

70

.0

2.8

4.2

0.8

56.3

2.

3 8.

7 1.

7 40

.1

28.0

B1D

9 O

0-1

0.01

39

1.01

17

300

51.5

23

.9

29.9

20

0 40

.0

2.7

89.9

3.

6 5.

7 1.

1 66

.3

2.7

10.3

2.

1 52

.9

33.8

B1D

10

F0-1

0.

0083

0.

9950

30

0 51

.5

23.6

29

.6

212

42.4

2.

8

75

.8

3.0

5.2

1.0

39.5

B

1D11

# F0

-1

0.00

87

1.03

52

300

51.5

22

.9

28.9

19

7 39

.4

2.6

63.9

2.

6 3.

9 0.

8 66

.5

2.7

6.4

1.3

32.5

34

.7

B

1D12

F0

-1

0.00

87

1.03

52

300

51.5

21

.1

27.1

21

1 42

.2

2.8

74.9

3.

0 4.

8 1.

0

37

.5

B

ox 2

B

2D1

E0-

2 0.

0195

0.

5261

0

0

0.0

169

33.8

2.

3

68

.9

2.8

4.9

1.0

52.2

2.

1 9.

2 1.

8 61

.5

39.1

B2D

2 E

0-2

0.02

04

0.57

89

102

18.8

16.7

16

6 33

.2

2.2

71.8

2.

9 4.

0 0.

8 58

.2

2.3

8.9

1.8

65.0

46

.9

B

2D3

E0-

2 0.

0213

0.

6317

12

5 22

.8

11.1

17

.1

166

33.2

2.

2

69

.9

2.8

4.7

0.9

55.6

2.

2 9.

7 1.

9 60

.1

41.8

B2D

4 E

0-2

0.02

13

0.63

17

150

27.2

14

.0

20.0

17

1 34

.2

2.3

72.2

2.

9 5.

9 1.

2 57

.6

2.3

10.5

2.

1 59

.5

41.8

B2D

5 E

0-2

0.02

13

0.63

17

175

31.4

14

.7

20.7

17

2 34

.4

2.3

78.2

3.

1 3.

3 0.

7 62

.1

2.5

7.5

1.5

66.0

46

.7

B

2D6

E0-

2 0.

0213

0.

6317

12

5 22

.8

9.5

15.5

16

4 32

.8

2.2

68.1

2.

7 3.

3 0.

7 54

.9

2.2

7.7

1.5

59.2

41

.9

B

2D7

E0-

2 0.

0213

0.

6317

20

0 35

.6

19.4

25

.4

182

36.4

2.

4

78

.0

3.1

3.5

0.7

65.9

2.

6 7.

8 1.

6 58

.8

45.8

B2D

8 E

0-2

0.02

21

0.68

45

225

39.7

20

.9

26.9

18

0 36

.0

2.4

85.9

3.

4 4.

3 0.

9 69

.0

2.8

8.4

1.7

66.2

48

.4

B

2D9

E0-

2 0.

0221

0.

6845

25

0 43

.7

21.3

27

.3

184

36.8

2.

5

67

.6

2.7

3.6

0.7

56.6

2.

3 6.

7 1.

3 44

.9

33.8

B2D

10

E0-

2 0.

0207

0.

6170

27

5 47

.7

198

39.6

2.

6

76

.0

3.0

3.9

0.8

58.1

B

2D11

E

0-2

0.02

07

0.61

70

300

51.5

19

3 38

.6

2.6

75.3

3.

0 4.

5 0.

9 53

.1

2.1

5.0

1.0

60.0

34

.4

Box

3

B3D

1# IE

0-1

0.02

57

0.56

34

200

35.6

23.4

B

3D2#

IE0-

1 0.

0257

0.

5634

20

0 35

.6

19.8

25

.8

221

44.2

2.

9

92

.2

3.7

9.2

1.8

67.4

2.

7 9.

5 1.

9 45

.5

29.1

# E

mbe

dmen

t dep

th d

ata

not i

nclu

ded

in a

naly

sis Tab

le 5

.10

Bea

m c

entr

ifuge

test

dat

a –

norm

ally

con

solid

ated

cla

y

s u

= a

z2 + b

z D

rop

Hei

ght

Vel

ocity

E

mbe

dmen

t R

econ

. tim

e, t

Cap

acity

1 D

isp.

1

Cap

acity

2 D

isp.

2

Nor

m. C

apac

ity

Sam

ple

Tes

t A

ncho

r a

b h d

,m

h d,e

q v m

v i

z e

,m

z e,p

z e/L

M

odel

P

roto

type

Fv1

,m F

v1,p

z 1,m

z 1

,p

Fv2

,m

Fv2

,p

z 2,m

z 2

,p

FN

1 F

N2

(k

Pa/

m2 ) (

kPa/

m)

(mm

) (m

) (m

/s) (

m/s

) (m

m)

(m)

(h

h:m

m:s

s) (

yy:d

dd)

(N)

(MN

) (m

m)

(m)

(N)

(MN

) (m

m)

(m)

Box

3

B3D

3 IE

0-1

0.02

23

0.67

31

300

51.5

28.7

19

8 39

.6

2.6

74.6

3.

0 10

.4

2.1

58.0

2.

3 14

.6

2.9

42.4

28

.7

B

3D4#

IE0-

1 0.

0223

0.

6731

30

0 51

.5

21.9

27

.9

198

39.6

2.

6

68

.4

2.7

6.2

1.2

55.9

2.

2 10

.5

2.1

37.3

27

.0

B

3D5

IE0-

1 0.

0223

0.

6731

30

0 51

.5

22.9

28

.9

191

38.2

2.

5

84

.7

3.4

9.4

1.9

64.2

2.

6 13

.3

2.7

54.3

36

.3

B

3D6

IE0-

1 0.

0223

0.

6731

25

0 43

.7

20.8

26

.8

199

39.8

2.

7

87

.7

3.5

10.8

2.

2 65

.7

2.6

15.0

3.

0 52

.6

34.7

B3D

7 IE

0-1

0.02

23

0.67

31

150

27.2

13

.6

19.6

17

7 35

.4

2.4

78.5

3.

1 6.

9 1.

4 61

.3

2.5

12.4

2.

5 56

.6

39.2

B3D

8 IE

0-1

0.01

88

0.78

27

100

18.4

4.

8 10

.8

157

31.4

2.

1

80

.4

3.2

8.0

1.6

59.5

2.

4 10

.4

2.1

72.4

46

.3

B

3D9

IE0-

1 0.

0188

0.

7827

12

5 22

.8

12.3

18

.3

173

34.6

2.

3

71

.2

2.8

14.8

3.

0 52

.5

2.1

18.6

3.

7 50

.9

31.3

B3D

10

IE0-

1 0.

0188

0.

7827

17

5 31

.4

16.0

22

.0

185

37.0

2.

5

76

.0

3.0

11.6

2.

3 59

.3

2.4

18.4

3.

7 49

.4

33.9

B3D

11

IE0-

1 0.

0188

0.

7827

22

5 39

.7

16.5

22

.5

182

36.4

2.

4

64

.4

2.6

7.9

1.6

51.3

2.

1 13

.7

2.7

39.8

27

.3

B

3D12

IE

0-1

0.01

88

0.78

27

250

43.7

17

.4

23.4

19

0 38

.0

2.5

59.9

2.

4 12

.7

2.5

45.3

1.

8 16

.7

3.3

32.8

19

.9

B

3D13

# IE

0-1

0.01

88

0.78

27

250

43.7

20

.4

26.4

19

8 39

.6

2.6

74.8

3.

0 16

.3

3.3

57.4

2.

3 21

.5

4.3

42.6

28

.3

B

3D14

# IE

0-1

0.02

11

0.79

43

275

47.7

21

.6

27.6

18

7 37

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2.5

93.9

3.

8 7.

4 1.

5 68

.2

2.7

11.5

2.

3 61

.1

39.0

B3D

15#

IE0-

1 0.

0211

0.

7943

30

0 51

.5

22.9

28

.9

188

37.6

2.

5

84

.5

3.4

5.9

1.2

63.5

2.

5 10

.9

2.2

52.5

34

.6

B

3D16

IE

0-1

0.02

11

0.79

43

150

27.2

9.

5 15

.5

163

32.6

2.

2

56

.9

2.3

5.6

1.1

44.2

1.

8 8.

9 1.

8 38

.0

24.0

B

ox 4

B

4D1

IE0-

1 0.

0107

0.

7288

30

0 51

.5

28

.7

209

41.8

2.

8 00

:06:

34

00:1

82

B

4D2#

IE0-

1 0.

0107

0.

7288

25

0 43

.7

26

.2

B4D

3# IE

0-1

0.01

07

0.72

88

250

43.7

26

.0

26.0

19

7 39

.4

2.6

00:1

5:13

01

:058

84

.0

3.4

4.6

0.9

69.3

2.

8 5.

5 1.

1 65

.5

49.7

B4D

4# IE

0-1

0.01

07

0.72

88

200

35.6

23

.2

23.2

20

1 40

.2

2.7

00:1

4:34

01

:040

80

.8

3.2

11.1

2.

2

60

.0

B4D

5 IE

0-1

0.01

07

0.72

88

150

27.2

21

.3

21.3

19

4 38

.8

2.6

00:1

5:04

01

:054

75

.4

3.0

8.7

1.7

69.5

2.

8 12

.1

2.4

57.8

51

.3

B

4D6

IE0-

2 0.

0107

0.

7288

10

0 18

.4

16.8

16

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189

37.8

2.

5 00

:14:

30

01:0

38

66.0

2.

6 14

.6

2.9

56.5

2.

3 18

.1

3.6

48.4

37

.5

B

4D7

IE0-

2 0.

0107

0.

7288

50

9.

4 11

.8

11.8

17

5 35

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2.3

00:1

3:52

01

:020

73

.1

2.9

11.0

2.

2 62

.5

2.5

13.4

2.

7 64

.6

50.7

B4D

8 IE

0-2

0.00

94

0.80

43

300

51.5

28

.1

28.1

19

2 38

.4

2.6

00:0

7:42

00

:214

80

.8

3.2

11.4

2.

3 62

.2

2.5

13.5

2.

7 61

.5

41.4

B4D

9 IE

0-2

0.00

94

0.80

43

300

51.5

28.7

19

3 38

.6

2.6

88.6

3.

5 8.

0 1.

6 65

.1

2.6

9.1

1.8

69.3

44

.1

B

4D10

IE

0-2

0.00

94

0.80

43

300

51.5

29

.1

29.1

19

4 38

.8

2.6

00:1

4:46

01

:045

81

.7

3.3

9.3

1.9

63.1

2.

5 10

.4

2.1

61.4

41

.6

B

4D11

IE

0-2

0.00

94

0.80

43

300

51.5

28

.6

28.6

19

0 38

.0

2.5

00:1

4:28

01

:037

90

.1

3.6

7.6

1.5

72.7

2.

9 10

.8

2.2

72.8

53

.7

# Em

bedm

ent d

epth

dat

a no

t inc

lude

d in

ana

lysi

s

Tab

le 5

.10

(con

tinue

d) B

eam

cen

trifu

ge te

st d

ata

– no

rmal

ly c

onso

lidat

ed c

lay

s u

= a

z2 + b

z D

rop

Hei

ght

Vel

ocity

E

mbe

dmen

t R

econ

. tim

e, t

Cap

acity

1 D

isp.

1

Cap

acity

2 D

isp.

2

Nor

m. C

apac

ity

Sam

ple

Tes

t A

ncho

r a

b h d

,m

h d,e

q v m

v i

z e

,m

z e,p

z e/L

M

odel

P

roto

type

Fv1

,m F

v1,p

z 1,m

z 1

,p

Fv2

,m

Fv2

,p

z 2,m

z 2

,p

FN

1 F

N2

(k

Pa/

m2 )

(kP

a/m

) (m

m)

(m)

(m/s

) (m

/s) (

mm

) (m

)

(hh:

mm

:ss)

(yy

:ddd

) (N

) (M

N) (

mm

) (m

) (N

) (M

N) (

mm

) (m

)

Box

4

B4D

12

IE0-

2 0.

0094

0.

8043

20

0 35

.6

23.9

23

.9

194

38.8

2.

6 00

:14:

48

01:0

46

78.6

3.

1 7.

4 1.

5 58

.8

2.4

9.7

1.9

58.1

37

.0

B

4D13

# IE

0-2

0.00

58

1.03

10

200

35.6

23

.9

23.9

17

9 35

.8

2.4

00:0

6:58

00

:194

66

.5

2.7

4.8

1.0

55.3

2.

2 8.

5 1.

7 46

.5

34.3

B4D

14#

IE0-

2 0.

0058

1.

0310

15

0 27

.2

20.7

20

.7

179

35.8

2.

4 00

:26:

59

02:0

20

78.8

3.

2 9.

7 1.

9 66

.1

2.6

12.9

2.

6 59

.9

46.0

B4D

15#

IE0-

2 0.

0058

1.

0310

15

0 27

.2

20

.3

178

35.6

2.

4

63

.7

2.5

7.1

1.4

55.8

2.

2 12

.9

2.6

43.8

35

.1

B

4D16

IE

0-2

0.00

58

1.03

10

0 0

0.

0 15

7 31

.4

2.1

00:0

5:45

00

:160

41

.2

1.6

6.5

1.3

34.5

1.

4 8.

7 1.

7 23

.5

14.6

B

ox 5

B

5D1

E0-

2 0.

0119

0.

8110

15

0 27

.2

20.4

20

.4

184

36.8

2.

5 00

:59:

40

04:1

97

79.7

3.

2 8.

6 1.

7 58

.6

2.3

12.8

2.

6 61

.1

38.3

B5D

2 E

0-2

0.01

60

0.85

52

150

27.2

20

.7

20.7

18

0 36

.0

2.4

00:5

9:57

04

:205

79

.5

3.2

6.0

1.2

55.4

B

5D3

E0-

2 0.

0160

0.

8552

15

0 27

.2

20.3

20

.3

176

35.2

2.

3 00

:01:

57

00:0

54

64.1

2.

6 4.

9 1.

0 56

.5

2.3

11.3

2.

3 41

.9

34.1

B5S

US1

E

0-2

0.01

60

0.85

52

150

27.2

20

.6

20.6

18

8 37

.6

2.5

01:0

0:32

04

:221

B5S

US2

E

0-2

0.01

72

0.79

93

150

27.2

21

.2

21.2

18

4 36

.8

2.5

01:0

0:11

04

:212

88

.8

3.6

10.0

2.

0 65

.6

2.6

11.3

2.

3 63

.0

40.7

B5S

US3

E

0-2

0.01

72

0.79

93

150

27.2

21

.1

21.1

18

2 36

.4

2.4

00:5

9:58

04

:206

84

.3

3.4

9.0

1.8

59.8

B

5SU

S4

E0-

2 0.

0184

0.

7433

15

0 27

.2

21.2

21

.2

178

35.6

2.

4 01

:00:

22

04:2

17

78.6

3.

1 8.

2 1.

6 58

.8

2.4

10.2

2.

0 57

.4

36.9

B5S

US5

E

0-2

0.01

84

0.74

33

150

27.2

21

.2

21.2

18

1 36

.2

2.4

00:5

9:51

04

:202

74

.9

3.0

8.5

1.7

52.0

B

5CY

C1

E0-

2 0.

0184

0.

7433

15

0 27

.2

20.9

20

.9

182

36.4

2.

4 00

:59:

51

04:2

02

73.0

2.

9 7.

2 1.

4

49

.5

B5C

YC

2 E

0-2

0.01

84

0.74

33

150

27.2

21

.0

21.0

17

8 35

.6

2.4

01:0

0:08

04

:210

87

.7

3.5

9.1

1.8

67.4

2.

7 11

.3

2.3

66.9

45

.8

B

5CY

C3

E0-

2 0.

0179

0.

8285

15

0 27

.2

20.6

20

.6

178

35.6

2.

4 01

:00:

05

04:2

09

88.4

3.

5 7.

6 1.

5 66

.4

2.7

8.6

1.7

64.1

42

.5

B

5CY

C4

E0-

2 0.

0179

0.

8285

15

0 27

.2

20.3

20

.3

180

36.0

2.

4 00

:59:

57

04:2

05

B

5CY

C5

E0-

2 0.

0179

0.

8285

15

0 27

.2

20.9

20

.9

179

35.8

2.

4 01

:00:

02

04:2

08

87.2

3.

5 7.

7 1.

5

62

.3

B5C

YC

6 E

0-2

0.01

79

0.82

85

150

27.2

20

.4

20.4

17

9 35

.8

2.4

01:0

0:03

04

:208

68

.9

2.8

7.6

1.5

44.5

B

5CY

C7

E0-

2 0.

0173

0.

9137

15

0 27

.2

20.3

20

.3

175

35.0

2.

3 01

:00:

10

04:2

11

85.4

3.

4 8.

6 1.

7 62

.1

2.5

9.8

2.0

59.9

37

.5

Box

6*

B6D

1 E

0-2

0.01

58

1.08

17

0 0

0.

0 66

13

.2

0.9

01:0

6:50

05

:031

42

.2

1.7

4.9

1.0

106.

9

B

6D2

E0-

2 0.

0158

1.

0817

10

0 18

.4

16.4

16

.4

93

18.6

1.

2 01

:01:

31

04:2

49

51.0

2.

0 6.

7 1.

3

79

.4

B6D

3 E

0-2

0.01

58

1.08

17

200

35.6

23

.3

23.3

10

9 21

.8

1.5

01:0

1:08

04

:238

59

.6

2.4

6.3

1.3

75.4

B

6D4

E0-

2 0.

0088

1.

3792

30

0 51

.5

27.6

27

.6

117

23.4

1.

6 01

:01:

49

04:2

57

71.6

2.

9 6.

3 1.

3

77

.2

B6D

5w

E0-

2 0.

0088

1.

3792

30

0 51

.5

27.7

27

.7

90

18.0

1.

2 00

:04:

38

00:1

29

63.9

2.

6 4.

4 0.

9

10

6.0

# E

mbe

dmen

t dep

th d

ata

not i

nclu

ded

in a

naly

sis;

* Box

6 e

mbe

dmen

t and

cap

acit

y da

ta n

ot in

clud

ed in

ana

lysi

s; w

No

surf

ace

wat

er la

yer

pres

ent d

urin

g te

st

Tab

le 5

.10

(con

tinue

d) B

eam

cen

trifu

ge te

st d

ata

– no

rmal

ly c

onso

lidat

ed c

lay

s u

= a

z2 + b

z D

rop

Hei

ght

Vel

ocity

E

mbe

dmen

t R

econ

. tim

e, t

Cap

acity

1 D

isp.

