Del Vecchio - Light Weight Materials for Deep Water Moorings - 1992

UNIVERSITY OF READING

LIGHT WEIGHT MATERIALS FOR DEEP WATER MOORINGS

A thesis submitted for the degree of Doctor of Philosophy

by

Cesar Josè Moraes Del Vecchio

Department of Engineering

June 1992

This work is dedicated to my wife Thais and my sons Andrê and Filipe.

ABSTRACT

The use of light weight materials for deep water moorings has been

investigated. Based on a survey of the literature, mechanical properties of a

number of candidate tethers were used in a "pilot study", reported elsewhere,

to select one material, polyester, and two low twist rope constructions, parallel

sub-rope and parallel strand, for further investigation.

For the tethers selected, a characterisation of the mechanical, rheological and

environmentally influenced properties was performed, under the relevant

loading conditions pertaining to deep water spread mooring systems.

It was found that low twist polyester fibre ropes have high strength efficiency,

good fatigue and creep properties, and low sensitivity to hydrolysis in sea

water, even in combination with high constant loads. It was also found that the

axial stiffness of these components is strongly dependent on the cyclic load

limits and frequency.

Using the properties measured, an analysis was performed of the behaviour

and cost of spread mooring systems incorporating polyester fibre ropes,

compared with wire rope-chain systems. Two extreme environmental

conditions, one relevant to the Campos Basin (offshore Brazil) and the other to

the West of Shetlands (offshore UK), and three water depths, 500, 1000 and

2000 m, were investigated.

It was concluded that low twist polyester fibre ropes provide practical cost

effective options for spread mooring systems for deep water vessels. Optimum

cost systems based on polyester ropes, having a lower chain component and

a drag embedment anchor, were found to reduce the first order wave

frequency tensions compared with steel wire rope-chain systems. Therefore to

meet the same tension safety factor requirements, substantially lower

minimum breaking loads were necessary. It was also observed that the time

and load dependent stiffness properties of these ropes should be considered

in the design process.

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ACKNOWLEDGEMENTS

I would like to tank my supervisor Dr. C. Richard Chaplin for his restless help

in all aspects of this work, from illuminating discussions to every day

encouragement.

I would also like to acknowledge the support received from my friends Mr. Luiz

Cldudio de M. Meniconi and Miss Isabel M. L. Ridge and the interesting

discussions with Dr. George Jeronimidis.

I gratefully acknowledge the sponsorship of PETROBRAS PetrOleo Brasileiro

S.A.

AKZO Fibres B.V., Brascorda S.A., DSM High Performance Fibers and Marlow

Ropes have kindly supplied the fibres and ropes tested.

ii

CONTENTS

Section page

ABSTRACT (i)

ACKNOWLEDGEMENTS (ii)

1. INTRODUCTION 1

1.1 Background 1

1.2 Scope of the Thesis 6

2. MOORING CONCEPTS 11

2.1 Alternative Concepts for Deep Water Moorings 11

2.2 Environmental Loads 12

2.3 Tension Leg Platforms 13

2.3.1 General Characteristics 13

2.3.2 Light Weight TLP Tethers 14

2.4 Spread Mooring Systems 16

2.4.1 Introduction 16

2.4.2 Offsets 17

2.4.3 Environmental Forces 18

2.4.4 Basic Response 22

2.4.5 Quasi-Static Analysis 22

2.4.6 Dynamic Analysis 22

2.4.7 Codes of Practice 26

3. DESIGN OF CATENARY MOORING SYSTEMS INCORPORATING LWT 29

3.1 State of the Art 29

3.2 The "Pilot Study" 35

4. CHARACTERISTICS OF SYNTHETIC FIBRE ROPES 41

4.1 Introduction 41

4.2 Textile Units 42

4.3 Yarns 43

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4.3.1 General Considerations 43

4.3.2 Yarn Finishes 44

4.3.3 Yarn Properties 45

4.4 Polyester (Polyethylene Terephthalate) Fibres 51

4.5 Fibre Ropes 59

4.5.1 Rope Constructions 59

4.5.2 Terminations 62

4.5.3 Jacketing 66

4.6 Rope Properties 68

4.6.1 Introduction 68

4.6.2 Modelling the Mechanical Behaviour of Fibre Ropes 69

4.6.3 Static Strength 70

4.6.4 Stiffness 71

4.6.5 Weight 75

4.6.6 Cost 75

4.6.7 Creep 75

4.6.8 Tension-Tension Cycling ("Fatigue") 77

4.6.9 Hysteresis 81

4.6.10 Field Experience 83

5. IDENTIFICATION OF PARAMETERS & TESTING PLAN 87

5.1 Identification of Parameters 87

5.2 Material Testing Programme 91

5.2.1 Strength Testing 93

5.2.2 Stiffness Testing 93

5.2.3 Creep and Environmentally Assisted Degradation 94

5.2.4 "Fatigue" 95

6. MATERIAL PROPERTIES: TEST METHODS 96

6.1 Strength Testing 96

6.1.1 Yarn 96

6.1.2 Ropes 98

6.2 Stiffness and Hysteresis 102

6.2.1 Yarn 102

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6.2.2 Ropes 103

6.2.2.1 Stiffness 103

6.2.2.2 Hysteresis 105

6.3 Creep and Environmentally Assisted Degradation 106

6.3.1 Yarn 106

6.3.1.1 Creep 107

6.3.1.2 Environmentally Assisted Degradation 108

6.3.2 Ropes 109

6.4 "Fatigue" 112

7. MATERIAL PROPERTIES: RESULTS 114

7.1 Strength 114

7.1.1 Yarn 114

7.1.2 Ropes 116

7.1.2.1 Superline 116

7.1.2.2 Brascorda Parallel 118


7.2.1 Yarn Stiffness 118

7.2.2 Rope Stiffness 120

7.2.2.1 Superline 120

7.1.2.2 Brascorda Parallel 122

7.2.3 Rope Hysteresis 123


7.3.1 Yarn 124

7.3.1.1 Creep 124


7.3.2 Ropes 126

7.3.2.1 Creep 126


7.4 "Fatigue" 128

8. MATERIAL PROPERTIES: DISCUSSION 130

8.1 Strength 130

8.1.1 Yarn 130

V

8.1.2 ropes 133


8.2.1 Yarn Stiffness 136

8.2.2 rope Stiffness 138

8.2.2.1 Wave Frequency and Low Frequency 138

8.2.2.2 Quasi-Static 142

8.2.3 Hysteresis 143


8.3.1 Yarn 146

8.3.1.1 Creep 146


8.3.2 Ropes 152

8.3.2.1 Creep 152


8.4 "Fatigue" 157

9. CASE STUDIES 161

9.1 Background 161

9.2 Design Cases and Methods 163

9.3 Results 168

9.4 Discussion 170

9.4.1 Dynamic Analyses 171

9.4.2 Quasi-Static Analyses 177

10. CONCLUSIONS AND RECOMMENDATIONS 179

10.1 Conclusions 179

10.2 Further Work 184

11. REFERENCES 186

APPENDIX 1 198

APPENDIX 2 200

APPENDIX 3 202

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1. INTRODUCTION

1.1 - Background

In the search for liquid hydrocarbons men started drilling on the ocean floor as

early as 1897. A wooden pier was then used to support a conventional drilling

rig. As drilling effort moved deeper into the ocean wooden platforms became

islands, disconnected from shore. Since that time the advantages of having a

mobile platform were very much appreciated by prospectors.

To fulfil this need early concepts like the submersible drilling rig evolved.

These were floating structures that could be towed to location with all the

drilling equipment on board and ballasted to rest on the ocean floor. Although

these were used in quite shallow waters, their concept is still relevant to

modern gravity based offshore platforms.

Moving to deeper waters and harsher environments produced the first steel

jacket in 1934. To limit the size of the fixed structure used, the "tender" ship

was born. The latter carries all facilities for drilling, completion, energy

generation and accommodation, and is moored alongside the platform.

Linking the ship to the platform there is a foot bridge known as the "widow

maker.

As exploitation went on and better exploration prospects evolved at increasing

depths the concept of self-elevating (Jack-up) platforms was devised and the

first unit constructed in 1955. Like the submersible, it could be moved afloat to

location. Once there, legs lowered to the sea floor allow the hull to be jacked-

up out of water, thereby tremendously reducing wave and current loading on

the platform.

Almost simultaneously another concept, the drilling-ship, arose bringing with it

a whole collection of technical innovations and allowing for the first time,

drilling from a floating platform.

In 1961 a revolutionary floating unit, the semi-submersible platform, made its

debut. It consisted of a platform connected to flotation elements by columns. A

huge reduction in water plane area was obtained in comparison with ships.

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Semi-submersible platforms are much less sensitive to environmental loading

and direction than ships.

Both drilling-ships and semi-submersible platforms were originally conceived

with catenary type spread mooring systems. These systems consist of a set of

mooring lines spread in radiating directions in order to resist the

environmental forces. Each mooring line typically consists of a length of chain

or wire rope and an anchor.

From 1961, however, some drilling-ship and later some semi-submersibles

had their mooring systems replaced by a dynamic positioning (DP) system

consisting of thrusters and a closed loop-control with linear and angular

feedback.

Parallel developments in deep water drilling technology, such as riser

systems, have maintained the trend in increasing maximum water depth

explored (Salama (1984)).

While in the North Sea fields maximum water depths reach about 500 metres,

drilling activity to the West of Shetlands is taking place in excess of 500 m. On

the other side of the Atlantic, both in the Gulf of Mexico, in North America and

in Campos Basin, in the Continental slope offshore Brazil, wells are being

drilled and large discoveries being made, in maximum water depths ranging

from 2,000 to 3,000 metres.

Apart from development wells being drilled from fixed structures or structures

designed for production, the current usage of drilling platforms as a function of

water depth is as follows:

(i) Jack-ups - frequently used up to 120 m. Current designs aiming to

reach 160 m.

(ii) Semi-submersible platforms and drill-ships with spread mooring

systems - frequently used between 80 and 500 m. Current

designs aiming to reach 1000 m with thruster assistance.

(iii) Drill-ships and semi-submersible platforms with DP systems -

frequently used in water depths in excess of 300 m.

Because of its much longer operational lifetime oil production, having started

2

offshore from the same piers and platforms where drilling was successful, has

concentrated mostly on bottom founded structures.

Both steel tubular jackets and reinforced concrete have been widely used

over the past decades to house: wellheads, work-over rig, production

equipment, pumping and compression facilities, living quarters, and auxiliary

equipment (such as power generation). A number of these platforms have

been also used for development drilling before and during production.

Although reinforced concrete platforms usually provide better oil storage

facilities, they have been greatly outnumbered by steel jackets due to their

higher capital cost and the scarcity of manufacturing yards.

The capital cost of fixed structures escalates in geometric progression with

water depth (Lewis (1982)). This is due to:

(i) the amount of material needed to carry the self weight of the

structure;

(ii) the increase in fabrication cost due to the use of heavier equipment;

(iii) the additional cost associated with loading and transportation

stresses imposed on the structure; and,

(iv) the cost penalty on deep waterinstallation operations.

For this reason, alternative solutions for deep water production have been

constantly developing over the past 20 years. Figure 1.1 shows some of the

concepts proposed for deep water application together with with a fixed steel

jacket.

As early as 1975 a semi-submersible platform was used for production in the

Argyll field in the North sea in 79 m water depth. That was not the only concept

devised to produce marginal fields, In 1977 a ship moored to an articulated

tower was used in the Mediterranean sea in 117 m.

By making use of existing semi-submersible platforms and converted tankers,

these systems made possible the exploitation of fields previously thought

unprofitable. The major difference between these systems and conventional

jackets was the use for the first time of subsea wellheads.

An even more successful concept has been adopted offshore Brazil: that of

3

Anticipated Production Systems. Under pressure to develop new finds as

quickly as possible to reduce oil imports, since 1977, Petrobrds (the Brazilian

state oil company) has been putting its newly found offshore fields in

production in record time by the use of underwater wet wellheads. These are

connected to spread moored semi-submersible platforms by flexible flowlines

and control bundles.

The technology is similar to some marginal field developments, but the

underlying concepts are: quick oil recovery and accurate evaluation of the

reservoir potential, before committing to a much bigger investment.

Such a strategy would have certainly prevented the huge loss made by Placid

in its Green Canyon development in the Gulf of Mexico. A Penrod 72 semi-

submersible was installed there in 1987 in 500 metres water depth. The

platform, which was heavily modified, was withdrawn in early 1990 due to low

production.

Several other concepts have been proposed for production of hydrocarbon

accumulations in water depths in excess of 300 m like the guyed tower and

the tension leg platform (TLP).

The guyed tower consists of a steel structure piled to the sea floor like a

conventional jacket with the addition of mooring lines to help in resisting the

horizontal components of the environmental loads.

The only structure of this kind installed to date is Exxon's Lena Guyed Tower,

operating in 305 metres of water in the Gulf of Mexico since 1983. Its mooring

lines consist of 137 mm and 127 mm steel wire ropes, of a spiral strand

construction, in combination with clump weights and piled anchors.

Tension leg platforms or tethered buoyant platforms are compliant structures

vertically moored to the sea bed by tethers that should be kept under tension

in all environmental conditions. Their shape is similar to that of semi-

submersibles in that a reduction of the water-plane area is obtained by the

use of columns.

Two of these platforms are presently installed: Conoco's Hutton, operating

since 1984, in the North Sea in 148 metres of water with an operational

4

displacement of 64,000 tonnes, and Conoco's Jolliet, since 1989, in the Gulf

of Mexico in 536 metres water depth and with a displacement of only 16,500

tonnes. The former is a full production platform, while the later is only a

wellhead platform.

The tethers used in these platforms are: 795 MPa yield strength (1.25% Cr,

3.5% Ni, 0.30% Mo, and 0.15%V) small bore steel tubes, with a diameter of

260 mm for Hutton (Salama & Tetlow (1983)); and, 450 MPa (65 ksi) yield

strength, 600 mm diameter by 20 mm thickness line pipe for Jolliet.

Saga Petroleum's Snorre TLP is scheduled to be installed in May 1992

offshore Norway in 310 m of water.

Auger TLP from Shell will greatly extend the water depth in which TLPs are

installed when, in 1993, it will be set in 872 metres. In addition to its vertical

tethers, a spread mooring system will also be used, both for facilitating

positioning for drilling but also for sharing the horizontal environmental loads

with the vertical tendons.

In the early 70's spread mooring systems with single component (wire or

chain) lines started to be challenged by systems with lines composed of a

combination of wire rope (top segment) and chain in the lower section

(Childers (1974)). This technology was already in use in barges and ships. At

that time only drilling was envisaged. Although combination systems have had

some use for deep water drilling, dynamically positioned vessels usually work

out to be cheaper. It was not since production was involved that the time on

location was sufficient to justify economically the use of combination systems.

As early as 1978 (Riewald et al. (1986)) it was perceived that spread mooring

systems, having in each line an upper component of light weight rope with

chain in the lower segment, could provide very effective solutions for semi-

submersible platforms and drill-ships in deep waters.

The key to improved performance is the horizontal component of line tension.

By operating at a lower angle to the horizontal, systems incorporating light

weight tethers achieve higher restoring forces than all steel systems for the

same tether tensions. Since changes in tension are also bigger for a given

5

excursion, the whole system becomes more efficient, with windward lines

picking-up load quicker and leeward lines being slackened faster. Figure 1.2

shows a two-dimensional representation of the features discussed.

A taut inclined system, using light weight ropes and piles on a spread mooring

arrangement, was proposed by Baxter (1988). This relied on rope stretch to

accommodate dynamic tensions. In all the other spread moored systems, this

compliance is mostly provided by the catenary geometry.

1.2 - Scope of the Thesis

The purpose of this work is to advance the knowledge of synthetic fibre ropes

in the context of mooring systems for deep water floating vessels. The

behaviour of a moored vessel with lines incorporating light weight tethers is a

problem of a complex nature. The stiffness of the mooring system, which is a

function of the geometry of the mooring lines, and of the mechanical

properties of the tether components, determines the response of the system to

the environmental loads, i.e. its station keeping characteristics. However light

weight tethers (LVVTs) have properties that are highly dependent on the load

levels in the tethers and on the time characteristics of the loading. Therefore

the properties of the tethers, which are relevant to the system analysis, will

themselves be a function of the system response.

At the start of this study very little had been done on the use of LVVTs for

offshore station keeping, therefore both system behaviour and material

properties were unknown. Having perceived the interactive nature of the

problem, it was realised that only an iterative approach was suitable to

address the subject. A "pilot study" (Reading Rope Research & Global

Maritime Ltd. (1988)) was devised to perform the first iteration. The study was

funded jointly by: Brasnor AS, British Petroleum Ltd., British Ropes Ltd. and

Conoco (UK) Limited.

Within the "pilot study" a review of tether properties thought to be relevant to

two classes of mooring systems, direct tension and spread mooring systems,

was performed. These "first approximation" properties were used to analyse

6

the behaviour of the systems incorporating LVVTs, to develop means of

comparing their performance with the performance of all steel mooring

systems, and to select the most attractive LWTs for further investigation.

A second phase was devised to provide a detailed assessment of the relevant

properties of the tethers selected, to refine the comparative analyses

performed in the "pilot study", and to enhance the analysis tools developed in

the "pilot study" to optimise and compare the performance of spread mooring

systems ((Chaplin (1989) and Global Maritime Ltd. (1989,3)).

This dissertation gives an overview of all the work performed in the "pilot

study", but concentrates on the investigation of material properties initiated in

the "pilot study" and carried on according to the proposal for the second phase

(Global Maritime Ltd. (1989,3)).

The study culminates with a feedback of the properties obtained for selected

fibre ropes into design cases, leading to recommendations concerning both

the relevant properties of LWTs to be used in spread mooring systems, and the

design of these systems.

To provide the industry with an early account of the work performed, a

preliminary publication of the outcome of this study was made by Chaplin &

Del Vecchio (1992). Since the major content of this paper is a summary of the

discussion presented in Chapters 8 and 9, no further reference to it will be

made.

Chapter 2 reviews the concepts used for deep water production systems.

Starting with a brief characterisation of the environmental loading, it reviews

the design of vertically moored vessels, i.e. tension leg platforms (TLP), and

the performance and opportunity for light weight tethers to be used with this

concept. The bulk of the chapter is dedicated to the concept that has been

selected as the most promising for the use of light weight tethers (LVVTs), i.e.

spread mooring systems. Design limitations, environmental loading and

response, analysis methods and relevant codes of practice are reviewed.

Chapter 3 narrows down the discussion to systems incorporating LVVTs. First

the very few papers published on the subject are reviewed, with main

7

emphasis on the analysis methods employed and system response observed.

The chapter then concentrates on a "Comparison of the performance of

lightweight and conventional catenary mooring systems" carried out by Global

Maritime Ltd. (1989,1) as part of the "pilot study" above mentioned.

The analysis methods developed and employed are discussed. -Particular

attention is given to the results obtained. Enough evidence was found to

insure the cost effectiveness of combined systems based on fibre ropes made

of Polyethylene Terephthalate (polyester) fibres assembled in stiff, low twist

constructions. The system response and corresponding tether loads for these

line configurations were carefully annotated.

Chapter 4 is a review of the characteristics of synthetic fibre ropes, with the

prospective application in view. Part of this chapter was conducted

simultaneously and interactively with the mooring design work discussed in

chapter 3 as part of the same "pilot study".

A brief overview of fibre ropes is followed by a general review of the properties

of industrial fibres currently available for rope making. Based on

environmental resistance and the strength and stiffness characteristics when

made into ropes, taking due account of the results of the comparison of design

performance, polyethylene terephthalate (polyester, PET) fibres were selected

for further study. A detailed review of the mechanical properties of this fibre is

presented, taking into consideration rheological and environmental effects

deemed relevant.

The bulk of chapter 4 discusses the fibre ropes themselves. First, attention is

given to the rope constructions and terminations, with particular attention to

strength conversion efficiency. Rope properties pertinent to the application are

reviewed. Modelling the mechanical behaviour is briefly touched upon, since

it has had restricted attention by previous workers. The key issues of strength,

stiffness, creep and hydrolysis are given particular attention. Limited testing of

the strength and stiffness characteristics of a small diameter PET fibre rope,

which was performed to focus better the experimental effort to come, is also

described.

Chapter 5 consolidates the outcome of chapters 3 and 4 and outlines the main

8

experimental testing programme. Spread mooring systems consisting of an

upper segment of wire rope or chain, an intermediate section of low twist PET

fibre ropes and a lower segment of steel chain have been selected for further

study. The installation and operational loads in such systems are spelt out. A

justified description of the materials testing programme follows including:

scale of the elements tested, strength, stiffness, creep, environmental assisted •

degradation and "fatigue" tests.

Chapter 6 describes: the materials tested, the apparatus used and the testing

procedures employed. A description is given of the actual yarns and ropes

tested. For each of the characteristics investigated, the equipment used, either

available at the University or purpose built for this study, is described. Of

particular interest are the rope creep testing machines developed. Testing

procedures, generally amalgamating the recommendations of standards with

the particular characteristics of the application envisaged, are detailed.

The results obtained from the materials investigation are given in Chapter 7. A

statistical analysis of the data is conducted, and major trends noted. A detailed

discussion of the data is left for Chapter 8. Yarn and rope strength are

compared with the literature available and the tests performed in the "pilot

study". Recommendations are given on minimum breaking strength to be used

for design purposes. The apparent Young's modulus of the yarns and ropes in

the relevant load cases are compared with the scarce previous work. A simple

structural model is presented to predict rope dynamic stiffness from yarn

figures. Recommendations for design are also given. Hysteresis results are

compared with wire rope results and damping model assumptions discussed.

Total rope creep is compared with the application requirements and creep

rates used to discuss operational procedures. The measured environmentally

assisted degradation is compared with previous work and a suggestion is

made for incorporating the effect into the design procedure. The damage

caused by cycling under severe, but not unrealistic, conditions is discussed in

relation to the single comparable set of published results. Failure mechanisms

and the influence of "fatigue" in design are discussed.

Chapter 9 presents a set of case studies where systems incorporating the fibre

ropes studied are compared with wire rope chain combination moorings and a

9

single case with a system based on an aramid fibre rope. Frequency domain

dynamic and quasi-static analysis techniques are used to verify the influence

of the measured material properties in the comparative performance of these

systems, and on the conclusions drawn in the "pilot study". Different analysis

techniques are briefly compared with findings reported elsewhere and

suggestions are given concerning methods to be used.

Chapter 10 presents conclusions relevant to the technical and economic

feasibility of using spread mooring systems incorporating light weight

materials for deep water station keeping. Recommendations are given on

design methods and further work necessary to implement these systems is

also identified.

Note - The following trade marks are acknowledged (no further

acknowledgement is made in the rest of the dissertation):

Brascorda Parallel - parallel strand rope from Brascorda S.A.;

Dacron - polyester fibre from E. I. du Pont de Nemours & Co.;

Diolen - polyester fibre from AKZO;

Dyneema - high molecular weight polyethylene fibre from DSM;

Hytrel - polyester elastomer from E. I. du Pont de Nemours & Co.;

Jetstran - wire rope type, fibre rope construction from Whitehill

Manufacturing Corporation;

Kevlar - aramid fibre from E. I. du Pont de Nemours & Co.;

Mylar - polyester film from E. I. du Pont de Nemours & Co.;

Parafil - parallel yarn fibre rope construction from Linear Composites

Ltd;

Spectra - high molecular weight polyethylene fibre from Allied-Signal

Corporation;

Superline - parallel sub-rope fibre rope construction from Marlow

Ropes;

Technora - aramid fibre from Teijin;

Vectran - liquid crystal polymer fibre from Hoechst Celanese

Corporation; and,

Zytel - nylon resin from E. I. du Pont de Nemours & Co.

10

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2. MOORING CONCEPTS

2.1. Alternative Concepts for Deep Water Production

According to Lewis (1982), for a Gulf of Mexico location, Tension Leg

Platforms and Guyed Towers become cheaper than fixed jackets after 300 m

of water depth. Bleakley (1984) suggests that in the North Sea the break even

point happens at larger depths, but points out that in 300 m floating production

systems based on spread moored semi-submersibles and weather vaning

tankers connected by a yoke to a monobuoy are half the cost of a fixed jacket

(without considering the extra cost of subsea wellheads). It is clear that, with

the current technology, fixed structures are not likely to be used in waters

deeper than 500 metres.

Guyed Towers have intermediate characteristics between fixed jackets and

floating structures and were not found to provide economically attractive

solutions. When an option is made to have the wellheads at the platform deck

level, the most attractive solution in deep water has been the TLP.

Floating production systems based in weather vaning ships have the

advantage of cargo capacity, but there are no facilities for drilling or workover

operations, they also require more extensive adaptation than semi-

submersible platforms, increasing lead time and cash flow requirements.

Therefore, when an underwater production system is chosen a floating

production system based on a semi-submersible platform is usually preferred.

For these reasons this study will concentrate its attention in TLPs and Semi-

submersible platforms. In this chapter each concept will be discussed

individually in order to identify the main characteristics of each design. The

mooring systems of both concepts, limit horizontal vessel motions to comply

with restrictions pertinent to:

(i) the kind of equipment connecting the platform to the sea floor, and

(ii) interference with other installations.

Before discussing the characteristics of the two systems, we will first briefly

examine the environment which acts on any offshore structure.

11

2.2 Environmental Loads

Offshore structures are subject to loading from winds, waves and currents, all

of which are complex functions of time and stochastic in nature. The following

description is limited to components in the frequency range between

approximately 3x10-3 and 0.3 Hz, thought to be relevant to floating platforms.

Wind speed has variable direction and intensity being a function of height

above the sea level. Wind has a turbulent component consisting of vortices

varying in length from a few centimetres to more than one thousand metres

(Global Maritime Ltd. (1989,1)). At typical wind speeds of 25 m/s vortices of

wave lengths between 750 m and 5000 m have frequencies in the range of

the natural frequencies of horizontal motions for both semi-submersible and

tension leg platforms. These lengths are well correlated over typical length

scales of these types of platforms, making it possible for them to excite

resonant motions (Global Maritime Ltd. (1989,1)). Several spectral forms have

been used to describe wind speed, the most common ones being: Harris,

Davenport, Kaimal and Ochi & Shin (1988).

Waves at a given location can be the summation of several systems which

have been generated in different areas. In this way a full description of the sea

state must include a distribution of wave direction as well as of wave height.

For mooring design purposes the wave spectrum is usually considered uni-

directional and spectral forms most commonly used are: ISSC, Pierson

Moskowitz, Wallops and Jonswap (Noble Denton (1986). Once a formulation

is chosen, a height parameter (for example the significant height) and a period

parameter (for example the peak period) are enough to fully describe the

spectrum.

Current generation is associated with tidal movements and winds. At a given

location current speed may vary with depth, but it is normally considered

steady in time over periods of up to 1 hour.

12

2.3 Tension Leg Platforms

2.3.1 General Characteristics

TLPs are systems compliant to horizontal components of platform motion and

stiff to vertical components. Surge and sway are resisted by the horizontal

component of tether tension that arises as the platform is displaced away from

the direct vertical of the rest position. Natural frequencies for horizontal

motions are lower than first order wave frequencies, in order to avoid the

resonances which limit fixed jackets (Salama (1984)).

Vertical components of platform motion are directly resisted by tether tension.

For current designs, natural periods of heave roll and pitch are kept below

wave periods by a very stiff tether system, to avoid problems with dynamic

amplification, i.e. loads significantly in excess of those corresponding to a

quasi-static process (Salama (1984). In doing so, all vertical motions,

including those due to pay load variation and tides are kept to such low levels

that rigid steel risers can be used and the wellheads installed in the platform.

The API RP 2T (1987) gives guidance on the design of TLPs. Figure 2.1 from

the API code illustrates the tension superpositions leading to maximum and

minimum tendon tensions. Tether pretension at Mean Water Level should be

enough to avoid tether slackening or excessive surge.

Maximum allowable stresses under extreme environmental conditions are

restricted to 60% of the yield or 50% of the ultimate strength for the net axial

stress and to 90% of yield or 70% of ultimate for local bending stresses,

whichever is less. Tubular tethers should also be designed to resist

hydrostatic collapse (Hanna et al. (1987) and API RP 2T (1987)).

Hanna et al. (1987) also point out that, for tubular tethers, the stresses due to

hydrostatic pressure should be combined with the stresses due to direct

loading of the tether to assess the actual safety factor against yield.

Using a tethering system that places the system natural frequency of vertical

motions above the peak frequency of wave spectrum makes the dynamic

amplification always higher than unity but if the difference between natural

13

and forcing frequencies is substantial or damping is high, dynamic

amplification tends to unity.

Usually the platform geometry is optimised (Horton et al. (1972)) by

proportioning of columns and pontoons to obtain heave force cancellation at

the most significant loading conditions. This is a function of wave length, wave

frequency, column and pontoon cross sectional areas and pontoon length.

2.3.2 Light Weight TLP Tethers

Early TLP tether systems were based on small bore steel tubular tethers. The

Hutton TLP for example, after considering: chain, wire rope, parallel strand

wire rope and threaded tubulars as candidates, settled for the heavy weight

steel tubes (Salama (1984)).

The tubes used have a diameter to thickness ratio (D/t) of 2.8 and so cannot

make effective use of buoyancy to reduce apparent weight. This kind of tether

would impose a severe weight penalty on deep water TLPs unless external

buoyancy was added. For this reason tethers based on light weight materials,

like aramid fibre ropes and carbon fibre composites have been considered for

deep water applications (Salama (1984) & (1986), Salama et al. (1985) and

Kim et al. (1988)).

The use of thin walled tubes, with a diameter to thickness ratio of 30, made

neutrally buoyant by closing their ends, has extended the water depth in

which tubular tethers can be used. However with increasing water depth

hydrostatic collapse becomes a problem. According to Hanna (1987) buoyant

steel tubes made of 345 N/mm2 yield strength material could be use for water

depths between 300 and 600 metres.

Lim (1988) assessed platform design and cost for a number of tether types:

small bore steel tubulars, thin walled buoyant steel tubes, steel spiral strands

and carbon fibre, glass fibre and aramid-fibre stranded composites. Water

depths of 300 and 600 metres were investigated. Buoyant steel tubulars were

considered to be the most cost effective tether option.

Global Maritime Ltd. (1989,2) found that 450 N/mm 2 yield strength buoyant

14

tubulars could be used down to 945 metres. By restricting the maximum

number of tethers per platform corner to six and maximum net tether weight to

10% of total platform displacement, water depth limits for steel tubulars of the

same grade of material were found to vary between 1350 and 1850 metres for

large and small displacement platforms respectively (Global Maritime Ltd.

(1989,2)).

Light weight tethers (LWT) considered to date for TLPs have encompassed:

ropes, tubulars and strands. Ropes made of aramid fibres and high molecular

weight polyethylene (HMPE) in stiff parallel lay or wire rope constructions

have been considered. Glass fibre, high modulus aramid and a number of

carbon fibre grades have been discussed for both tubular and stranded

tethers.

The major advantages of most light weight options proposed as compared to

their steel counterpart are: weight reduction, simpler installation, corrosion

resistance and fatigue performance (Walton & Yeung (1986) and Salama

(1984)).

The major disadvantages of LWTs are: low stiffness on an area basis (Walton

& Yeung (1986)), high cost and difficulty in the production of very large

capacity tethers (Lim (1988)). For example, Global Maritime Ltd. (1989,2)

calculated that the number of 250 mm diameter carbon fibre pultruded strands

tethers required per platform corner for a large displacement TLP (156000

tonnes) in 1350 m of water would be 18. This diameter is in the limit of the

current manufacturing technology available and still the number of tethers

needed is unrealistically large in terms of handling limitations.

Although light weight tethers were shown by Salama (1986) to be cost

competitive with steel tubulars similar to those used in Hutton, Lim (1988) and

Global Maritime Ltd. (1989,2) found LWTs substantially more expensive than

thin walled tubulars.

As pointed out by Global Maritime Ltd. (1989,2), LVVTs have to be sized for

stiffness in all but the shallowest water depths. For example a TLP, with high

modulus carbon fibre pultruded strand tethers, must have its tethers sized for

stiffness in waters deeper than 800 metres, this imposes a cost penalty since

15

the material cannot be stressed to its available limit.

For these reasons both Lim (1988) and Global Maritime Ltd. (1989,2)

considered LWTs useful only in very deep waters (possibly •deeper than 1500

metres) where steel tethers could not provide a technically feasible solution. A

typical maximum limit for tether tension as a percentage of platform

displacement would be 10% Global Maritime Ltd. (1989,2).

As discussed by Salama (1986), deep water TLPs need complicated and

expensive tensioning and motion compensation systems in their steel risers in

order to cope with the effects of: pressure, thermal expansion, current and

wave loading and platform movements. McCabe (1991) describes the

tensioners in the Auger platform (in 872 metres) as having a stroke of 1.83 m

(6 ft.). Salama (1984) has proposed the use of composite risers in deep water.

Composite risers can have a different stiffness in the axial and radial

directions.

An option that has not been explored so far, is the use of much lower stiffness

tethers in combination with low axial stiffness composite risers. By having

adequately low axial stiffness risers the riser compensators could be made

redundant. Using low stiffness tethers the natural periods of vertical motions

can be well above the wave periods. Tide amplitudes would be a key

parameter in the feasibility of this sort of tethering system.

For example, in Campos basin, where tides are quite low (100 year

recurrence total tide = 1.45 metres), maximum tether strain due to tidal

variation plus a 6% of water depth offset would not exceed 0.25% (2500 Ile)

for a TLP in 2000 m of water. Trimming the frequency response of the system,

fatigue loading on tethers and risers can be minimised.

2.4 Spread Mooring Systems

2.4.1 Introduction

Spread moorings are generally compliant systems, i. e. have low stiffness, in

relation to all vessel motions. Significant vessel offsets are needed to develop

16

enough restoring forces to balance the mean environmental loads. This

comes to their advantage in "filtering" the dynamic components of the

environmental forces.

The main function of the mooring system is to restrict the vessel offset to

acceptable limits. For the system to operate adequately and safely, however,

other conditions also have to be fulfilled. Typically, limits are imposed on the

maximum load in the individual components of the mooring system as a

percentage of their minimum guaranteed breaking load. If cyclic loads are

significant, components must also have adequate endurance to survive the

foreseen lifetime. Other requirements, such as avoiding non-horizontal loads

on drag-embedment anchors, will be dictated by individual system

characteristics.

The following sections briefly review the most relevant design parameters, the

interaction of the system with the environment, the commonly used design

procedures and the main requirements of the relevant codes of practice.

2.4.2 Offsets

Offset requirements for drilling vessels are a function of drilling riser in use

and detailed guidance concerning a particular installation can be sought from

API RP 20 (1984). General information can be obtained from API RP 2P

(1987), which states that usually an offset between 3% and 6% of the water

depth (WD) is acceptable while drilling and a 3% to 10% of WD offset can be

tolerated with drilling suspended but with the riser still connected to the

seafloor.

Production units will normally have their offset limits dictated by wellhead

risers and pipelines. API RP 17A (1987) and API RP 17B (1988) give

guidance on design of such systems.

General guidance can be obtained from API RP 2FP1 (1991), which states

that typical offset limits are: (i) 8% to 12% of WD for units with rigid risers, (ii)

10% to 15% of WD if flexible risers are used in deep water and (iii) 15% to

25% of WD for similar systems in shallow water.

17

2.4.3 Environmental Forces

Current, wind and waves have mean components that act on floating units to

produce a steady state force for any given sea state and direction. Wind and

waves also have oscillatory components that excite the vessel dynamically.

Current forces are usually considered as steady for the purpose of mooring

analysis. They act on the vessel, on the risers and on the mooring lines.

Current forces should preferably be obtained by model testing (API RP 2P

(1987)). If test results are not available current forces, Fc, can be calculated by

simplified formulas (API RP 2P (1987), API RP 2FP1 (1991)) of the form:

Fc = C . V2

where: Vc = current speed, and

C = function of the drag coefficient and the vertically projected area of

immersed members.

For productions units, forces on the riser system will be a significant proportion

of total current loading.

Although current forces can be considered steady over short periods of time

Larsen & Fylling (1982) point out that current action on mooring lines induces

vortex shedding which excites transverse vibrations. Such motions can

increase the drag coefficient of the lines by a factor between 1.5 and 2.5 and

will be seen to alter the dynamic response of the mooring lines significantly.

The action of wind on floating offshore units for the purpose of mooring

analysis can be taken into account in two different ways: (i) by considering it

steady and averaged over a short period of time (one minute in API RP 2P

(1987) and API RP 2FP1 (1991), and 10 minutes in DnV POSMOOR (1989))

or (ii) by treating it as a steady force based on average speed over a longer

period, say one hour, plus a time varying component based on an empirical

wind spectrum ( API RP 2FP1 (1991)).

The steady force component Fw is either obtained by model testing or

calculated by equations of the form:

18

Fw = Cw . Vw2

where: Vw = design wind speed; and,

Cw = function of the area, shape and height of an installation or

structural component.

A detailed description of the procedures for carrying out such a calculation

can be found on API RP 2FP1 (1991). Not much guidance is given on any of

the rules for calculating the forces due to the spectral component of wind

speed.

For the purpose of analysis, the effect of the waves on a floating unit can be

conveniently split in three components: (i) a steady loading (mean wave drift),

(ii) a loading spectrum associated with the first order peak or peaks of the

wave spectrum (high frequency, wave frequency or first order response) and

(iii) a loading spectrum associated with the second order energy present in

the wave spectrum and the gusty nature of wind, encompassing the natural

frequencies of the moored vessel (low frequency, slow-drift or second order

response).

According to API RP 2P (1987), the steady component can be determined by

model testing or evaluated from graphs contained in this code. API RP 2FP1

(1991) recommends the use of model tests or motion analysis computer

programmes. Simplified formulations, based on a mean wave drift coefficient

and the significant wave height, have also been used.

First order wave forces can be evaluated by: (i) model testing (API RP 2P

(1987), API RP 2FP1 (1991) and DnV POSMOOR (1989), (ii) computer

analysis (API RP 2 FP1 (1991)) or (iii) simplified equations as a function of

significant wave height and a coefficient, which for semi-submersible

platforms is predominantly a function of mean wave period.

Due to the huge masses and relatively high frequencies involved, first order

forces, although associated with relatively small platform displacements, are

very big and cause motions in the six degrees of freedom of the vessel (Morch

& Moan (1985)). It is usual in some design procedures to account directly for

wave frequency vessel motions by means of a response amplitude operator

19

(RAO), translating wave heights into vessel motions, for each degree of

freedom, over the wave frequency range (usually from model tests or

computer simulations of vessel motions). In this way first order wave forces on

the vessel do not need to be spelt out.

According to API RP 2P (1987) and API RP 2FP1 (1991) low frequency wave

forces can be obtained by model testing or by analytical methods. The former

also provides graphs for maximum forces and motions obtained by computer

simulations for a range of vessels. API RP 2FP1 (1991), however, warns that

these graphs should not be used for large floating production units owing to

their different displacement.

2.4.4 Basic Response

Spread mooring systems resist the steady component of environmental forces

(current, wind and waves) by offsetting from the equilibrium position and

generating a net increase on the summation of the horizontal component of

the tension acting on all mooring lines (windward lines will experience a

tension increase and leeward lines will be slackened). Figure 1.2 shows a

two-dimensional representation of this behaviour.

Excluding current effects on the mooring lines, the static behaviour of each

individual mooring line is governed by the catenary equation (see for example

Timoshenko & Young (1965). Figure 2.2 (API RP 2P (1987)) shows a typical

load x offset plot for a single component line and the total system restoring

force as a function of offset. The non linearity of both graphs should be noted.

For the purpose of mooring analysis, dynamic response of floating systems

can be conveniently divided in two time scales: high frequency and low

frequency, in a similar way as was done for the environmental forces.

High frequency response is the system behaviour when excited by forces with

frequencies ranging from about 0.04 to 0.25 Hz. These predominantly wave

induced forces are very large indeed. Net forces involved, for a range of

semi—submersible platforms, range from 50000 kN to 150000 kN and a typical

displacement amplitude would be 5 metres (Global Maritime Ltd. (1989,1)).

Considering the low stiffness of the mooring system, say between 50 kNim

20

and 300 kN/m, no more than 3% of the net force can be absorbed by the

moorings. Therefore first order forces are usually considered as acting on the

unrestrained vessel, i.e. being opposed only by inertia and drag.

As water depth increases, the contribution of the first order motions to total

platform offset becomes less important. Nonetheless these motions can still

excite significant dynamic tensions in the mooring lines. This will be discussed

in more detail below (Section 2.4.5).

Low frequency response is the behaviour in the frequency range

corresponding to the natural modes of the horizontal motions(yaw, sway and

surge) of the moored unit. Second order waves and wind forces provide the

excitation for the low frequency response.

Typical periods for these motions are from 30 to 200 seconds. Since periods

are long, the lines behave essentially in a quasi-static manner, each line

following its statically determined load excursion curve and the system having

the same (quasi-static) restoring force-offset characteristics.

Second order wave forces are too small to excite motions in the vertical plane,

due to the high hydrostatic restoring forces. However they act at frequencies

close to resonance for the horizontal motions. Since the periods are long, the

relative speed between the vessel and the water is small and so is the

damping. Also, because the effective stiffness of the mooring system is usually

small, large motions can result, and a good estimate of damping is a key factor

in the reliability of the analysis of motions due to these forces.

Maximum system offset is a summation of the steady component with a

combination of low frequency and wave frequency motions. As discussed

below, different codes of practice advocate different ways of accounting for the

statistical nature of the dynamic components when doing this sum.

Considering that mooring lines do not provide any effective restriction to first

order wave frequency movements, maximum line tensions can be assessed

by considering the fairlead motions at wave frequency as imposed

displacements in each line from their equilibrium position for the system under

the steady plus the low frequency force. Once again the way in which the

21

statistics of the dynamic tensions are considered varies according to the code

adopted.

The analysis of the response of the system can be based onlyon the static

catenary equations, or can take into account the dynamic effects mainly from

drag and inertia.

2.4.5 Quasi-Static Analysis

The quasi-static method analyses the system as if no dynamic amplification

exists, i.e., by considering that each mooring line responds with a static

catenary behaviour. The procedure consists of:

(i) calculating the equilibrium position of the vessel and of the mooring

lines as well as their tensions due to the action of the steady

components of current, wind and waves;

(ii) taking the low frequency response into consideration by either using

a wind speed averaged over a small period, say one minute, as a

steady component, or by calculating the low frequency vessel

motions based in the stiffness at the displaced position found in (i)

and adding these motions as a static offset; and,

(iii) calculating the tension on individual lines by superimposing the

wave frequency motions translated to the fairlead on the mean plus

low frequency equilibrium position.

2.4.6 Dynamic analysis

The dynamic response of mooring lines to wave frequency excitation departs

from the catenary equation more and more as the water gets deeper. The

main reason for this behaviour lies in the dynamic changes in the axial

stiffness of the mooring components and the dynamic interaction between the

cable and the environment.

The axial stiffness behaviour is strongly influenced by phenomena occurring

at the touch down point and in the grounded region (Larsen & Fylling (1982).

The mooring components themselves show non linear stress-strain

22

characteristics. Chaplin & Potts (1991) discuss results obtained by a series of

other workers and conclude that for six strand wire ropes axial stiffness can

vary up to 15% when loading conditions vary from full-slip between the wires

to no-slip, however they conclude that this variation is unlikely to be of major

concern.

Synthetic mooring lines can have a marked time dependent behaviour due to:

(i) viscoelastic material behaviour; and,

(ii) significant constructional contractions present in all but parallel laid

ropes.

This issue will be discussed in more detail later.

Two major effects are associated with the cable water interaction:

(i) current effect on drag coefficient; and,

(ii) drag associated with platform induced line movements.

Currents are known to excite (vortex induced) vibrations on cables. The

influence of these vibrations on drag force can be dramatic. Larsen & Fylling

(1982) point out that drag coefficients in the range of 1.5 to 2.5 should be used

rather than 1.0 to 1.2 as for rigid cylinders. In recent measurements on a

vertical tow cable Yoerger et al. (1991) found drag coefficients varying

between 2.2 and 2.5.

As the mooring line is dragged in an accelerated movement through the water

it is opposed by a force normal to each cable element that can be calculated

by the dominant drag component of Morrison's equation:

Fd = 1/2 . p . Cd . v2 . D ,

where: Ed = drag force,

p .-.-- density of water,

Cd = drag coefficient,

v = relative velocity normal to the line, and

D = cable diameter.

The dynamic behaviour of spread moored vessels and mooring lines can be

analysed in the frequency domain or in the time domain. In both methods it is

23

usual to assume that the low frequency and the high frequency responses of

the vessel are decoupled.

On a frequency domain analysis, RMS (root mean square) low frequency

motions are usually calculated using a one degree of freedom model, with the

stiffness of the mooring system at the static equilibrium position. Second order

motions are then considered as an additional offset and a new equilibrium

position for the platform calculated based in the quasi-static system response.

First order RMS vessel motions are calculated in the unmoored condition. An

appropriate combination of these motions with the mean offset dictates the

maximum platform offset.

A typical procedure for calculating first order line tensions via a frequency

domain analysis consists of:

(i) obtaining a response amplitude operator (RAO), translating wave

heights into vessel motions for each degree of freedom over the

wave frequency range (usually from model tests or computer

simulations of vessel motions);

(ii) calculating a response spectrum by integrating the RAO with the

wave spectrum; and,

(iii) integrating the response spectrum and taking its square root to

obtain the RMS response.

Significant and maximum values can then be estimated by assuming a

statistical distribution. Assuming a narrow band Gaussian process with

Rayleigh distribution of peaks leads to the following estimates:

(i) significant value = 2. RMS value; and,

(ii) maximum value = (1(2. In(T/Ta))) . RMS value

where:

T = specified duration for the sea state; and,

Ta = the average zero up crossing period.

DnV POSMOOR (1989) recommends a minimum duration T of 2 hours.

Time domain analysis procedures typically consist of a low frequency and a

24

wave frequency calculation. The low frequency module transforms the

second order combined spectrum of environmental forces in a time series

which is then applied iteratively in a quasi-static model to obtain a time series

of line tensions. The wave frequency module uses the first 'order spectrum of

line motions at the fairlead to *generate a motion time history, which is then

applied iteratively to the line. A time series of line tensions is obtained at

selected line points. The tension time series obtained in both modules can

them be combined and the maximum total tension for the simulation period

obtained.

Dynamic mooring line behaviour is nowadays analysed with the use of

computers. Discretization methods commonly used are the lumped mass

(Larsen & Fylling (1982), van den Boom (1985), and Global Maritime Ltd.

(1989,1)), and more complex finite element methods. The former concentrates

all the mass at nodes connected by massless springs. The later uses

interpolation functions to describe the values of the variables at intermediate

positions on each element as a function of nodal values.

The solution for the system of equations obtained can be developed in the

time domain or in the frequency domain. According to Noble Denton (1986)

the time domain solution can take up to 2 orders of magnitude more

computing time than the frequency domain solution. The solution in the

frequency domain uses the principle of superposition, and so all non-

linearities have to be linearised. A time domain solution can take full account

of all non-linearities present since for each time step individual mass,

damping, stiffness and loading terms are recalculated. Because of the huge

computer effort involved it is unusual to use the time domain method except

for the analysis of the extreme loading condition on the most tensioned

mooring line.

Larsen & Fylling (1982) calculated the dynamic response of wire rope

mooring lines and chain moorings in water depths between 70 and 300 m.

The input motion was an harmonic horizontal oscillation. For wire rope lines a

pseudo axial elastic, also called "frozen catenary", behaviour was found to

prevail for most of the relevant range of frequencies and pretensions.

Figure 2.3 shows the results obtained in 150 m of water.

25

A similar trend was found by Global Maritime Ltd. (1989,1) for wire rope, and

wire rope chain combinations in water depths from 500 to 2000 m.

Results reported by GVA (1990) for a floating production platform in Campos

Basin in 1000 m water depth, using combined chain/wire rope/chain mooring

lines, showed a different trend. The results of a frequency domain analysis

accounting for both horizontal and vertical fairlead movements showed that:

(i) Considering the full length of all components as working axially in

the calculation of the axial elastic stiffness, the effective dynamic

line tension turns out to be 52% of the tension calculated assuming

a pseudo axial elastic, i.e. frozen, behaviour.

(ii) If we consider that only 600 m of the lower chain component

contribute to the axial stiffness of the line (which should be the

approximately the amount of chain lifted off the sea floor), the actual

dynamic line tensions become 42% of the tension in a "frozen

catenary".

2.4.7 Codes of Practice

Depending on the country where the vessel is going to operate, it has to

comply with rules set by national authorities, certification societies and or

standards organisations. These codes basically address:

(i) the kind of vessel and application envisaged (scope);

(ii) the mooring materials and equipments;

(iii) the loads;

(iv) the design criteria; and,

(v) the acceptable analysis methods.

Code procedures and requirements referring to the first three items have

already been discussed. Design criteria and acceptable methods are

discussed below for the 3 codes that are likely to be applied in the areas

where deep water activity is currently more intense. These are: DnV

POSMOOR (1989), API RP 2P (1987) and API RP 2FP1 (1991).