1

Cap

acity

2 D

isp.

2

Nor

m. C

apac

ity

Sam

ple

Tes

t A

ncho

r a

b h d

,m

h d,e

q v m

v i

z e

,m

z e,p

z e/L

M

odel

P

roto

type

Fv1

,m F

v1,p

z 1,m

z 1

,p

Fv2

,m

Fv2

,p

z 2,m

z 2

,p

FN

1 F

N2

(k

Pa/

m2 )

(kP

a/m

) (m

m)

(m)

(m/s

) (m

/s) (

mm

) (m

)

(hh:

mm

:ss)

(yy

:ddd

) (N

) (M

N) (

mm

) (m

) (N

) (M

N) (

mm

) (m

)

B

ox 6

* B

6D6w

E

0-2

0.00

88

1.37

92

300

51.5

28

.7

28.7

81

16

.2

1.1

00:0

2:34

00

:071

40

.2

1.6

4.4

0.9

57.9

B

6D7

E0-

2 0.

0057

1.

3349

25

0 43

.7

26.2

26

.2

93

18.6

1.

2 00

:15:

43

01:0

72

49.9

2.

0 5.

5 1.

1

70

.3

B6D

8w

E0-

2 0.

0057

1.

3349

10

0 18

.4

16.3

16

.3

77

15.4

1.

0 00

:15:

59

01:0

79

B

6D9w

E

0-2

0.00

57

1.33

49

100

18.4

16

.8

16.8

69

13

.8

0.9

00:1

3:24

01

:007

32

.5

1.3

5.8

1.2

48.0

B

6D10

E

0-2

0.00

57

1.33

49

150

27.2

20

.4

20.4

96

19

.2

1.3

00:1

4:32

01

:039

46

.9

1.9

4.7

0.9

59.0

B

6D11

E

0-2

0.00

57

1.33

49

250

43.7

26

.4

26.4

10

8 21

.6

1.4

# Em

bedm

ent d

epth

dat

a no

t inc

lude

d in

ana

lysi

s; * B

ox 6

em

bedm

ent a

nd c

apac

ity

data

not

incl

uded

in a

naly

sis;

w N

o su

rfac

e w

ater

laye

r pr

esen

t dur

ing

test

Tab

le 5

.10

(con

tinue

d) B

eam

cen

trifu

ge te

st d

ata

– no

rmal

ly c

onso

lidat

ed c

lay

s u

= a

z2 + b

z D

rop

Hei

ght

Vel

ocity

E

mbe

dmen

t R

econ

. tim

e, t

Cap

acity

1 D

isp.

1

Cap

acity

2 D

isp.

2

Nor

m. C

apac

ity

Sam

ple

Tes

t A

ncho

r a

b h d

,m

h d,e

q v m

v i

z e

,m

z e,p

z e/L

M

odel

P

roto

type

Fv1

,m F

v1,p

z 1,m

z 1

,p

Fv2

,m F

v2,p

z 2,m

z 2

,p

FN

1 F

N2

(k

Pa/

m2 ) (

kPa/

m)

(mm

) (m

) (m

/s) (

m/s

) (m

m)

(m)

(h

h:m

m:s

s) (

yy:d

dd)

(N)

(MN

) (m

m)

(m)

(N)

(MN

) (m

m)

(m)

Dru

m 1

D

1D1

H0-

1

40

6.

3

9.5

39

7.8

6.5

2.0

0.08

3.

99

0.8

2.2

0.09

6.

44

1.3

D

1D2

H0-

1

15

0 20

.4

16

.2

45

9.0

7.5

3.2

0.13

4.

71

0.9

D

1D3

H0-

1

10

0 14

.5

14.2

14

.2

46

9.2

7.7

3.5

0.14

6.

24

1.2

D

1D4#

H0-

1

20

0 25

.3

18.2

18

.2

29

5.8

4.8

2.3

0.09

9.

29

1.9

D

1D5

H0-

2

40

6.

3 9.

3 9.

3 51

10

.2

5.7

5.1

0.20

8.

48

1.7

D

1D6

H0-

2

10

0 14

.5

14.3

14

.3

59

11.8

6.

6

5.

2 0.

21

6.67

1.

3

D1D

7 H

0-2

150

20.4

16

.8

16.8

62

12

.4

6.9

6.1

0.24

5.

66

1.1

D

1D8

H0-

3

40

6.

3

9.5

57

11.4

4.

8

5.

1 0.

20

4.45

0.

9

D1D

9 H

0-3

150

20.4

17

.6

17.6

70

14

.0

5.8

5.5

0.22

5.

59

1.1

D

1D10

H

0-3

100

14.5

15

.3

15.3

71

14

.2

5.9

D

1D11

H

0-4

40

6.3

9.5

9.5

70

14.0

3.

9

6.

7 0.

27

3.58

0.

7 7.

5 0.

30

5.42

1.

1

D1D

12

H0-

4

15

0 20

.4

16.2

16

.2

86

17.2

4.

8

9.

9 0.

40

5.97

1.

2

D1D

13

H0-

4

20

0 25

.3

20.1

20

.1

89

17.8

4.

9

7.

6 0.

30

3.27

0.

7 8.

9 0.

36

5.41

1.

1

D1D

14

H0-

5

40

6.

3 9.

9 9.

9 89

17

.8

3.7

10.2

0.

41

4.99

1.

0 11

.8

0.47

7.

41

1.5

D

1D15

H

0-5

150

20.4

19

.0

19.0

10

6 21

.2

4.4

14.4

0.

58

6.57

1.

3

D1D

16

H0-

5

25

0 29

.2

20.3

20

.3

111

22.2

4.

6

14

.6

0.58

4.

49

0.9

15.2

0.

61

6.91

1.

4

D1D

17

H0-

6

40

6.

3

9.5

112

22.4

3.

1

20

.2

0.81

5.

40

1.1

20.3

0.

81

8.71

1.

7

D1D

18

H0-

6

10

0 14

.5

14.1

14

.4

114

22.8

3.

2

19

.4

0.78

4.

21

0.8

21.2

0.

85

6.59

1.

3

D1D

19

H0-

6

20

0 25

.3

18.0

18

.0

128

25.6

3.

6

22

.4

0.90

4.

21

0.8

22.6

0.

90

6.65

1.

3

D1D

20

H0-

7

40

6.

3 9.

5 9.

5 43

8.

6 1.

8

2.

7 0.

11

5.74

1.

1

D1D

21

H0-

7

10

0 14

.5

13.9

13

.9

44

8.8

1.8

3.0

0.12

3.

25

0.7

D

1D22

H

0-7

150

20.4

17

.1

17.1

49

9.

8 2.

0

2.

8 0.

11

2.99

0.

6

# E

mbe

dmen

t dep

th d

ata

not i

nclu

ded

in a

naly

sis Tab

le 5

.11

Dru

m c

entr

ifuge

test

dat

a –

norm

ally

con

solid

ated

cla

y

s u

= a

z2 + b

z D

rop

Hei

ght

Vel

ocity

E

mbe

dmen

t R

econ

. tim

e, t

Cap

acity

1 D

isp.

1

Cap

acity

2 D

isp.

2

Nor

m. C

apac

ity

Sam

ple

Tes

t A

ncho

r a

b h d

,m

h d,e

q v m

v i

z e

,m

z e,p

z e/L

M

odel

P

roto

type

Fv1

,m F

v1,p

z 1,m

z 1

,p

Fv2

,m F

v2,p

z 2,m

z 2

,p

FN

1 F

N2

(k

Pa/

m2 ) (

kPa/

m)

(mm

) (m

) (m

/s) (

m/s

) (m

m)

(m)

(h

h:m

m:s

s) (

yy:d

dd)

(N)

(MN

) (m

m)

(m)

(N)

(MN

) (m

m)

(m)

Dru

m 1

D

1D23

H

0-8

40

6.3

9.5

9.5

47

9.4

1.3

4.7

0.19

2.

70

0.5

4.5

0.18

3.

61

0.7

D

1D24

H

0-8

150

20.4

16

.6

16.6

62

12

.4

1.7

5.4

0.22

4.

16

0.8

D

1D25

H

0-8

250

29.2

19.7

63

12

.6

1.8

5.3

0.21

2.

42

0.5

5.7

0.23

4.

5 0.

9

D1D

26#

H0-

9

40

6.

3 9.

0 9.

0 43

8.

6 1.

2

3.

6 0.

14

3.28

0.

7

D1D

27

H0-

9

25

0 29

.2

19.1

19

.1

66

13.2

1.

8

3.

6 0.

14

4.84

1.

0

D1D

28#

H0-

9

25

0 29

.2

19.7

19

.7

59

11.8

1.

6

4.

1 0.

16

2.92

0.

6

D1D

29

H0-

10

100

14.5

13

.5

13.5

65

13

.0

1.4

5.8

0.23

5.

46

1.1

D

1D30

H

0-10

20

0 25

.3

16.7

16

.7

69

13.8

1.

4

6.

7 0.

27

2.99

0.

6 5.

8 0.

23

4.27

0.

9

D1D

31

H0-

10

40

6.3

10.2

10

.2

56

11.2

1.

2

4.

6 0.

18

3.60

0.

7 4

0.16

4.

22

0.8

D

1D32

H

0-11

20

0 25

.3

15.2

15

.2

79

15.8

1.

3

7.

2 0.

29

2.14

0.

4 5.

6 0.

22

5.59

1.

1

D1D

33

H0-

11

100

14.5

14

.2

14.2

78

15

.6

1.3

8.5

0.34

2.

08

0.4

8.3

0.33

5.

08

1.0

D

1D34

H

0-11

15

0 20

.4

15.1

15

.1

80

16.0

1.

3

9.

3 0.

37

2.54

0.

5 9.

5 0.

38

5.01

1.

0

D1D

35

H0-

11

200

25.3

18.1

81

16

.2

1.4

9.4

0.38

1.

85

0.4

9.3

0.37

3.

75

0.8

D

1D36

H

0-12

10

0 14

.5

13.5

13

.5

84

16.8

1.

2

10

.7

0.43

2.

35

0.5

10.5

0.

42

4.49

0.

9

D1D

37

H0-

12

150

20.4

15

.3

15.3

87

17

.4

1.2

11.2

0.

45

4.50

0.

9

D1D

38

H0-

12

200

25.3

16

.5

16.5

89

17

.8

1.2

11.3

0.

45

4.71

0.

9

D1D

39

H0-

13

150

20.4

15

.2

15.2

85

17

.0

1.2

8.9

0.36

2.

16

0.4

9.8

0.39

3.

72

0.7

D

1D40

H

0-13

10

0 14

.5

12.8

12

.8

80

16.0

1.

1

9.

3 0.

37

1.79

0.

4 9.

5 0.

38

3.6

0.7

D

1D41

H

0-13

20

0 25

.3

18

.1

87

17.4

1.

2

11

.0

0.44

2.

41

0.5

12

0.48

4.

21

0.8

D

1D42

H

0-14

20

0 25

.3

16.2

16

.2

97

19.4

1.

2

12

.8

0.51

3.

62

0.7

9.6

0.38

6.

04

1.2

D

1D43

H

0-14

10

0 14

.5

12.5

12

.5

88

17.6

1.

0

11

.1

0.44

2.

99

0.6

7.9

0.32

7.

48

1.5

D

1D44

H

0-14

15

0 20

.4

14.4

14

.4

91

18.2

1.

1

12

.7

0.51

2.

18

0.4

9.7

0.39

4.

99

1.0

# E

mbe

dmen

t dep

th d

ata

not i

nclu

ded

in a

naly

sis

Tab

le 5

.11

(con

tinue

d) D

rum

cen

trifu

ge te

st d

ata

– no

rmal

ly c

onso

lidat

ed c

lay

s u

= a

z2 + b

z D

rop

Hei

ght

Vel

ocity

E

mbe

dmen

t R

econ

. tim

e, t

Cap

acity

1 D

isp.

1

Cap

acity

2 D

isp.

2

Nor

m. C

apac

ity

Sam

ple

Tes

t A

ncho

r a

b h d

,m

h d,e

q v m

v i

z e

,m

z e,p

z e/L

M

odel

P

roto

type

Fv1

,m F

v1,p

z 1,m

z 1

,p

Fv2

,m F

v2,p

z 2,m

z 2

,p

FN

1 F

N2

(k

Pa/

m2 ) (

kPa/

m)

(mm

) (m

) (m

/s) (

m/s

) (m

m)

(m)

(h

h:m

m:s

s) (

yy:d

dd)

(N)

(MN

) (m

m)

(m)

(N)

(MN

) (m

m)

(m)

Dru

m 1

D

1D45

H

0-15

40

6.

3 8.

5 8.

5 48

9.

6 5.

3

10

.4

0.42

8.

43

1.7

D

1D46

H

0-15

10

0 14

.5

14.3

14

.3

61

12.2

6.

8

14

.1

0.56

7.

51

1.5

D

1D47

H

0-16

40

6.

3 9.

5 9.

5 76

15

.2

4.2

22.4

0.

90

8.59

1.

7

D1D

48

H0-

16

100

14.5

15

.2

15.2

89

17

.8

4.9

29.2

1.

17

9.51

1.

9

D1D

49

H0-

17

40

6.3

9.7

9.7

96

19.2

3.

6

33

.4

1.34

9.

57

1.9

D

1D50

H

0-17

10

0 14

.5

15.0

15

.0

114

22.8

4.

2

47

.5

1.90

7.

81

1.6

D

1D51

H

0-18

40

6.

3 10

.0

10.0

43

8.

6 1.

6

7.

9 0.

32

5.66

1.

1

D1D

52

H0-

18

100

14.5

14

.7

14.7

52

10

.4

1.9

8.1

0.32

4.

41

0.9

D

1D53

H

0-19

40

6.

3 9.

2 9.

2 64

12

.8

5.3

24.9

1.

00 1

2.19

2.

4

D1D

54

H0-

19

100

14.5

15

.5

15.5

73

14

.6

6.1

29.2

1.

17

9.31

1.

9

D1D

55

H0-

20

40

6.3

9.0

9.0

103

20.6

4.

3

54

.5

2.18

14.

12

2.8

D

1D56

H

0-20

10

0 14

.5

15.5

15

.5

115

23.0

4.

8

69

.1

2.76

9.

50

1.9

D

1D57

E

4-1

0 0

0.0

0.0

116

23.2

1.

5

54

.5

2.18

13.

22

2.6

D

1D58

# E

4-1

50

7.7

9.

3 98

19

.6

1.3

42.2

1.

69

6.62

1.

3

D1D

59#

E4-

1

10

0 14

.5

11

.8

102

20.4

1.

4

28

.1

1.12

6.

91

1.4

D

1D60

# E

4-1

100

14.5

11.8

10

5 21

.0

1.4

22.4

0.

90

6.93

1.

4

D1D

61

E4-

1

0

0 0.

0 0.

0 10

8 21

.6

1.4

57.8

2.

31

4.50

0.

9 47

.6

1.90

6.

03

1.2

D

1D62

E

4-1

0 0

0.0

0.0

110

22.0

1.

5

61

.9

2.48

6.

33

1.3

51.4

2.

06

8.14

1.

6

D1D

63

E4-

1

0

0 0.

0 0.

0 12

4 24

.8

1.7

55.9

2.

24

8.14

1.

6 46

.2

1.85

10.

28

2.1

D

1D64

# E

4-1

0 0

0.0

0.0

142

28.4

1.

9

53

.0

2.12

16.

47

3.3

44.7

1.

79 1

8.59

3.

7

D1D

65

E4-

1

0

0 0.

0 0.

0 11

2 22

.4

1.5

62.0

2.

48

5.64

1.

1 52

.6

2.10

7.

16

1.4

D

1D66

# E

4-1

0 0

0.0

0.0

140

28.0

1.

9

65

.1

2.60

14.

62

2.9

55.6

2.

22 1

6.39

3.

3

# E

mbe

dmen

t dep

th d

ata

not i

nclu

ded

in a

naly

sis

Tab

le 5

.11

(con

tinue

d) D

rum

cen

trifu

ge te

st d

ata

– no

rmal

ly c

onso

lidat

ed c

lay

s u

= a

z2 + b

z D

rop

Hei

ght

Vel

ocity

E

mbe

dmen

t R

econ

. tim

e, t

Cap

acity

1 D

isp.

1

Cap

acity

2 D

isp.

2

Nor

m. C

apac

ity

Sam

ple

Tes

t A

ncho

r a

b h d

,m

h d,e

q v m

v i

z e

,m

z e,p

z e/L

M

odel

P

roto

type

Fv1

,m F

v1,p

z 1,m

z 1

,p

Fv2

,m F

v2,p

z 2,m

z 2

,p

FN

1 F

N2

(k

Pa/

m2 ) (

kPa/

m)

(mm

) (m

) (m

/s) (

m/s

) (m

m)

(m)

(h

h:m

m:s

s) (

yy:d

dd)

(N)

(MN

) (m

m)

(m)

(N)

(MN

) (m

m)

(m)

Dru

m 2

D

2D1

E0-

3 0.

0037

0.

9590

0

0 0.

0 0.

0 10

9 21

.8

1.5

00:1

4:40

01

:042

27

.4

1.1

3.9

0.8

25.4

1.

0 7.

3 1.

5 47

.1

41.8

D2D

2 E

0-3

0.00

37

0.95

90

100

14.5

12

.6

12.5

11

8 23

.6

1.6

00:1

4:07

01

:027

32

.1

1.3

3.8

0.8

27.3

1.

1 7.

3 1.

5 51

.6

40.6

D2D

3 E

0-3

0.00

37

0.95

90

200

25.3

14

.4

14.5

12

4 24

.8

1.7

00:1

4:57

01

:050

40

.3

1.6

5.0

1.0

32.2

1.

3 8.

2 1.

6 64

.9

47.6

D2D

4 E

0-3

0.00

37

0.95

90

50

7.7

9.3

9.3

117

23.4

1.

6 00

:14:

39

01:0

42

27.7

1.

1 3.

5 0.

7 25

.6

1.0

6.6

1.3

42.1

37

.2

D

2D5

E0-

3 0.