26

API RP 2P (1987) is a code for drilling vessels and so sets excursion limits

based on the drilling riser used. Three design conditions are identified:

maximum operating, maximum connected and maximum design.

Maximum offset is defined as the mean offset plus:

(i) significant wave frequency motion plus maximum low frequency

motion; or,

(ii) maximum wave frequency motion plus significant low frequency

motion,

whichever is greater.

Maximum line tension is defined in a similar way as maximum offset. It should

not exceed 50% of the nominal strength of the line for the maximum design

condition and 33% for the operating condition.

The quasi-static analysis procedure, taking into account the low frequency

motions, is recommended.

DnV POSMOOR (1989) applies to mobile offshore units in general and is a

concise standard. It defines 2 operating conditions:

(i) "Condition ri corresponds to situations where a single line failure is

not critical (for example, a drilling vessel with riser disconnected and

far from other structures); and,

(ii) "Condition II" should be applied where any failure in the positioning

system leads to a critical situation for the overall unit (for example, a

production unit using rigid risers where loss of position is critical for

the overall safety of the unit and those aboard).

The rules require that the tension safety factors shown in Table 2.1 be met.

More general restrictions are imposed on offset limits. The rules do not give

guidance on how high frequency and low frequency tensions are combined to

obtain maximum tension. When a quasi-static analysis is performed, low

frequency (XLF) and wave frequency (XFF) offsets are combined as:

Xior = "V XFF2 + XLF2

The quasi-static analysis method is accepted for vessels in waters shallower

than 450 metres. When a dynamic analysis is used, a time domain procedure

27

is preferred.

API RP 2FP1 (1991) is a draft code which applies specifically for floating

production units.

Maximum offset is defined in the same way as API RP 2P (1987) and the user

is referred to specific riser rules for guidance on admissible offsets values.

Maximum line tensions are obtained from the mean, low frequency and high

frequency tensions by a combination similar to that described in API RP 2P

(1987).

Maximum allowable tensions for the intact system and for one line broken are

respectively 60% and 75% of the nominal strength of the line.

In addition to the offset and maximum tension requirements the mooring lines

have to be assessed for endurance. A safety factor of three on life is

recommended for the Miners summation. For both the extreme response and

the fatigue analysis a dynamic analysis is recommended. Time domain or

frequency domain procedures are accepted.

With regard to the use of synthetic fibre ropes API 2FP1 (1991) states:

"Because of a lack of long term service experience and concern regarding

handling problems, synthetic materials are generally not used in permanent

mooring systems, although research is ongoing to develop synthetic materials

that may prove acceptable". DnV POSMOOR (1989) only mentions that: "NV -

certification will be required for synthetic fibre rope and fibre rope end

attachments". Apart from these brief mentions the codes do not provide for the

use of fibre ropes.

28

Operationcondition.

Quas'staticana ysis

Dynamicanalysis

POSMOOR POSMOOR V I) POSMOOR POSMOOR V I)

Intactsystem 1,80 2,00 1,50 1,65

TransientI motion 1.10 1.10 1,00 1,00

Temporary mooringafter singleline failure 1,25 1,40 1,10 1,25

Intactsystem 2,70 3,00 2,30 2,50

TransientH motion 1,40 1.40 1,20 1,20

Temporary mooringafter singleline failure 1,80 2,00 1,50 1,65

1) Applies for anchor lines which are located within a critical sector, normally in a 180 degrees sector facing away from the installation, seefigures 1 and 2.

— For d5L, the anchor lines outside the critical sector may be designed according to operation condition I. POSMOOR V.— For d>L, the anchor lines outside the critical sector may be designed according to operation condition I. POSMOOR.

Upon special consideration a narrower sector may be accepted.

Table 2.1 - Permissible tension safety factors according to DnV POSMOOR

(1989).

FOUNDATION MISPOSITIONING MINIMUM TENDON TENSIONDOWN WAVE LEG

WAVE

WINDOFFSET

TIDE/SURGEPRETENSION

WIND

FOUNDATIONMISPOSMON

WAVE

OFFSET—

PRETENSION

TIDE/SURGE

MAXIMUM TENDON TENSIONUP WAVE LEG

Figure 2.1 - Tension components leading to maximum and minimum tendon

tensions ( from API RP 2T (1987) ).

restoring force

2000 -

2_v

020 1000 -U.

......ow..

ago.......

mow.

maw. n••••

.--...-....-

..... most loaded line tension

I0 10 20 30

Offset (m)

Figure 2.2 - Restoring force and tension in the most loaded line based in the

static catenary equation. Adapted from API RP 2P (1987).

1.2 -

ao•._(I)

04-,

0•...Ealc>.

G)cr,• ....

caE

oz

all

01

_ ____.4.

C.

V.

V.

1.0

0.8 -

-

0.6

0.4-

0.2 --

/

_

Static tension level

70 tonnes

---140 tonnes

- --- 220 tonnes

'0.0 1 . I

0.0 1.0 2.0

Frequency (rad/s)

Figure 2.3 - Dynamic tensions in the upper end of a steel wire rope mooring

line in 150 m water depth, presented as a fraction of the tension

obtained assuming a slow (quasi-static) axial elastic deformation

of the line without change in catenary shape (from Larsen &

Fylling (1982)).

3. DESIGN OF CATENARY MOORINGS INCORPORATING LWT

3.1 State of the Art

As early as the mid seventies the potential advantages of using synthetic fibre

ropes in deep water moorings started to attract research attention. Already in

1976, Niedzwecki & Casarella (1976), working on design curves for combined

wire rope and chain mooring lines, reported the intention of producing design

curves for synthetic rope-chain combination moorings.

Niedzwecki (1978), used a quasi-static model to compare the behaviour of:

chain, wire rope, chain-wire rope and chain-synthetic rope moorings in 100

metres and 1000 metres water depth. No consideration was given to dynamic

loads. The model took into account the non-linear nature of the axial stiffness

of fibre ropes by considering a semi-empirical constitutive equation of the

form:

Ta / b = cosh (c.e) - 1,

where: Ta = applied tension;

b = rope breaking strength;

e = percentage elastic elongation; and,

c = an characteristic experimental constant.

In 100 metres water depth no advantage was found in using synthetic ropes.

In 1000 metres, systems having the same minimum breaking load (MBL)

were designed to reach the same tension (1/3 of the MBL) at an offset of 5%.

A polyester rope with a characteristic constant (c) equal to 18, in a length

equal to the water depth, was used in combination with chain. The rope

construction was not specified, but from the graphs presented in the paper it is

possible to infer that it was a low twist construction, possibly a parallel strand

rope. The necessary pretension was 20% lower and the restoring force was

1.5 times bigger than on the chain only mooring. When compared with a wire

rope-chain combination mooring, the pretension was 4% lower and the

restoring force was 14% bigger at the 5% excursion.

Niedzwecki (1978) concluded that, as depth increases, nonmetallic ropes

become viable alternatives for all steel moorings provided their elongation is

29

not excessive.

Riewald (1979) reported confidential work done by Nachlinger in 1978

comparing the performance of a combination Kevlar (aramid) fibre rope-chain

with a steel wire rope-chain system. The analysis has shown that the optimum

Kevlar-chain system provided a bigger restoring force and need much lower

pretensions than the optimum wire rope-chain system.

E. I. du Pont de Nemours & Co. (undated) discusses Nachlinger's work in

more detail. They state that the mooring analysis programme used performed

a "static analysis with the addition of dynamic terms", taking into account:

surge, sway and yaw. The following materials were used: 3" diameter ORQ

chain, 3-1/2" diameter steel wire rope and 3-1/2" diameter Kevlar rope. The

procedures used and results disclosed are discussed in the paragraphs

below.

First, systems were compared using a two-point mooring model. Water depth

(224, 488, 732 and 1067 m) and chain length (426, 610 and 793 m) were

considered independent variables. Rope length was calculated so that anchor

uplift would start at the maximum anchor holding power. Pretension was

selected to have a maximum tension of 40% of BL at an offset of 6% of the

water depth.

Under these conditions, Kevlar rope-chain systems produced a 17% to 75%

bigger restoring force than wire rope-chain. Line pretension was 11% to 87%

lower than the wire rope-chain values. On the other hand Kevlar lines had to

be 3% to 45% longer than steel wire ropes for the same length of chain.

Since the performance achieved by the synthetic system was so much better

than the wire rope combination system, a second comparison was done

adjusting the Kevlar rope length to obtain the same performance, i.e. same

restoring force at an excursion of 6% of the water depth. The result was that

Kevlar lines could be made 14% to 40% shorter than steel wire ropes, the

bigger difference corresponding to the deepest condition.

Finally, a drillship using an eight point mooring in 1070 metres water depth

was also briefly discussed. The report states that the Kevlar rope-chain system

30

was able to maintain the vessel in location under the worst environmental

conditions, while the steel wire rope-chain system could only obtain the same

result by using very high pretensions and slackening the leeward lines.

The first known design incorporating fibre ropes in an actual application was

intended to moor a production barge in 700 metres water depth offshore

Spain (Pollack & Hwang (1982)). Figure 3.1 shows the system with the turret

and its swivel as an integral part of the production barge.

Each of the six mooring legs had an aramid fibre rope upper component

700 metres long with 800 m of chain leading to an anchor. The aramid rope

was selected for:

(i) its light weight, so that it would be taken to the surface by a small

buoy in the event of an emergency disconnection;

(ii) the strict offset design requirements; and,

(iii) the lower pretension needed and lower static and dynamic peak

loads in comparison with a wire rope-chain combination system.

Model testing, at a 160:1 scale, was performed for static wind and current

forces in combination with regular waves and a wave spectrum. The tether

components were geometrically similar to the prototype but their stiffness in

the model was too high.

Low frequency damping in the model was found to be high enough to damp

out the free system response in 2 cycles. No whipping or formation of ripples

was observed in the chain.

The coupled barge and the mooring system were simultaneously analysed by

means of a time domain three-dimensional computer model. Mooring legs

were modelled by 2 node straight truss elements with zero bending and

compressive stiffness, with the mass concentrated in the nodes.

The programme could not handle a wave spectrum, so analysis considered

steady current and wind plus regular waves. The length of time used in the

simulation was said to be enough for "all the results to converge to a stable

cyclical solution".

Static and dynamic tensions were found to be substantially smaller than on a

31

wire rope-chain combination system. It was also observed that mooring leg

tensions increased nonlinearly with the stiffness of the aramid rope as shown

in Figure 3.2. In this way, dynamic loads could be reduced by increasing the

flexibility of the lightweight rope.

Although the technical concept has been developed to a very advanced state,

the oil reserves were found to be small and the field was never brought to

production.

A completely different use for fibre ropes was made in the temporary mooring

of the Hutton TLP at the deck mating site (Smith et al. (1985)). The design

environmental conditions were quite severe and the water depth was only 55

metres. The restriction on maximum load and loading angle in the padeyes of

the TLP precluded the use of a simple catenary tether in steel. Instead, an

intermediate barge had to be installed on each of the 8 mooring lines, having:

a chain on the side leading to the anchor and a nylon rope connecting it to the

platform via chaffing chains.

Maximum allowable line tensions were taken as 70% and 30% of the

breaking load respectively for the chain and the fibre rope in the intact

condition and 95% and 40% respectively for chain and rope with a single line

failed.

Static catenary equations were used throughout the calculations. First, the

equilibrium position due to mean loads was found. Then, low frequency

motions and forces due to waves were calculated based on the stiffness at the

position under mean load. First order platform movements were considered to

be decoupled from the steady and second order components. Forces due to

these motions were added to the previously calculated tensions to get the

maximum tension between the barges and the TLP. The maximum tension on

the section between the barge and the anchor, on the windward side, was

then obtained by adding the environmental load on that barge.

The use of a low stiffness fibre rope segment between each barge and the

TLP, efficiently kept the maximum tension within acceptable limits. The system

performed satisfactorily during almost two months that the TLP remained in

the mating site.

32

Taylor et al. (1987) reported on the design and installation of a triangular

shape semi-submersible platform, in 887 m water depth, offshore California,

USA. The platform displaced 96.4 tonnef and was moored by three lines.

Each leg had: a 152 m long upper component of 1" chain, a 1.5" diameter

1067 m long Superline polyester rope (see Section 4.5.1 for a description of

this construction), and a lower component of 122 m of 2" chain, leading to an

anchor. The platform had no line tensioning equipment.

The design process was fairly sophisticated. First, platform response (motions

and tensions) to all environmental load cases was computed based on the

static catenary equations for multi-component mooring legs. At this stage,

hydrodynamic and inertial effects on the mooring lines were not considered.

The dynamic response of the lines to the given motions imposed by the

platform was then computed at the average equilibrium position. This was

done using SEADYN, a finite element programme for time domain simulation

of cable response.

Finally the coupled response of the platform and the mooring system was

analysed in the time domain. In this analysis, the mooring lines were modelled

by non-linear truss elements. Chain lift-off and ground interaction were

included. According to Taylor et al. (1987) the full set of loading , material and

geometrical non-linearities were taken into account.

The maximum line tension under survival condition was 84.5 kN (19000 lbf)

and the maximum tension range obtained in the simulation was 45.5 kN.

These values correspond to 24% and 13% respectively of the minimum

breaking load (MBL) of the rope, as quoted by the manufacturer (H & T Marlow

(1985).

The system was reported to have been installed without problems. No

information has been found on the subsequent operational performance of

this system.

An appraisal of the use of parallel laid polyester and aramid ropes in

moorings for semi-submersible platforms was reported by Baxter (1988). A

platform displacing 60000 tonnes was evaluated in: 300, 500 and 900 m

33

water depth, subjected to a 100 year recurrence North sea environment. A 16

line symmetric mooring pattern was employed, having an upper component of

fibre rope and a chain leading to a drag embedment anchor. Some systems

were designed with clump weights between the chain and the rope,

increasing system stiffness and reducing the length of chain required.

The information available concerning the analysis procedures used is limited.

It was possible to find out that a quasi-static procedure was used and it seems

that only the steady component of: wind, waves and current was taken into

account. There was no optimisation of the mooring system. Results obtained

are summarised in Table 3.1.

The influence of the addition of clump weights on offset is striking, with

maximum excursion being reduced from between 3% and 4.3% to between

0.3% and 1.1%, depending on whether an aramid or a polyester rope was

used. Since no dynamic effects have been considered, the addition of clump

weights did not cause any increase in maximum tension. For systems using

aramid ropes a reduction in maximum tension was reported. This was

probably associated with a reduction in pretension, although there is no

mention of such a change.

The difference between the results obtained using aramid and polyester ropes

is not great. While systems with aramid ropes showed somewhat lower offsets,

systems with polyester ropes generally had lower maximum tensions (except

for the systems with clump weights).

Baxter (1988) also presents some results for a taut inclined system based on

the the synthetic ropes mentioned above, using piles instead of anchors, in

450 m of water depth. In this case, system compliance is mainly due to the

axial stiffness of the rope as opposed to the geometric compliance afforded by

catenary systems. Results for two chain systems one in the same depth and

another in 79 m are presented for comparison purposes. Rope breaking load

and length are not mentioned.

Table 3.2, after Baxter (1988), shows the results obtained. The systems with

fibre ropes in 450 m depth showed very small static offsets, comparable to that

obtained for the chain mooring in 79 m. The aramid rope system had an

34

excursion of 0.5% of the water depth and a reasonable maximum tension, but

a natural period of 23.5 seconds, prone to be excited by long waves. This

characteristic would discourage its implementation. The system based on the

polyester rope, with a natural period of 44 s, was found to be comfortably

removed from the first order wave spectrum. It should be noted that, as far as

excursions are concerned, the behaviour of the taut systems was quite similar

to the systems with clump weights.

3.2 - The "Pilot Study"

Within the framework of a joint industry study jointly performed by the

University of Reading and Global Maritime Ltd. in 1989, a fresh look was taken

into the potential of light weight materials for deep water moorings. The study

considered spread (catenary) and direct tension (TLP) mooring systems. The

results obtained for TLPs have already been discussed in Chapter 2 and will

not be discussed further.

At the outset of this study very little was known concerning both the dynamic

behaviour of light weight tethers and the response of spread mooring systems

incorporating LWTs with different dynamic characteristics. As discussed in

Chapter 2 the quasi-static compliance of an all steel mooring line is basically

derived from its catenary shape, with a small contribution of tether axial

compliance. At increasing frequencies the mooring lines show dynamic

tensions in excess of what would be predicted by the static catenary

equations, partly due to their accelerated movement in the water, and

therefore, a function of their: axial stiffness, linear weight, area and shape. The

incorporation of a component with markedly different stiffness and weight

characteristics, and which also shows rheological behaviour over the

timescales involved, was expected to produce a substantial change in the

behaviour of the complete system. This in turn would be expected to result in a

different loading pattern of the mooring lines.

From the early start it was concluded that light weight tethers should not be

compared with steel wire rope or chain as a substitute material, solely on the

basis of their mechanical properties and cost. Technically feasible solutions

35

could only be compared on the basis of complete mooring systems designed

to meet similar tension and offset requirements.

Two main areas of activity were clearly present:

(i) the development of analysis methods and procedures to enable a

meaningful comparison between all steel mooring systems and

systems incorporating LWTs; and,

(ii) to obtain the relevant material characteristics to be used in the

analysis.

Given the restricted amount of previous work in both fields, and the highly

interactive nature of the two areas of activity, in the systems studied, it was

necessary to conduct both activities simultaneously and iteratively.

The review of the properties of available light weight tethers (Del Vecchio

(1989)) performed in the "pilot study" included synthetic fibre ropes and

composite strands. The relevant information obtained in this review has been

incorporated in Chapter 4. Values for: weight, strength, dynamic stiffness and

cost, obtained in the "pilot study" are shown in Table 3.3 and formed the basis

for the analytical studies carried out by Global Maritime Ltd. (1989,1) which

are discussed below.

The study based its comparison in two types of semi-submersible platforms:

(i) a drilling unit; and,

(ii) a floating production system.

Three combinations of water depth and location were selected:

(i) 500 m in the West of Shetlands;

(ii) 1000 m in Campos Basin; and,

(iii) 2000 m in the Gulf of Mexico.

Eight leg, symmetric pattern, two component mooring systems were selected,

with an upper length of fibre or wire rope connected to a chain, leading to a

drag embedment anchor. A steel wire rope (in 500 m) and a steel wire rope-

chain system (in 1000 and 2000 m) were used as a reference for comparison.

In order to obtain a meaningful comparison between different tether options,

optimum systems had to be found for each of them. In this study, systems were

36

optimised to achieve the same tension safety factor at minimum cost.

The analysis procedure made the following simplifying assumptions:

(i) the systems were operated actively (the leeward lines slackened

and the tension on the windward lines equalised);

(ii) the low frequency response was simulated by using one minute

wind speed in the static analyses; and,

(iii) the first order effect on the mooring lines was represented by an

harmonic horizontal movement of the line top corresponding to the

horizontal fairlead motion of the unmoored platform.

A substantial part of the work consisted in investigating the dynamic tensions

arising on individual legs due to the harmonic horizontal movement of the

uppermost point of the line (corresponding to the fairlead), in the plane of the

line. A computer programme (TRANSDYN), based on a proven lumped mass

discretization of the line and a frequency domain solution, was used for these

analyses. Chain, wire rope, wire rope-chain and fibre rope-chain combination

lines were investigated.

The trend found was similar to what has been reported by Larsen & Fylling

(1982), i.e., dynamic stiffness similar to the total axial elastic stiffness, at

periods between 10 and 15 seconds, in all but the chain only lines. Dynamic

stiffness was defined as the actual dynamic tension divided by the amplitude

of motion. Total axial elastic stiffness was calculated as the equivalent spring

constant (EA/I) of all line components associated in series as springs without

mass.

Based in these results a further assumption was made: that the dynamic

tensions on the lines can be calculated by multiplying the top oscillation by the

equivalent spring constant.

This assumption was used to develop an optimisation programme

(LWDESGN) to find the cheapest configuration (diameter and length) of two

component mooring lines for a number of upper components with grounding

chain, satisfying anchor uplift and tension safety factor criteria. Figure 3.3, after

Global Maritime Ltd. (1989,1), shows the flowchart of LWDESGN. For discrete

variations of the length of the upper component, minimum cost systems are

37

calculated and printed.

The programme included a buoyancy cost penalty, associated with the vertical

component of tether tension, This was estimated by assuming that each 10

tonnes of additional buoyancy requires 2 tonnes of structural steel work at a

fabricated cost of US$6,400/tonne (Lim (1988)). It should be noted from the

flowchart that the platform offset was not a design parameter.

Preliminary runs of LWDESGN with systems incorporating polyester fibre

ropes showed a weak but clear cost minimum as a function of the length of the

upper component. For example, results in 1000 m water depth, for a mean

horizontal force and an imposed surge compatible with the Campos Basin

location, showed a cost minimum for a 2000 m long PET rope. However, for

lengths of the PET rope between 1500 and 3000 m maximum cost penalty

was 5.5%.

To test the accuracy of the designs obtained with the above programme the

optimum configurations derived by LWDESGN for six load cases were

analysed by TRANSDYN.

In the West of Shetlands location in 500 m water depth, a wire rope only

system (3750 m of 110 mm 6 strand rope) and a fibre rope-chain combination

(2000 m of 140 mm polyester Superline and 500 m of 90 mm ORQ chain)

were analysed. Tension safety factors obtained by TRANSDYN were 2.08 and

2.22 respectively. A quasi-static analysis for the same configurations showed

safety factors of 3.09 and 2.10 respectively.

In 1000 m water depth, for the Campos Basin environmental conditions, a wire

rope-chain (127 mm diameter 6 strand rope and 129 mm ORQ chain) and a

fibre rope-chain combination (174 mm polyester Superline and 110 mm ORQ

chain) were verified by TRANSDYN. Tension safety factors obtained were

2.17 and 2.03 respectively. Safety factors obtained from a quasi-static analysis

were 2.59 and 2.05 respectively.

For the Gulf of Mexico environment, a verification was performed in 2000 m

water depth. The wire rope-chain combination was sized by LWDESGN as

5000 m of 120 mm diameter 6 strand rope and 550 m of 120 mm ORQ chain.

38

The fibre rope-chain system selected consisted of 5000 m of 154 mm diameter

polyester Superline rope and 850 m of 97 mm ORQ chain. Safety factors

calculated by TRANSDYN were 2.5 and 2.05, and by a quasi-static analysis

were 2.59 and 2.05 respectively.

In general the results obtained demonstrated the adequacy of the simplified

optimisation procedure (LWDESGN). Of the six cases analysed, only in

2000 m for the wire rope-chain mooring is the safety factor substantially

greater (25%) than 2.0 and also 22% greater than obtained by the fibre rope

system. In this case the approximate procedure is penalising the wire rope by

being over conservative.

The maximum dynamic tension range observed for the systems incorporating

PET ropes was found to be 19.5% of the MBL. As expected this happened in

500 m in the West of Shetlands, since that is the shallower location and also

the one that causes the highest platform surge.

The results of the quasi-static analysis showed the importance of taking into

account first order line dynamics, especially for the wire rope system. As water

gets deeper it was found that there is a tendency for the wave frequency

tensions to represent a smaller proportion of the total tension. In this way the

safety factor derived from the quasi-static analysis gets closer to that obtained

from the dynamic analysis.

The generally good agreement between the quasi-static and dynamic results

for the system containing the fibre rope is probably due to a good match

between the axial stiffness of this fibre rope and the geometric catenary

stiffness. However, no explanation could be found for the bigger safety factor

obtained for the dynamic analysis in comparison with the quasi-static analysis

in the West of Shetlands case study.

Having proved that the performance of the optimisation programme was

satisfactory, the software was used to:

(i) compare the costs of optimised solutions incorporating LWTs with

optimum all steel systems; and,

(ii) sort the candidate light weight materials on a cost basis.

39

Table 3.4 shows results obtained with LWDESGN for different tether options

sorted by cost (Global Maritime Ltd. (1989,1)). Results are pertinent to a

drilling platform in the Gulf of Mexico in 1000 m water depth (horizontal line

load of 2000 kN and surge of 7.5 m).

Ropes based on polyester fibres showed a clear advantage over the other

options. The system based on the Parafil rope came out 22% cheaper than

the standard wire rope-chain combination, closely followed by the Superline

and the parallel laid rope at 16% and 12% respectively. Although changing

the way in which the buoyancy penalty was calculated could alter their

attractiveness in relation to the optimum steel system, it should not influence

their relative order.

The Minimum breaking load required by all the systems based on PET ropes

was about 75% of the MBL of the optimum six strand steel wire rope-chain

mooring.

The system based on standard modulus aramid wire rope come out 43%

more expensive than the reference steel system, with an MBL that was 90% of

that of the optimum all steel system.

The high modulus aramid pultruded strand-chain system was too stiff for the

application, as can be seen from its MBL which is 8% higher than the MBL of

the reference system. The cost of this option was 2.6 times the cost of the

reference system. Although a system using a glass fibre pultrusion would

certainly perform better than the high modulus aramid one, it is apparent from

its cost and stiffness characteristics that it would not be able to challenge the

reference steel system. On these grounds composite pultrusions will not be

further addressed in this study.

40

water depth

m

rope material

-

rope BL

tonnes

rope length

m

chain BL

tonnes

chain length

m

clump weight

tonnes

static offset

m

max tension

kN

300 polyester 800 600 1245 700 - 11.7 3804

500 polyester 800 850 1245 800 -

,

21.7 3240

500 aramid 800 850 1245 800 - 17.9 3609

500 polyester 800 850 1245 300 150 3.9 3345

500 aramid 800 750 1245 300 150 1.7 2884

900 polyester 800 1500 1245 900 - 30.9 3150

900 aramid 800 1500 1245 900 - 26 3348

900 polyester 800 1400 1245 300 130 9.7 3128

900 aramid 800 1300 1245 300 130 7.3 2818

Table 3.1 - Configuration and performance characteristics of combined light

weight rope and chain moorings (from Baxter (1988)).

water depthm

rope material_

static offsetm

max. tensionkN

79 ORO chain 3.6 2030

450 ORO chain 57 2080

450 polyester Parafil 5.9 1875

450 aramid Parafil 2.4 2020

Table 3.2 - Tensions and offsets for taut inclined light weight mooring systems

compared with all chain moorings (from Baxter (1988)).

Material-

StrengthGPa

StiffnessGPa

Linear Mass Drykg/mmA2 . 100m

CostUS$/kg

polyester double braid 0.22 2.8 0.097 8.4polyester Superline 0.30 5.0 0.096 7.5

polyester parallel strand 0.47 9.0 0.096 10.5polyester Parafil 0.38 9.7 0.096 6.5

Kevlar29 wire rope const. 0.66 26.5 0.096 27.0Kevlar29 Parafil 1.10 48.3 0.101 48.8

Kevlar49 wire rope const. 0.66 41.6 0.096 27.0Kevlar49 Parafil 1.10 76.7 0.101 58.6

Spectra900 double braid 0.47 18.0 0.067 37.4Kevlar49 pultruded strand 0.86 57.7 0.124 50.0

6x36 wire rope 0.84 67.7 0.532 2.6spiral strand wire rope 1.02 108.9 0.633 3.4

Table 3.3 - Selected light weight and steel tether properties used in the "pilot

study" (adapted from Del Vecchio (1989)).

Upper Leg Material-

Lengthm

Total Cost/LegUS$1000

Relative Cost-

Breaking LoadkN

'Relative BL

polyester Parafil 3500 458 0.78 4689 0.76polyester Superline 3000 496 0.84 4593 0.75

polyester parallel strand 3000 519 0.88 4669 0.766x36 wire rope 5000 588 1.00 6153 1.00

polyester double braid 2000 673 1.14 4813 0.78Kevlar29 Parafil 3000 684 1.16 5313 0.86Kevlar49 Parafil 3500 782 1.33 5760 0.94

spiral strand wire rope 5000 829 1.41 6896 1.12Kevlar29 wire rope const. 2500 842 1.43 5546 0.90Kevlar49 wire rope const. 3000 967 1.64 5936 0.96Spectra900 double braid 2000 1018 1.73 5968 0.97

Kevlar49 pultruded strand 2500 1543 2.62 6635 1.08

Table 3.4 - Results calculated with the the mooring line optimisation

programme for a typical drilling semi-submersible platform in

1000 m in the Gulf of Mexico ( from Global Maritime Ltd. (1989,1)).

4” ALGA TOWER

600'

PRODUCTIONBARGE

164R

FLEXIBLEPRODUCT &CONTROLLINES

ALGA//TOWER

MAXIMUMEXCURSION OFMOORINGSYSTEM

PLAN VIEW2300'

ARAMID FIBER ROPEPORTION OF MOORING LEG2300 ft LONG

3 . CHAIN PORTION OFMOORING LEG 2625 ft LONG

ANCHOR POINT

Figure 3.1 - Elevation and layout of turret moored production barge (from

Pollack & Hwang (1982)).

3000 -

1000 -

00 500 1000 1500 2000

60°

DERRICK11(=,...„......„,,PRODUCTION BARGE MOORING LEGS

(6 TOTAL)

WELLHEADS

-4*

2000 -

Modulus x Area, AE (kN)

Figure 3.2 - Peak tension in aramid fibre rope as a function of EA (from

Pollack & Hwang (1982)).

IINPUT

Water depthMean Horizontal Force HFirst Order Max SurgeTarget Safety FactorMinimum Uplift TensionLower Comp. Wear Margin

L2 loop

Yes

END

Print out resultsfor this value ofupper componentlength

L2

1Set Length of Upper

Component Set Initial Valuefor Design MinimumBreaking Load (MBL)

Solve catenary eqns.using diameter set byMBL and select lowercomponent length tosatisfy safety factorsand uplift criteria

( BEGIN ) Correct MBL undercontrol ofoptimizationalgorithm

MBL loop

Yes

Figure 3.3 - Flowchart of combined catenary line optimisation programme

(redrawn from Global Maritime Ltd. (1989,1)).

4. CHARACTERISTICS OF SYNTHETIC FIBRE ROPES

4.1 Introduction

Fibre ropes are light flexible structures used as tensile members in

applications as diverse as ship moorings and bow strings. Known by man for

at least five thousand years (Borwick (1971)), it was in the past 50 years that,

due to the availability of synthetic polymeric fibres, the rope industry has

experienced a rapid technical development.

The research effort by Carothers and Staudinger since the early 1920s up to

the 2nd World War was responsible for the development of synthetic fibres as

we know them today (Roberts (1984)). After World War II, nylon 6.6, product of

the direct work of Carothers at Du Pont in North America in the 1930s, became

the first commercially available man-made fibre. Nylon 6 , developed by I. G.

Farbenindustrie, was first available in the late 1930s and is still more common

in Europe. Polyester (Polyethylene Terephthalate) fibres were developed into

commercial products in the late 40s and early 50s by Winfield and Dickson

(1946) in the United Kingdom.

For rope making, polymeric fibres can be in the form of:

(i) coarse filaments (monofilament);

(ii) fine filaments (multifilament);

(iii) fibrillated tape; or,

(iv) discontinuous coarse filaments, also called staple fibres (to simulate

the surface handling characteristics of natural fibres).

Multifilaments typically have a diameter between 10 and 100 micron and

come in lightly twisted or discontinually entangled (by a jet of hot air) bundles

of 100 to 2000 filaments. Each bundle is called a single yarn or simply a yarn.

The tensile strength obtained from multifilament yarns is usually higher than

from the other forms of yarn.

In most rope constructions, a number of single yarns are twisted together into

plied yarns, these being further combined into rope yarns and strands, by

sequential twisting operations. Strands can be used to produce either

41

3—strand ropes, by further twisting, or braided into 8-strand, 12-strand or

double braided (core and cover) rope constructions. Over 90% of all fibre

ropes are made in one of these constructions. Figure 4.1 shows schematically

these constructions, as well as other constructions of interest for offshore

moorings which will be discussed below.

4.2 Textile Units

Mechanical properties of synthetic fibres are generally quoted in textile units.

Due to the size of the filaments involved, and to the variations in apparent

cross sectional area with packing it is more convenient to think in terms of

strength on a mass basis than on an area basis. Fibre strength and stress are

usually normalised in terms of the yarn mass as opposed to its cross sectional

area, i.e., breaking load is divided by linear density. In the textile industry this

measure of fibre strength is known as tenacity and the corresponding stress

as specific stress.

Linear density is normally measured in grams per kilometre, or tex. The tex

corresponds to 10 -6 kg/m and is obviously far more convenient for fibres and

yarns than kg/m. Tenacity and specific stress are then expressed in units of

N/tex which is exactly the same as MN/(kg/m).

It can easily be seen that multiplying the specific stress in N/tex (MN/(kg/m)) by

the material density (in kg/m3) one gets stress in MPa referred to the actual

cross sectional area of all the fibres in a yarn. It should be noted that it is very

difficult to arrive at precise figures for the circumscribed or apparent area of

the yarn or at any stress calculated as a function of this sort of area.

For the same reasons discussed above, it is more convenient to normalise

modulus in a mass basis. Specific modulus (in N/tex) is defined as the

relation between specific stress and strain. Again, a conventional engineering

modulus can be obtained by multiplying the specific modulus by the material

density.

42

4.3 Yarns

4.3.1 General Considerations

The world production of synthetic fibres in 1987 reached a total of 14.8 million

tons. Polyesters, Polyamides and Acrylics accounted for approximately 95% of

the total production. Table 4.1, after Davies (1989), presents production

figures for the main synthetic fibres from 1970 to 1987. It can be seen that

polyester has become by far the largest production fibre group, with about

50% of the market. As pointed out by Ford (1988) this is mainly due to to its

favourable price in comparison with less durable fibres such as cotton and

viscose.

Yarn used for rope making, tire cords, conveyor belt, reinforcing seat belts and

similar applications is known as industrial yarn as opposed to the textile

filament used in clothing. Ford (1988), referring to 1984 statistics points out

that the production of polyamide (nylon) industrial yarn was still twice the

production of the equivalent polyester yarn, although polyester was increasing

its market share. Over the past years yarn cost per kg for nylon industrial yarn

has been around 1.2 to 1.4 times the cost of industrial polyester yarn (Kirk &

Othmer (1984) and Ford (1988)). The production of aramid fibres is typically

two order of magnitude lower than the production of polyester fibres, most of it

used in a chopped form as an asbestos substitute for brake linings. Other high

modulus fibres, like high modulus polyethylene, have an even lower

production.

Polymeric fibres used in rope making are mostly made from petrochemical

feed stock. Fibres are formed by processes such as polymerisation and

polycondensation of basic components or monomers. The filaments are

formed by extrusion through a spinneret in one of three different spinning

methods shown schematically in Figure 4.2.

After spinning most fibres have poor strength (tenacity) and stiffness, since the

molecules of the polymer are not preferentially oriented in the direction of the

filaments. Orientation is obtained by drawing. For polyamide and polyester

fibres typical drawing ratios vary between 3:1 and 5:1 (Davis & Talbot (1985)).

43

In general terms tenacity increases with: the average molecular weight of the

material, its degree of cristalinity, the degree of axial orientation and the lack of

imperfections in the fibre structure. An adequate molecular weight is obtained

in the polymerisation process. Cristalinity and orientation are normally a

function of spinning speed, drawing ratio and heat treatment.

Man-made fibres currently used in marine ropes are: polypropylene (PP),

polyamide 6 (PA6, nylon 6), polyamide 6.6 (PA6.6, nylon 6.6), polyethylene

terephthalate (PETP, PET, polyester), and, on a much smaller scale, Aromatic

polyamide (aramid) and high molecular weight polyethylene (HMPE). New

fibres and improved versions are regularly introduced in the market. Liquid

crystal polymers, like Vectran (Beers & Ramirez (1990)) are examples of the

former case and Technora aramid (Stidd (1990)) is an example of the later.

4.3.2 Yarn Finishes

Spinning (standard) finishes are substances applied to the surface of yarns

during the manufacturing process. They prevent static charging, hold the

filaments together and lubricate them to reduce abrasion damage during rope

making. A standard finish is usually water soluble.

After finish is an additional lubricant applied to the yarn for different purposes.

Yarns with non water soluble (marine) finishes are used in several rope

constructions and play an important role in reducing friction and internal

abrasion in service.

Since yarn manufacturers usually do not release technical information on the

finishes they use (Flory (1988)) and the application envisaged does not cause

severe cyclic loading (see Section 3.2), no further attempt was made to

develop this subject except for an experimental verification. This took the form

of the "fatigue" tests performed in model fibre ropes, discussed in Chapter 6,

where one of the ropes used a yarn with marine finish and another rope was

manufactured from yarn without after finish.

44

4.3.3 Yarn Properties

Table 4.2 shows a compilation of mechanical and physical properties of yarns

selected as viable options for mooring rope manufacture (Enka (1985,1),

Kirschbaum (undated), E. I. du Pont du Nemours & Co. (1987) and Flory et al.

(1988)). Data presented for polyester and both nylons correspond to high

strength (tenacity) yarns. Polypropylene results are for good quality

multifilament yarns.

Conventional industrial yarns (polypropylene, nylon and polyester) all have

strengths that are approximately half the tensile strength of steel rope wire, on

an area basis, or 3.5 times in terms of weight. Aramids and HMPEs have all

strengths about 50% higher than wire, but the difference being an order of

magnitude on a weight basis. Initial modulus is spread over a huge range,

from 6 to 200 GPa, leaving room for the user to build a tether with a tailored

system response. It should be noted however that, because of the visco-

elastic nature of their behaviour, the initial modulus of synthetic fibres does not

represent the behaviour in an application involving load cycling.

Tensile testing of yarns should normally be done according to standards

produced by national standards organisations (BSI 1932: Part 1 (1989) or

other types of associations (ASTM 0855-85 (1985) and ASTM 02256-88

(1988)). Typical gauge length for these tests vary from 250 to 500 mm. A

testing speed of 10% of the gauge length per minute is normally used for high

modulus yarns such as aramid and HMPE. A testing speed of 100% of the

gauge length per minute is normally used for conventional materials such as

polyesters and nylons. Yarns of conventional materials can be tested with or

without twist but yarns of high modulus materials need twist to avoid excessive

numbers of failures in the grips. Tensile strength results presented in Table 4.2

refer to yarns in standard conditions of humidity, typically 55c/oRH, tested

according to ASTM D855-85 (1985) or any similar standard.

Published data on the long term strength of fibres and yarns in fresh and sea

water is limited to a few materials and conditions. Morton and Hearle (1975)

and Flory (1988) reported a decrease of about 15% in the tensile strength of

nylon in water. Although absorbing 7% of water, Kevlar 49 aramid showed

45

only 1.5% strength loss after 1 year immersion in salt water as reported by E.I.

du Pont du Nemours & Co. (1987). ENKA (1985,2) indicates a loss of 3 to 5%

for its aramid yarn, Twaron, fully saturated in sea water. Polypropylene and

polyethylene do not absorb water and are not thought to suffer any strength

reduction due to immersion in water. Results published by Enka (1985,1), for

external yarns of 24 mm diameter polyester ropes, kept 50 m below the sea

surface for 3 years, show retained strength of 93%. The same test was

performed in ropes made of nylon yarns, with and without additives to improve

ultra violet and heat resistance. Retained strengths were 91% and 71%

respectively. More detailed investigations performed for polyester fibres are

going to be discussed in Section 4.4. For the time being it is sufficient to say

that the rate of strength degradation reported for polyester fibres in water at

ambient temperature is very small (McMahon et al. (1959) and ICI (undated)).

Initial modulus, as shown in Table 4.2 is calculated from the slope of the

tangent to the load elongation curve in its first reasonably straight region.

Figure 4.3, after ASTM D855-85 (1985), shows load-elongation graphs for two

types of materials and their respective tangent lines used in computing

modulus.

Early results for individual filaments under very small (unquantified) elastic

deformations (Hadley et al. (1969)) showed an initial modulus between

14 GPa and 18 GPa for polyester yarns (draw ratios 5-8) and circa 4.7 GPa for

nylon at a draw ratio of 6:1. Hadley et al. (1969) also reported a very

significant decrease in modulus by nylon fibres with increasing relative

humidity as shown in Figure 4.4.

Van der Meer (1970) reported on the dynamic properties of polyester and

nylon yarns. Average dynamic modulus values quoted were respectively

20 GPa and 7.5 GPa for a cycling frequency of 10 Hz. Results were also

presented for hysteresis, in the form of tan 8 (also called loss coefficient or

loss factor, the ratio between the loss modulus and the storage modulus).

Appendix 1 defines the terminology used to describe hysteresis. Dry polyester

and nylon textile yarns showed loss coefficient values of 0.013 and 0.019

respectively, while in the wet condition results were 0.013 and 0.050.

46

Kenney (1983) measured the hysteretic energy absorption in nylon and

polyester yarns, manufactured by Du Pont, cycled dry between 1% and 20%

of their breaking load, for frequencies between 0.00028 and 6.2 Hz. The

results were reported in absolute energy units (J) absorbed per cycle. Total

energy absorbed per cycle for nylon was approximately 10 times bigger than

absorbed by the PET yarn. From a knowledge of the yarn tested and making

the assumption that the yarn dynamic modulus at 0.1 Hz is equal to 13.8 GPa

(average measured by Van der Meer (1970)) it is possible to infer the loss

factor at this frequency. The value so obtained is 0.017.

Failure strain is a dominant parameter in determining the ability of the tethers

to equalise small imbalances in construction and the care necessary when

handling the fibres, i.e. the higher the strain to failure the easier to handle the

fibre and to make a well balanced rope.

The density of the fibres reviewed ranges from 0.91 to 1.45 g/cm 3. In sea water

both polypropylene and high molecular weight polyethylene float, while the

other fibres show a small but positive apparent weight. The density of these

materials is such that tethers based on them assume catenaries with very

small sag (or hog). The tethers can usually be considered neutrally buoyant

when compared to steel tethers.

Kinking susceptibility relates to the compression behaviour of some high

strength fibres. Shear bands are produced under alternate tension-

compression (Riewald (1986) and Greenwood & Rose (1974)). The kinked

fibres lose strength and are more susceptible to: chemical attack, hydrolysis

and oxidation (E.I. du Pont du Nemours & Co. (1987)). Figure 4.5 shows kinks

in an aramid filament.

Figure 4.6 after E.I. du Pont du Nemours & Co. (1987) shows creep results for:

nylon, polyester, two grades of aramid (Kevlar) yarns and steel wire for ropes,

at ambient temperature, loaded at 50% of their respective breaking load.

Creep strain, here defined as total strain minus strain after 1 minute, is plotted

as percentage of initial yarn length. In the same graph results now obtained at

Reading for a HMPE yarn (Dyneema SK 60), at 30% of its nominal breaking

load and 20±2°C, have been plotted.

47

Figure 4.7 shows mean stress rupture, or creep rupture, data for: nylon 6.6,

polyester and aramid yarns. As well as being directly related to the capacity of

the fibres to sustain constant load, which may be relevant, to the application

envisaged, creep rupture is also one of the mechanisms of fibre failure under

cyclic load as described below.

"Fatigue" (cyclic loading) behaviour of nylon 6.6, polyester and Kevlar 49

yarns and fibres has been shown to derive from a simple process of

accumulating creep strain (Kenney et al. (1985), Mandell (1987)) and is

therefore totally different from any concept of fatigue in metals. This behaviour

has been observed under the following conditions: wet and dry testing,

minimum to maximum load ratios (R) between 0 and 1, frequencies from 0.1 to

20 Hz, and at maximum stresses above: 30% to 40%, 60% to 70%, and 70%

to 80% of the initial strength, respectively for nylon, polyester and Kevlar 49.

The presence of water produced a 10% to 20% strength reduction in nylon 6.6

while the polyester yarn was almost unaffected (Kenney et al. (1985), Mandell

(1987)).

Figure 4.8 shows data for the maximum load versus time to failure, presented

by Mandell, plotted on a logarithmic time scale.

For the wet polyester and nylon 6.6 yarns, the following equations respectively

fitted to the test data:

P/Po = 1.02 - 0.0570 log (t); (1)

P/Po = 0.98 - 0.1008 log (t). (2)

where: P = the maximum cyclic load ;

Po = the initial strength; and,

t = the cumulative time to failure in seconds.

The number of cycles to failure was found to be independent of frequency and

obtained simply by multiplying t by the frequency in Hz.

It should be noted that the difference in behaviour between nylon and

polyester is considerable. For example, a time to failure of 1 month could be

obtained by loading a polyester yarn to 65% of its breaking load while to get

failure of a nylon yarn in the same time requires cycling to a maximum load of

only 33% of its breaking load!

48

Results presented by Bunsell & Hearle (1974) for nylon 6.6 and by Oudet &

Bunsell (1987) for polyester yarns disagree with the results presented by

Mandell (1987) in that a different and faster mechanism of failure, identified as

"actual" fatigue, was found to be responsible for fibre failures if R <0.25,

approximately.

However the same trend of much better "fatigue" performance of polyester

than nylon 6.6 was verified by Bunsell & Hearle (1974). For example, nylon

fibres cycled between zero and 55% of their breaking load typically survived

50,000 cycles, while polyester fibres cycled between zero and 65% of their

breaking strength survived an average of 200,000 cycles.

The residual strength of polyester yarns at various fractions of their average

failure time in fatigue was investigated by Steckel (1984). No degradation was

found for yarns cycled at 80%, 85% and 90% of their breaking load after up to

80% of their life.

No results have been found in the literature concerning the residual strength

of yarns under: moderate loads (constant or cyclic), temperatures from 0°C to

25°C and immersion on sea water, for long periods of time. These conditions

are the most relevant for yarns used in the manufacture of tethers for use in

spread mooring systems.

Photo-oxidation of polymers involves complex chemical and physical

interactions. Since light has to be absorbed before any photochemical

reaction may occur, a significant parameter in photo-oxidation is the optical

density of the polymer over the solar energy spectrum incident upon it.

Because polymers like polypropylene are quite sensitive to photochemical

degradation, being transparent to sunlight, reactions must involve impurities

and be affected by molecular mobility. Another important effect concerning

strength reduction is the polymer structure, i.e. crystalline and semi-crystalline

polymers tend to be more sensitive to degradation than those with amorphous

structure (Wiles (1976)).

To simulate this sort of degradation, special equipment capable of generating

ultra violet radiation is used in accelerated laboratory tests (Global UV tester

(Tabor & Wagenmakers (1991))). Although results obtained in this test can be

49

correlated to outdoors weathering for individual polymeric fibres, comparative

tests on different fibres using the Global UV tester do not agree with

environmental exposure results (Tabor & Wagenmakers (1991)).

Three years exposure results in Wuppertal, Germany, have shown that the

loss in strength is two times greater for a stabilised nylon yarn than for a high

tenacity polyester yarn without additives (Tabor & Wagenmakers (1991)).

Enka (1985,2) states that photo degradation results for aramid yarns exposed

for 5 years are similar to nylon yarns.

For large diameter mooring ropes photo-oxidation is not thought to be a

problem. The self screening effect and/or the use of thick plastic jackets

effectively block the access of radiation to the load bearing material.

Yarn on yarn abrasion plays an important role in the fatigue behaviour of

ropes incorporating high levels of twist and/or braiding, cycled with medium to

low loads (Parsey (1982)). Yarn on yarn abrasion behaviour is strongly

dependent on fibre finish but also influenced by: environment, load and yarn

twist. It should be assessed if the expected rope failure mode is internal

abrasion (Flory (1988)). A standardised test method was proposed by Goksoy

(1986). Figure 4.9, after E. I. du Pont du Nemours & Co. (1987), shows results

for one particular experimental set-up that illustrate the influence of some of

the variables mentioned. The detrimental effect of water on nylon is

remarkable.

Friction coefficients between yarns and different materials can also be

obtained from yarn manufacturers. They are relevant in yarn care during rope

making and for ropes failing by abrasion at terminations. Particularly in barrel

and spike terminations and eye splices fibres are known to fail by friction

against metallic components. There are no published equations relating

friction coefficients and abrasion resistance, so specific values are not

mentioned here.

As discussed above, nylon 6 and nylon 6.6 yarns have several characteristics

that limit their suitability for ropes for platform moorings:

(i) excessive creep;

(ii) poor stress rupture characteristics;

50

(iii) poor fatigue performance in the wet condition; and,

(iv) low modulus especially when wet.

The cost of nylon and polyester is approximately the same on a volume basis

and, as seen in Table 4.2, their dry tensile strength is very . similar. However

taking into account all the drawbacks discussed for nylon fibres and the bonus

modulus offered by polyester, it is considered that there is no justification for

using a nylon yarn for the sort of application envisaged unless a low modulus

fibre is needed. Nylon yarns will not be considered any further in this analysis.

Polypropylene, despite its low cost and good wet behaviour, will only be

considered as a possible jacketing material. Its poor creep properties (a

function of its low glass transition temperature) can cause premature failure

due to stress-rupture and its low strength on an area basis penalise the

required tether diameter.