0037

0.

9590

15

0 20

.4

14.8

14

.8

124

24.8

1.

7 00

:14:

49

01:0

47

31.0

1.

2 2.

7 0.

5 32

.5

1.3

5.8

1.2

45.1

48

.3

D

2D6

E0-

3 0.

0037

0.

9590

0

0 0.

0 0.

0 10

3 20

.6

1.4

00:3

1:07

02

:134

36

.7

1.5

3.1

0.6

29.6

1.

2 5.

1 1.

0 79

.3

58.7

D2D

7 E

0-3

0.00

37

0.95

90

0 0

0.0

0.0

106

21.2

1.

4 00

:00:

44

00:0

20

25.5

1.

0 2.

1 0.

4 23

.1

0.9

8.0

1.6

44.3

37

.6

D

2D8

E0-

3 0.

0037

0.

9590

0

0 0.

0 0.

0 10

6 21

.2

1.4

00:0

3:13

00

:089

29

.1

1.2

3.2

0.6

23.0

0.

9 4.

7 0.

9 54

.2

37.4

D2D

9 E

0-3

0.00

37

0.95

90

0 0

0.0

0.0

108

21.6

1.

4 00

:09:

47

00:2

72

33.9

1.

4 3.

1 0.

6 27

.3

1.1

6.2

1.2

65.3

47

.6

D

2D10

E

0-3

0.00

37

0.95

90

0 0

0.0

0.0

101

20.2

1.

3 01

:30:

43

06:3

30

33.4

1.

3 3.

8 0.

8 27

.2

1.1

5.9

1.2

72.3

53

.6

D

2D11

E

0-3

0.00

37

0.95

90

0 0

0.0

0.0

105

21.0

1.

4 03

:00:

17

13:2

63

39.1

1.

6 3.

5 0.

7 31

.2

1.2

5.9

1.2

83.3

61

.1

D

2D12

E

0-3

0.00

37

0.95

90

0 0

0.0

0.0

109

21.8

1.

5 00

:13:

46

01:0

17

32.8

1.

3 3.

5 0.

7 26

.2

1.0

6.6

1.3

62.3

44

.6

D

2D13

E

0-3

0.00

37

0.95

90

0 0

0.0

0.0

105

21.0

1.

4 14

:53:

27

67:3

63

46.7

1.

9 3.

9 0.

8

10

4.7

D2D

14#

E0-

4 0.

0037

0.

9590

20

0 25

.3

13.1

13

.1

00

:09:

10

00:2

55

D

2D15

# E

0-4

0.00

37

0.95

90

200

25.3

12

.7

12.7

D

2D16

# E

0-4

0.00

37

0.95

90

200

25.3

14.0

00:1

4:12

01

:029

D2D

17

E0-

4 0.

0037

0.

9590

20

0 25

.3

14.1

14

.1

108

21.6

1.

4 00

:05:

51

00:1

62

26.7

1.

1 3.

3 0.

7 22

.5

0.9

6.7

1.3

56.9

45

.6

D

2D18

E

0-4

0.00

37

0.95

90

200

25.3

13

.1

13.1

10

2 20

.4

1.4

00:3

4:07

02

:218

27

.8

1.1

3.9

0.8

22.4

0.

9 6.

0 1.

2 66

.4

50.4

D2D

19

E0-

4 0.

0037

0.

9590

20

0 25

.3

12.8

12

.8

107

21.4

1.

4 00

:00:

46

00:0

21

13.6

0.

5 2.

4 0.

5 13

.1

0.5

9.3

1.9

22.2

20

.8

D

2D20

E

0-4

0.00

37

0.95

90

200

25.3

12

.7

12.7

10

8 21

.6

1.4

00:0

0:55

00

:025

15

.1

0.6

1.9

0.4

13.5

0.

5 8.

5 1.

7 25

.8

21.5

D2D

21

E0-

4 0.

0037

0.

9590

20

0 25

.3

12.5

12

.5

104

20.8

1.

4 01

:32:

26

07:0

13

34.1

1.

4 3.

9 0.

8 29

.1

1.2

6.0

1.2

82.1

67

.8

D

2D22

E

0-4

0.00

37

0.95

90

200

25.3

12

.9

12.9

11

3 22

.6

1.5

20.1

0.

8 6.

0 1.

2 16

.7

0.7

9.3

1.9

36.2

27

.7

D

2D23

E

0-4

0.00

37

0.95

90

200

25.3

12

.7

12.7

11

2 22

.4

1.5

00:0

2:07

00

:059

24

.1

1.0

4.9

1.0

20.6

0.

8 8.

9 1.

8 46

.8

38.0

D2D

24

E0-

4 0.

0037

0.

9590

20

0 25

.3

13.5

13

.5

108

21.6

1.

4 00

:08:

46

00:2

44

26.8

1.

1 4.

1 0.

8 22

.2

0.9

6.9

1.4

57.2

44

.8

D

2D25

E

0-4

0.00

37

0.95

90

200

25.3

14.0

11

1 22

.2

1.5

15:3

9:47

71

:190

46

.6

1.9

5.9

1.2

105.

1

# Em

bedm

ent d

epth

dat

a no

t inc

lude

d in

ana

lysi

s

Tab

le 5

.11

(con

tinue

d) D

rum

cen

trifu

ge te

st d

ata

– no

rmal

ly c

onso

lidat

ed c

lay

s u

= a

z2 + b

z D

rop

Hei

ght

Vel

ocity

E

mbe

dmen

t R

econ

. tim

e, t

Cap

acity

1 D

isp.

1

Cap

acity

2 D

isp.

2

Nor

m. C

apac

ity

Sam

ple

Tes

t A

ncho

r a

b h d

,m

h d,e

q v m

v i

z e

,m

z e,p

z e/L

M

odel

P

roto

type

Fv1

,m F

v1,p

z 1,m

z 1

,p

Fv2

,m F

v2,p

z 2,m

z 2

,p

FN

1 F

N2

(k

Pa/

m2 ) (

kPa/

m)

(mm

) (m

) (m

/s) (

m/s

) (m

m)

(m)

(h

h:m

m:s

s) (

yy:d

dd)

(N)

(MN

) (m

m)

(m)

(N)

(MN

) (m

m)

(m)

Dru

m 2

D

2D26

E

0-4

0.00

37

0.95

90

200

25.3

12

.7

12.7

10

2 20

.4

1.4

00:1

4:08

01

:028

28

.6

1.1

3.5

0.7

23.8

1.

0 5.

7 1.

1 68

.7

54.5

D2D

27

E0-

4 0.

0037

0.

9590

50

7.

7 8.

5 8.

5 96

19

.2

1.3

00:1

3:15

01

:003

23

.2

0.9

4.3

0.9

19.6

0.

8 7.

0 1.

4 59

.1

47.2

D2D

28

E0-

4 0.

0037

0.

9590

50

7.

7 8.

7 8.

7 88

17

.6

1.2

00:1

4:28

01

:037

21

.2

0.8

2.6

0.5

17.5

0.

7 4.

6 0.

9 62

.4

47.9

D2D

29#d

E

0-4

0.00

37

0.95

90

150

20.4

11

.9

11.9

96

19

.2

1.3

00:1

3:30

01

:010

28

.1

1.1

3.3

0.7

19.2

0.

8 5.

2 1.

0 75

.3

45.9

D2D

30#d

E

0-4

0.00

37

0.95

90

50

7.7

8.

7 83

16

.6

1.1

00:1

3:10

01

:001

17

.6

0.7

2.2

0.4

17.0

0.

7 4.

8 1.

0 54

.7

52.1

D2D

31#d

E

0-4

0.00

37

0.95

90

100

14.5

10

.6

10.6

94

18

.8

1.3

00:1

3:33

01

:011

24

.2

1.0

2.5

0.5

18.9

0.

8 5.

0 1.

0 65

.0

46.8

D2D

32#d

E

0-4

0.00

37

0.95

90

0 0

0.0

0.0

75

15.0

1.

0 00

:14:

01

01:0

24

17.6

0.

7 2.

2 0.

4 14

.2

0.6

5.2

1.0

69.1

50

.3

D

2D33

#d

E0-

4 0.

0037

0.

9590

20

0 25

.3

12.9

12

.9

93

18.6

1.

2 00

:13:

46

01:0

17

19.6

0.

8 2.

5 0.

5 17

.6

0.7

5.1

1.0

50.2

43

.2

D

2D34

#d

E0-

4 0.

0037

0.

9590

75

11

.3

9.4

9.4

91

18.2

1.

2 00

:13:

45

01:0

17

20.6

0.

8 2.

3 0.

5 17

.1

0.7

5.1

1.0

56.1

43

.3

D

2D35

#d

E0-

4 0.

0037

0.

9590

12

5 17

.6

12.2

12

.2

101

20.2

1.

3 00

:12:

29

00:3

47

26.0

1.

0 2.

8 0.

6 19

.8

0.8

5.7

1.1

62.1

43

.5

D

2D36

E

0-5

0.00

37

0.95

90

0 0

0 0.

0 69

13

.8

0.9

00:1

9:55

01

:188

12

.4

0.5

2.8

0.6

12.3

0.

5 4.

9 1.

0 51

.7

51.1

D2D

37

E0-

5 0.

0037

0.

9590

10

0 14

.5

12.4

12

.4

95

19.0

1.

3 00

:15:

41

01:0

71

17.0

0.

7 3.

1 0.

6 16

.4

0.7

6.2

1.2

43.8

41

.8

D

2D38

E

0-5

0.00

37

0.95

90

50

7.7

9.9

9.9

87

17.4

1.

2 00

:17:

18

01:1

16

13.9

0.

6 5.

6 1.

1

39

.9

D2D

39

E0-

5 0.

0037

0.

9590

20

0 25

.3

13.6

13

.6

93

18.6

1.

2 00

:16:

05

01:0

82

22.6

0.

9 2.

8 0.

6 19

.7

0.8

5.3

1.1

65.4

55

.2

D

2D40

E

0-5

0.00

37

0.95

90

150

20.4

13

.0

13.0

98

19

.6

1.3

00:1

7:35

01

:123

18

.7

0.7

3.2

0.6

15.3

0.

6 5.

8 1.

2 46

.7

35.9

D2D

41#d

E

0-5

0.00

37

0.95

90

0 0

0.0

0.0

69

13.8

0.

9 00

:13:

19

01:0

05

17.9

0.

7 2.

7 0.

5 13

.7

0.5

4.9

1.0

85.4

59

.7

D

2D42

E

4-1

0.00

37

0.95

90

0 0

0.0

0.0

121

24.2

1.

6 00

:15:

09

01:0

56

78.6

3.

1 6.

4 1.

3 63

.2

2.5

8.9

1.8

82.9

60

.3

D

2D43

#d

E4-

1 0.

0037

0.

9590

50

7.

7 8.

7 8.

7 12

2 24

.4

1.6

00:1

4:05

01

:026

72

.3

2.9

6.4

1.3

59.3

2.

4 8.

9 1.

8 72

.6

53.8

D2D

44#d

E

4-1

0.00

37

0.95

90

100

14.5

12

.0

12.0

12

0 24

.0

1.6

00:1

4:31

01

:038

72

.6

2.9

6.1

1.2

58.4

2.

3 7.

7 1.

5 75

.2

54.0

D2D

45#d

E

4-1

0.00

37

0.95

90

200

25.3

15

.0

15.0

13

0 26

.0

1.7

00:1

3:59

01

:023

88

.9

3.6

6.3

1.3

74.6

3.

0 8.

9 1.

8 86

.8

68.1

D2D

46#d

E

4-2

0.00

37

0.95

90

0 0

0.0

0.0

103

20.6

1.

4 00

:14:

53

01:0

48

56.8

2.

3 6.

8 1.

4 45

.6

1.8

9.5

1.9

78.7

57

.1

D

2D47

#d

E4-

2 0.

0037

0.

9590

0

0 0.

0 0.

0 10

4 20

.8

1.4

00:0

0:52

00

:024

43

.9

1.8

4.8

1.0

41.0

1.

6 9.

2 1.

8 52

.8

47.4

D2D

48

E4-

2 0.

0037

0.

9590

0

0 0.

0 0.

0 10

3 20

.6

1.4

00:0

5:05

00

:141

52

.5

2.1

4.9

1.0

42.1

1.

7 5.

5 1.

1 70

.4

50.4

D2D

49

E4-

2 0.

0037

0.

9590

0

0 0.

0 0.

0 10

3 20

.6

1.4

02:0

2:02

09

:105

68

.5

2.7

6.2

1.2

56.4

2.

3 8.

4 1.

7 10

1.3

77.9

# E

mbe

dmen

t dep

th d

ata

not i

nclu

ded

in a

naly

sis;

d Tes

t con

duct

ed in

pre

viou

sly

dist

urbe

d si

te

Tab

le 5

.11

(con

tinue

d) D

rum

cen

trifu

ge te

st d

ata

– no

rmal

ly c

onso

lidat

ed c

lay

s u

= a

z2 + b

z D

rop

Hei

ght

Vel

ocity

E

mbe

dmen

t R

econ

. tim

e, t

Cap

acity

1 D

isp.

1

Cap

acity

2 D

isp.

2

Nor

m. C

apac

ity

Sam

ple

Tes

t A

ncho

r a

b h d

,m

h d,e

q v m

v i

z e

,m

z e,p

z e/L

M

odel

P

roto

type

Fv1

,m F

v1,p

z 1,m

z 1

,p

Fv2

,m F

v2,p

z 2,m

z 2

,p

FN

1 F

N2

(k

Pa/

m2 ) (

kPa/

m)

(mm

) (m

) (m

/s) (

m/s

) (m

m)

(m)

(h

h:m

m:s

s) (

yy:d

dd)

(N)

(MN

) (m

m)

(m)

(N)

(MN

) (m

m)

(m)

Dru

m 2

D

2D50

E

4-2

0.00

37

0.95

90

0 0

0.0

0.0

108

21.6

1.

4 49

:28:

13

225:

325

93.2

3.

7 7.

1 1.

4

13

6.8

D2D

51#d

E

4-3

0.00

37

0.95

90

200

25.3

14

.4

14.4

10

6 21

.2

1.4

00:1

4:45

01

:045

45

.2

1.8

5.6

1.1

37.4

1.

5 8.

1 1.

6 63

.4

49.1

D2D

52

E4-

3 0.

0037

0.

9590

20

0 25

.3

15.1

15

.1

104

20.8

1.

4 02

:46:

30

12:2

45

66.5

2.

7 6.

4 1.

3

10

6.0

D2D

53

E4-

3 0.

0037

0.

9590

20

0 25

.3

15

.1

105

21.0

1.

4 14

:58:

55

68:1

50

74.3

3.

0 6.

0 1.

2

11

8.7

D2D

54

E4-

3 0.

0037

0.

9590

20

0 25

.3

15.1

15

.1

107

21.4

1.

4 00

:00:

59

00:0

27

30.8

1.

2 4.

6 0.

9 28

.2

1.1

9.4

1.9

36.3

31

.6

D

2D55

E

4-3

0.00

37

0.95

90

200

25.3

16

.2

16.2

11

2 22

.4

1.5

00:0

7:11

00

:200

47

.8

1.9

5.2

1.0

37.7

1.

5 7.

9 1.

6 61

.8

44.9

D2D

56#d

E

4-4

0.00

37

0.95

90

0 0

0.0

0.0

71

14.2

0.

9 00

:16:

41

01:0

98

19.0

0.

8 4.

2 0.

8 15

.9

0.6

6.9

1.4

54.7

42

.5

D

2D57

#d

E4-

4 0.

0037

0.

9590

50

7.

7 8.

9 8.

9 84

16

.8

1.1

00:1

5:47

01

:073

25

.9

1.0

4.1

0.8

24.6

1.

0 6.

2 1.

2 59

.5

55.8

D2D

58#d

E

4-4

0.00

37

0.95

90

100

14.5

12

.6

12.6

83

16

.6

1.1

00:1

5:42

01

:071

25

.2

1.0

4.3

0.9

22.4

0.

9 6.

3 1.

3 59

.0

50.8

D2D

59#d

E

4-4

0.00

37

0.95

90

200

25.3

15.1

84

16

.8

1.1

00:1

6:12

01

:085

23

.5

0.9

3.8

0.8

20.4

0.

8 5.

8 1.

2 52

.6

43.8

D2D

60

H0-

3 0.

0037

0.

9590

10

0 14

.5

13.5

13

.5

69

13.8

5.

8 00

:14:

23

01:0

35

8.3

0.3

7.4

1.5

10.1

D

2D61

H

0-3

0.00

37

0.95

90

50

7.7

10.1

9.

1 57

11

.4

4.8

00:1

5:02

01

:053

7.

2 0.

3 4.

7 0.

9

10

.2

D2D

62

H0-

3 0.

0037

0.

9590

20

0 25

.3

15.3

15

.3

69

13.8

5.

8 00

:14:

25

01:0

35

7.5

0.3

6.3

1.3

8.6

D2D

63

H0-

5 0.

0037

0.

9590

50

7.

7

9.1

86

17.2

3.

6 00

:13:

58

01:0

23

14.2

0.

6 4.

6 0.

9

11

.2

D2D

64

H0-

5 0.

0037

0.

9590

20

0 25

.3

14.7

14

.7

104

20.8

4.

3 00

:12:

54

00:3

58

20.9

0.

8 6.

2 1.

2

16

.9

D2D

65

H0-

5 0.

0037

0.

9590

10

0 14

.5

12.6

12

.6

96

19.2

4.

0 00

:14:

35

01:0

40

18.0

0.

7 5.

7 1.

1

14

.8

D2D

66

H0-

6 0.

0037

0.

9590

50

7.

7 9.

3 9.

3 11

2 22

.4

3.1

00:1

3:31

01

:010

D2D

67

H0-

9 0.

0037

0.

9590

50

7.

7 9.

0 9.

0 51

10

.2

1.4

00:1

5:46

01

:073

4.

8 0.

2 3.

1 0.

6

14

.9

D2D

68

H0-

9 0.

0037

0.

9590

20

0 25

.3

15.5

15

.5

64

12.8

1.

8 00

:15:

18

01:0

60

6.8

0.3

4.3

0.9

15.7

D

2D69

H

0-9

0.00

37

0.95

90

100

14.5

11

.4

11.4

56

11

.2

1.6

00:1

4:41

01

:043

5.