4.4 Polyester (Polyethylene Terephthalate) Fibres

Polyester fibres are obtained from long chain synthetic polymers containing at

least 85% in weight of an ester of a dihydric alcohol and terephthalic acid

(Davis & Hill (1984)). The polyester most widely used in fibres (the one

investigated in this study) is polyethylene terephthalate (PET), the structural

formula of which is shown below:

0 13

II r_

H—OCHaCH2OC C H_ -n

A number average molecular weight (M n) of 15000 is considered as a

minimum to obtain adequate textile properties (Davis & Hill (1984). The yarn

tested in this study has a M n of 17000 (Tabor & Wagenmakers (1991)).

There are two manufacturing processes for PET fibres in current use, based

in: dimethyl terephthalate (DMT) and ethylene glycol (GE) or terephthalic acid

51

(TA) and GE. The processes involve first an ester interchange (DMT) or

esterification (TA) and then a polycondensation with the elimination of glycol.

The second process is presently preferred, because it is continuous, allowing

for a higher degree of polymerisation without thermal degradation.

Fibre formation is obtained by melt spinning. The speed at which the spun

yam is pulled is called take-up speed and controls the structure of the material

produced. After spinning the fibres undergo a several fold drawing operation

followed by a relaxation. This treatment confers the fibre with a highly oriented

semi-crystalline structure.

The arrangement of the molecules in crystalline PET was determined by X-ray

diffraction, such a configuration is pictured in Figure 4.10. after Ward (1990).

To represent oriented semi-crystalline polymers, several different structural

models have been proposed (Hearle (1967) & (1991)). All models incorporate

highly ordered crystalline regions and zones of oriented amorphous material.

The indirect evidence to support these models comes from: X-ray diffraction,

birefringence, sonic velocity and electron microscopy (Hearle (1991)).

A schematic representation of such a model for PET is shown in Figure 4.11

(Prevorsek & Kwon (1976)). Its major component is the microfibril with

alternating crystalline zones (crystallites) and amorphous domains. Between

the microfibrils lie extended non-crystalline molecules, some of which

penetrate the crystallites. The crystallites contain some folded molecules and

are considered to be perfectly oriented in the direction of the fibre. The axial

orientation of both crystalline and amorphous zones is used to explain the

excellent axial properties of drawn polymers.

Hearle (1991) suggests that the extent of crystallite misorientation in the actual

fibre can explain the better fatigue performance of polyester over nylon. The

orientation of the crystallites in polyester, being more perfect, would explain

why fatigue cracks run almost parallel to the fibre axis, as opposed to a

propagation at approximately 10 0 to the fibre axis found in nylon (Bunsell &

Hearle (1974)).

Recent work by Rim & Nelson (1991) shows that the structural model

described above is able to explain the main properties of three high modulus

52

high tenacity PET industrial yarns. Tenacity increased linearly with the

orientation of the amorphous region. A similar but less strong trend was found

for a measure of fibre stiffness, the load at 5% elongation (LASE-5, ASTM

D855-85 (1985)), in a typical loading regime for tire yarns. Initial static

modulus and dynamic modulus under conditions of: low pretension, low

amplitude and ambient temperature, also increased with amorphous

orientation. However, a decrease in hysteresis with amorphous orientation

under the same conditions, measured as tan 5, could not be explained.

Dortmans (1988) has used a similar model to explain the observed relations

between spinning speed and yarn properties, when investigating PET fibres

obtained by high-speed spinning (HSS). Defining the overall orientation (fm)

by applying the rule of mixtures to the orientation of amorphous and crystalline

regions, gave quite a good correlation between modulus (measured by the

LASE-5) and f ov, as shown in Figure 4.12. Since at higher spinning speeds

the cristalinity increased and the orientation of both regions did not change,

the modulus increased with spinning speed. Because of the higher modulus,

HSS fibres showed an improved creep performance. However tenacity was

reduced by the increase in spinning speed. This was explained by an

increase in the number of folded chains in the crystallites and a more

scattered distribution of length of the molecules in the amorphous region.

Fatigue performance was improved in HSS fibres. This was associated with

the decrease in the number of crystals and consequent increase in mobility in

the amorphous zone.

Tensile strength of high tenacity industrial yarn used in rope making quoted by

the manufacturers is between 1.1 GPa (0.80 N/tex) and 1.2 GPa (0.87 N/tex)

(AKZO (undated), E. I. du Pont du Nemours & Co. (1987) and Rim & Nelson

(1991)). AKZO (1991) production data for the yarn tested indicates a

coefficient of variation of 2.4%, over the year of 1990, for the yarn breaking

load. For this particular yarn, batches are rejected if the sample means fall

below 5% of the average specified value.

Fibre modulus is of paramount importance when the application concerns

imposed cyclic strains. Figure 4.13, after ENKA (1985,3), shows a typical

53

stress-strain plot for the yarn tested. Yarn tangent modulus is shown in the

same graph. These results highlight the non-linearity of the extensional

behaviour presented by polyester fibres.

Another way of measuring modulus is by the tangent to the isochronous stress

versus creep strain relation (isochronal modulus). Results obtained by Croll

(1973) for highly oriented PET sheet, parallel to the sheet axis, showed the

same overall non-linear behaviour, but displayed a region of linear

viscoelastic behaviour between 0.06 and 0.19 GPa, where the relaxed

modulus (t was ca. 4.7 GPa.

It should be kept in mind that there is no direct correlation between any of the

above mentioned measurements of modulus, be it initial modulus (ASTM

D855-85 (1985)), tangent modulus or secant modulus between any stress

values, and the dynamic modulus displayed by the fibre when cycled between

specific load limits at a specific frequency. As explained in Section 3.2, this

later stiffness measurement is the value pertinent to the response of mooring

ropes.

Dynamic modulus measurements of an experimental PET yarn have been

made by Van Der Meer (1970) at a frequency of ca. 10 Hz, using a damped

free vibration method. Results obtained at 20°C as a function of yarn mean

stress are shown in Figure 4.14. A strong influence of mean tension can be

observed. Rim & Nelson (1991) reported a average dynamic modulus of

approximately 12.3 GPa for three PET high tenacity tire yarns at room

temperature. Samples had a pre-stress of 0.03 GPa and were cycled with a

strain amplitude of 0.17% at a frequency of 10 Hz. This value is a bit low

compared with Van Der Meer (1970) results. Apart from these references, all

early dynamic modulus results have been obtained at very low mean stresses

and stress ranges.

In the same tests mentioned above for dynamic modulus, Van Der Meer

(1970) measured the loss coefficient (tan 8) and found out that hysteresis

decreased with increasing mean tension. The results ranged from ca. 0.02 to

ca. 0.035. In another PET yarn a loss factor of ca. 0.013 was obtained (see

Appendix 1 for definitions). Rim & Nelson (1991) in the experiments above

54

mentioned found loss coefficients between 0.02 and 0.03 for the three yarns

tested, in the same range as the Van Der Meer data. Results for yarn

hysteresis at frequencies relevant to the application in focus could not be

found in the literature.

Various authors have stated that PET is unusually resistant to hydrolysis when

immersed in cold or warm water, but warned that this behaviour changes for

boiling water or steam (Ludewig (1971). ICI (undated), Parsey et al. (1989)

and Flory et al. (1990) mention hydrolysis as having a long-term degrading

effect on polyester ropes. Studies of the degradation of PET fibres by

hydrolysis (of the ester bond) have been mainly directed to conditions relevant

to process that happen with clothes such as dyeing and heat setting, or in the

manufacture of tires.

Moisture was found to be preferentially absorbed by the amorphous regions of

the polymer (Hasegawa et al. (1989)). When chain scissions occur, some

crystallisation may happen, mainly above the glass transition temperature,

reducing the volume fraction of amorphous material. Since the density of the

crystalline PET is higher than the density of amorphous PET, a density

increase has been reported by many authors in association with hydrolysis

processes (McMahon et al. (1959), Ellison et al. (1982) and Ballara & Verdu

(1989)).

Hydrolysis has been studied in:

(i) boiling water (Ludewig (1971), D'Alo & Ciaperoni (1977), ICI

(undated) and Ballara & Verdu (1989);

(ii) dye baths (Ingamells et al. (1981));

(iii) aqueous solutions of NaOH (Ellison et al. (1982); and,

(iv) hot water and high temperature,controlled humidity environments

(McMahon et al. (1959) and ICI (undated).

Although none of the works mentioned above relates directly to the

environment and temperatures found in moorings ropes, some useful

information could be found.

Ellison et al. (1982), found a 5% average reduction in breaking strength

(significant at a 97.5% level) in yarns that were kept in water at 60°C for 2

55

hours, while Ludewig (1971) reports an average reduction in strength of 3.3%

for a yarn boiled for 5 hours. Ludewig (1971) also found that yarns boiled

under tension did not degrade any quicker than those boiled under no

tension.

The most interesting work on this subject was conducted by McMahon et al.

(1959), who tested a polyester fibre (Dacron) and two thickness of PET film

(Mylar) in water and at relative humidities of 20%, 50%, 75% and 95%, in

temperatures of 50, 60, 71, 82, 90 and 99°C, for up to 309 days.

The extent of hydrolytic degradation (EHD) was represented by:

EHD = Log (A / ( A - x )) (1)

where:

A = initial molar concentration of ester links; and,

x = number of moles of water that have reacted with 1 mole of polymer.

EHD was found to be a linear function of exposure time (t) for every

combination of material, temperature and environment tested. Results for the

PET fibre are shown for two relative humidities at 71°C in Figure 4.15.

Since no instantaneous hydrolysis can occur, at

t = 0,

EHD = 0,

and we can write

EHD k(T, RH) . t, (2)

where:

t = time in days; and,

k(T, RH) = constant, for temperature T and relative humidity RH.

It was also observed that, for the polyester fibre, the retained tensile strength

fell linearly with EHD up to 50% of the original strength, as shown in

Figure 4.16. The regression equation obtained for the strength loss (SL) as a

percentage of the initial strength was:

SL= 141.2. EHD . 100. (3)

Considering that the lower level of temperature in this tests, i.e. 71°C, is below

56

the glass transition temperature, McMahon et al. (1959) point out that there is

no reason to believe that equation (3) is not valid at lower temperatures.

From equations (2) and (3) it would seem that, for any particular combination

of temperature and environment, strength loss will be a linear function of time.

To estimate the influence of temperature on degradation, the gradient of EHD

with time, i.e. k(T, RH), obtained by McMahon et al. (1959), for the three

materials tested, at 100% R.H., was plotted versus temperature in Figure 4.17.

As suggested by ICI (undated) and Parsey et al. (1989), an exponential curve

fit was performed for each material. The fit was very good. The equation

obtained for the PET fibre was:

k (T, 100%) = 8.53E-22. 10 A (4.49E-2 . T) , (4)

where: T = temperature in °K.

The square of the coefficient of correlation obtained was 0.962 (the proportion

of the variation of the dependent variable that can be attributed to the linear

relationship with the independent variable is given by the square of the

coefficient of correlation (Miller et al. (1990)).

Substituting (4) in (2) and (2) in (3) we get:

SL = 1.20E-17 . t. 10 A (4.49E-2 . T) . (5)-

Assuming, for the time being, that a polyester mooring rope in service remains

at a temperature close to the sea water, equation (5) predicts a retained

strength in excess of 98% after 20 years immersion at 20°C.

McMahon et al. (1959) also exposed stretched samples of the 0.0127 mm

thickness film to hydrolysis at 90°C and 95% RH for 35 days. Retained

strength of the stretched portions of the samples was approximately twice the

strength of the unstretched regions. McMahon et al. (1959) concluded that

polymer orientation reduces the sensitivity of the material to hydrolytic

degradation.

ICI (undated), in its Industrial Fibres Manual, gives guidance on the amount of

hydrolytic degradation of PET fibres for a wide range of environmental

conditions. The actual data in which the recommendations are based is not

57

presented. Therefore a number of uncertainties remain on the applicability of

the results presented. It is not possible, for example, to assess either the

actual coverage of the tests undertaken (and, in consequence, the

extrapolations made) or the scatter of the results obtained.

In agreement with McMahon et al. (1959), strength loss was reported to be

proportional to time. Strength loss was found to increase exponentially with

temperature, but at a higher rate than reported by McMahon et al. (1959), as

shown in Figure 4.18.

The equation recommended by ICI to calculate the strength loss as a

percentage of breaking strength is:

SL= 2.88. t. (1.082 A (T - 373.15)) (6).

According to this equation exposure for 20 years at 20°C would cause a

strength reduction of 37.6%.

Creep strain measurements presented by E. I. du Pont du Nemours & Co.

(1987) for a polyester yarn, Dacron T-67, loaded at 50% of the breaking

strength, at 22°C, show an approximately constant creep rate of 0.135% per

decade, between 1.8*10 3 and 7.2*1 0 6 seconds (30 minutes to 83 days)

(Figure 4.6).

Tests reported by ENKA (1985,3) on Diolen 855T as tested in the present

study, at 20% of the breaking strength at 20°C, up to 3. 10 5 seconds show a

different trend. The creep rate has been found to decrease with time. For

example, between 10 2 and 103 s the increase in strain was 0.26% while

between 103 and 104 it was 0.16%. The same paper presents results for yams

loaded at a higher percentage of the breaking strength. The data shows that,

after the first 1000 seconds, the creep rate decreases for increasing loads up

to 40% of the breaking load. For example, at 30% of the breaking load, the

creep rate between 10 3 and 104 s was 0.13% per decade.

Tabor & Wagenmakers (1991), testing two PET yarns processed to obtain a

higher dimensional stability (Diolen 770 and Diolen 2500), for up to 107

seconds, found the same trend of decreasing creep rate with time. Between

106 and 107 s rates for Diolen 770 were as low as AKZO's standard modulus

58

aramid yarn, around 0.035% per decade. Creep rate was also found to

decrease with increasing load up to ca. 50% of YBL. For Diolen 770 immersed

in water at 60°C an increase in initial elongation but no change in creep rate

as compared with the yarn tested at 20°C and 65% RH was also observed.

Oudet & Bunsell (1987) tested two PET industrial yarns used for rubber

reinforcement, manufactured by Viscousuisse, at very high loads. Only the

yarns tested at the lowest loading level, 50% of YBL, showed creep rates

decreasing with time.

Apart from results already mentioned for creep-rupture (E. I. du Pont du

Nemours & Co. (1987)), which lack information on the conditions under which

the results were obtained, only very short duration tests could be found for

PET yarns. Mandell et al. (1987) gave results for Du Pont's Dacron 608 for

rupture in up to ca. 4.5 days. The load level needed to produce failure in that

time was found to be 70% of YBL. These results are also shown in Figure 4.7.

Oudet & Bunsell (1987), reported two failures in samples loaded at 80% and

82% of YBL. Lives were ca. 3 *10 4 and 105 seconds respectively, well within

the scatter band of data from similar tests on aramid yarns in Figure 4.7.

No reliable data could be found on the long term creep-rupture properties of

PET yarns tested dry or immersed in either fresh or sea water.

Fatigue behaviour of polyester yarns has been shown to be very good at high

stress ranges and high testing frequencies, as discussed in the previous

section. The failure mechanisms found (creep-rupture and fatigue) were not

investigated at the low mean, low range regimes, typical of a spread mooring

system, due to the long testing times necessary.

4.5 Fibre Ropes

4.5.1 Rope Constructions

The geometrical way in which the yarns are assembled into a rope is called its

construction. Since the end of the Second World War there has been a rapid

development of rope constructions as alternatives to the traditional three-

59

strand type.

Today, apart from a number of hybrid constructions, one can conveniently

classify constructions in six groups (Parsey et al. (1989)): three-strand, plaited,

double-braid, wire rope type, parallel sub-rope and parallel yarn. In this

terminology low twist parallel strand ropes are grouped together with parallel

yarn ropes. Figure 4.1 illustrates these rope types.

The following description of rope type characteristics is based on: Van

Leeuwen (1981), Parsey (1982), Lewis (1982), Ractliffe & Parsey (1985),

Parsey et al. (1985), Flory et al. (1988) and Flory et al. (1990).

Three-strand ropes incorporate several levels of twist in their manufacture and

therefore have a highly compliant structure. Their main characteristics are:

(i) high elongation;

(ii) low bending stiffness;

(iii) good energy absorption;

(iv) low strength efficiency;

(v) poor torque balance;

(vi) irregular outer surface; and,

(vi) low cost.

Eight-strand plaited ropes, using similar strands as 3-strand ropes, have

strands plaited or braided in pairs, four running clockwise and four anti-

clockwise. These ropes have:

(i) medium to high elongation;


(iii) good energy absorption;

(iv) low strength efficiency;

(v) good torque balance characteristics;

(vi) irregular outer surface; and,

(vi) low cost (although higher than 3-strand ropes).

Braid-on-braid or double-braid ropes incorporate strands in two concentric

circular braids one over the other. They have:

(i) medium elongation;


60

(iii) medium energy absorption capacity;

(iv) reasonably good strength efficiency;

(v) very good torque balance;

(vi) smooth outer surface; and,

(vi) generally a medium cost (higher than 8-strand ropes).

The need for high strength low stretch (high modulus) ropes has led to the

development of low-twist constructions. All these ropes have generally:

(i) low elongation;

(ii) low energy absorption capacity;

(iii) high strength efficiency;

(iv) smooth outer surface; and,

(vi) medium to high cost.

Wire rope type constructions are either similar to six-strand or spiral-strand

wire ropes, with a long helical pitch. Depending on rope size, strands may be

formed by direct combination of industrial yarns or from plied yarns as in a

three-strand rope. Some constructions have braided covers over each strand.

The torque balance properties of these ropes vary with the details of the

construction but they can be made with good torque balance characteristics.

The use of eye splices as a termination is still possible.

Parallel strand ropes are made by encapsulating within the same cover sub-

ropes which are either individually torque balanced or are paired with

opposite torque characteristics. Parallel strand constructions are torque-free,

but are less easy to splice efficiently.

Parallel yarn and parallel strand ropes have either slightly twisted or parallel

yarns laid parallel to the rope axis, encapsulated within a jacket to hold them

together. These ropes have the highest possible modulus and are non-

rotating. However they are hard to bend, perform badly over sheaves, may

subject fibres to kinking induced by bending and have to be terminated with

resin potted or wedge and cone type fittings, that can be expensive and

limited efficiency.

Generally speaking we can say that:

(i) braiding operations are more expensive than twisting but cheaper

61

than handling lower levels of twisted bundles;

(ii) the higher the twist and the number of construction levels of the

structure the lower the strength translation and stiffness obtained;

and,

(iii) high twist levels generate ropes that are flexible and easy to

handle.

In the mooring application which is the subject of this investigation, typical

pretensions are about 20% of the rope minimum breaking load, and maximum

quasi-static levels can be as high as 50% of MBL. It has been shown by

McKenna (1990) that 3-strand polyester ropes of a size compatible with

offshore moorings elongate elastically ca. 6% when tensioned between 20%

and 50% of BL. Considering that such loading can be due to a weather

condition lasting for something like one week, in addition to this 6% there

would be a creep elongation of at least another 3% (according to

measurements taken by Crawford & McTernan (1983) on stiffer rope

constructions). In a system using combined mooring lines, the lower end of the

synthetic rope will also display a movement due to change in the catenary

shape of the lower component. For a passively operated system, it is clear that

a 3-strand polyester rope sized for its strength, will not be able to keep the

vessel within a typical offset of 10% of the water depth. This means that, to

meet offset requirements, the ropes would have to be oversized, leading to

high capital and installation costs. Therefore this construction will not be

considered any further.

4.5.2 Terminations

The type of end fitting used to connect the rope is called the termination. As

the rope itself is very uniform, there is a tendency for the terminations to be the

"weakest link". Ropes incorporating high levels of twist or braid are inherently

inefficient in tension. By careful design, i. e. gradually reducing the twist

angles and or the braid pitch, it is possible to terminate such ropes with 100%

termination efficiency in quasi-static situations (a termination efficiency of

100% is indicated where failure is remote from the termination i.e. the full

62

strength of the rope is achieved).

Constructions which have high tensile efficiencies are difficult to terminate,

since the fibres are mainly oriented in the axial rope direction. In such ropes,

failure on quasi-static testing tends to be shifted from the free length to the

transition between the rope and the termination where the rope construction is

disturbed and radial tensions in the filaments are increased.

Terminations perform differently according to the rope with which they are

used. A direct assessment of termination efficiency is not possible if, for a

particular rope, no other termination providing clear breaks can be found. In

this situation, it is only possible to obtain a comparative evaluation of different

end fittings. This is done by calculating the strength conversion or strength

realisation of the terminated rope, as obtained with the different end fittings.

Strength conversion is defined as the average terminated rope breaking

strength divided by the aggregate breaking strength of all the yarns in the

rope. This kind of comparison is only significant for one particular rope, i.e.

yarn, construction and diameter.

A slightly different and more appropriate way of comparing the cost efficiency

of a terminated rope is by comparing the rope tenacity (say in Nitex) with the

tenacity of the yarn used to make the rope (tenacity conversion). This is more

appropriate since it relates to the quantity of yarn per unit length of rope.

Although there are a number of ways of terminating fibre ropes, for the

demanding application of a permanent offshore mooring only three types of

terminations can provide the efficiencies needed to justify consideration.

These are: splices, resin potted, and cone and plug (also known as barrel and

spike) terminations.

Splicing

Splicing is the standard termination for three-strand, plaited and double-

braided ropes. It can also be used with wire rope type and parallel sub-rope

constructions.

Splicing details vary mainly with rope construction but also with yarn material

and finish. In general terms splicing is done by forming an eye on the end of

63

the rope by tucking individual rope strands back into the rope construction.

While splicing simple constructions is straightforward, large double braided

ropes can be so complicated that a rope makers catalogue can spend 8

pages to describe it (Cordoaria São Leopoldo (undated)).

Eye splices are often protected by thimbles and, if long term heavy duty

cycling is foreseen, additional linings such as: polyester cloth sheeting

(Crawford & McTernan (1983) and urethane moulding of the eye (McKenna

(1980), Werth (1980)) are employed between the eye and the thimble.

Polyester cloth sheeting was reported by (Crawford & McTernan (1983) to

increase the "fatigue" life of spliced double braided polyester ropes by a factor

of five.

The efficiency of properly made splices is effectively 100% for most fibres and

constructions that allow splicing (Lewis (1982)), including small Kevlar wire

rope construction ropes (Horn et al. (1977), polyester double-braided

construction (National Coal Board (1979)) and polyester wire rope

construction ( McKenna (1991)). In ropes made of high strength fibres in low

twist constructions, very sophisticated splicing techniques have been used in

an attempt, not always successful, to avoid termination failures (Riewald et al.

(1986)).

As with other types of terminations, cyclic loading tends to generate splice

failures (Horn et al. (1977) and (Crawford & McTernan (1983). As will be

discussed later tensile tests are not sufficient to prove termination efficiency

and reliability under significant "fatigue" loading.

Resin Potting

Resin potting consists of distributing the yarns in a conical socket which is

then filled with a cold curing resin. Figure 4.19 illustrates the operation of

pouring the resin into the prepared socket. Care must be taken in fibre

cleaning, distribution, alignment and tension balancing. This method is used

mainly for ropes with high strength fibres. Commercial resins used are epoxy

and polyester.

Resin cast sockets develop their holding power by generating high pressure

64

in the bulk of the resin as the conical plug is pulled into the socket by the rope.

Chaplin & Sharman (1984), working with wire ropes, showed that this

pressure applies a normal force on the rope constituents so that the latter are

effectively held in position by friction and not by adhesion. Adhesion is only

responsible for holding the fibres inside the socket in the initial stages of

loading. This work also verified that in uniform taper conical sockets the

pressure generated close to neck is much higher than in the rest of the socket.

It is concluded that an improved design, with a more even pressure

distribution, could avoid having the highest shear stresses in the wires (or

fibres) where the tensile stresses are already maximum, and also reduce

socket stresses.

The behaviour of resin socket terminations for fibre ropes made with high

strength low stretch fibres such as aramids and HMPE, is very similar to that

for wire ropes, the frictional grip on the fibres being even greater because of

their larger overall surface area as compared with a wire rope. The situation

with fibres like PET is complicated by its relatively low modulus and high initial

creep compared with the properties of the socketing resins commonly used.

Resin cast terminations of polyester fibre ropes could possibly profit more than

wire ropes by a design with a more even pressure distribution.

High efficiencies are reported for small diameter (up to 25 mm) wire rope type

and parallel yarn Kevlar (aramid) ropes with resin socket connections (Lewis

(1982) and Horn et al. (1977)). There is no data available for large diameter

ropes. Heat generation during resin curing seems to be a possible limitation

for large diameter ropes.

Cone and Plug Socketing

Cone and plug socketing consists of a conical socket with a co-axial conical

plug. The fibres are evenly distributed filling the gap between the two cones.