5 0.

2 4.

0 0.

8

15

.1

D2D

70

H0-

13

0.00

37

0.95

90

50

7.7

9.

1 75

15

.0

1.0

00:1

5:48

01

:074

10

.3

0.4

2.4

0.5

10.3

0.

4 3.

6 0.

7 22

.5

22.5

D2D

71

H0-

13

0.00

37

0.95

90

200

25.3

13

.0

13.0

85

17

.0

1.2

00:1

4:18

01

:032

16

.3

0.7

2.7

0.5

17.2

0.

7 5.

1 1.

0 31

.9

34.0

D2D

72

H0-

13

0.00

37

0.95

90

100

14.5

11

.1

11.1

85

17

.0

1.2

00:1

5:36

01

:068

12

.5

0.5

4.7

0.9

23.0

# Em

bedm

ent d

epth

dat

a no

t inc

lude

d in

ana

lysi

s; d T

est c

ondu

cted

in p

revi

ousl

y di

stur

bed

site

Tab

le 5

.11

(con

tinue

d) D

rum

cen

trifu

ge te

st d

ata

– no

rmal

ly c

onso

lidat

ed c

lay

D

rop

Hei

ght

Vel

ocity

E

mbe

dmen

t C

apac

ity

Dis

plac

emen

t

Sam

ple

Tes

t A

ncho

r h d,

m

h d,e

q v m

v i

z e

,m

z e,p

z e/L

F

v,m

Fv,

p z m

z p

(mm

) (m

) (m

/s)

(m/s

) (m

m)

(m)

(N

) (M

N)

(mm

) (m

)

Box

7

B7D

1 E

0-1

200

35.6

19

.0

25.0

11

2 22

.4

1.5

47.8

1.

9 8.

2 1.

6

B

7D2

E0-

1 20

0 35

.6

23

.4

B

7D3

E0-

1 20

0 35

.6

23

.4

103

20.6

1.

4 43

.0

1.7

4.1

0.8

B

7D4

E0-

1 20

0 35

.6

23

.4

105

21.0

1.

4 46

.3

1.9

5.8

1.2

B

7D5

E0-

1 20

0 35

.6

12.1

18

.1

96

19.2

1.

3 40

.4

1.6

7.4

1.5

B

7D6

E0-

1 21

0 37

.3

19.8

25

.8

84

16.8

1.

1 46

.9

1.9

3.3

0.7

B

7D7

E0-

1 21

0 37

.3

19.9

25

.9

84

16.8

1.

1 50

.8

2.0

4.0

0.8

B

7D8

E0-

1 21

0 37

.3

18.8

24

.8

105

21.0

1.

4 43

.1

1.7

3.6

0.7

B

7D9

E0-

1 15

0 27

.2

13.2

19

.2

90

18.0

1.

2 46

.8

1.9

3.5

0.7

B

7D10

E

0-1

300

51.5

23

.1

29.1

11

0 22

.0

1.5

54.8

2.

2 3.

3 0.

7

B

ox 8

* B

8D1

E0-

1 0

0 0.

0 0.

0 17

3.

4 0.

2

B

8D2

E0-

1 12

5 22

.8

8.5

14.5

46

9.

2 0.

6

B

8D3

E0-

1 17

5 31

.4

13.8

19

.8

51

10.2

0.

7 46

.3

1.9

3.8

0.8

B

8D4

E0-

1 30

0 51

.5

23.0

29

.0

61

12.2

0.

8 45

.6

1.8

3.0

0.6

Box

9

B9D

1 E

0-1

0 0

0.0

0.0

47

9.4

0.6

30.1

1.

2 4.

8 1.

0

B

9D2

E0-

1 12

5 22

.8

7.7

13.7

60

12

.0

0.8

39.5

1.

6 5.

2 1.

0

B

9D3

E0-

1 25

0 43

.7

20.7

26

.7

91

18.2

1.

2 53

.1

2.1

4.5

0.9

B

9D4

E0-

1 30

0 51

.5

23.7

29

.7

85

17.0

1.

1 46

.9

1.9

4.3

0.9

B

9D5

IE0-

1 30

0 51

.5

23.1

29

.1

91

18.2

1.

2 51

.0

2.0

17.5

3.

5

B

9D6

IE0-

1 30

0 51

.5

22.5

28

.5

89

17.8

1.

2 50

.6

2.0

6.3

1.3

B

9D7

IE0-

1 30

0 51

.5

23.4

29

.4

91

18.2

1.

2 54

.1

2.2

9.7

1.9

* Box

8 e

mbe

dmen

t and

cap

acit

y da

ta n

ot in

clud

ed in

ana

lysi

s

Tab

le 6

.2 B

eam

cen

trifu

ge te

st d

ata

– ca

lcar

eous

san

d

231

FIGURES

Figure 1.1 Average annual shallow-water and deepwater oil and gas production in the Gulf of Mexico (French et al.2006)

Figure 1.2 Offshore development systems(http://www.gomr.mms.gov)

Figure 1.3 Tension leg platform(http://www.offshore-technology.com)

Figure 1.4 Semi-submersible(http://www.offshore-technology.com)

Figure 1.5 Spar platform(http://www.globalsecurity.org)

Figure 1.6 Floating production, storage and offloading facility (http://www.sbmmalaysia.com)

Figure 1.7 Catenary and taut leg mooring systems (Vryhof 1999)

Figure 1.8 Anchor piles (Eltaher et al. 2003)

Figure 1.9 Suction caissons(http://www.delmarus.com)

Figure 1.10 Drag embedment anchor (Vryhof 1999)

Figure 1.11 Drag-in plate anchor – Stevmanta VLA (Vryhof 1999)

Figure 1.12 Suction embedded plate anchor (http://www.energetics.com)

Figure 1.13 Torpedo anchor (Araujo et al. 2004)

Figure 1.14 Deep Penetrating Anchor (Lieng et al. 1999)

Figure 2.1 Marine sediment penetrometer (after Colp et al. 1975)

Figure 2.2 Laboratory scale Marine impact penetrometer (after Dayal & Allen 1973)

Figure 2.3 Undrained shear strength profiles from Doppler penetrometer tests in normally consolidated terrigenous clayey silt

(after Beard 1981)

Figure 2.4 Free fall cone penetrometer (after Brooke Ocean Technology 2007)

Figure 2.5 Expendable Bottom Penetrometer (after Shi 2005)

Figure 2.6 Interpreted XBP and miniature vane shear strength profiles (after Aubeny & Shi 2006)

Figure 2.7 Great Meteor East and Nares Abyssal Plain test sites in the Atlantic Ocean (after Freeman & Burdett 1986)

Figure 2.8 European Standard Penetrometer (after Freeman & Burdett 1986)

Figure 2.9 DOMP II penetrometer designs (after Freeman & Burdett 1986)

Figure 2.10 True’s Method – calculation procedure flow chart (NCEL 1985)

Is

vi > 3 ft/s

Determine object characteristics

L, D, Deq, Ap, As, Ws, m, CD

Yes

Use static penetration

method

Obtain soil parameters

su, St, ρ, Se*, Ce, Co

No

Select depth increment

∆z

Initialise iterative values

i = 0, z = 0, v0 = v

i = i + 1

zi = i(∆z)

Calculate

Ws

Calculate

Fbi, sui(nose), Sei, Nti

Calculate

Fsi, sui(side), Sti, Sei

Does

i = 1?

Estimate Fdiusing v0

Yes

Estimate v1

Calculate

Fdi

No

Calculate

Fi

Calculate

vi+1

Is

vi+1 < 0?

Penetrate one more

depth increment

No

Calculate final embedment

z

Yes

Equations 2.16, 2.17 & 2.19

Equations 2.18 & 2.19

Equation 2.8

Equation 2.15

Equation 2.22

Equation 2.24

Equation 2.8

Equation 2.23

Figure 2.11 Dependence of pile capacity on time after installation (after Fleming et al. 1985)

Figure 2.12 Dependence of torpedo anchor capacity on time after installation (after Audibert et al. 2006)

Figure 2.13 Regain in DPA capacity with time after installation (D = 1.2 m, wflukes = 0.2 m, ch = 5 m2/yr; after Lieng et al. 1999)

Figure 2.14 Dissipation curves from cavity expansion solutions for the radial consolidation of soil around a solid driven pile

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.001 0.01 0.1 1 10 100 1000

Non-dimensional time, T = cht/D2

Exc

ess

pore

pre

ssur

e, ∆∆ ∆∆u/

∆∆ ∆∆u m

ax

Ir = 50

Ir = 500

Figure 2.15 Torpedo anchors (a) after Medeiros (2001) (b) after Araujo et al. (2004)

(a)

(b)

Figure 2.16 Torpedo anchor handling and offloading during field tests (after Araujo et al. 2004)

Figure 2.17 Proposed Deep Penetrating Anchor structural design (after Lieng et al. 1999)

10 – 15 m

Figure 2.18 Deep Penetrating Anchor installation procedure (after Lieng et al. 2000)

Permanent mooring line

Installation line

Release unit

300

-30

00 m

Penetration depth

Anchor

Seabed

Chain

Drop height, typically < 100 m

Figure 2.19 Deep Penetrating Anchor reduced scale field tests

Figure 2.20 SPEAR anchor (a) Crane handling (b) Field trials in the Gulf of Mexico (after Zimmerman 2007)

(a)

(b)

Figure 2.21 Model Deep Penetrating Anchors (a) Four fluke anchor (b) Three fluke anchor (c) Zero fluke anchor

(a)

(b)

(c)

Figure 2.22 Model anchor tip embedments with impact velocity (after O’Loughlin et al. 2004b)

Figure 2.23 Model anchors used in drum centrifuge aspect ratio study

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Stress

No

rma

lised

dep

th,

z/h sa

mpl

ePrototype

Model

Under stress

Over stress

Stress similitude

Figure 3.1 Stress variation with depth (model and prototype)

Swinging Platform

Counter Weight

Strong-box

Flight Computer

Figure 3.2 Beam centrifuge

Figure 3.3 Beam centrifuge strong-box

Figure 3.4 Beam centrifuge actuator

Horizontal Axis

Vertical Axis

Motor

Encoder

50 mm

Pore pressure transducer

Figure 3.5 Sub-Terrain Oil impregnated Multiple Pressure Instrument (STOMPI)

Sample Channel Tool Table Actuator

Figure 3.6 Drum centrifuge (with cover removed)

Figure 3.7 Drum centrifuge sample channel

Sample channel Sample surface

Figure 3.8 Drum centrifuge tool table actuator

Figure 3.9 Rowe cell test - coefficient of vertical consolidation

0 100 200 300 400 500 6000

1

2

3

4

5

6

7

Coe

ffici

ent o

f Con

solid

atio

n, c v (

m2 /y

r)

Vertical Effective Stress, σ'v (kPa)

Figure 3.10 Hopper positioned above drum centrifuge

Hopper

Clamshell

Cover

Coupling

Figure 3.11 Rotating coupling and slurry placement nozzle

Hose

Rotating coupling

HoseNozzle

Tool table actuator

20

5

SIDE VIEW END VIEW

Figure 3.12 T-bar penetrometer

Load cell Shaft

T-bar

Figure 3.13 25 MPa, 10 mm diameter cone penetrometer

Load cell

Cone tip

Shaft

Figure 3.14 100 MPa, 7 mm diameter cone penetrometer

Load cell

Cone tip

Shaft

Figure 3.15 Zero fluke model anchor

Ltip

Lshaft

D

L

0

2

4

6

8

10

12

-8 -6 -4 -2 0 2 4 6 8x (mm)

y (m

m)

a

b

Figure 3.16 Ellipsoid anchor tip shape

Figure 3.17 Interchangeable zero fluke model anchor segments

Tip & shaft

Padeye

Tip

Shaft

Padeye

Figure 3.18 Four fluke model anchor

L

D

Ltip

Lfluke1

Lfluke2

Lfluke3

wfluke

(a)

(b)

Figure 3.19 Model anchors – varying tip geometry (a) Conical tip (b) Ogive tip (c) Flat tip

(c)

Ltip

L

D

D

Lshaft

Ltip

Lshaft

L

D

L

Figure 3.20 Instrumented model anchor

Piezoelectric material

Test massStrain gauged

section

Figure 3.21 Model anchors – varying aspect ratio

Figure 3.22 Model anchor with hemispherical tip and padeye sections

Anchor shaft

Padeye section Insert

Anchor chain

Release cord

Figure 3.23 Anchor chain and release cord connection

Figure 3.24 Zero fluke anchor installation guide

Slot

Zero fluke model anchor

Slot PERPs

Rails

Bracket

Slot

Model anchor

Groove

Figure 3.25 Four fluke anchor installation guide

Slot

Groove

Rails

Bracket

PERPs

Figure 3.26 Comparison of single and multiple PERP installation guides (a) Photograph (b) Typical output (c) Velocity profile

(a)

(b)

(c)

0 5 10 15 20 25 30

-100

-50

0

50

100

150

200

250

300Single PERPMultiple PERP

Hei

ght a

bove

sam

ple

surf

ace

(mm

)

Velocity (m/s)

0.000 0.002 0.004 0.006

2.5

3.0

3.5

4.0

4.5

5.0

5.5

Out

put V

olta

ge (

V)

Time (sec)

∆t ∆t1 ∆t2 ∆t3 ∆t4

∆t5 ∆t6 ∆t7 ∆t8

0.122 0.124 0.126 0.128 0.130-1

0

1

2

3

4

5

6

O

utpu

t Vol

tage

(V

)

Time (sec)

Figure 3.27 Release mechanism

Release cord

Resistor

Clamp

Anchor chain

Load cell

Connecting screw

Figure 3.28 Load cell

Water

650 mm

325

mm

1

2

Installation guide

Model DPA

Load cell Actuator

Kaolin clay

Strongbox

Load cell

Release mechanism

Installation guide

PERPs

Actuator

Figure 3.29 Dynamic anchor test arrangement in the beam centrifuge

Figure 3.30 Embedment depth calculation procedure

Drop height

Embedment depth

Load cell

zslack

zchain

L

zLC

Sample surface

Installation guide

Model anchor

Figure 3.31 Dynamic anchor static installation adaptor

Model anchor

Anchor chain

Adaptor

T-bar shaft

Load cell

Installation guide

Sample surface

Figure 3.32 Dynamic anchor test arrangement in the drum centrifuge

Installation guide

Load cell

Sample surface

10°

PERPs

Anchor chain

Figure 4.1 Drag coefficient dependence on object shape (after Hoerner 1965)

Figure 4.2 Drag coefficient as a function of Reynolds number for a smooth sphere and a smooth cylinder (after Young et al. 1997)

5D 20DD

10D

Figure 4.3 Problem domain for FLUENT analysis of a smooth sphere

Axis of symmetry

SphereVelocity inlet Outflow

Figure 4.4 Drag coefficient of a smooth sphere from FLUENT analysis

0.01

0.1

1

10

100

1000

0.1 10 1000 100000 10000000Reynolds number, Re

Dra

g co

effic

ient

, CD

Theoretical

FLUENT

(a)

(b)

(c)

(d)

Figure 4.5 Axis-symmetric problem domains for FLUENT analysis (a) Ellipsoid nose (b) Conical nose (c) Ogive nose (d) Flat nose

Velocity inlet Outflow

Anchor

(a)

(b)

(c)

Figure 4.6 Velocity contours - ellipsoid nosed anchor (a) v = 1 × 10-6 m/s(b) v = 1 × 10-4 m/s (c) v = 60 m/s

(a)

(b)

(c)

Figure 4.7 Velocity contours - conical nosed anchor (a) v = 1 × 10-6 m/s(b) v = 1 × 10-4 m/s (c) v = 60 m/s

(a)

(b)

(c)

Figure 4.8 Velocity contours - ogive nosed anchor (a) v = 1 × 10-6 m/s(b) v = 1 × 10-4 m/s (c) v = 60 m/s

(a)

(b)

(c)

Figure 4.9 Velocity contours - flat nosed anchor (a) v = 1 × 10-6 m/s(b) v = 1 × 10-4 m/s (c) v = 60 m/s

Figure 4.10 Zero fluke anchor drag coefficients from FLUENT analysis.

0.1

1

10

100

1E-05 0.0001 0.001 0.01 0.1 1 10 100

Velocity, v (m/s)

Dra

g co

effic

ient

, CD

Ellipsoid

Cone

Ogive

Flat

Figure 4.11 (a) Dependence of impact velocity on drop height

0

5

10

15

20

25

30

35

40

0 50 100 150 200 250 300Model drop height, hd,m (mm)

Impa

ct v

eloc

ity,

vi (

m/s

)

0 10 20 30 40 50 60Nominal prototype drop height, hd,p (m)

Uniform g field

Beam g field

Drum g field

0

10

20

30

40

50

60

0 50 100 150 200 250 300Model drop height, hd,m (mm)

Equ

ival

ent

prot

otyp

e dr

op h

eigh

t, h

d,e

q (m

)

Uniform g field

Beam g field

Drum g field

Figure 4.11 (b) Equivalent prototype drop heights

Sha

ft fr

ictio

n (F

s)

Iner

tial d

rag

(F d)

End

be

arin

g (F b

)

(a)

Com

plet

e ho

le c

losu

re(b

) P

artia

l hol

e cl

osur

e(c

) N

o ho

le c

losu

re

Sub

mer

ged

wei

ght (

W s)

Rev

ers

e en

d be

arin

g (F r

)

Fig

ure

4.12

Hol

e cl

osur

e be

hind

adv

anci

ng a

ncho

r du

ring

inst

alla

tion

Figure 4.13 Forces acting on a zero fluke dynamic anchor during installation

Shaft friction (Fs)

Submerged weight (Ws)

Inertial drag (Fd)

End bearing (Fb)

Figure 4.14 Forces acting on a four fluke dynamic anchor during installation

End bearing (Fb)

Inertial drag (Fd)

Submerged weight (Ws)

Shaft friction (Fs)

Fluke bearing (Fbf)

Fluke friction (Fsf)

Fluke reverse end bearing (Frf)

Figure 4.15 Flow chart showing calculation procedure for embedment prediction method

Determine object characteristics

L, Ltip, D, Ap, As, m, W, CD, vi, Nc

Determine soil properties

su, k, ρ, λ, β, α

Select time increment

∆t

Initialise iterative values

i = 0, z = 0, v = vi

i = i + 1

zi = i(∆z)

Calculate

Ws

Calculate

Fb, su,tip

Calculate

Fs, su,ave

Calculate

Fd

Calculate

F

Calculate

zi+1

Is

vi+1 < 0?

Penetrate another

increment

No

Calculate final embedment

z

Yes

Equation 4.16

Equation 4.20 or 4.21

Equation 4.22

Equation 4.23

Equation 4.24

Equation 4.25

ti-1 = -∆t

zi-1 = -∆t(vi)

Calculate

Rf

Calculate

a

Calculate

vi+1

Equation 4.15

Equation 4.4

Figure 4.16 Variation in bearing capacity factor with depth (after Skempton 1951 as cited by Whitlow 2001)

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5Normalised depth, z/D

Bea

ring

ca

paci

ty fa

cto

r, N

c

Circle

Strip

Figure 4.17 Forces acting on a zero fluke dynamic anchor during extraction

Reverse end bearing (Fr)

Submerged weight (Ws)

Shaft friction (Fs)

Padeye bearing (Fb)

Cable tension (Fv)

Figure 4.18 Forces acting on a four fluke dynamic anchor during extraction

Cable tension (Fv)

Padeye bearing (Fb)

Fluke reverse end bearing (Frf)

Fluke bearing (Fbf)

Fluke friction (Fsf)

Reverse end bearing (Fr)

Shaft friction (Fs)

Submerged weight (Ws)

Figure 4.19 Bearing capacity of shallow footings on sand (after Poulos & Chua 1985)

Figure 4.20 Variation in ββββCALC values with pile length (after Abbs et al. 1988)

Figure 4.21 Comparison of vertically loaded plate anchor with padeye pullout bearing mechanism

Figure 4.22 Bearing capacity factors for vertically loaded plate anchors in sand (after Rowe & Davis 1982)

Figure 5.1 Linear and polynomial approximations of a typical undrained shear strength profile

Figure 5.2 Undrained shear strength profiles in Box 1

0

4

8

12

16

20

24

28

32

36

0 10 20 30 40Undrained shear strength, su (kPa)

Pro

toty

pe d

epth

, zp (

m)

0

20

40

60

80

100

120

140

160

180

Mod

el d

epth

, zm (

mm

)

Measured

Linear

Polynomial

0

4

8

12

16

20

24

28

32

36

0 10 20 30 40 50 60Undrained shear strength, su (kPa)

Pro

toty

pe d

epth

, zp

(m)

0

20

40

60

80

100

120

140

160

180

Mod

el d

epth

, zm (

mm

)BeforeAfterAverage

k = 1.17 kPa/m

Figure 5.3 Undrained shear strength profiles in Box 2

Figure 5.4 Undrained shear strength profiles in Box 3

0

4

8

12

16

20

24

28

32

36

0 10 20 30 40 50Undrained shear strength, su (kPa)

Pro

toty

pe d

epth

, zp

(m)

0

20

40

60

80

100

120

140

160

180

Mod

el d

epth

, zm (

mm

)

Before

After

Average

k = 0.83 kPa/m

0

5

10

15

20

25

30

35

40

0 10 20 30 40 50 60 70Undrained shear strength, su (kPa)

Pro

toty

pe d

epth

, zp

(m)

0

25

50

75

100

125

150

175

200

Mod

el d

epth

, zm (

mm

)

Before

After

Average

k = 1.09 kPa/m

Figure 5.5 Undrained shear strength profiles in Box 4

Figure 5.6 Undrained shear strength profiles in Box 5

0

4

8

12

16

20

24

28

32

36

0 10 20 30 40 50

Undrained shear strength, su (kPa)

Pro

toty

pe d

epth

, zp

(m)

0

20

40

60

80

100

120

140

160

180

Mod

el d

epth

, zm (

mm

)

BeforeAfterAverage

k = 1.00 kPa/m

0

4

8

12

16

20

24

28

32

36

0 10 20 30 40 50 60

Undrained shear strength, su (kPa)

Pro

toty

pe d

epth

, zp

(m)

0

20

40

60

80

100

120

140

160

180

Mod

el d

epth

, zm (

mm

)

Before

After

Average

k = 1.03 kPa/m

Figure 5.7 Undrained shear strength profiles in Box 6

Figure 5.8 Average undrained shear strength profiles for the beam centrifuge samples

0

4

8

12

16

20

24

28

32

36

0 10 20 30 40 50 60 70Undrained shear strength, su (kPa)

Pro

toty

pe d

epth

, zp

(m)

0

20

40

60

80

100

120

140

160

180

Mod

el d

epth

, zm (

mm

)

BeforeAfterAverage

k = 1.45 kPa/m

0

4

8

12

16

20

24

28

32

36

0 10 20 30 40 50 60Undrained shear strength, su (kPa)

Pro

toty

pe d

epth

, zp

(m)

0

20

40

60

80

100

120

140

160

180

Mod

el d

epth

, zm (

mm

)

Box 1

Box 2Box 3

Box 4Box 5

Box 6

k = 1.07 kPa/m

Figure 5.10 Sensitivities from cyclic T-bar tests in Box 6

Figure 5.9 Cyclic T-bar test in Box 6

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25

Number of cycles

Sen

sitiv

ity,

S t

Test 1

Test 2

Test 3

Test 4

0

40

80

120

160

200

-80 -60 -40 -20 0 20 40 60 80Undrained shear strength, su (kPa)

Mo

del

dep

th, z

m (

mm

)

Extraction

Installation

Cycling

Figure 5.11 Measured single PERP velocities from current and previous beam centrifuge tests

Figure 5.12 Measured single and multiple PERP velocities from the beam centrifuge tests

0

10

20

30

40

50

60

0 5 10 15 20 25 30Impact velocity, vi (m/s)

Equ

ival

ent

prot

otyp

e dr

op h

eigh

t, h

d,e

q (m

)

Current

Previous

Note: Equivalent drop heights represent model

drop heights of 0 - 300 mm

0

10

20

30

40

50

60

0 5 10 15 20 25 30Impact velocity, vi (m/s)

Equ

ival

ent

prot

otyp

e dr

op h

eigh

t, h

d,e

q (m

)

Single PERP

Multiple PERP

Note: Equivalent drop heights represent model

drop heights of 0 - 300 mm

-50

0

50

100

150

200

250

0 10 20 30

Velocity, v (m/s)

Hei

gh

t abo

ve s

am

ple

surfa

ce,

h s (m

m)

Point of impact

Figure 5.13 Adjusted impact velocities from beam centrifuge tests

Figure 5.14 Typical velocity profile for a dynamic anchor test conducted from a drop height of 200 mm in the beam centrifuge

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35Impact velocity, vi (m/s)

Equ

ival

ent

prot

otyp

e dr

op h

eigh

t, h

d,e

q (m

)

Multiple PERP

Single PERP

Note: Equivalent drop heights represent model

drop heights of 0 - 300 mm

Figure 5.15 Anchor chain slack length from load displacement curve

Figure 5.16 Dependence of embedment depth on impact velocity for 0FA tests in the beam centrifuge

0

10

20

30

40

50

60

70

0 50 100 150Vertical displacement (mm)

Loa

d (

N)

Slack length

Point of load onset

Maximum capacity

0

5

10

15

20

25

30

35

40

45

50

0 5 10 15 20 25 30 35Impact velocity, vi (m/s)

Pro

toty

pe

embe

dm

ent,

z e,p (

m)

0

25

50

75

100

125

150

175

200

225

250

Mo

del e

mb

edm

ent,

z e,m (

mm

)

Ellipsoid nose 0FA

mave = 14.5 g

L = 75 mmD = 6 mm

Figure 5.17 Extrapolated embedments for dynamic anchors based on beam centrifuge test results

Figure 5.18 Embedment depth discrepancy with tip shape (after O’Loughlin et al. 2004b)

0

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80Impact velocity, vi (m/s)

Pro

toty

pe e

mb

edm

ent,

z e,p (

m)

0

50

100

150

200

250

300

Mo

del

em

bed

men

t, z e,m

(m

m)

Waste disposal test datam = 1800 - 2645 kgL = 2.00 - 5.75 mD = 0.23 - 0.50 m

0

5

10

15

20

25

30

35

40

45

50

0 5 10 15 20 25 30 35Impact velocity, vi (m/s)

Pro

toty

pe e

mbe

dmen

t, ze

,p (

m)

0

25

50

75

100

125

150

175

200

225

250

Mod

el e

mbe

dmen

t, ze

,m (

mm

)0FA - sharp (m = 16.75 g)

0FA - blunt (m = 16.75 g)

Figure 5.19 Variation in embedment with impact velocity for different anchor tip shapes

Figure 5.20 Variation in embedment with kinetic energy for different anchor tip shapes

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40Impact velocity, vi (m/s)

Pro

toty

pe e

mb

edm

ent,

z e,p (

m)

0

25

50

75

100

125

150

175

200

225

250

Mo

del e

mb

edm

ent,

z e,m (

mm

)

Ellipsoid (m = 14.3 - 14.8 g)

Cone (m = 14.7 g)

Ogive (m = 14.8 g)

Flat (m = 15.5 g)

0

5

10

15

20

25

30

35

40

45

50

0 20 40 60 80Prototype kinetic energy, Ek,p (MJ)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

25

50

75

100

125

150

175

200

225

250

0 2.5 5 7.5 10Model kinetic energy, Ek,m (J)

Mo

del e

mb

edm

ent,

z e,m (

mm

)

Ellipsoid (m = 14.8 g)

Cone (m = 14.7 g)

Ogive (m = 14.8 g)

Flat (m = 15.5 g)

Figure 5.21 Bearing mechanism beneath a deep circular foundation(after Meyerhof 1951)

Figure 5.22 Dependence of embedment depth on the presence of anchor flukes (impact velocity)

0

5

10

15

20

25

30

35

40

45

50

0 5 10 15 20 25 30 35Impact velocity, vi (m/s)

Pro

toty

pe

embe

dmen

t, z e,p

(m

)

0

25

50

75

100

125

150

175

200

225

250

Mo

del

em

bed

men

t, z e,m

(m

m)

0FA (m = 14.5 g)

3FA (m = 12.5 g)

4FA (m = 12.5 g)

Figure 5.24 Dependence of embedment depth on the presence of the surface water layer

Figure 5.23 Dependence of embedment depth on the presence of anchor flukes (kinetic energy)

0

5

10

15

20

25

0 10 20 30 40Impact velocity, vi (m/s)

Pro

toty

pe e

mbe

dmen

t, z e,p

(m

)

0

25

50

75

100

125

Mo

del e

mbe

dmen

t, z e,m

(m

m)

Surface water

No surface water

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40 50 60Prototype kinetic energy, Ek,p (MJ)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

25

50

75

100

125

150

175

200

225

250

0 1.25 2.5 3.75 5 6.25 7.5Model kinetic energy, Ek,m (J)

Mo

del e

mb

edm

ent,

z e,m (

mm

)

0FA (m = 14.5 g)

3FA (m = 12.5 g)

4FA (m = 12.5 g)

Figure 5.25 Excavated beam centrifuge sample showing the inclination of a model dynamic anchor

Figure 5.26 Typical load displacement response for the vertical monotonic extraction of a dynamic anchor in the beam centrifuge

Model anchor

Sand drainagelayer

Clay

0

10

20

30

40

50

60

70

80

90

0 5 10 15 20 25 30Model displacement, zm (mm)

Mo

del l

oa

d,

F v,m

(N

)

Peak 1

Peak 2

Figure 5.27 Load displacement response from static installation, vertical monotonic extraction test in Box 5

Figure 5.28 Typical load displacement response for model anchors with various tip shapes

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50Model displacement, zm (mm)

Mo

del

loa

d, F

v,m (

N)

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25 30Model displacement, zm (mm)

Mo

del

loa

d, F

v,m (

N)

Ellipsoid

Cone

Ogive

Flat

Figure 5.29 Measured 0FA Peak 1 vertical monotonic holding capacities

0

5

10

15

20

25

30

35

40

45

50

0 1 2 3 4 5Prototype capacity, Fv,p (MN)

Pro

toty

pe e

mbe

dmen

t, ze

,p (

m)

0

25

50

75

100

125

150

175

200

225

250

0 25 50 75 100 125Model capacity, Fv,m (N)

Mod

el e

mbe

dmen

t, ze

,m (

mm

)

Current 0FA (m = 14.5 g)

Previous 0FA (m = 16.75 g)

Torpedo anchor (m = 63200 kg, L = 12 m, D = 1.07 m)

Figure 5.30 Measured 0FA Peak 2 vertical monotonic holding capacities

0

5

10

15

20

25

30

35

40

45

50

0 1 2 3 4 5Prototype capacity, Fv,p (MN)

Pro

toty

pe e

mbe

dmen

t, ze

,p (

m)

0

25

50

75

100

125

150

175

200

225

250

0 25 50 75 100 125Model capacity, Fv,m (N)

Mod

el e

mbe

dmen

t, ze

,m (

mm

)Current 0FA - Peak 2 (m = 14.5 g)

Previous 0FA - Peak 1 (m = 16.75 g)

Torpedo anchor (m = 63200 kg,L = 12 m, D = 1.07 m)

Figure 5.32 Normalised 0FA Peak 2 vertical monotonic holding capacities

Figure 5.31 Normalised 0FA Peak 1 vertical monotonic holding capacities

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40 50 60 70 80Normalised capacity, FN = (Fv -Ws)/su,aveAp

Pro

toty

pe e

mb

edm

ent,

z e,p (

m)

0

25

50

75

100

125

150

175

200

225

250

Mo

del

em

bedm

ent,

z e,m (m

m)

Current 0FA (m = 14.5 g)

Previous 0FA (m = 16.75 g)

Torpedo anchor (m = 63200 kg,L = 12 m, D = 1.07 m)

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40 50 60 70 80Normalised capacity, FN = (Fv -Ws)/su,aveAp

Pro

toty

pe e

mb

edm

ent,

z e,p (

m)

0

25

50

75

100

125

150

175

200

225

250

Mo

del

em

bed

men

t, z e,m

(mm

)

Current 0FA - Peak 2 (m = 14.5 g)

Previous 0FA - Peak 1 (m = 16.75 g)

Torpedo anchor (m = 63200 kg,L = 12 m, D = 1.07 m)

Figure 5.33 Variation in normalised Peak 1 capacity with anchor tip shape

Figure 5.34 Variation in normalised Peak 2 capacity with anchor tip shape

25

30

35

40

45

50

0 10 20 30 40 50 60 70Normalised capacity, FN = (Fv -Ws)/su,aveAp

Pro

toty

pe e

mb

edm

ent,

z e,p (

m)

125

150

175

200

225

250

Mo

del

em

bed

men

t, z e,m

(m

m)

Ellipsoid (m = 14.8 g)

Cone (m = 14.7 g)

Ogive (m = 14.8 g)

Flat (m = 15.5 g)

25

30

35

40

45

50

0 10 20 30 40 50

Normalised capacity, FN = (Fv -Ws)/su,aveAp

Pro

toty

pe e

mbe

dmen

t, ze

,p (

m)

125

150

175

200

225

250

Mod

el e

mbe

dmen

t, ze

,m (

mm

)

Ellipsoid (m = 14.8 g)

Cone (m = 14.7 g)

Ogive (m = 14.8 g)

Figure 5.36 Variation in load and displacement for sustained loading test B5SUS2

Figure 5.35 Dependence of anchor efficiency on fluke configuration

0

10

20

30

40

50

0 1 2 3 4 5Efficiency, Ef

Pro

toty

pe e

mbe

dmen

t, ze

,p (

m)

0

50

100

150

200

250

Mod

el e

mbe

dmen

t, ze

,m (

mm

)

0FA (m = 14.5 g)

3FA (m = 12.5 g)

4FA (m = 12.5 g)

0

0.2

0.4

0.6

0.8

1

1.2

0 50 100 150 200 250 300Time, t (sec)

Rel

ativ

e lo

ad

, F s

us/F

mo

n

0

1

2

3

4

5

6

No

rma

lised

dis

pla

cem

ent,

z/D

Load

Displacement Failure

Switch to disp. control

Figure 5.37 Variation in load and displacement for sustained loading test B5SUS3

Figure 5.38 Variation in load and displacement for sustained loading test B5SUS4

0

0.2

0.4

0.6

0.8

1

1.2

0 150 300 450 600 750 900Time, t (sec)

Rel

ativ

e lo

ad

, F s

us/F

mo

n

0

0.5

1

1.5

2

2.5

3

3.5

4

No

rma

lised

dis

pla

cem

ent,

z/D

Load

Displacement Failure

Switch to disp. control

0

0.2

0.4

0.6

0.8

1

1.2

0 100 200 300 400 500Time, t (sec)

Rel

ativ

e lo

ad, F

sus/

F mo

n

0

0.5

1

1.5

2

2.5

3

3.5

4

No

rma

lised

dis

pla

cem

ent,

z/D

Load

DisplacementFailure

Figure 5.39 Variation in load and displacement for sustained loading test B5SUS5

Figure 5.40 Normalised load displacement response for sustained loading tests B5SUS2, B5SUS4 and B5SUS5

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 100 200 300 400 500 600Time, t (sec)

Rel

ativ

e lo

ad,

Fsu

s/Fm

on

0

0.5

1

1.5

2

2.5

3

3.5

4

No

rma

lised

dis

pla

cem

ent,

z/D

Load

Displacement

Failure

0

10

20

30

40

50

60

70

0 1 2 3 4 5Normalised displacement, z/D

Nor

mal

ised

load

, FN

=(Fv

-Ws )

/su

,aveA

p

0

0.2

0.4

0.6

0.8

1

No

rma

lised

ca

paci

ty r

atio

, N

CR 1

B5SUS2

B5SUS4

B5SUS5

Fsus/Fmon = 50 %

70 %

90 %

80 %

Figure 5.41 Normalised load displacement response for sustained loading tests B5SUS2, 4 and 5

Figure 5.42 Normalised load displacement response for tests B5D1, B5SUS2 and B5SUS3

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 100 200 300 400 500

Time, t (sec)

Nor

mal

ised

dis

plac

emen

t, z

/D

B5SUS2

B5SUS4

B5SUS5

Fsus/Fmon = 80 %

50 %

70 %

90 %

0

10

20

30

40

50

60

70

0 2 4 6 8Normalised displacement, z/D

Nor

mal

ised

load

, FN

=(Fv

-Ws )