When tension is applied, the internal cone is pulled in and acts as a wedge

that presses the fibres against the outer cone, holding them inside the socket.

Figure 4.20 shows a section of a barrel and spike termination.

Used mainly with parallel yarn ropes, this is the standard type of end fitting for

Linear Composites' polyester and Kevlar Parafil ropes (Kingston (1988)).

65

Cone and plug socketing is also used for small diameter wire rope type Kevlar

ropes (Lewis (1982)). It is not possible to assess efficiency of this kind of

termination directly because, for the constructions that use them, no clear

breaks have been consistently obtained with any kind of termination.

An idea of the static termination performance can be obtained from the result

of a breaking load test reported on a 124 mm core diameter Kevlar 29 Parafil

rope (Linear Composites Ltd. (undated)). Based on a 72.5% fibre filling factor,

the strength conversion of the terminated rope was 61.7%. From data

presented by Crawford & McTernan (1988) for a 17 mm core diameter

polyester Parafil, a strength conversion of 69% can be inferred.

Fatigue tests for this kind of termination are only published for Parafil ropes to

a maximum core diameter of 38 mm (Crawford & McTernan (1988)). All the

failures were due to fretting at the terminations.

Since termination failure is the expected failure mode for the more efficient

constructions under both static and dynamic loading, there still seems to be

some room for improvement, mainly in resin socketed, and cone and plug

terminations. Quality control is also a crucial issue for both these systems with

present designs.

For each particular application full size static and dynamic (where needed)

termination tests are recommended to assess both strength and reliability.

4.5.3 Jacketing

Parallel yarn and parallel strand ropes rely on jacketing to maintain their

shape. All constructions benefit from jacketing which provides: wear

resistance (particularly useful during deployment), fish bite protection

(Berteaux et al. (1990)), and acts as a barrier to ultra-violet radiation.

Polyurethane Jackets are recommended where severe abrasion is foreseen

(Linear Composites Ltd. (1983) and McKenna (1980)). Ethylene vinyl acetate

copolymer and Hytrel polyester elastomer have also been used offshore. The

last two are applied by extrusion over the rope and seem to be the more

66

convenient option for long lengths of tether.

Braided jackets have been used in small ropes and also in large ropes.

According to McKenna (1987), nylon and polyester braided jackets are

normally less rugged but leave the rope more flexible and are cheaper than

extruded jackets. Berteaux et al. (1990) reported that Kevlar and Spectra

braids were more effective than a Zytel (nylon resin) extruded plastic jacket in

protecting synthetic fibre ropes against fish bites.

Mayo (1972) reports on the good performance of 48 mm and 72 mm diameter

nylon ropes with polyurethane coating used to fire and pre-load explosive

embedment anchors. Polyurethane jackets have also been used over braided

jackets (Karnoski & Liu (1988)) for extra protection. Koralek & Barden (1987)

reported good performance from a Hytrel jacket on a Kevlar wire rope

construction mooring line used for 5 months on a drilling semi-submersible

platform. The same rope was deployed for 6 months in one of the mooring

lines of a floating production platform offshore Brazil. Although no damage

was caused by the sea exposure, the jacket was cut by a shackle pin when it

was coiled on the anchor handling boat's winch (Del Vecchio (1988)),

showing that special handling precautions are needed when installing ropes

with this type of jacket.

For most ropes an extruded jacket of approximately 5 mm thickness seems to

be sufficient, as long as the rope does not touch the sea bed and does not

bear against sharp corners during handling. Parallel yarn ropes need a

heavier (say 10 mm) jacket. A polyester braided jacket seems to be able to

provide the same level of protection as an extruded jacket, except against

penetration by sharp objects.

The subject of jacket adhesion to the rope itself is one that is still a matter of

some dispute and needs further investigation. For the very low stretch

fibre/construction combinations this does not seem to be a problem, but, for

moderate stretch ropes, a partially loose jacket can lead to rope—jacket

abrasion (Banfield (1989)). So, in applications with significant cyclic loads, a

jacket with a high degree of adherence should be used, particularly for

polyester—based ropes.

67

4.6 Rope Properties

4.6.1 Introduction

In order to evaluate the likely performance of light weight mooring materials, a

critical review of the literature on this subject was undertaken. This review had

two main purposes:

(i) to obtain approximate values for properties to allow a preliminary

selection of the most attractive candidate tethers on the basis of a

mooring design optimisation exercise (Global Maritime Ltd.

(1989,1));

(ii) to identify the areas where data to be used for mooring design were

missing, incomplete or unreliable; and,

(iii) to establish the additional areas of investigation, not accounted for

in the analysis of all steel mooring systems, which needed to be

addressed to support a full design using the light weight tethers

selected.

Table 4.3 shows the properties used in the analysis of the "pilot study" but

presented here in a different format. As in Table 3.3, the following

characteristics have been tabulated: tensile strength, axial modulus, dry

weight, and cost. As the most influential properties are strength and stiffness,

additional columns were produced to represent the strength (Str. Value) and

stiffness (Stiff. Value) which can be obtained for an unit cost (1 US$) in a 100

metres length of tether. These values were also tabulated normalised in terms

of the steel wire rope figures (Rel. Str. Val. and Rel. Stiff. Val.), representing

how much strength or stiffness can be purchased for a given expenditure

compared with a wire rope typically used for catenary mooring systems.

An inspection of the last two columns of Table 4.3 provides a quick way of

ranking the performance of substitute light weight tethers. As shown by

Chaplin (1989) and as further discussed in Chapter 5, this is a crude

approximation since, when used in the same system, compliant tethers need a

substantially lower breaking strength than stiffer steel elements.

68

The following paragraphs discuss the way the figures in this table were

obtained and their reliability. Consideration is also given to relevant data

published after the conclusion of the "pilot study". Additional tether

characteristics that are not considered directly in a streamlined mooring

analysis but which are essential to the implementation of a design

incorporating LVVTs are also discussed.

4.6.2 Modelling the Mechanical Behaviour of Fibre Ropes

With the advent of ever cheaper computing power a number of researchers

have recently explored the numerical modelling of fibre ropes. Numerical

formulations for both the helical geometry of twisted fibre bundles (Phoenix

(1979) and the sinusoidal helix of braids (Wu (1990)) have been proposed.

Phoenix (1979) working with stranded constructions has considered random

distribution of: fibre strength (and failure strain), fibre slack and fibre migration

in twisted yarns. Using his model, the strength conversion obtained for a rope

with 3 layer Kevlar 29 wire rope construction with low helix angles (< 15°) was

typically 85%. No experimental results are presented to validate this model

but the efficiency obtained is greater than the average of 70% quoted by

Lewis (1982) for very small 2 layer Kevlar 29 stranded ropes. It seems as

though his model is quite optimistic.

As far as simulating the quasi-static load-extension behaviour of small to

medium size 3 strand ropes, Chen (1988) has obtained quite good results for

25.4 mm diameter nylon and polyester cables. Failure loads though were

typically 30% higher in the model than in the ropes tested.

Recent work by Wu (1990), modelling the strength of 6.35 mm diameter nylon

and PET ropes in double braided constructions, has found that, including the

failure probability of the fibres in the numerical model, the experimental

strength falls between the numerical results obtained considering no friction

(+6%) and infinite friction (-3%) between the yarns.

Burgoyne & Flory (1990) have modelled the load strain behaviour of small

parallel yarn Kevlar 49 ropes, taking into account yarn strength and slack

69

variability. The biggest rope modelled had a breaking load of approximately

180 kN, and the strength conversion indicated by the model was 84%. No

comparison with experimental data was presented.

All the models discussed above have been applied to the behaviour of fibre

ropes under quasi-static loading conditions, corresponding to either a single

loading cycle to failure on a new rope, or a similar cycle on a rope that has

been worked to bed in the construction and rested. This sort of information is

only relevant to an assessment of the amount of rope take-up during

installation.

Considering the results published so far, we are forced to conclude that

modelling has not covered the ropes and rope properties relevant to a

mooring analysis.

4.6.3 Static Strength

Tensile strength data is readily available for more traditional constructions

such as plaited and double braided ropes from manufacturers' catalogues

and form a number of technical papers. The later have been preferred

whenever available.

Since different rope manufacturers use jackets of different materials and

thicknesses and jacket thickness is not geometrically similar for different

diameters, the strength (in kNimm2 ) presented in Table 4.3 was calculated

based on the full enclosed area without any protective jacket.

Strength values are given for steel wire rope and strand for comparison

purposes. These are catalogue figures (Minimum Breaking Load) and as such

are less than the mean, which would typically be 10% higher.

Strength quoted for the fibre ropes corresponds to mean test data minus 9%,

so as to be compatible with the wire rope values. This somewhat arbitrary

value is considered justified since, although at the present time, typical spread

in experimental data is greater for the light weight products, the development

and improved production controls that must precede any mooring rope

application may be expected to reduce the spread and improve the means for

70

these light weight constructions to obtain a level of consistency equivalent to

that of steel. Appendix 2 gives details of the references and further

assumptions upon which the figures were based.

It is important to point out that, particularly for more efficient constructions, the

scatter in strength found in the literature was very large. For example, tests

carried out at NEL (Crawford & McTernan (1988)) on nominally 10 tonne PET

Parafil and 60 tonne Kevlar 49 Parafil showed average tensile strengths

corresponding to respectively +16% and -10.5% of the manufacturers average

values.

Even bigger discrepancy was found for a 52 mm diameter PET Superline

parallel strand construction. The guaranteed minimum breaking strength

quoted by H&T Marlow Ltd. (1985) is 0.30 kN/mm 2. According to Banfield

(1989) the average breaking strength should be 10% higher than the

catalogue value, i.e. 0.33 kN/mm 2. A 53 mm diameter Superline, tested by

Karnoski & Liu (1988) showed a strength of 0.52 kNimm 2, which is 58% higher

than expected!

4.6.4 Stiffness

Several papers ( for example: Crawford & McTernan (1983), Ractliffe & Parsey

(1985) and Taylor et al. (1987)) discuss the subject of rope stiffness, but none

presents an adequate formulation encompassing the frequency range

relevant to catenary moored platforms. McKenna (1979) gives a good

description of the quasi-static tensile behaviour of fibre ropes. Referring to

Figure 4.21, the different components of rope elongation are described as:

ALr = residual elongation (mainly due to constructional setting);

ALh = elongation recovered by the rope after cycling at working

loads and rested for 30 minutes;

ALn = non-elastic elongation;

ALw = working elongation (non-linear elastic); and,

ALt = total elongation relative to unused rope.

Data supplied by manufacturers usually corresponds to the first cycle of

71

Figure 4.21. This is relevant only for assessing final length after line

deployment and anchor setting. Some rope makers provide data for ropes

that have been worked and rested (say for 24 hours).

Wave frequency stiffness is shown in Table 4.3 in kN/mm2 (GPa). The area

referred to is the area of the circle circumscribing the core section. Since very

few papers quote results from direct dynamic stiffness measurements, giving

detailed rope dimensions, the figures given in Table 4.3 were derived making

several different assumptions, as a function of the available data for each

material and construction combination. Appendix 2 gives details of the

references and further assumptions upon which the values were based. Four

papers are particularly relevant for the ropes studied and are discussed

below, giving an idea of the process used to obtain the data contained in

Table 4.3.

Bitting (1980) reported on the dynamic stiffness behaviour of small diameter

(12.7 to 31.75 mm) braided ropes. A mild stiffness dependence on frequency,

a strong dependence on mean load and a moderate dependence on load

range were found. A factor of three to four times was reported between quasi-

static and dynamic (wave frequency) stiffness for nylon ropes.

For 12.7 mm diameter double braided polyester rope the new dynamic

stiffness and the dynamic stiffness after 4 years in the sea were found to be

respectively 60% and 90% greater than quasi-static stiffness. The actual

dynamic stiffness, Kap (in 10 4 lbf), measured for this polyester rope when new,

followed the equation:

Kap = 9.457 - 0.578 f2 - 0.196* Fm2 - 0.284* AF2 + 0.271 *f +

+ 1.973*Fm - 0.319*AF- 0.067*f*Fm+0.100*f*AF+

+ 0.464 * Fm * AF,

where: f = (frequency (in Hz) - 0.3)1 0.2;

Fm = (mean load as percentage of BL - 21) / 9; and,

AF = (load range as percentage of BL - 17) / 7.

Using this equation for a loading of 21% ± 8.5% of the BL at a frequency of

0.3 Hz, a modulus of 3.3 GPa is obtained, based on the area of the circle

enclosing the rope section.

72

Recent work by Toomey et al. (1990) on 12.7 mm diameter double braided

polyester ropes cycled between fixed strain limits, reports much higher values

for dynamic modulus. Most of the testing concentrated on frequencies and

load ranges much bigger than those found in spread moorings of large

floating structures, and caused the ropes to overheat. However a few tests

were performed under milder conditions and the samples were kept cool. For

a mean tension of 20% of the nominal BL and a strain range corresponding to

a load range of ±7.5% of the BL, at 0.2 Hz, a modulus of 5 GPa was

measured.

Karnoski & Liu (1988), from the US Naval Civil Engineering Laboratory, tested

a polyester Superline (parallel sub-rope construction) with an additional

extruded polyurethane jacket. The rope had a diameter of 53.34 mm without

the extruded jacket. A typical core diameter would be 47.34 mm (not

mentioned in the paper). The rope extension limits are given for a cycling load

corresponding to 8% to 50% of MBL at 0.1 Hz. Based on this figures, the

dynamic modulus including the braided jacket would be ca. 8.4 GPa and the

core only would have a modulus of approximately 9.6 GPa (considering that

without the cover the strength of the rope is reduced by 10%).

The data contained in Karnoski & Liu (1988) had not been analysed in the

"pilot study", because Taylor et al. (1987), also with the US Naval Civil

Engineering Laboratory, gave direct results for the dynamic stiffness of a

38.1 mm Superline (3.6 GPa). The latter figures, reduced by an estimated

10% to account for scale effects to a breaking load of about 5000 kN, are

shown in Table 4.3.

Ractliffe & Parsey (1985) studied the dynamic behaviour of 8 strand and

Superline (parallel sub-rope) nylon and polyester ropes. It is worth

remembering that the Superline has a braided cover and a core containing

the main load carrying 3 strand sub-ropes. The model presented does not

account for any influence of mean stress on modulus. The discussion

presented in the paper only allows the calculation of maximum and minimum

modulus, corresponding to the high frequency and the quasi-static conditions.

For the polyester 8 strand rope these values were respectively 0.57 GPa and

1.61 GPa. The maximum dynamic modulus obtained using the equations

73

presented by Ractliffe & Parsey for a PET Superline for a load range of 20% of

UBL, was 2.51 GPa. Even for a result incorporating the braided jacket this is

very low. Considering this result is substantially lower than .reported by Bitting

(1980) and by Toomey et al. (1990) for nominally much more compliant ropes,

and less than 1/3 the modulus measured by Kamoski & Liu (1988) for a rope

of similar construction, the only possible conclusion about this result is that it

should be treated with caution as should the model used.

Considering the large discrepancies found in the results in the literature a

limited amount of testing was done at this stage on a small diameter parallel

strand polyester rope (Brascorda Parallel). The rope consisted of 24 strands

laid in parallel, enclosed on a polypropylene braided cover. The approximate

diameter of the core was 9.5 mm and the average breaking load of the rope

with the cover removed was ca. 40 kN.

Testing was done in a Dartec servo-hydraulic tension testing machine. Load

was measured with the built in load cell. Strain was measured with an

extensometer directly attached to the rope free length (Figure 4.22). The

extensometer used was designed specifically for this project. It is a full bridge

90 mm gauge length extensometer, for ±10 mm deflection. Its sensitivity

(indicated strain / actual strain) is 0.02115 at a gauge factor of 2, and its

stiffness is 0.0063 N/mm. A Measurements Group model P-3500 digital strain

indicator was used as conditioner, the results being plotted on a Gould Series

60000 XY plotter.

From these exploratory tests the main trends reported by Bitting (1980),

concerning modulus dependency on the loading parameters were verified.

The results obtained for the dynamic modulus were quite high. Typical

modulus at a loading of 20% ± 10% of the BL was about 15.5 GPa, based on

the estimated area of the circle enclosing the rope core. No effect of frequency

was measured in the dry condition. An increase of 4% in stiffness was found

on the wet tests, between 0.01 and 0.2 Hz. Stiffness variation with load range

was 12%, for ranges from 10% to 20% of the BL (stiffness decreasing with

increasing load range). Stiffness variation was found to be 26% for mean

loads varying between 10% and 30% of the BL.

74

4.6.5 Weight

The dry weight data shown in Table 4.3 came mainly from manufacturers'

catalogues and is presented as weight (kgf) per unit area (enclosing circle,

mm2) for 100 m of rope. Submerged weights were based on yarn densities

assuming the ropes to be completely flooded. This will normally be the case

since: (i) it is very difficult to guarantee that there are no leaks in the jacket or

in the termination, (ii) only fibres with little sensitivity to sea water are likely to

be used, (iii) a flooded rope will exchange any heat (generated by hysteresis)

better than a dry rope, and flooding is necessary to eliminate hydrostatic

pressure.

4.6.6 Cost

Every effort was made to obtain consistent and relevant cost data. Most data

shown on Table 4.3 came from rope makers, who were asked to consider a

price based on a requirement for:

- eight mooring lines;

- 1000 metres long; and,

- 500 metric tonnes breaking strength.

Jacket and termination costs were excluded for normalisation wherever

possible since exact needs would depend on the full lengths required and

handling procedures.

Costs shown in Table 4.3 refer only to the capital cost of the tether. It is

appreciated that apart from the interaction between the tether properties and

the mooring system behaviour, which is discussed in Chapters 3 and 9, a full

comparison of the cost implications of different tether systems would take into

account:

(i) the vertical load imposed on the rig by the lines;

(ii) the cost of installation;

(iii) jacketing cost;

(iv) the cost of termination; and,

75

(v) the life cycle costs (inspection, replacement and removal).

4.6.7 Creep

Very little has been published concerning the long term elongation behaviour

of fibre ropes under constant load. Although more elaborate constructions

present a residual or permanent elongation after a few cycles at any

significant load level , for more parallel rope constructions this effect is

reduced to very small levels. McKenna (1979) quoted a residual elongation of

4.5% for a double braided polyester rope cycled between 10% and 20% of the

BL. No precise figures were found for any other construction.

Total elongation with time including initial elongation could not be found for

any fibre rope. Two references present partial elongation results for small

diameter ropes.

Lewis (1982) presented measurements of "creep strain", possibly meaning the

additional elongation measured subsequent to an "initial" elongation, for

several small diameter Kevlar 29 and Kevlar 49 ropes. The actual

measurements are not presented but the curves pictured start approximately

10 minutes after loading and the results are shown as linear on a logarithmic

time scale. Table 4.4 shows the creep rates quoted, in % per time decade. It

was not possible to identify whether the loading was based on the nominal or

in the average breaking load of the ropes tested.

Linear Composites Ltd. (1983) tested small diameter Kevlar 29 and polyester

parallel lay ropes (Parafil) up to 7 years under constant loads corresponding

to fixed percentages of the nominal (catalogue) breaking load. Presentation of

results is similar to Lewis (1982) in that the initial elongation of the rope is not

given, but the actual test data is tabulated. Although Linear Composites Ltd.

(1983) did not attempt to fit a linear logarithmic time law to the data, a

reasonable fit was obtained, and the rates obtained are also shown in Table

4.4. Since the data is quite sparse and has some scatter other curve fits give

similar coefficients of correlation. LCL, for example, fitted a straight line on a

linear time scale for the data points after 230 days.

76

Results obtained by Lewis (1982) and Linear Composites Ltd. (1983) show

consistent creep rates of around 0.045% per time decade for parallel laid

Kevlar 29 ropes over the useful range of loads in .catenary mooring

applications, well in agreement with Kevlar 29 yarn data (0.050% per time

decade) at 50% of the breaking load.

The result for the PET Parafil, 0.089% per time decade, is lower than values

for PET yarn given by ENKA (1985,3), 0.12% per time decade between 103

and 104 s, under a load of 40% of the yarn actual breaking load. Differences in

yarn characteristics, are not a plausible explanation for such a difference in

favour of the rope. A more sensible explanation is that the rope shows the

same trend as the yarn (Tabor & Wagenmakers (1991) and ENKA (1985,3))

with decreasing creep rate as time passes. The scatter in the data presented

by LCL does not permit a verification of this hypothesis.

The wire rope construction tested by Lewis had a creep rate almost three

times the parallel lay ropes. This clearly shows how, even on a small rope, the

effect of twist can predominate over the yarn behaviour.

4.6.8 Tension-Tension Cycling ("Fatigue")

The subject of "fatigue" resistance has been investigated mainly for ropes

used in hawsers which connect shuttle tankers to buoys in single point

moorings (Parsey (1982) and (1983), Parsey et al. (1987), Heade & Parsey

(1983), Van Leeuwen (1981) and Werth (1980)) and as part of a wave energy

recovery system programme (Crawford & McTernan (1983), (1985) and

(1988)). Plaited and double braided ropes mostly of nylon and PET yarns

were tested generally under severe loading conditions, i.e. load ranges above

30% of MBL and very low minimum loads (below 5% of UBL), in various

frequencies and environmental conditions (wet, dry, partially wet and drying).

Parsey (1982) and Hearle & Parsey (1983) have postulated the following

mechanisms of "fatigue": creep, hysteresis, filament fatigue, structural fatigue

and abrasion.

Similarly to what has been discussed in Section 4.3.3 with respect to yarns, a

77

creep mechanism under cyclic load was shown to dominate failures when

cycling with very high maximum loads ( Parsey (1982), Hearle & Parsey

(1983)). Small ropes were found to fail at the same strains , measured in creep

rupture tests according to the total time under load, following the model

presented for yams in Section 4.3 (Kenney (1983) & Mandell (1987)).

Synthetic fibre ropes, when cycled, absorb energy due to mechanisms

inherent to the material structure (material hysteresis), and due to inter-fibre

effects, i.e. flattening, twist migration and friction (Parsey (1983). For

temperatures below the glass transition temperature very little of this energy is

expended in changing the molecular structure and in plastic deformation of

the material. Therefore, after a few cycles during which a significant amount of

energy can be absorbed for accommodation of the rope structure, most of the

energy absorbed appears as heat. Since synthetic fibres have generally poor

heat conductivity hysteretic heating is clearly cause for concern. Parsey

(1983) describes hysteresis as the predominant failure mode of large

diameter non-immersed ropes at load ranges above 50% of breaking strength

at periods around 25 seconds. At lower cycling periods of 6 seconds, 112 mm

diameter parallel strand was shown to fail by this mechanism when loaded to

only 23% of its wet breaking load (Parsey et al. (1987)). The ropes tested were

made of nylon, polyester and polypropylene fibres, all of which lose strength

quite quickly with increasing temperature. No failure due to excessive

hysteretic heating has been reported for ropes cycled in water.

Very little evidence has been found of filament fatigue as described by Bunsell

& Hearle (1974),on mooring hawsers retired from service (Parsey et al.

(1987)).

Structural fatigue was described as the gradual failure of individual filaments

by tensile overload due to tension imbalance between rope yarns and strands

(Parsey et al. (1987)). No "fatigue" failure of such kind has been reported

either in laboratory tests or in the field for ropes based on nylon,

polypropylene or polyester fibres. Aramid fibre ropes are more susceptible to

this failure mechanism due to the sensitivity of the material to kinking.

Abrasion failures were found to dominate at load ranges below around 30% of

78

breaking strength and usually happened in splices by yarn on yarn abrasion

and/or abrasion on the thimble. Lives under this kind of loading have been

improved by appropriate yarn finish selection, splice design and protection. In

ropes subject to abrasion, no endurance limit has been found as yet (Parsey

(1982) and Mandell (1987).

For the endurance of wet braided polyester ropes, Mandell (1987) has

proposed a bi-modal heuristic model which incorporates a creep-rupture

behaviour up to 3,000 cycles and an abrasion failure mechanism over 3,000

cycles. The creep model follows the equations given in Section 4.3.1. The

following equation was fitted to the data in the abrasion regime:

N . (1 - S / So) . (Ao / k) . (So / 5)111

where: N . number of cycles to failure,

So = new rope wet strength,

S = maximum force,

Ao = initial rope cross-sectional area,

k . rate of material removal due to abrasion, and

m = sensitivity to load level.

With m assumed to be 3, a value of 10 35 for Ao/k was found to give a good fit

to available data for tests on polyester ropes without protection to the inside of

the eye of the spliced termination(failing due to external abrasion). A value of

1043 gave a good fit for PET ropes with eye protection (failing due to internal

abrasion in the splice).

Figure 4.23 shows data gathered by Mandell from: Van Leeuwen (1981),

Crawford & McTernan (1983) and (1985) and others (proprietary work). The

load range is presented as a percentage of the measured ultimate breaking

load for the ropes (UBL). The strait line corresponds to the creep rupture

model and the S-shaped curves to the abrasion model.

Crawford & McTernan (1988) tested a 28 mm diameter 8 strand polyester

rope. A sample cycled between 1.5% and 15% of the actual BL broke after

3.33 million cycles. A run-out at 6 million cycles from 1.5% to 10% was also

reported. These results are also plotted in Figure 4.23 and can be seen to

agree well with Mandell's prediction.

79

Parsey et al. (1987) gives results for a PET rope tested wet (also included in

Figure 4.23) but no information is given about rope construction, size or other

testing conditions, except the load range. The data presented corroborates

Mandell's model in the higher loading regimes, but at load ranges of 30% and

25% of the BL two samples were considered run-outs with 1 million and ca.

2.5 million cycles respectively. Both performed better than predicted by

Mandell's abrasion model even at the lower abrasion rate (Ao/k = 104-3).

Also plotted in Figure 4.23 is a mean life SN curve proposed by Chaplin &

Potts (1991) for six strand steel wire rope with independent wire rope core

based on carefully selected published work (rope samples showing:

termination failures, too short samples, overheated samples and other

anomalies have not been considered).

It should be noted that for load ranges lower than 40% of the UBL all results

for the wet polyester ropes fall to the right, i.e. on the safe side, of the curve

proposed by Chaplin & Potts, except for 4 run-outs. These results correspond

to lives between 10 5 and ca. 5 * 10 6 cycles. On the other hand under more

severe regimes wire ropes seems to perform better. However, since some of

the tests on the fibre ropes have not been performed under immersion and the

internal temperature in the fibre ropes has not been monitored, it is possible

that excessive heating has been the cause of some of the failures observed

well below the creep rupture line. In the very high cycle regime, Chaplin &

Potts predict a fatigue limit for wire ropes. No such limit has been forecasted

for the braided constructions of fibre ropes due to abrasion.

Other materials and more efficient constructions have been investigated,

mainly in small diameters with the exception of:

(i) some early NEL data on parallel yarn "PARAFIL" rope (Crawford &

McTernan (1988);

(ii) a small number of tests done by Karnoski & Liu (1988) on

approximately 100 tonne breaking load Kevlar 29 parallel lay and

polyester parallel sub-rope construction ropes; and,

(iii) three test results on a 450 tonne Kevlar 29 wire rope construction

(E. I. du Pont du Nemours & Co. (undated).

80

Figure 4.24 shows these results together with the curve proposed by Chaplin

& Potts. The load range is presented as a percentage of UBL. In order to

avoid reducing even more an already quite small database, tests conducted:

dry, wet, drying and at different frequencies have all been included in this

graph.

The tendency shown is similar to that of the braided ropes, but the results at

low load ranges are superior. This is not unexpected since these constructions

have much lower relative motions between adjacent fibres than braided

ropes.

Figure 4.25 is an extract from Figure 4.24 containing only the polyester ropes.

Two results are on the unsafe side of Chaplin & Potts' curve and are

discussed below:

(i) A Superline parallel sub-rope sample with a braided cover and an

additional polyurethane jacket was soaked in water prior to testing

but had no cooling during testing and was cycled at a load range of

62% at 0.1 Hz. There is a strong possibility of overheating in this

test at such a high load range.

(ii) A 10 tonne parallel yam rope sample was fitted with an early model

of a socket and plug termination. Three other tests were conducted

with improved terminations under the same loading conditions and

performed markedly better than the proposed wire rope curve.

The run-out at 2 million cycles retained 93% of the original strength. The

number of test results available here is very small to draw any conclusions but

the trend is still for fatigue lives superior to those of steel wire ropes at cycling

ranges below 50% of ultimate.

4.6.9 Hysteresis

The net energy absorbed inside a rope during cycling, called rope hysteresis,

is composed of: material damping and energy spent by the relative movement

under pressure between fibres in the rope. In generic terms, stiffer yarns and

low twist constructions lead to lower hysteretic energy dissipation. Appendix 1

81

gives the relevant definitions for damping and hysteresis..

Hysteresis energy is of great concern and has been discussed in several

papers on single point mooring hawsers and towing cables. These ropes are

frequently cycled dry or wet, but not immersed. Depending on the rope

diameter and the cycling regime, quite high equilibrium temperatures in the

centre of the rope can be achieved. For example, core temperatures as high

as 130°C have been reported by Toomey et al. (1990), for a 12.5 mm diameter

double braided polyester rope, cycled at 1 Hz with a fixed strain amplitude of

22000

Parsey (1983) cycled previously wet 48 mm diameter 8-strand polyester rope

samples between: 10% and 28%, 10% and 50% and 10% and 70% of UBL at

6 second period. He defined normalised hysteresis as the area within the

loop, on a load elongation plot, divided by the area bounded by the loading

curve, a vertical tangent at the right of the loop and the lower horizontal

tangent to the loop. This definition is loosely associated by Parsey with the

logarithm decrement (Parsey (1983) and with the loss factor, in a later paper

(Parsey et al. (1985)).

Considering the very flat shape of the loading curve found in cycling

hysteresis loops of braided ropes, as shown in Figure 4.26 after National Coal

board (1979), the definition adopted by Parsey is approximately equal to the

relative damping, Drel, as defined in Appendix 1 (i.e. half the logarithm

decrement and n./2 times the loss coefficient or loss factor).

The values quoted by Parsey for his normalised hysteresis quickly collapsed

to about 0.25 after ca. 50 cycles at the lower cycling regime. In the more

severe loadings maximum value measured was 0.29. These values

correspond to a loss coefficient of 0.16 or a logarithm decrement of 0.5 and

are approximately ten times higher than results presented by Van Der Meer

(1970) and by Kenney (1983) for polyester yarn (see Section 4.3.3).

Parsey (1983) also measured the thermal conductivity of dry compacted

polyester strands, and found 0.17 W/m.°C.

Toomey et al. (1990) tested 12.7 mm diameter braided PET rope dry and wet

82

at constant strain ranges for frequencies between 0.0667 and 1 Hz. His results

do not allow a direct evaluation of the energy dissipated in the wet tests

because only the temperature rise in the rope is given. Nevertheless it is

interesting to note that even when cycled at 1 Hz at a strain rate of 0.44 s 4 the

rise in temperature in the centre of the rope was limited to 5°C.

Li et al. (1990) used Toomey et al. (1990) data to adjust a thermal model to

simulate the heating of braided fibre ropes subject to cycling. The estimated

rope conductivity dry was found to be 0.12 W/m.°C. The heat transfer

coefficient in the wet tests varied between 1000 and 3000 W/m 2.°C which was

considered could be taken as infinity with negligible error, i.e. the external

temperature of the rope wall was effectively equal to the water temperature.

Hobbs & Raoof (1985) reported on hysteresis in large steel spiral strands.

Results were presented as damping capacity which corresponds to twice the

logarithmic decrement (Appendix 1). Peak values were found to be about

0.30 corresponding to a logarithmic decrement of 0.15 and a loss coefficient of

0.048. This result is an order of magnitude bigger than results compiled by

Lazan (1968) for a variety of carbon steels. No influence of frequency has

been measured in wire ropes.

To assess the hysteretic behaviour of a more parallel construction a 10 mm

diameter parallel strand rope (Brascorda Parallel) was cycled wet, at 0.2 Hz,

between 10% and 30% of UBL. After 100 cycles the loss coefficient was down

to approximately 0.02, which is quite close to the yarn results (Section 4.4).

The difference between this result and the 0.16 reported by Parsey (1983) is

striking, although expected, since the construction of rope tested by Parsey

incorporates several levels of twist and a braiding operation as well.

4.6.10 Field Experience

Large diameter stranded and braided polyester ropes have a good reported

performance as single point mooring hawsers, however tension load histories

are quite different in catenary mooring systems. Hawsers operate

discontinuously, being generally left floating unloaded when there is no ship

83

moored to the buoy. When the rope is being used, its mean load is normally

lower than in the legs of a spread mooring system, but tensions due to low

frequency movements from the tanker in relation to the buoy can be very high.

The number of handling operations is also much higher than in a catenary

system leg. The detrimental effect of sun light and the formation of salt crystals

inside the rope structure are additional factors that make the application of

synthetic fibre rope in hawsers generally more severe than in spread mooring

systems.

Concerning the long term strength degradation of ropes made from polyester

fibres continuously immersed in seawater, data is limited to two conflicting

references described below.

Bitting (1980) tested 12.7 mm diameter double braided and plaited ropes after

immersion for up to 5 years as part of several buoy moorings. Some samples

of the double braided rope were partly in contact with the sea bed. The

nominal tensile load in the samples was very small. The samples of the

braided rope removed from different mooring locations showed retained

strengths linearly decreasing with time, and after 5 years the retained strength

was 50% of the original measured breaking load, five samples of the 8 strand

rope were removed after being installed for 5 years in moorings without

touching the sea floor. The average retained strength was 76%. It should be

noted that none of the samples had protective jackets and the upper end was

ca. 1.5 m below the water surface. Although photochemical degradation

caused by the sun light was not mentioned by Bitting it is more than likely that

it had some effect on the samples.

Linear Composites Ltd. (1983) reports that polyester parallel yarn (Parafil)

ropes recovered from seawater moorings after 10 years showed no strength

degradation of the rope or of yarns removed from the rope. No details of the

installation are given.

Two types of ropes have been used in actual catenary mooring installations: a

polyester parallel sub-rope construction (Superline) and an aramid wire rope

construction (Jetstran, made by Whitehill in USA).

Three 38.1 mm (1.5 inch) diameter 1067 m long Superline ropes in

84

combination with chain and anchors were installed by the US Navy in a

triangular shaped semi submersible in 887 m of water off the coast of

California. More details of the installation are given in , Section 3.1. The

installation was considered successful (Taylor et al. (1987)) but no report was

found on the log term performance of this mooring.

The only rope with recorded experience as part of mooring lines of the size

compatible with the application now studied is the aramid, Kevlar 29, wire

rope construction made by Whitehill.

A 63.5 mm (2.5 inch) diameter, 1.87 MN (420,000 lbf) breaking strength, 18-

strand Jetstran rope was used for the Ocean Builder I moorings in 1983

(Riewald (1986) with very poor performance, resulting of several line failures

at very low loads. This was found to be due to unpredicted alternate

compression loading in the rope fibres, causing kinking, and subsequent

tension fatigue damage, during system pre-deployment (Riewald et al.

(1986)).

A 36-strand construction, nominally 4.45 MN (1 million lbf) breaking strength,

101.6 mm (4 inch) diameter (including jacket), 305 m (1000 ft) length of rope,

of the same material and manufacturer was installed as part of the catenary

mooring system of a semi-submersible drilling in 468 m of water in the Gulf of

Mexico in 1985 (Koralek & Barden (1987). The average dry breaking strength

of the rope was 4.40 MN and a single sample tested after 2 weeks immersion

in tap water broke with 4.00 MN.

The rope was retrieved after five months. The only signs of damage were on

the cover inside one of the eyes. Subsequent breaking tests on two

specimens taken from the rope gave an average strength of 4.09 MN and all

broke at the new splice. As the specimens bled water during testing, it was

considered a wet test. The load obtained corresponds to a loss of 7% on the

average obtained for the new dry rope and to a 2% gain over the only wet test

performed on a new specimen.

Two 50 meter lengths of this used rope were re-spliced and sent to Brazil. The

first was installed in 1987 in a semi-submersible production platform operating

in 240 metres water depth in Campos Basin in combination with 76 mm (3

85

inch) ORQ chain, in a lightly loaded mooring leg. During the installation the

rope was coiled in the drum of the anchor handling boat over a shackle and

the jacket was locally cut by the shackle pin. No damage was apparent in the

rope strands, so the rope was deployed. The rope was removed after five

months. The eyes showed no damage. The wet breaking strength recorded

was 3827 kN and the rope broke in the region were the jacket had been

damaged, showing that somehow the rope had been damaged.

The other rope sample was installed in the same rig and location, but in

another mooring line (facing the strongest weather), in June 1988. The

specimen performed well for 18 months. Upon recovery the sample was found

to be mechanically damaged. A deep cut was found in the rope cover away

from the terminations. It was not possible to visually assess the presence of

damage in the rope strands. Tested to failure the rope showed a residual

breaking load of 3182 kN. Failure happened in two locations, 4 strands broke

at the mechanically damaged section, and several others broke at the splice

situated closer to the damage.

The experience with wire rope construction aramid mooring lines has shown

that the susceptibility of the material to kinking and handling damage has to

be taken into account. Up to now there are no reliable models to predict the

stresses in all fibres of a complex braided or twisted rope construction under

various cyclic loading conditions. This puts a question mark in the use of these

ropes in a non redundant structure with fixed risers.

86

1970 1975 1980 1985 1987

('000 tons) (%) ('000 tons) (%) ('000 tons) (%) ('000 tons) (%) ('000 tons) (%)PolyamideWestern Europe 606 32 603 24 637 20 639 19 629 17USA 606 32 854 34 1,083 34 1,042 31 1,147 34Japan 303 16 276 11 319 10 303 9 333 7Other regions 379 20 779 31 1,147 36 1,379 41 1,555 42World 1,895 100 2,512 100 3,185 100 3,364 100 3,702 100

PolyesterWestern Europe 458 28 638 19 707 14 889 14 848 11USA 654 40 1,377 14 1,819 36 1,524 24 1,619 21Japan 311 19 437 13 606 12 634 10 617 8Other regions 213 13 907 27 1,920 38 3,301 52 4,627 60World 1,635 100 3,359 100 5,053 100 6,349 100 7,712 100

AcrylicsWestern Europe 402 40 526 38 688 34 842 35 821 32USA 221 22 235 17 344 17 289 12 282 11Japan 262 26 235 17 344 17 385 16 411 16Other regions 121 12 388 28 648 32 890 37 1,052 41World

tellulosics

1,006 100 1,385 100 2,024 100 2,405 100 2,567 100

Western Europe 1,092 30 769 24 872 25 702 21 688 21

USA 717 20 470 15 550 15 253 8 228 7

Japan 498 14 391 12 432 12 388 12 372 11

Other regions 1,293 36 1,571 49 1,703 48 1,940 59 2,001 60

World 3,600 100 3,201 100 3,557 100 3,283 100 3,289 108

Table 4.1 - Production figures for man-made fibres from 1970 to 1987

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6

CDC°.-

-00) CZC CL2..)065

CVCM

ciCDCOci

h.-'szrci

COCOci.

CDCOci.

CD1-.-:

CDCO

c;CD.-i-:

rn-•crci

COcoci

..4-a)ci.

(NJc,..

rc.=0 •Tcs.

I)Es._

JDa)

.-c7)70

IDon-77.30>.

TD0.

a)c='-a)a=

U);a517;a)>,

o•0 a,

CEa..—cn

Tu—*FsZ 6

,0tii

-�.-0C)-

=,.-Ct$‘-(1'CL'a- 5

64>.0cp.

Cr)Co0a)aoL._

112

0),(11co-5a)Y

=E

(150_

C S)

ca>a)Y

C/)Coc.)a)c.0L_

a)

a)-a.as7cuY

=

C'30_

a)

as'5a)Y

7C)C-s-6

-0 a)

-0=0-0

c)47),,—1-.5a)CI

(/)

CE.0 ./Tn.-0a)-0m.._..

a0)Tr_cz—>a,Y

a)00'-'0

• t=

toc,-)(>8

a)CX2a)•-.-

IDcEto

—Es.-0.u)

Material Construction Diameter

mm

Load

% of BL

Strain Rate

% / decade

Reference

Kevlar 49 parallel lay 11 20 0.027 Lewis (1982)

Kevlar 29 parallel lay 9.5 50 0.051 Lewis (1982)

Kevlar 29 braided 6.35 50 0.088 . Lewis (1982)

Kevlar 29 wire rope 6.35 40 0.124 Lewis (1982)

Kevlar 29 parallel lay 5.4 20 0.041 LCL (1983)

Kevlar 29 parallel lay 5.4 40 0.038 LCL (1983)

Polyester parallel lay 10 40 0.089 LCL (1983)

Table 4.4 - Creep rates reported in the literature for small fibre ropes.

double - braided

eight - strand

parallel sub - rope

three - strand

wire rope parallel yarn

Figure 4.1 - Conventional and low twist rope constructions.

.0

C 13.)

g-4 0 r.., t-I

CD ...4 a) 0 C) -CE 41-, C CD JD CD

>. 7 C. C 4-E ..-c

4-1 4-4 E ..-1 ca co C

CO 7 0- a) -C ..-t

a CO C. Lo = C.) C.,_

4.J-•-n •—n E-C a) 7

(-)

t

Aload load

•elongation

/t

/ tangent

High Modulus

elongation

Normal Modulus

Figure4.3 - Load - elongation curves for normal and high modulus fibres

(from ASTM - D855-85 (1985))

40 60 „ 80 100RELATIVE HUMIDITY (%)

Figure 4.4 - Effect of relative humidity on the initial modulus of nylon

(from HadIley et al. (1969).

RIEWALJ3

flIflul7 u

i0-2 aiu 111 035

Figure 4.5- Kinks in aramid fibres (from E.I. du Pont du Nemours & Co. (1987)).

Twist 1.1T.M.72°F, 55% R.H.50% OF ULTIMATE STRENGTH

Dynema SK60

0 30% of YBL

^

POLYESTER

"=" 100 yr

— 1 yr

114

0.1 1.0 10

100

1000

lime, Hours

Figure 4.6 - Creep results for selected man-made fibres and steel wire

(adapted from E.I. du Pont du Nemours & Co. (1987)).

20

16

C)

12

0i-tif 8F-

4

0.2 0.4 0.6 0.6

10

FRACTION OF NOMINAL (1 SEC.) BREAKING LOAD

Figure 4.7 - Stress-rupture of selected man-made fibres

(adapted from E.I. du Pont du Nemours & Co. (1987)).

0

100

80

60

40

20

0o2 4 6LOG (TOTAL TIME TO FAILURE. SEC.)

Figure 4.8 - Cyclic endurance ("fatigue") trend lines for nylon 6.6 and

polyester yarns (from Mandell (1987)).

Moving Yam 0

FIBER

STRENGTH LOSS. %

DRY WET

Nylon (T-707) 8 (3220)

DACRON* Polyester (T-67) 34 52

Steel Wire 2 0

KEVLAR* 29 Aramid No Finish (1-962) (380) (45)

KEVLAR 29 Aramid Standard Finish (1-961) - (65)

KEVLAR 29 Aramid Cordage Finish (1-960) 10-20 20-30

Figure 4.9 - Schematical set up and results of yarn on yarn abrasion for

10000 cycles at 20% of YBL. Results in parentesis indicate cycles

to failure (from E.I. du Pont du Nemours & Co. (1987)).

Figure 4.10 - Arrangement of atoms in the molecule and molecules in the

crystalline structure of polyethylene terephthalate (from Ward

(1990)).

MICRO FIBRILS/

( b )

EXTENDEDNON-CRYSTALLINE

MOLECULES

CRYSTALLITES

DISORDEREDDOMAINS

Figure 4.11 - Structural model of polyester fibres (fibre axis vertical) (from

Prevorsek & Kwon (1976)).

50

Z40z...,--..U1

30Lov)a-J

20

10

0

0.70 0.75 0.80 0.85 0.90

fcv = Vc . fc + ( 1 - Vc ) . fc

Figure 4.12 - Polyester fibre modulus (LASE-5) as a function of overall

structural orientation (from Dortmans (1988)).

0.80

-0.40

• 05

10strain ('%)

Figure 4.13 Specific stress and tangent modulus of Diolen 855T yarn

(redrawn from ENKA (1985,3)).

30

00

0.1

0.2

0.3

Mean Stress (GPa)

Figure 4.14- Influence of mean stress on the dynamic modulus of PET yarn

(data from Van Der Meer (1970)).

140

120

60

400.001 0.002

extent of deg rationLog (A/(A-x))

0.0040.003

13 95% R.H.

• 75°/0R.H.

Figure 4.15 - Influence of time on the hydrolytic degradation of PET yarn

(data from McMahon et al. (1959)).

o

100

200

300

time (days)

.ctoc

Figure 4.16 - Retained strength of PET yarn at different levels of hydrolytic

degradation (redrawn from McMahon et al. (1959)).

7.5e-5

5.0e-5 -

El PET fibre

• 10-ra PETsheet

D 0.5-rni PETfilm

320

340

360

380temperature (°K)

2.5e-5 -

Figure 4.17 - Influence of temperature on the hydrolysis of polyester fibre and

film (data from McMahon et al. (1959)).

ICI (undated) SL 4.7617e-13 10'(3.4248e-2T) (a)

McMahon (1959) SL 1.2038e-17* 10'(4.4889e-21) (b)

02 5 0 300

350

temperature ( °K )

Figure 4.18 - Degradation of PET yarn in immersion as a function of

• temperature according to ICI (undated) and data from

McMahon et al. (1959).

400

115

Figure 4.19- Resin socket termination.

Figure 4.20 - Cone and plug (barrel and

spike) termination.

packing

ELONGATION

I 10 50

L r L

1-4

ALn

t

Figure 4.21 - Quasi-static load elongation behaviour during initial rope.

cycling (from McKenna (1979)).

Figure 4.22 - Photograph of extensometer mounted on rope sample.

• • \ • NX Xo X XIX

• • • Mandell•••n..

•IC • X A

0

••••

Chaplin & Potts

1 0 1 0 3 1 0 4

Log cycles to failure

1 0 710 10

100

90

:3 80

70

60

50

Es 40

D30

20

10

.10

Figure 4.23 Fatigue data for several constructions of PET fibre ropes tested

wet (data from several authors), and model proposed by

Mandell (1987) to predict rope life. Steel wire rope mean life

curve (Chaplin and Potts (1991)) also shown.

70

60 —

10 —

"o. • ---r9 . ......, . •. .."1 . • .1T1-1-11 • • • •TrT71 •

1 0 2 1 0 3 1 0 4 1 0 5 1 0 6 1 0 7 1 0 8

Cycles to failure

Figure 4.24 - Fatigue data for low twist rope constructions (various test

conditions).

70

60 —

aco 50 —ne

40-0C)Cco• 30-

0o...s 20—

0

CI 101f Parafi Term.1

• 101f Parafil Term2

O 10 tf Parafi Term3

118 tf Superfine0

III 118 11 Superfine run out

— 6 strand wire we

o

10—

0 -• w TT CITY' • • • • • a I .1 v • • "1.9 11 0 2 1 0 3 1 0 4 1 0 5

Cycles to failure

i I 1-1 . -9 •

1 o6

I. II I W.I., 1 II . 11.111111

1 0 7 1 0 8

Figure 4.25 - Fatigue data for low twist PET fibre ropes (various test

conditions).

ITH,4-00

i.

• :

•

. i

•

14.50_ 12'1s% 3 1-3•1 HAX

:

OGZ.b kEtJGTH

I ;:

I ;

• : I • ! •

_ .16r I. oADIO

tr ONLOAD

; •-

• i ' i

: I

• ! , . ! . i

I • 1 . l'nfirre : EVERY 10771 404D tpla. 2

n .: 1 : 1

1

— 7- - i—i —1 - : 11 VA 14.0 A b ii 1/416 ...A.1.-.50411.419

' 1 :1 1

-.L I • .1______ . • - 5

. i ... I i

. .. n : . • 1

. , .

• "

, •

I. 11)

I .

i

• i

le :

I . :

+11 (IOW

':;.—

(IOW

TO% Ny .10 FIRXI ID 20 .

;&:—.-.. OXIG47'104.1 70 • •

• 1 • .

. . .

;•

"• •

Figure 4.26 - Load strain measurements on a 870kN double braid PET rope.

First and 120th cycles between 1 and 52% of UBL shown

(from National Coal board (1979)).

Lowt,iNia__ •

120 rt-i Un_n_optbit,jd

5. IDENTIFICATION OF PARAMETERS & TESTING PLAN

5.1 Identification of Parameters

This section summarises the outcome of the background work done

highlighting:

(i) the choice of the most attractive light weight tether systems for

catenary moorings;

(ii) the behaviour of the moored vessel using these systems;

(iii) the typical loadings expected to be seen by the LINTs during the

installation and the operational phases of the system;

(iv) the unknown tether properties when subject to these typical

loadings; and,

(v) the missing or unreliable information concerning the long term

behaviour of the LWTs selected.

Since most of the work mentioned in this section has already been extensively

discussed in previous chapters, only the conflicting references are spelt out.