/su

,ave

Ap

0

0.2

0.4

0.6

0.8

1N

orm

alis

ed c

apac

ity r

atio

, N

CR1

B5D1

B5SUS2

B5SUS3Fsus/Fmon ~ 80 %

Figure 5.43 Variation in normalised displacement under sustained loading sequences for tests B5SUS2 and 3

Figure 5.44 Variation in load and displacement for cyclic loading test B5CYC1

0

0.05

0.1

0.15

0.2

0.25

0.3

0 200 400 600 800Time, t (sec)

No

rma

lised

dis

pla

cem

ent,

z/D

B5SUS2

B5SUS3

Fsus/Fmon = 80 %

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80Time, t (sec)

Rel

ativ

e lo

ad

, F c

yc/F

mo

n

0

0.5

1

1.5

2

2.5

3

3.5

4N

orm

alis

ed d

isp

lace

men

t, z/

D

Load

Displacement

Failure

Figure 5.45 Variation in load and displacement with time for cyclic loading test B5CYC2

Figure 5.46 Variation in load and displacement with time for cyclic loading test B5CYC3

0

0.2

0.4

0.6

0.8

1

1.2

0 50 100 150 200 250 300Time, t (sec)

Rel

ativ

e lo

ad

, F c

yc/F

mo

n

0

0.5

1

1.5

2

2.5

3

3.5

4

No

rma

lised

dis

pla

cem

ent,

z/D

LoadDisplacement

Failure

Switch to disp. control

0

0.2

0.4

0.6

0.8

1

1.2

0 50 100 150 200 250 300Time, t (sec)

Rel

ativ

e lo

ad,

Fcy

c/Fm

on

0

0.5

1

1.5

2

2.5

3

3.5

4

No

rma

lised

dis

pla

cem

ent,

z/D

Load

DisplacementFailure

Switch to disp. control

Figure 5.47 Variation in load and displacement with time for cyclic loading test B5CYC5

Figure 5.48 Variation in load and displacement with time for cyclic loading test B5CYC6

0

0.2

0.4

0.6

0.8

1

1.2

0 200 400 600 800 1000Time, t (sec)

Rel

ativ

e lo

ad

, F c

yc/F

mo

n

0

0.5

1

1.5

2

2.5

3

3.5

4

No

rma

lised

dis

pla

cem

ent,

z/D

Load

DisplacementFailure

Switch to disp. control

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80Time, t (sec)

Rel

ativ

e lo

ad

, F c

yc/F

mo

n

0

0.5

1

1.5

2

2.5

3

3.5

4

No

rma

lised

dis

pla

cem

ent,

z/D

Load

Displacement

Failure

Figure 5.49 Variation in load and displacement with time for cyclic loading test B5CYC7

Figure 5.50 Mean load and cyclic load amplitude

0

0.2

0.4

0.6

0.8

1

1.2

0 50 100 150 200 250 300Time, t (sec)

Rel

ativ

e lo

ad,

Fcy

c/Fm

on

0

0.5

1

1.5

2

2.5

3

3.5

4

No

rma

lised

dis

pla

cem

ent,

z/D

Load

DisplacementFailure

Switch to disp. control

Time

Lo

ad

Mean load

Cyclic load amplitude

Figure 5.51 Normalised load displacement response for cyclic loading tests B5CYC3 and B5CYC7

Figure 5.52 Variation in normalised displacements under cyclic loading sequences for tests B5CYC3 and B5CYC7

0

10

20

30

40

50

60

70

0 2 4 6 8Normalised displacement, z/D

Nor

mal

ised

load

, FN

=(Fv

-Ws )

/su

,aveA

p

0

0.2

0.4

0.6

0.8

1

Nor

mal

ised

cap

acity

rat

io,

NC

R1

B5CYC3

B5CYC7

Fcyc/Fmon = 50 - 80 %

70 - 80 %

0

0.05

0.1

0.15

0.2

0.25

0 50 100 150 200Time, t (sec)

Nor

mal

ised

dis

plac

emen

t, z

/D

B5CYC3

B5CYC7

Fcyc/Fmon = 50 - 80 %

70 - 80 %

Figure 5.53 Variation in normalised displacements for tests B5SUS2 and B5CYC3

Figure 5.54 Normalised load displacement response for tests B5D1 and B5CYC7

0

0.05

0.1

0.15

0.2

0.25

0 50 100 150 200Time, t (sec)

No

rma

lised

dis

pla

cem

ent,

z/D

B5SUS2

B5CYC3

Fsus/Fmon = 80 %

Fcyc/Fmon = 50 - 80 %

0

10

20

30

40

50

60

70

0 2 4 6 8Normalised displacement, z/D

Nor

mal

ised

load

, FN

=(Fv

-Ws )

/su

,ave

Ap

0

0.2

0.4

0.6

0.8

1N

orm

alis

ed c

apac

ity r

atio

, N

CR1

B5D1

B5CYC7

Fcyc/Fmon = 70 - 80 %

Figure 5.55 Variation in normalised displacements under cyclic loading sequences for tests B5CYC3 and B5CYC5

Figure 5.56 Variation in normalised displacements under cyclic loading sequences for tests B5CYC3 and B5CYC5

0

10

20

30

40

50

60

70

0 2 4 6 8Normalised displacement, z/D

Nor

mal

ised

load

, FN

=(Fv

-Ws )

/su

,aveA

p

0

0.2

0.4

0.6

0.8

1

Nor

mal

ised

cap

acity

rat

io,

NC

R1

B5CYC3

B5CYC5

Fcyc/Fmon = 50 - 80 %

0

0.05

0.1

0.15

0.2

0.25

0.3

0 200 400 600 800Time (sec)

No

rma

lised

dis

pla

cem

ent,

z/D

B5CYC5

B5CYC3

Fcyc/Fmon = 50 - 80 %

Figure 5.57 Variation in static penetration resistance with anchor tip shape

Figure 5.58 Undrained shear strength profiles with depth from Drum 1 showing the influence of unbalance

0

4

8

12

16

20

24

28

32

36

0 0.4 0.8 1.2 1.6 2 2.4Prototype static resistance, Fs,p (MN)

Pro

toty

pe

dep

th,

z p (m

)

0

20

40

60

80

100

120

140

160

180

0 10 20 30 40 50 60Model static resistance, Fs,m (N)

Mo

del

dep

th,

z m (

mm

)

Ellipsoid

Cone

Ogive

Flat

0

4

8

12

16

20

24

28

0 10 20 30 40Undrained shear strength, su (kPa)

Pro

toty

pe d

epth

, zp

(m

)

0

20

40

60

80

100

120

140

Mod

el d

epth

, zm

(m

m)

Unbalance = 0.43 g

Unbalance = 0.57 g

Unbalance = 0.72 g

k = 1 kPa/m

Figure 5.59 Undrained shear strength profiles with depth from Drum 2 showing the influence of centrifuge unbalance

Figure 5.60 Linear and polynomial approximations of the undrained shear strength profile for the zero unbalance T-bar test

0

4

8

12

16

20

24

28

0 5 10 15 20 25 30Undrained shear strength, su (kPa)

Pro

toty

pe d

epth

, zp

(m)

0

20

40

60

80

100

120

140

Mo

del d

epth

, z m

(m

m)

Linear

Polynomial

k = 1.03 kPa/m

a = 0.0037b = 0.9590

0

4

8

12

16

20

24

28

0 5 10 15 20 25 30Undrained shear strength, su (kPa)

Pro

toty

pe d

epth

, zp

(m

)

0

20

40

60

80

100

120

140

Mod

el d

epth

, zm

(m

m)

Unbalance = 0 gUnbalance = 0.35 - 0.4 gUnbalance = 0.6 g

k = 1 kPa/m

Figure 5.61 Variation in impact velocity with drop height for 0FA tests in the drum centrifuge

Figure 5.62 Variation in impact velocity with drop height for 4FA tests in the drum centrifuge

0

5

10

15

20

25

30

35

0 5 10 15 20Impact velocity, vi (m/s)

Equ

ival

ent

prot

otyp

e dr

op h

eigh

t, h

d,e

q (m

) Note: Equivalent drop heights represent model

drop heights of 0 - 200 mm

0

5

10

15

20

25

30

35

0 5 10 15 20Impact velocity, vi (m/s)

Equ

ival

ent

prot

otyp

e dr

op h

eigh

t, h

d,e

q (m

) Note: Equivalent drop heights represent model

drop heights of 0 - 200 mm

Figure 5.63 Variation in impact velocity with drop height for L/D < 7 tests in the drum centrifuge

Figure 5.64 Variation in impact velocity with drop height for L/D > 7 tests in the drum centrifuge

0

5

10

15

20

25

30

35

0 5 10 15 20 25Impact velocity, vi (m/s)

Equ

ival

ent

prot

otyp

e dr

op h

eigh

t, h

d,e

q (m

) Note: Equivalent drop heights represent model

drop heights of 0 - 250 mm

0

5

10

15

20

25

30

35

0 5 10 15 20Impact velocity, vi (m/s)

Equ

ival

ent

prot

otyp

e dr

op h

eigh

t, h

d,e

q (m

)

Note: Equivalent drop heights represent model

drop heights of 0 - 200 mm

Figure 5.66 Dependence of embedment depth on impact velocity for 0FA tests in the drum centrifuge

Figure 5.65 Variation in best-fit impact velocities with drop height for 0FA and hemispherically tipped anchor tests

0

5

10

15

20

25

30

35

0 5 10 15 20Impact velocity, vi (m/s)

Equ

ival

ent

prot

otyp

e dr

op h

eigh

t, h

d,e

q (m

)

0FA

L/D < 7

L/D > 7

0

5

10

15

20

25

30

0 5 10 15 20Impact velocity, vi (m/s)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

25

50

75

100

125

150

Mo

del e

mb

edm

ent,

z e,m (

mm

)E0-3 (m = 8.2 g)

E0-4 (m = 6.2 g)

E0-5 (m = 5.4 g)

0

5

10

15

20

25

30

35

0 5 10 15 20Impact velocity, vi (m/s)

Equ

ival

ent

prot

otyp

e dr

op h

eigh

t, h

d,e

q (m

)

0FA

L/D < 7

L/D > 7

Figure 5.68 Dependence of embedment depth on impact velocity for anchors with varying aspect ratio in the drum centrifuge

0

5

10

15

20

25

30

0 5 10 15 20Impact velocity, vi (m/s)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

25

50

75

100

125

150

Mo

del e

mb

edm

ent,

z e,m (

mm

)

E4-2 (m = 12.7 g)

E4-3 (m = 9.6 g)

Figure 5.67 Dependence of embedment depth on impact velocity for 4FA tests in the drum centrifuge

0

5

10

15

20

25

30

0 5 10 15 20 25Impact velocity, vi (m/s)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

25

50

75

100

125

150

Mo

del

em

bed

men

t, z e,m

(m

m)

H0-2 (L/D=1.5, m=1.8 g)

H0-5 (L/D=4, m=4.7 g)

H0-11 (L/D=10, m=4.2 g)

Figure 5.69 Extrapolated 0FA embedment depths

Figure 5.70 Variation in embedment depth with impact velocity for anchors H0-5 and H0-13

0

5

10

15

20

25

30

35

40

45

0 20 40 60 80Impact velocity, vi (m/s)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

25

50

75

100

125

150

175

200

225

Mo

del e

mb

edm

ent,

z e,m (

mm

)

E0-3 (m = 8.2 g)

E0-4 (m = 6.2 g)

E0-5 (m = 5.4 g)

Waste disposal test datam = 1800 - 2645 kgL = 2.00 - 5.75 mD = 0.23 - 0.50 m

0

5

10

15

20

25

30

0 5 10 15 20 25Impact velocity, vi (m/s)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

25

50

75

100

125

150

Mo

del

em

bed

men

t, z e,m

(m

m)

H0-5 (L/D=4, m=4.7 g)

H0-13 (L/D=12, m=4.7g)

Tip

Padeye

Figure 5.71 Variation in embedment depth with impact velocity for anchors H0-15 and H0-18

Figure 5.72 Variation in embedment depth with impact velocity for anchors H0-5 and H0-7

0

5

10

15

20

25

30

0 5 10 15 20 25Impact velocity, vi (m/s)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

25

50

75

100

125

150

Mo

del

em

bed

men

t, z e,m

(m

m)

H0-5 (L/D=4, m=4.7 g)

H0-7 (L/D=4, m=1.4 g)

Tip

Padeye

0

5

10

15

20

0 5 10 15 20Impact velocity, vi (m/s)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

25

50

75

100

Mo

del e

mb

edm

ent,

z e,m (

mm

)

H0-15 (L/D=1, m=3.0 g)

H0-18 (L/D=3, m=3.0 g)

Tip

Padeye

Figure 5.73 Variation in embedment depth with impact velocity for anchors H0-6 and H0-8

Figure 5.74 Variation in embedment depth with impact velocity for anchors H0-1, H0-4 and H0-6

0

5

10

15

20

25

30

35

0 5 10 15 20 25Impact velocity, vi (m/s)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

25

50

75

100

125

150

175

Mo

del

em

bed

men

t, z e,m

(m

m)

H0-6 (L/D=6, m=7.4 g)

H0-8 (L/D=6, m=2.3 g)

Tip

Padeye

0

5

10

15

20

25

30

35

0 5 10 15 20 25Impact velocity, vi (m/s)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

25

50

75

100

125

150

175

Mo

del e

mb

edm

ent,

z e,m (

mm

)

H0-1 (L/D=1, m=0.9 g)H0-4 (L/D=3, m=3.0 g)H0-6 (L/D=6, m=7.4 g)

Tip

Padeye

Figure 5.75 Influence of consolidation time on the load displacement response for anchor E4-3

Figure 5.76 Influence of the anchor aspect ratio on the load displacement response

0

10

20

30

40

50

60

70

80

0 10 20 30 40Model displacement, zm (mm)

Mo

del l

oa

d,

F v,m

(N

)

t = 59 s

t = 431 s

t = 9990 s

t = 53935 s

0

2

4

6

8

10

12

0 10 20 30 40Model displacement, zm (mm)

Mo

del

loa

d, F

v,m (

N)

L/D = 2

L/D = 6L/D = 8

L/D = 12

Figure 5.77 0FA Peak 1 holding capacity dependence on embedment depth in the drum centrifuge

Figure 5.78 0FA Peak 2 holding capacity dependence on embedment depth in the drum centrifuge

0

5

10

15

20

25

30

0 0.5 1 1.5 2Prototype capacity, Fv,p (MN)

Pro

toty

pe

embe

dmen

t, z e,p

(m

)

0

25

50

75

100

125

150

0 10 20 30 40 50Model capacity, Fv,m (N)

Mo

del e

mbe

dmen

t, z e,m

(m

m)E0-3 (m = 8.2 g)

E0-4 (m = 6.2 g)

E0-5 (m = 5.4 g)

0

5

10

15

20

25

30

0 0.5 1 1.5 2Prototype capacity, Fv,p (MN)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

25

50

75

100

125

150

0 10 20 30 40 50Model capacity, Fv,m (N)

Mo

del e

mb

edm

ent,

z e,m (

mm

)E0-3 (m = 8.2 g)

E0-4 (m = 6.2 g)

E0-5 (m = 5.4 g)

Figure 5.79 Variation in holding capacity with embedment depth for anchors H0-5 and H0-13

Figure 5.80 Variation in holding capacity with embedment depth for anchors H0-15 and H0-18

0

5

10

15

20

25

30

35

0 0.2 0.4 0.6 0.8 1Prototype capacity, Fv,p (MN)

Pro

toty

pe

embe

dmen

t, z e,p

(m

)

0

25

50

75

100

125

150

175

0 5 10 15 20 25Model capacity, Fv,m (N)

Mo

del e

mbe

dmen

t, z e,m

(m

m)

H0-5 (L/D=4, m=4.7 g)

H0-13 (L/D=12, m=4.7 g)

Tip

Padeye

0

5

10

15

20

0 0.2 0.4 0.6 0.8 1Prototype capacity, Fv,p (MN)

Pro

toty

pe e

mbe

dmen

t, ze

,p (

m)

0

25

50

75

100

0 5 10 15 20 25Model capacity, Fv,m (N)

Mod

el e

mbe

dmen

t, ze

,m (

mm

)

H0-15 (L/D=1, m=3.0 g)

H0-18 (L/D=3, m = 3.0 g)

Tip

Padeye

0

0.5

1

1.5

2

2.5

3

3.5

4

1 10 100 1000 10000 100000 1000000Consolidation time, t (sec)

Pro

toty

pe c

apa

city

, F v

,p (M

N)

0

10

20

30

40

50

60

70

80

90

100

Mod

el c

apac

ity, F

v,m (

N)

E0-3 (m=8.2 g, h=0 mm)

E0-4 (m=6.2 g, h=200 mm)

E4-2 (m=12.7 g, h=0 mm)

E4-3 (m=9.6 g, h=200 mm)

Figure 5.81 Variation in anchor capacity with consolidation time for anchors E0-3, E0-4, E4-2 and E4-3

Figure 5.82 Variation in normalised capacity with non-dimensional time for anchors E0-3, E0-4, E4-2 and E4-3

0

20

40

60

80

100

120

140

160

0.001 0.01 0.1 1 10 100 1000Non-dimensional time, T=cht/D

2

No

rma

lised

ca

pa

city

, FN =

(F v

-Ws)

/su,

aveA

p

E0-3 (m=8.2 g, h=0 mm)

E0-4 (m=6.2 g, h=200 mm)

E4-2 (m=12.7 g, h=0 mm)

E4-3 (m=9.6 g, h=200 mm)

0

0.2

0.4

0.6

0.8

1

1.2

0.001 0.01 0.1 1 10 100 1000Non-dimensional time, T=cht/D

2

Deg

ree

of C

onso

lidat

ion

E0-3 (m=8.2 g, h=0 mm)

E0-4 (m=6.2 g, h=200 mm)

E4-2 (m=12.7 g, h=0 mm)

E4-3 (m=9.6 g, h=200 mm)

Torpedo (m=0.6 kg, L/D=12)

Figure 5.83 Variation in normalised capacity ratio with non-dimensional time for anchors E0-3, E0-4, E4-2 and E4-3

Figure 5.84 Degree of consolidation for anchors E0-3, E0-4, E4-2 and E4-3

0

0.2

0.4

0.6

0.8

1

1.2

0.001 0.01 0.1 1 10 100 1000Non-dimensional time, T=cht/D

2

No

rma

lised

ca

paci

ty r

atio

, F N

/FN

,ma

x E0-3 (m=8.2 g, h=0 mm)

E0-4 (m=6.2 g, h=200 mm)

E4-2 (m=12.7 g, h=0 mm)

E4-3 (m=9.6 g, h=200 mm)

Dynamic

Quasi-static

Figure 6.1 Silica sand cone resistance profiles with depth

Figure 6.2 Zero fluke model anchor embedded in silica sand sample

0

4

8

12

16

20

24

28

32

0 20 40 60 80Cone tip resistance, qc (MPa)

Pro

toty

pe d

epth

, zp

(m

)0

20

40

60

80

100

120

140

160

Mod

el d

epth

, zm

(m

m)

CPT 1

CPT 2

CPT 3

CPT 4

Figure 6.3 Comparison of tip embedments in silica sand and normally consolidated clay

Figure 6.4 Calcareous sand cone resistance profiles with depth

0

5

10

15

20

25

30

35

40

45

50

0 5 10 15 20 25 30 35Impact velocity, vi (m/s)

Pro

toty

pe e

mbe

dmen

t, ze

,p (

m)

0

25

50

75

100

125

150

175

200

225

250

Mod

el e

mbe

dmen

t, ze

,m (

mm

)

NC clay

Silica sand

0

4

8

12

16

20

24

28

32

36

40

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Cone tip resistance, qc (MPa)

Pro

toty

pe d

epth

, zp

(m)

0

20

40

60

80

100

120

140

160

180

200

Mod

el d

epth

, zm (

mm

)

Box 7

Box 8

Box 9 (before)

Box 9 (after)

Figure 6.5 Variation in measured velocity with drop height

Figure 6.6 Variation in adjusted impact velocity with drop height

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35Impact velocity, vi (m/s)

Equ

ival

ent

prot

otyp

e dr

op h

eigh

t, h

d,eq

(m

)

Multiple PERP

Single PERP

Calcareous sand

Note: Equivalent dropheights represent model

drop heights of 0 - 300 mm

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35Impact velocity, vi (m/s)

Equ

ival

ent

prot

otyp

e dr

op h

eigh

t, h

d,eq

(m

)

Multiple PERP

Single PERP

Calcareous sand

Note: Equivalent dropheights represent model

drop heights of 0 - 300 mm

Figure 6.7 Variation in embedment depth with impact velocity in calcareous sand

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35Impact velocity, vi (m/s)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

50

100

150

200

250

300

Mo

del e

mbe

dm

ent,

z e,m (

mm

)

NC clay

Silica sand

Calcareous sand

Figure 6.8 Extrapolated embedment depths for dynamic anchors in calcareous sand

0

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80Impact velocity, vi (m/s)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

50

100

150

200

250

300

Mo

del e

mbe

dm

ent,

z e,m (

mm

)

NC clay

Silica sand

Calcareous sand

Figure 6.10 Comparison of vertical capacities for calcareous sand and normally consolidated clay

Figure 6.9 Typical load displacement plot in calcareous sand

0

5

10

15

20

25

30

35

40

45

50

0 5 10 15 20Vertical displacement, z (mm)

Mo

del

loa

d,

F v,m

(N

)

0

10

20

30

40

50

0 1 2 3 4 5Prototype capacity, Fv,p (MN)

Pro

toty

pe e

mbe

dmen

t, z e,p

(m

)

0

50

100

150

200

250

0 25 50 75 100 125Model capacity, Fv,m (N)

Mod

el e

mbe

dmen

t, z e,

m (

mm

)Calcareous sandNC clay - Peak 1NC clay - Peak 2

Figure 6.11 Static resistance force from static penetration tests in calcareous sand

0

5

10

15

20

25

30

35

40

0 2 4 6 8 10Prototype resistance, Fp (MN)

Pro

toty

pe d

epth

, zp

(m)

0

25

50

75

100

125

150

175

200

0 50 100 150 200 250Model resistance, Fm (N)

Mod

el d

epth

, zm (

mm

)

Test 1

Test 2

Figure 7.1 Measured and theoretical impact velocities in the beam centrifuge

Figure 7.2 Typical velocity profiles from embedment depth prediction calculations

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35Impact velocity, vi (m/s)

Equ

ival

ent

prot

otyp

e dr

op h

eigh

t, h

d,e

q (m

)

Multiple PERP

Single PERP

Theoretical

Note: Equivalent dropheights represent model

drop heights of 0 - 300 mm

0

10

20

30

40

50

60

0 10 20 30 40Velocity, v (m/s)

Pro

toty

pe d

epth

, zp

(m)

0

50

100

150

200

250

300

Mod

el d

epth

, zm (

mm

)Impact velocity

Embedment depth su = 1.0 kPa/m

(a)

Figure 7.3 Back-calculated strain rate parameter (a) Semi-logarithmic rate law (b) Power rate law

(b)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 5 10 15 20 25 30 35Impact velocity, vi (m/s)

Stra

in r

ate

pa

ram

eter

, ββ ββ

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 5 10 15 20 25 30 35Impact velocity, vi (m/s)

Stra

in r

ate

pa

ram

eter

, λλ λλ

Figure 7.5 Measured and predicted embedment depths for the 0FA in the beam centrifuge

0

5

10

15

20

25

30

35

40

45

50

0 5 10 15 20 25 30 35

Impact velocity, vi (m/s)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

25

50

75

100

125

150

175

200

225

250

Mo

del e

mb

edm

ent,

z e,m (

mm

)

β = 0.08

β = 0.14

βave = 0.12

0

0.5

1

1.5

2

2.5

3

3.5

4

1 10 100 1000 10000 100000Normalised strain rate, γγγγ/γγγγref

No

rma

lised

res

ista

nce

, s u/

s u,r

ef

Log - λ = 0.2

Log - λ = 0.4

Power - β = 0.1

Figure 7.4 Strain rate effects for semi-logarithmic and power rate laws

Figure 7.7 Sensitivity of embedment depth predictions to bearing capacity factor

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35

Impact velocity, vi (m/s)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

50

100

150

200

250

300

Mo

del e

mb

edm

ent,

z e,m (

mm

)

Nc = 8

Nc = 20

Nc = 12

Figure 7.6 Embedment depth predictions for impact velocities of up to 80 m/s

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80

Impact velocity, vi (m/s)P

roto

type

em

bed

men

t, z e,p

(m

)

0

50

100

150

200

250

300

350

400

Mo

del

em

bed

men

t, z e,m

(m

m)

β = 0.12

Figure 7.9 Sensitivity of embedment depth predictions to undrained shear strength gradient

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35

Impact velocity, vi (m/s)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

50

100

150

200

250

300

Mo

del e

mb

edm

ent,

z e,m (

mm

)

k = 1 kPa/m

k = 1.5 kPa/m

k = 1.07 kPa/m(a = 0.013, b = 0.870)

Figure 7.8 Sensitivity of embedment depth predictions to shaft adhesion factor

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35

Impact velocity, vi (m/s)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

50

100

150

200

250

300

Mo

del e

mb

edm

ent,

z e,m (

mm

)

α = 0

α = 1

α = 0.4

Figure 7.11 Measured and predicted Peak 1 vertical monotonic holding capacities

0

5

10

15

20

25

30

35

40

45

50

0 1 2 3 4 5Prototype capacity, Fv,p (MN)

Pro

toty

pe e

mbe

dmen

t, ze

,p (

m)

0

25

50

75

100

125

150

175

200

225

250

0 25 50 75 100 125Model capacity, Fv,m (N)

Mod

el e

mbe

dmen

t, ze

,m (

mm

)

α = 1

α = 0.8

Figure 7.10 Sensitivity of embedment depth predictions to drag coefficient

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35

Impact velocity, vi (m/s)P

roto

typ

e em

bed

men

t, z e,p

(m

)

0

50

100

150

200

250

300

Mo

del e

mb

edm

ent,

z e,m (

mm

)

CD = 0

CD = 0.7

CD = 0.24

Figure 7.13 Holding capacity predictions for embedment depths of up to 360 mm (72 m at prototype scale)

0

10

20

30

40

50

60

70

80

0 1 2 3 4 5 6 7 8Prototype capacity, Fv,p (MN)

Pro

toty

pe e

mbe

dmen

t, ze

,p (

m)

0

50

100

150

200

250

300

350

400

0 25 50 75 100 125 150 175 200Model capacity, Fv,m (N)

Mod

el e

mbe

dmen

t, ze

,m (

mm

)

α = 1

α = 0.5

Figure 7.12 Measured and predicted Peak 2 vertical monotonic holding capacities

0

5

10

15

20

25

30

35

40

45

50

0 1 2 3 4 5Prototype capacity, Fv,p (MN)

Pro

toty

pe e

mbe

dmen

t, ze

,p (

m)

0

25

50

75

100

125

150

175

200

225

250

0 25 50 75 100 125Model capacity, Fv,m (N)

Mod

el e

mbe

dmen

t, ze

,m (

mm

)

α = 0.5α = 1

Figure 7.15 Sensitivity of holding capacity predictions to padeye bearing resistance

0

10

20

30

40

50

0 1 2 3 4 5Prototype capacity, Fv,p (MN)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

50

100

150

200

250

0 25 50 75 100 125Model capacity, Fv,m (N)

Mo

del e

mb

edm

ent,

z e,m (m

m)

f.Nc = 0.9

(f = 0.1, Nc = 9)

f.Nc = 9

f.Nc = 0

Figure 7.14 Sensitivity of holding capacity predictions to tip bearing capacity factor

0

10

20

30

40

50

0 1 2 3 4 5Prototype capacity, Fv,p (MN)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

50

100

150

200

250

0 25 50 75 100 125Model capacity, Fv,m (N)

Mo

del e

mb

edm

ent,

z e,m (m

m)

Nc = 20

Nc = 8

Nc = 12

Figure 7.17 Sensitivity of holding capacity predictions to undrained shear strength gradient

0

10

20

30

40

50

0 1 2 3 4 5Prototype capacity, Fv,p (MN)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

50

100

150

200

250

0 25 50 75 100 125Model capacity, Fv,m (N)

Mo

del e

mb

edm

ent,

z e,m (m

m)

k = 1 kPa/m

k = 1.5 kPa/m

k = 1.07 kPa/m(a = 0.013, b = 0.870)

Figure 7.16 Sensitivity of holding capacity predictions to shaft adhesion factor

0

10

20

30

40

50

0 1 2 3 4 5Prototype capacity, Fv,p (MN)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

50

100

150

200

250

0 25 50 75 100 125Model capacity, Fv,m (N)

Mo

del e

mb

edm

ent,

z e,m (m

m)

α = 0

α = 1

α = 0.8

Figure 7.19 Measured and theoretical impact velocities in the drum centrifuge

Figure 7.18 Variation in holding capacity predictions with impact velocity for shear strength gradients of 1 and 1.5 kPa/m

0

1

2

3

4

5

0 5 10 15 20 25 30 35Impact velocity, vi (m/s)

Pro

toty

pe c

apac

ity,

Fv,p (

MN

)

0

25

50

75

100

125

Mod

el c

apac

ity,

Fv,m

(N

)

k = 1 kPa/m

k = 1.5 kPa/m

0

5

10

15

20

25

30

35

0 5 10 15 20 25Impact velocity, vi (m/s)

Equ

ival

ent

prot

otyp

e dr

op h

eigh

t, h

d,e

q (m

)

0FA

4FA

L/D < 7

L/D > 7

TheoreticalNote: Equivalent drop

heights represent modeldrop heights of 0 - 250 mm

Figure 7.20 Back-calculated strain rate parameter for 0FA tests (a) Semi-logarithmic rate law (b) Power rate law

(a)

(b)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 5 10 15 20Impact velocity, vi (m/s)

Stra

in r

ate

pa

ram

eter

, λλ λλ

E0-3 (m = 8.2 g)

E0-4 (m = 6.2 g)

E0-5 (m = 5.4 g)

Overall best-fit

0

0.02

0.04

0.06

0.08

0.1

0 5 10 15 20Impact velocity, vi (m/s)

Stra

in r

ate

pa

ram

eter

, ββ ββ

E0-3 (m = 8.2 g)

E0-4 (m = 6.2 g)

E0-5 (m = 5.4 g)

Overall best-fit

Figure 7.21 Back-calculated strain rate parameter for 4FA tests (a) Semi-logarithmic rate law (b) Power rate law

(a)

(b)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 5 10 15 20Impact velocity, vi (m/s)

Stra

in r

ate

pa

ram

eter

, λλ λλ

E4-1 (m = 15.5 g)

E4-2 (m = 12.7 g)

E4-3 (m = 9.6 g)

Overall best-fit

0

0.02

0.04

0.06

0.08

0.1

0 5 10 15 20Impact velocity, vi (m/s)

Stra

in r

ate

pa

ram

eter

, ββ ββ

E4-1 (m = 15.5 g)

E4-2 (m = 12.7 g)

E4-3 (m = 9.6 g)

Overall best-fit

Figure 7.22 Back-calculated strain rate parameter for hemispherical nose anchor tests (a) Semi-logarithmic rate law (b) Power rate law

(a)

(b)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 5 10 15 20Impact velocity, vi (m/s)

Stra

in r

ate

pa

ram

eter

, λλ λλ

H0-3 (L/D=2, m=2.0 g)

H0-5 (L/D=4, m=4.7 g)

H0-9 (L/D=6, m=1.9 g)

H0-13 (L/D=12, m=4.7 g)

0

0.04

0.08

0.12

0.16

0.2

0 5 10 15 20Impact velocity, vi (m/s)

Stra

in r

ate

pa

ram

eter

, ββ ββ

H0-3 (L/D=2, m=2.0 g)

H0-5 (L/D=4, m=4.7 g)

H0-9 (L/D=6, m=1.9 g)

H0-13 (L/D=12, m=4.7 g)

Figure 7.23 Measured and theoretical embedment depths for anchor E0-3

Figure 7.24 Measured and theoretical embedment depths for anchor E0-4

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25

Impact velocity, vi (m/s)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

25

50

75

100

125

150

175

200

Mo

del e

mb

edm

ent,

z e,m (

mm

)

0FA

Overallβ = 0.07

β = 0.06

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25

Impact velocity, vi (m/s)P

roto

typ

e em

bed

men

t, z e,p

(m

)

0

25

50

75

100

125

150

175

200

Mo

del e

mb

edm

ent,

z e,m (

mm

)

0FA

Overall

β = 0.07

β = 0.06

Figure 7.25 Measured and theoretical embedment depths for anchor E0-5

Figure 7.26 Measured and theoretical embedment depths for anchor E4-2

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25

Impact velocity, vi (m/s)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

25

50

75

100

125

150

175

200

Mo

del e

mb

edm

ent,

z e,m (

mm

)

0FA

Overallβ = 0.07

β = 0.06

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25Impact velocity, vi (m/s)

Pro

toty

pe e

mbe

dmen

t, z e,p

(m

)

0

25

50

75

100

125

150

175

200

Mo

del

em

bed

men

t, z e,m

(m

m)

4FA

Overall

β = 0.07

β = 0.08

Figure 7.27 Measured and theoretical embedment depths for anchor E4-3

Figure 7.28 Measured and theoretical embedment depths for anchor H0-3

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25Impact velocity, vi (m/s)

Pro

toty

pe

embe

dmen

t, z e,p

(m

)

0

25

50

75

100

125

150

175

200

Mo

del

em

bed

men

t, z e,m

(m

m)

4FA

Overall

β = 0.07

β = 0.08

0

5

10

15

20

25

30

0 5 10 15 20 25Impact velocity, vi (m/s)

Pro

toty

pe

embe

dmen

t, z e,p

(m

)

0

25

50

75

100

125

150

Mo

del

em

bed

men

t, z e,m

(m

m)

H0-3

Overall

β = 0.07

β = 0.09

Figure 7.29 Measured and theoretical embedment depths for anchor H0-5

Figure 7.30 Measured and theoretical embedment depths for anchor H0-9

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25Impact velocity, vi (m/s)

Pro

toty

pe

embe

dmen

t, z e,p

(m

)

0

25

50

75

100

125

150

175

200

Mo

del

em

bed

men

t, z e,m

(m

m)

H0-5

Overall

β = 0.07

β = 0.11

0

5

10

15

20

25

30

0 5 10 15 20 25Impact velocity, vi (m/s)

Pro

toty

pe

embe

dmen

t, z e,p

(m

)

0

25

50

75

100

125

150

Mo

del

em

bed

men

t, z e,m

(m

m)

H0-9

Overall

β = 0.07

β = 0.03

Figure 7.31 Measured and theoretical embedment depths for anchor H0-13

Figure 7.32 Measured and theoretical holding capacities for anchor E0-3

0

5

10

15

20

25

30

0 5 10 15 20 25Impact velocity, vi (m/s)

Pro

toty

pe

embe

dmen

t, z e,p

(m

)

0

25

50

75

100

125

150

Mo

del

em

bed

men

t, z e,m

(m

m)

H0-13

Overallβ = 0.07

β = 0.06

0

5

10

15

20

25

30

35

40

0 0.5 1 1.5 2 2.5 3Prototype capacity, Fv,p (MN)

Pro

toty

pe e

mbe

dmen

t, ze

,p (

m)

0

25

50

75

100

125

150

175

200

0 25 50 75Model capacity, Fv,m (N)

Mod

el e

mbe

dmen

t, ze

,m (

mm

)

Peak 1

Peak 2

α = 0.8

α = 0.6

Figure 7.33 Measured and theoretical holding capacities for anchor E0-4

Figure 7.34 Measured and theoretical holding capacities for anchor E0-5

0

5

10

15

20

25

30

35

40

0 0.5 1 1.5 2 2.5 3Prototype capacity, Fv,p (MN)

Pro

toty

pe e

mbe

dmen

t, ze

,p (

m)

0

25

50

75

100

125

150

175

200

0 25 50 75Model capacity, Fv,m (N)

Mod

el e

mbe

dmen

t, ze

,m (

mm

)

Peak 1

Peak 2

α = 0.8α = 0.5

0

5

10

15

20

25

30

35

40

0 0.5 1 1.5 2 2.5 3Prototype capacity, Fv,p (MN)

Pro

toty

pe e

mbe

dmen

t, ze

,p (

m)

0

25

50

75

100

125

150

175

200

0 25 50 75Model capacity, Fv,m (N)

Mod

el e

mbe

dmen

t, ze

,m (

mm

)Peak 1

Peak 2

α = 0.6

α = 0.5

Figure 7.35 Measured and theoretical holding capacities for anchor E4-2

Figure 7.36 Measured and theoretical holding capacities for anchor E4-3

0

5

10

15

20

25

30

35

40

0 1 2 3 4 5Prototype capacity, Fv,p (MN)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

25

50

75

100

125

150

175

200

0 25 50 75 100 125Model capacity, Fv,m (N)

Mo

del e

mb

edm

ent,

z e,m (

mm

)

Peak 1

Peak 2α = 1

α = 0.7

0

5

10

15

20

25

30

35

40

0 1 2 3 4 5Prototype capacity, Fv,p (MN)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

25

50

75

100

125

150

175

200

0 25 50 75 100 125Model capacity, Fv,m (N)

Mo

del e

mb

edm

ent,

z e,m (

mm

)

Peak 1

Peak 2α = 1

α = 0.4

α = 0.7

Figure 7.37 Measured and theoretical holding capacities for anchor H0-3

Figure 7.38 Measured and theoretical holding capacities for anchor H0-5

0

5

10

15

20

25

30

0 0.5 1 1.5Prototype capacity, Fv,p (MN)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

25

50

75

100

125

150

0 10 20 30Model capacity, Fv,m (N)

Mo

del e

mb

edm

ent,

z e,m (

mm

)

α = 1

α = 0.8

0

5

10

15

20

25

30

0 0.5 1 1.5Prototype capacity, Fv,p (MN)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

25

50

75

100

125

150

0 10 20 30Model capacity, Fv,m (N)

Mo

del e

mb

edm

ent,

z e,m (

mm

)

α = 1

α = 0.8

Figure 7.39 Measured and theoretical holding capacities for anchor H0-9

Figure 7.40 Measured and theoretical holding capacities for anchor H0-13

0

5

10

15

20

25

30

0 0.5 1 1.5Prototype capacity, Fv,p (MN)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

25

50

75

100

125

150

0 10 20 30Model capacity, Fv,m (N)

Mo

del e

mb

edm

ent,

z e,m (

mm

)

α = 1

α = 0.4

0

5

10

15

20

25

30

0 0.5 1 1.5Prototype capacity, Fv,p (MN)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

25

50

75

100

125

150

0 10 20 30Model capacity, Fv,m (N)

Mo

del e

mb

edm

ent,

z e,m (

mm

)

Peak 1

Peak 2

α = 0.7

α = 0.5

0

0.2

0.4

0.6

0.8

1

1.2

0.001 0.01 0.1 1 10 100 1000Non-dimensional time, T=cht/D

2

Deg

ree

of C

onso

lidat

ion

E0-3 (m=8.2 g, h=0 mm)

E0-4 (m=6.2 g, h=200 mm)

E4-2 (m=12.7 g, h=0 mm)

E4-3 (m=9.6 g, h=200 mm)

Torpedo (m=0.6 kg, L/D=12)

Ir = 50

Ir = 500

Figure 7.41 Degree of consolidation from cavity expansion solutions

Figure 7.42 Variation in back-calculated adhesion factor with consolidation time

0

0.5

1

1.5

2

2.5

0.001 0.01 0.1 1 10 100 1000Non-dimensional time, T=cht/D

2

Adh

esio

n fa

ctor

, αα αα

E0-3 (m=8.2 g, h=0 mm)

E0-4 (m=6.2 g, h=200 mm)

E4-2 (m=12.7 g, h=0 mm)

E4-3 (m=9.6 g, h=200 mm)

Best-fit curve

Figure 7.43 Measured and theoretical holding capacities for anchor E0-3 with revised adhesion factors

Figure 7.44 Measured and theoretical impact velocities in calcareous sand tests

0

5

10

15

20

25

30

35

40

0 0.5 1 1.5 2 2.5 3Prototype capacity, Fv,p (MN)

Pro

toty

pe e

mbe

dmen

t, ze

,p (

m)

0

25

50

75

100

125

150

175

200

0 25 50 75Model capacity, Fv,m (N)

Mod

el e

mbe

dmen

t, ze

,m (

mm

)

α = 1.8

α = 0.4

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35Impact velocity, vi (m/s)

Equ

ival

ent

prot

otyp

e dr

op h

eigh

t, h

d,e

q (m

)

Theoretical

Figure 7.45 Back-calculated strain rate parameter – calcareous sand (a) Semi-logarithmic rate law (b) Power rate law

(a)

(b)

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 5 10 15 20 25 30 35

Impact velocity, vi (m/s)

Stra

in r

ate

pa

ram

eter

, λλ λλ

-0.02

0

0.02

0.04

0.06

0.08

0 5 10 15 20 25 30 35

Impact velocity, vi (m/s)

Stra

in r

ate

pa

ram

eter

, ββ ββ

Figure 7.46 Measured and theoretical embedment depth - calcareous sand

Figure 7.47 Embedment depth predictions for impact velocities of up to 80 m/s -calcareous sand

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35Impact velocity, vi (m/s)

Pro

toty

pe

embe

dmen

t, z e,p

(m

)

0

25

50

75

100

125

150

Mo

del

em

bed

men

t, z e,m

(m

m)

β = 0.03

0

10

20

30

40

50

0 10 20 30 40 50 60 70 80Impact velocity, vi (m/s)

Pro

toty

pe

embe

dmen

t, z e,p

(m

)

0

50

100

150

200

250

Mo

del

em

bed

men

t, z e,m

(m

m)

β = 0.03

Figure 7.48 Sensitivity of calcareous sand embedment predictions to bearing capacity factor

Figure 7.49 Sensitivity of calcareous sand embedment predictions to adhesion factor

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35Impact velocity, vi (m/s)

Pro

toty

pe

embe

dmen

t, z e,p

(m

)

0

25

50

75

100

125

150

Mo

del

em

bed

men

t, z e,m

(m

m)

Nq = 50

Nq = 20

Nq = 32

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35Impact velocity, vi (m/s)

Pro

toty

pe

embe

dmen

t, z e,p

(m

)

0

25

50

75

100

125

150

Mo

del

em

bed

men

t, z e,m

(m

m)

βCALC = 0.42

βCALC = 0

βCALC = 0.5

Figure 7.50 Sensitivity of calcareous sand embedment predictions to effective soil unit weight

Figure 7.51 Measured and theoretical holding capacities – calcareous sand

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35Impact velocity, vi (m/s)

Pro

toty

pe

embe

dmen

t, z e,p

(m

)

0

25

50

75

100

125

150

Mo

del

em

bed

men

t, z e,m

(m

m)

γ΄ = 6.8 kN/m3

γ΄ = 4.3 kN/m3

γ΄ = 5.2 kN/m3

0

10

20

30

40

50

0 1 2 3 4 5 6Prototype capacity, Fv,p (MN)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

50

100

150

200

250

0 25 50 75 100 125 150Model capacity, Fv,m (N)

Mo

del e

mb

edm

ent,

z e,m (

mm

)

Nq = 3.3, β = 0.42

Figure 7.52 Sensitivity of calcareous sand holding capacity predictions to padeye bearing resistance

Figure 7.53 Sensitivity of calcareous sand holding capacity predictions to adhesion factor

0

10

20

30

40

50

0 2 4 6 8Prototype capacity, Fv,p (MN)

Pro

toty

pe

embe

dmen

t, z e,p

(m

)

0

50

100

150

200

250

0 50 100 150 200Model capacity, Fv,m (N)

Mo

del e

mb

edm

ent,

z e,m (m

m)

f.Nq = 5.3

f.Nq = 0

f.Nq = 3.3

(f = 1, Nq = 3.3)

0

10

20

30

40

50

0 2 4 6 8Prototype capacity, Fv,p (MN)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

50

100

150

200

250

0 50 100 150 200Model capacity, Fv,m (N)

Mo

del e

mb

edm

ent,

z e,m (m

m)

βCALC = 0.5

βCALC = 0

βCALC = 0.42

Figure 7.54 Sensitivity of calcareous sand holding capacity predictions to effective soil unit weight

Figure 7.55 Variation in holding capacity predictions with impact velocity for effective soil unit weights of 4.3 and 6.8 kN/m3

0

10

20

30

40

50

0 2 4 6 8Prototype capacity, Fv,p (MN)

Pro

toty

pe

emb

edm

ent,

z e,p (

m)

0

50

100

150

200

250

0 50 100 150 200Model capacity, Fv,m (N)

Mo

del e

mb

edm

ent,

z e,m (m

m)

γ΄ = 6.8 kN/m3

γ΄ = 4.3 kN/m3

γ΄ = 5.2 kN/m3

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25 30 35

Impact velocity, vi (m/s)

Pro

toty

pe

cap

aci

ty,

F v,p

(MN

)

0

12.5

25

37.5

50

62.5

75

Mo

del c

apa

city

, F v

,m (N

)

γ΄ = 4.3 kN/m3

γ΄ = 6.8 kN/m3

Figure 7.56 Design chart – 0FA embedment depth, normally consolidated clay (a) su = 1 kPa/m (b) su = 1.5 kPa/m

(a)

(b)

0

20

40

60

80

100

120

0 20 40 60 80Impact velocity, vi (m/s)

Em

bedm

ent

dept

h, ze

(m

)

50 t

75 t

100 t

125 tβ = 0.09

Nc = 12

α = 0.4

L = 15 mD = 1.2 m

0

20

40

60

80

100

120

0 20 40 60 80Impact velocity, vi (m/s)

Em

bedm

ent

dept

h, ze

(m

)

50 t

75 t

100 t

125 t

β = 0.09

Nc = 12

α = 0.4

L = 15 mD = 1.2 m

(a)

(b)

Figure 7.57 Design chart – 0FA holding capacity, normally consolidated clay (a) su = 1 kPa/m (b) su = 1.5 kPa/m

0

1

2

3

4

5

6

7

8

9

0 20 40 60 80Impact velocity, vi (m/s)

Ho

ldin

g c

ap

aci

ty,

F v (

MN

)

50 t

75 t

100 t

125 t

L = 15 mD = 1.2 m

Extractiont = 1 year

ch = 5.5 m2/yr

Nc,tip = 12

Nc,pad = 9f = 0.1

Installationβ = 0.09

Nc = 12α = 0.4

0

1

2

3

4

5

6

7

8

9

0 20 40 60 80Impact velocity, vi (m/s)

Ho

ldin

g c

apa

city

, F v

(M

N)

50 t

75 t

100 t

125 t

L = 15 mD = 1.2 m

Extractiont = 1 year

ch = 5.5 m2/yr

Nc,tip = 12

Nc,pad = 9

f = 0.1

Installationβ = 0.09

Nc = 12

α = 0.4

(a)

(b)

Figure 7.58 Design chart – 0FA holding capacity, normally consolidated clay (a) ch = 3 m2/yr (b) ch = 30 m2/yr

0

1

2

3

4

5

6

0.001 0.01 0.1 1 10 100 1000

Consolidation time, t (years)

Hol

ding

cap

acity

, Fv

(M

N)

30 m/s

20 m/s

10 m/s

0 m/s

L = 15 mD = 1.2 mm = 100 t

su = 1 kPa/m

Nc,tip = 12

Nc,pad = 9

f = 0.1

0

1

2

3

4

5

6

0.001 0.01 0.1 1 10 100

Consolidation time, t (years)

Hol

ding

cap

acity

, Fv

(M

N)

30 m/s

20 m/s

10 m/s

0 m/s

L = 15 mD = 1.2 mm = 100 t

su = 1 kPa/m

Nc,tip = 12

Nc,pad = 9

f = 0.1

Figure 7.59 Design chart – 4FA embedment depth, normally consolidated clay (a) su = 1 kPa/m (b) su = 1.5 kPa/m

(a)

(b)

0

10

20

30

40

50

60

70

0 20 40 60 80Impact velocity, vi (m/s)

Em

bedm

ent

dept

h, ze

(m

)

50 t

75 t

100 t

125 t

β = 0.08

Nc = 12

Ncf = 7.5

α = 0.4

L = 15 mD = 1.2 m

0

10

20

30

40

50

60

70

0 20 40 60 80Impact velocity, vi (m/s)

Em

bedm

ent

dept

h, ze

(m

)

50 t

75 t

100 t

125 t

L = 15 mD = 1.2 m

β = 0.08

Nc = 12

Ncf = 7.5

α = 0.4

(a)

(b)

Figure 7.60 Design chart – 4FA holding capacity, normally consolidated clay (a) su = 1 kPa/m (b) su = 1.5 kPa/m

0

2

4

6

8

10

12

0 20 40 60 80Impact velocity, vi (m/s)

Ho

ldin

g c

apa

city

, F v

(M

N)

50 t

75 t

100 t

125 t

L = 15 mD = 1.2 m

Extractiont = 1 year

ch = 5.5 m2/yr

Nc,tip = 12

Nc,pad = 9

Ncf = 7.5

f = 0.1

Installationβ = 0.12

Nc = 12

Ncf = 7.5

α = 0.4

0

2

4

6

8

10

12

0 20 40 60 80Impact velocity, vi (m/s)

Ho

ldin

g c

apa

city

, F v

(M

N)

50 t

75 t

100 t

125 t

L = 15 mD = 1.2 m

Extractiont = 1 year

ch = 5.5 m2/yr

Nc,tip = 12

Nc,pad = 9

Ncf = 7.5

f = 0.1

Installationβ = 0.12

Nc = 12

Ncf = 7.5

α = 0.4

(a)

(b)

Figure 7.61 Design chart – 4FA holding capacity, normally consolidated clay (a) ch = 3 m2/yr (b) ch = 30 m2/yr

0

1

2

3

4

5

6

7

8

0.001 0.01 0.1 1 10 100 1000

Consolidation time, t (years)

Hol

ding

cap

acity

, Fv

(M

N)

30 m/s

20 m/s

10 m/s

0 m/s

L = 15 mD = 1.2 mm = 100 t

su = 1 kPa/m

Nc,tip = 12

Nc,pad = 9

Ncf = 7.5

f = 0.1

0

1

2

3

4

5

6

7

8

0.001 0.01 0.1 1 10 100

Consolidation time, t (years)

Hol

ding

cap

acity

, Fv

(M

N)

30 m/s

20 m/s

10 m/s

0 m/s

L = 15 mD = 1.2 mm = 100 t

su = 1 kPa/m

Nc,tip = 12

Nc,pad = 9

Ncf = 7.5

f = 0.1

(a)

(b)

Figure 7.62 Design chart – 0FA embedment depth, calcareous sand(a) γ΄ = 4.3 kN/m3 (b) γ΄ = 6.8 kN/m3

0

10

20

30

40

50

60

0 20 40 60 80Impact velocity, vi (m/s)

Em

bedm

ent

dept

h, ze

(m

)

50 t

75 t

100 t

125 tβ = 0.03

Nq = 32

βCALC = 0.42

L = 15 mD = 1.2 m

0

10

20

30

40

50

60

0 20 40 60 80Impact velocity, vi (m/s)

Em

bedm

ent

dept

h, ze

(m

)

50 t

75 t

100 t

125 t

L = 15 mD = 1.2 m

β = 0.03

Nq = 32

βCALC = 0.42

Figure 7.63 Design chart – 0FA holding capacity, calcareous sand (a) γ΄ = 4.3 kN/m3 (b) γ΄ = 6.8 kN/m3

(a)

(b)

0

1

2

3

4

5

6

7

0 20 40 60 80Impact velocity, vi (m/s)

Ho

ldin

g c

ap

aci

ty,

F v (

MN

)

50 t

75 t

100 t

125 t

L = 15 mD = 1.2 m

Extraction

βCALC = 0.42

Nq = 3.3f = 1

Installationβ = 0.03Nq = 32

βCALC = 0.42

0

1

2

3

4

5

6

7

0 20 40 60 80Impact velocity, vi (m/s)

Ho

ldin

g c

apa

city

, F v

(M

N)

50 t

75 t

100 t

125 t

L = 15 mD = 1.2 m

Extraction

βCALC = 0.42

Nq = 3.3

f = 1

Installationβ = 0.03

Nq = 32

βCALC = 0.42

(a)

(b)

Figure 7.64 Design example – holding capacity, normally consolidated clay(a) 0FA (b) 4FA

0

1

2

3

4

5

6

7

8

9

0 20 40 60 80Impact velocity, vi (m/s)

Ho

ldin

g c

apa

city

, F v

(M

N)

50 t

75 t

100 t

125 t

L = 15 mD = 1.2 m

Extractiont = 1 year

ch = 5.5 m2/yr

Nc,tip = 12

Nc,pad = 9

f = 0.1

Installationβ = 0.09

Nc = 12

α = 0.4

0

2

4

6

8

10

12

0 20 40 60 80Impact velocity, vi (m/s)

Ho

ldin

g c

apa

city

, F v

(M

N)

50 t

75 t

100 t

125 t

L = 15 mD = 1.2 m

Extractiont = 1 year

ch = 5.5 m2/yr

Nc,tip = 12

Nc,pad = 9

Ncf = 7.5

f = 0.1

Installationβ = 0.12

Nc = 12

Ncf = 7.5

α = 0.4

(a)

(b)

Figure 7.65 Design example – embedment depth, normally consolidated clay(a) 0FA (b) 4FA

0

20

40

60

80

100

120

0 20 40 60 80Impact velocity, vi (m/s)

Em

bedm

ent

dept

h, ze

(m

)

50 t

75 t

100 t

125 tβ = 0.09

Nc = 12

α = 0.4

L = 15 mD = 1.2 m

0

10

20

30

40

50

60

70

0 20 40 60 80Impact velocity, vi (m/s)

Em

bedm

ent

dept

h, ze

(m

)

50 t

75 t

100 t

125 t

β = 0.08

Nc = 12

Ncf = 7.5

α = 0.4

L = 15 mD = 1.2 m

Figure 7.66 Design example – consolidation time, normally consolidated clay

0

1

2

3

4

5

6

0.001 0.01 0.1 1 10 100 1000

Consolidation time, t (years)

Hol

ding

cap

acity

, Fv

(M

N)

20 m/s

10 m/s

0 m/s

30 m/s

su = 1 kPa/m

Nc,tip = 12

Nc,pad = 9

f = 0.1

L = 15 mD = 1.2 mm = 100 t