The background work can be summarised as follows:

Spread mooring systems with lines composed of:

(i) an upper component of steel wire rope or steel chain;

(ii) an intermediate component of fibre rope; and,

(iii) a lower component of steel chain leading to an anchor;

are viable alternatives to wire rope only, or wire rope (upper component) and

chain, for deep water moorings.

Systems based on ropes made of high strength polyester fibres in parallel

yarn, parallel strand or parallel sub-rope constructions can be cheaper than

the all steel alternatives. Not only that, these systems attract much lower loads

at wave frequency and consequently are able to meet the same tensile safety

factor using components of substantially lower breaking strength than the

equivalent wire rope-chain combination mooring.

Systems based in fibres with lower modulus, like nylon and polypropylene, are

not able to meet typical offset requirements (10% of water depth) when sized

87

based on obtaining a safety factor on strength. They would need to be made of

a larger diameter in order to obtain the stiffness necessary and in this way

become economically unattractive and inconvenient to handle.

Systems based on stiffer fibres, such as aramids and HMPE, would be

substantially more expensive than all steel components. They also attract

much higher loads at the wave frequency than the systems based on polyester

fibre. For typical loadings and offset requirements the latter systems are

preferred, however systems requiring extremely tight offset control can

possibly benefit from a stiffer LWT.

The wave frequency line tensions were found to increase as a function of line

stiffness. There is an apparent disagreement, in the literature, on the

quantitative nature of this tension increase. According to Global Maritime

(1989), at typical storm conditions, maximum wave frequency line tensions

tend to be similar to the tensions that would be developed in a straight tether

due to its axial stiffness, the so called "frozen catenary behaviour". Global

Maritime Ltd. (1989,1) warned that "in fact modes of oscillation are not

generally as simple as this suggests". These results were based on

harmonically oscillating the line top in an horizontal movement. Results

obtained by Larsen & Fylling support these observations. Results obtained by

Pollack and Hwang (1982) for harmonically oscillating the line top

simultaneously in horizontal and vertical directions in the plane of the line

showed the same trend to increasing tensions for increasing tether stiffness

but did not mimic the "frozen catenary behaviour". These results are supported

by work performed by GVA (1990).

As a consequence of the increase in line tensions with dynamic stiffness, as

water gets deeper, wave frequency tensions decrease and represent a lower

proportion of maximum line tension. In consequence the error in calculating

the maximum line tension via a quasi-static analysis decreases with water

depth. Polyester rope-chain combination systems, because of their lower wave

frequency tensions than all steel systems, show a lower discrepancy from

tensions calculated by a quasi-static analysis. In 1000 m in North Sea

conditions, differences as low as 1% between the two analysis methods have

been calculated.

88

Material damping, i.e. energy absorbed internally to the mooring line, is

considered low enough in comparison with hydrodynamic damping caused by

drag, to be discarded from most dynamic analyses of all steel systems. If light

weight tethers have substantially higher damping, this approximation may not

hold. Very little information was found on the damping factor of fibre ropes.

Results for polyester ropes were only found for 8 strand plaited ropes at 6 s

period. Although these were not clearly presented it is estimated that these

ropes have a damping factor ca. 3.5 times greater than the peak values for

steel wire ropes. Limited testing on a 10 mm diameter parallel strand polyester

rope indicated damping factors lower than peak wire rope values and almost

one order of magnitude lower than obtained for plaited PET ropes. Reliable

values for the damping factor of PET ropes in low twist construction, are not

available for the range of loading conditions relevant to spread mooring

systems. Also the hysteretic heating of large diameter ropes immersed in sea

water, including its effect on material hydrolysis, have not been addressed.

Very few tensile strength tests have been reported for parallel sub-rope,

parallel strand and parallel yarn ropes. There is disagreement between values

of rope tensile strength reported by manufacturers and independent test

results, concerning these rope constructions. Differences as great as 58%

have been reported! For these constructions information concerning the

diameter of the circle enclosing the rope core and/or the real weight per unit

length of the rope core is very scarce, making it difficult to obtain reliable

tensile strength and specific strength data.

The time dependent load-elongation behaviour of low stretch polyester fibre

ropes in a series of loading conditions pertinent to spread mooring system has

not been characterised. The most important conditions identified were:

(i )

Installation loading - typically represented by a single slow

tensioning to about 50% of MBL followed by 15 to 30 minutes at

this load level to bed the anchor and check that no anchor

movement is taking place. After that the load is lowered to a

working level of say 20% of BL. It is necessary to insure that under

these circumstances the connection with the upper steel

component does not reach the fairlead.

89

(ii) Quasi-static loading variation - typically represented by a slow

change in tension, for example ± 10% of UBL, about the pretension

level (say 20% of UBL). Changes between these limits may occur

with periods of between a few hours and say one week. The

apparent stiffness of the LVVT component in this loading condition

should be used to assess the mean offset.

(iii) Low frequency loading - represented by relatively slow tension

variations, associated with the system natural frequencies of surge,

sway and yaw. In deep water the natural periods will typically vary

between 50 and 200 seconds. The mean tension associated with

these loads can be anything from 10 to 50% of UBL. The limited

investigation performed in the "pilot study" suggests that the

amplitude of these motions is not likely to exceed 10% of UBL.

(iv) Wave frequency loading - typically consisting of small amplitude

tension variations, with periods between 5 and 17 seconds.

Maximum amplitudes should not exceed 15% of UBL for depths of

water larger than 500 m. The mean load for this condition can vary

over the operating range of the mooring lines, i. e. between about

5% and 50% of UBL.

(v) Long term mean environmental loading - represented by a slowly

changing sequence of constant loads, responsible for a creep

behaviour of the LVVT. For a typical pretension of 20% of MBL,

maximum mean line tension in the lines that face the prevailing

environmental direction should not exceed 30% of MBL, otherwise

a change in pretension level or line size would be adopted. This

loading condition can then be simulated by a constant loading, for

example, at 30% of MBL. As in the installation loading, it is

necessary to insure that the connection of the LVVT with the upper

steel component will not foul the fairlead. It is also important to

define the retensioning routine for the mooring lines.

For the ropes selected the limited amount of data available on the number of

cycles to failure in wet "fatigue" tests suggests that for load ranges between 20

and 50% of MBL, the endurance of these ropes is better than the endurance of

six strand steel wire rope. The effect of cycling with a small load range, on the

90

retained rope strength is not known.

Existing data on the long term degradation of polyester ropes or yarns under

the combined effect of moderate constant load and a sea water environment is

very restricted and conflicting (Linear Composites Ltd. (1983) and Bitting

(1980)). Available data on the long term effect of fresh water on polyester

yarns is unreliable for the time scales envisaged (20 years) and also

inconsistent. For example, a 20 years exposure at 20°C according to

McMahon et al (1959) would cause a 2% strength reduction while under the

same conditions ICI (undated) forecasts a strength loss of 37.6%.

The following section outlines the experimental programme set out to

investigate the lacuna highlighted.

5.2 Material Testing Programme

Three rope constructions were found from the preliminary investigations to

lead to mooring systems cheaper than all steel systems:

(i) a Parafil parallel yarn rope;

(ii) a Superline parallel sub-rope construction, made up of pairs of

three strand sub-ropes enclosed in a braided jacket; and,

(iii) a Brascorda Parallel, parallel strand construction, with twisted

strands running in parallel inside a braided cover.

Of these, the two latter were selected for testing. It was considered that the

parallel yarn rope, having no twist or braiding in its construction, could have

most of its properties assessed from tests on yarn and the filling factor reported

by the manufacturer.

Testing was carried out on two scales: industrial yarn and small diameter rope.

In choosing rope size the main constraints were:

(i) to have a strength low enough to make long term constant load

tests feasible; and,

(ii) to have a construction that would display most of the characteristics

of a full size rope.

Ropes with approximately 60 kN breaking load were selected. This size of

91

rope has ca. 250 yarns and 180,000 continuous filaments, and is therefore

able to represent the scatter in tensile properties to be found in a full size

mooring rope.

Unlike steel wire ropes, scaling up fibre ropes can not be done by increasing

fibre diameter. Since packing a large number of filaments in a single twisted

yarn has obvious handling problems, additional twisting operations may be

introduced in the rope structure in the process of scaling up. To account for

that, the ropes tested were not normal production items but model ropes.

Full size mooring ropes of the Superline construction typically have four

twisting operations, one more than the model rope. To compensate for that,

twist (turns per unit length) in the structure of the model rope was increased

accordingly (Street (1989)).

The Brascorda rope has only one twist operation in any scale. Packing a

larger number of yarns per strand increases its diameter and in consequence

decreases the modulus if the same twist is used (Hearle et al. (1969). To

compensate for the larger number of yarns per strand on the full size rope, the

strand twist in the model rope was made slightly greater than in a large

diameter rope.

Scaling down the cover of a rope is quite difficult. On the Superline model

rope, for example, the core represents 38% of the total rope weight and about

17% of its strength, while on a 5000 kN Superline, a braided cover would only

account for something like 13% of the rope weight and 6% of its strength. For

the Brascorda Parallel the difference in strength is even bigger because the

core is proportionately stiffer than the cover. To overcame this inconvenience, it

was decided to test both ropes without their covers.

For the purpose of description, the tests performed were grouped according to

the predominant loading mode or degradation agent under the following

headings:

(i) tensile testing;

(ii) stiffness testing;

(iii) creep and environmental assisted degradation; and,

(iv) cyclic endurance ("fatigue").

92

This headings are carried forward to the next three chapters, were the testing

performed is fully described, the results presented and discussed.

5.2.1 Strength Testing

Since the background work indicated that dynamic loads were not likely to

cause significant degradation of the ropes selected for this application, but

long term creep and environmental assisted degradation were cause for some

concern, relatively simple tension tests, used to determine retained strength,

performed a key function in the testing programme.

After proper gripping methods were developed, yarns as the basic component

of all ropes, had their strength characterised. Residual strength after different

treatments was compared with this data base. The yarn load elongation

behaviour was checked against manufacturers and literature data and gave

the first insight on the material. Models are presently being developed to

predict the tensile properties of parallel yarn ropes based on yarn data

(Burgoyne & Flory (1990)).

Tensile tests were applied to terminated ropes to characterise their initial

tensile strength, specific strength and later to assess their retained strength. To

account for the application in view, a testing sequence was developed to

simulate rope installation and initial loading as in a mooring system (the

procedure is detailed in Section 6.1.2). Elongation during the installation

simulation incorporates bedding in of the rope construction and material

creep. The installation stiffness was defined as the secant modulus measured

at the maximum overall elongation obtained during this process.

5.2.2 Stiffness Testing

Tether axial stiffness was found to dominate wave frequency tensions.

However mean offset is controlled by load elongation properties over a much

longer time scale. Owing to the reported non-linear viscoelastic behaviour of

PET fibres and to the complex structural mechanics of fibre assemblies a

thorough investigation of the behaviour of the elongation behaviour of yarn

93

and model ropes was performed.

Yarn was cycled over the range of wave and low frequencies in all tensile

loading regimes considered possible in this application, to obtain data

pertinent to parallel lay ropes and to allow future modelling of other

constructions.

Model ropes were similarly cycled at wave and low frequencies and also in a

simulated quasi-static cycle. The influence of long term cycling between fixed

load limits, and long term constant loads, on wave frequency stiffness was also

measured.

A limited number of tests were performed to evaluate the hysteretic energy

absorbed by the more compliant model rope, the Superline, at wave

frequency. The hysteresis of a small diameter steel wire rope was also

measured for comparison purposes.

5.2.3 Creep and Environmentally Assisted Degradation

Elongation under constant load was measured for model ropes and yarns at

load levels slightly higher than typical average tensions in a spread mooring

systems.

Yarn elongation results are important as a lower bound to the behaviour to be

found in ropes, but also directly relevant to parallel yarn ropes, as long as fibre

slack is not significant compared to total elongations measured (see Chapter

8).

Strength degradation was measured in yarns that had been under constant

load in laboratory conditions (no temperature or humidity control).

The effect of a range of temperatures (4 to 40°C), load durations (1 to 12

months) and load levels (20 to 40% of UBL) on the retained strength of yarn in

deionised and synthetic sea water was investigated in an attempt to sort out

discrepancies in the literature, and to provide design in support of the long

term use of PET fibre ropes.

Samples of the model ropes were also subjected to the simultaneous effects of

94

constant tension and a sea water environment for up to one year. The retained

strength of these samples was measured to investigate degradation of both

rope material and termination. Elongations measured relate directly to what is

expected in the real application. These results can be used to establish

operational retensioning procedures and, in combination with the elongation

measured in the installation procedure, to set the lower limit for the length of

the upper component.

5.2.4 "Fatigue"

The literature reviewed clearly demonstrates that the predominant failure

mode changes with loading condition. Currently available data is concentrated

at high to medium load ranges, while the outcome of the pilot study shows that

very small load ranges of any significant number of cycles can be expected.

Therefore it is clear that there is no point in performing tests at higher loading

regimes.

Testing was therefore targeted at gaining an insight into any possible failure

modes operating under the mild conditions foreseen in the application, and

obtaining an assurance that the cyclic endurance of these ropes was

satisfactory.

The procedure adopted to run wet "fatigue" tests on the model ropes to 1

million cycles with a load range slightly greater than calculated by Global

Maritime Ltd. (1989,1) as the maximum wave frequency tension range in the

worst design condition (100 years storm in the West of Shetlands in 500 m

water depth). After cycling, the ropes were inspected and their retained

strength measured.

95

6. MATERIAL PROPERTIES: TEST METHODS

6.1 Strength Testing

6.1.1 Yarn

The yarn tested was a high tenacity multi-filament polyester yarn with the

following nominal characteristics (AKZO (undated)):

Manufacturer - AKZO (Holland);

Type - Diolen 855TN;

Average molecular weight - 17000 (Tabor & Wagenmakers (1991));

Number of filaments - 210;

Twist - 0 , yam tangled discontinuously by hot air jet;

Linear weight - 1100 dtex (g/1000 m);

Breaking force - 92 N;

Tenacity (specific stress) - 84 mN/dtex;

Elongation at break - 12.5%;

Finish - marine rope finish;

The yarn is not normally supplied as an individual industrial yarn, but twisted

according to the rope maker's specification. The yarn tested was removed

from a twisted yarn supplied to Marlow Ropes from which the Superline model

rope described in Section 6.1.2 was made. All 20 individual yarns from this

twisted yarn were tensile tested and the one with the highest average

breaking load was selected.

The tests performed to select the yarn for further testing (from the twisted yarn

with 20 single yarns) were conducted dry in a laboratory without thermostatic

or humidity control. Sample length was 250 mm, with a loading rate of

400 mm/minute. Air operated, flat jaws, with rubber linings were used. The

yarns were tested without twist, and results from samples showing filament

breaks inside the jaws were not taken into account.

At the start of the testing programme a number of tensile tests were performed

on yarn Diolen 855T, without marine finish, also used in rope making. The

yarn was supplied by Marlow Ropes from their normal stock. Because it did

96

not have to be separated from other yarn, it was more convenient for testing

than the yarn with the marine finish. These tests were used to investigate the

influence of: gauge length, testing speed and gripping methods. A small

number of tests was run to compare the tensile strength of Diolen 855T with

the strength of Diolen 855TN. Since environmental assisted degradation was

one of the items being investigated the bulk of the testing programme

concentrated on yarn with marine finish.

A limited number of tests was performed on yarn disassembled from the other

model rope tested, a Brascorda Parallel rope (this rope is described in

Section 6.1.2.). This yarn is manufactured in Brazil by COBAFI S.A. and its

characteristics (COBAFI (undated)) are identical to those of the AKZO yarn

except for:

Breaking force - 90 N;

Elongation at break - 13%; and,

Finish - spinning finish only.

To facilitate long term experiments to evaluate the combined effect of constant

loads and a sea water environment, a termination system was devised to

allow direct transfer of samples from the long term loading facilities, into the

testing machine used to evaluate their retained breaking strength, without

need for re-termination.

Figure 6.1 shows a photograph of the termination used. Samples consisted of

pieces of yarn approximately 200 mm long in which each extreme was glued

between two thin tabs of acrylic sheet, leaving a free length of 100 mm. A

room temperature curing epoxy resin was used for this purpose. In order to

distribute stresses more evenly over the filaments as they go into the

termination, the region between the tabs closest to the gauge length

(approximately 10 mm), was filled with a nitrile rubber compound instead of

the epoxy glue.

Samples were prepared 8 at a time using a purpose built jig. Figure 6.2 shows

a photograph of this jig after manufacturing a batch of samples, with one

sample still to be removed from the jig. A template, used to position the acrylic

tabs precisely, is also shown by the side of the jig. The procedure for making

97

the samples was as follows:

position lower acrylic pieces on the jig base, using the template;

position upper acrylic pieces on closing strips, using the same

template;

lay a length of yam straight and centred over the gauge length and

the lower acrylic pieces, fixing the yarn ends to the base with

adhesive tape;

apply epoxy glue and nitrile rubber compound on lower tabs;

close the jig by positioning the strips over the lower tabs;

apply weight to squeeze excess glue; and,

cure for approximately 8 hours at 50°C.

Testing of this samples was performed in an lnstron model 1026 screw type

bench top universal testing machine, with a 500 N load cell. Speed was set at

100 mm/minute and air operated rubber lined flat grips, set 120 mm apart,

were used. Samples were tested wet after immersion in deionised water for

15 minutes.

This termination method gave very consistent performance. Typically,

filaments would break in the free portion of yarn with less than 5% of them

breaking within the rubber filled region. The results for the few samples

showing filament breaks in the region glued with epoxy resin or at the rubber-

epoxy interface have not been included in the analysis.

6.1.2 Ropes

Two model ropes were tested, both manufactured from high tenacity multi-

filament polyester yarns, as described below.

ROPE 1.

Manufacturer - Marlow Ropes, UK;

type - polyester Superline;

construction - fourteen 3-strand ropes enclosed in a braided jacket;

sub-rope construction - 50 turns per metre, 7 z-laid and 7 s-laid;

strand construction - 20 x 1100 dtex Diolen 855TN, 40 turns per

98

metre, s-laid in z-laid sub-ropes and z-laid in

s-laid sub-ropes;

cover - 16 plait polyester cover;

diameter with jacket -14.75 mm (average measured);

diameter without jacket -11.5 mm (average measured);

linear mass - 0.160 kg/m = 160000 tex (average measured);

linear mass of core - 0.0995 kg/m = 99500 tex (average measured).

ROPE 2.

Manufacturer - Brascorda S.A., Brazil;

type - Brascorda parallel;

construction - 34 strands (half z laid and half s laid) in parallel

enclosed in a braided jacket;

strand construction -27 x 1100 dtex PET 855T (from COBAFI), 25 turns

per metre;

cover - 16 plait multi-filament polypropylene cover;

diameter with jacket -18.1 mm (average measured);

diameter without jacket -11.5 mm (average measured);

linear mass - 0.198 kg/m = 198000 tex (average measured);

linear mass of core - 0.107 kg/m = 107000 tex (average measured).

As already discussed in Section 5.2, the cover of these ropes does not have

the same geometrical proportions or the carry the same proportion of the load

as large diameter ropes of the same constructions. Therefore the model ropes

were tested without their covers.

The constructions tested are quite stiff and the working length available in the

tensile testing machine was limited to 1260 mm between the load cell and the

piston attachment plate. Therefore, obtaining an equal distribution of load

between sub-ropes and strands in the terminated samples, was very important

to realise the rope potential strength. The limitation in length also ruled out the

use of splices, which would reduce the free rope length too much.

It was decided to make use of resin cast socket terminations. Trials were run

with different cone angles, cone lengths and resin composition ( formulation,

amount of filler and catalyst ).

99

Best results were obtained for the socket which cross section is shown in

Figure 6.3. This has a 145 mm long, 4.5° semi angle conical region and a

55 mm long 22.5 mm diameter cylindrical region.

The resin selected was an unsaturated polyester resin in styrene monomer

with 27% of filler based on calcium carbonate and 1.13 cm 3 of catalyst (methyl

ethyl ketone peroxide at 50% in phlegmatizer) per 100 g of resin.

Casting procedures normally used for fibre ropes mimic those used for wire

rope (BS 7035 (1989) and Philadelphia Resins Co. (1982)). The main

concern in using a wire rope procedure for a fibre rope is ensuring a uniform

distribution of the fibres inside the socket. Wire ropes are served and then

have the wires splayed to form a broom. When the broom is pulled back into

the socket and during resin pouring, there is no significant change in the

broom shape. That is not the case with fibre ropes, where the filaments do not

have enough stiffness to stay in position. If the socket is being cast in the

vertical position, as is usual, fibres will be washed down and accumulate in

the socket neck and against the wall. It is not a surprise that such terminations

do not provide good efficiency, and so are not normally selected for polyester

ropes.

To overcome this problem the positioning and tensioning frame shown in

Figure 6.4 was designed to be used with the selected socket. Rope

terminations were cast in the vertical position following the procedure

described below:

(i) cut a 2.5 m long piece of rope;

(ii) serve with yarn over the jacket at approximately 600 mm from one

end;

(iii) remove jacket from the serving to the nearer end;

(iv) pass the rope through the socket, taking the serving 80 mm into

the socket;

(v) install centraliser and seal the bottom of the socket with plasticine;

(vi) distribute the individual strands evenly using the top frame and

apply a uniform tension to them by means of dead weights;

(vii) pour the resin from the top and leave to cure;

(viii) remove frame and cut excess fibre flush with resin top.

100

The other socket is cast using the same procedure leaving a free sample

length of 700 ± 20 mm. After that the jacket is cut and removed from the free

rope length except for 50 mm adjacent to each termination.

Basically the same termination procedure and dimensions were used for the

stiffness, creep and fatigue tests.

A two column Dartec servo-hydraulic testing machine was used for the

strength measurements. A 250 kN strain gauge based load cell was used for

load measurement. Actuator stroke was measured by a linear variable

displacement transformer (LVDT) mounted concentrically to the actuator

piston. The extensometer described in Section 4.6.4 was used to measure

rope strain.

The test procedure for strength determination was designed with two

purposes in mind:

(i) to find out how much the rope sample would stretch under a

loading typical of an installation procedure at sea; and,

(ii) to determine the strength of a rope some hours after being installed

on a mooring leg.

Testing procedure was as follows:

(i) install rope in the test frame with the piston fully extended;

(ii) apply pre-load of 180N (ISO (1972);

(iii) measure distance between sockets and mark a gauge length on

the rope;

(iv) installation cycle - load sample to 50% of the expected breaking

load at a rate of 0.1 kN/s, hold for 30 minutes, reduce load to 10%

of the breaking load at the same rate and hold for another 30

minutes.

(v) working procedure - apply 100 cycles between 5 and 30% of the

expected breaking load at 0.1 Hz;

(vi) without touching the sample, reduce load to zero, change feedback

mode to stroke and load to failure at a stroke rate of 0.7 mm/s.

101

6.2 Stiffness and Hysteresis

6.2.1 Yarn

The same yarn,AKZO's Diolen 855 TN, described in Section 6.1.1 was tested

to determine its stiffness and hysteresis.

The termination consisted of gluing each side of a piece of yarn between two

pieces of acrylic sheet. A room temperature curing epoxy resin was used for

this purpose.

The procedure for making the samples was similar to that used on the

samples intended for strength testing but without the use of the nitrile rubber

compound. Free sample length between tabs was 370 mm.

The samples were tested in an Instron model 4302, microprocessor

controlled, screw type, bench top, universal testing machine. Simple clamp

type grips were made as shown in Figure 6.5 to minimise the influence of

machine stiffness.

Extension was measured in two ways:

(i) by means of the built-in encoder on the test machine; and,

(ii) by an extensometer (see Section 4.6.4) attached to the yarn.

The readout from the machine was only used for mean loads of 5% and 10%

of the yarn reference breaking load (YBL, see Section 7.1.1), since, at such

low loads, the weight of the extensometer attached to the yarn would have

influenced the measurements. For higher mean loads the extensometer was

used.

In order to be able to compare results with the rope data the test procedure it

was necessary to mimic the procedure adopted for the rope samples. First the

yarn was submitted to an equivalent 'installation' cycle ( taken to 50% of YBL

kept for 30 minutes, unloaded to 5% of YBL, left for 30 minutes).

The machine was then operated between load limits and cycled at constant

crosshead speed. The following mean loads and load ranges, shown as

percentages of YBL, were assessed in sequence:

102

5 ± 2.5;

10 ± 2.5, 10 ± 5;

15± 2.5, 15± 5;

20±2.5, 20±5, 20±10;

30 ± 2.5, 30±5, 30 ± 10;

40 ± 2.5, 40±5, 40±10;

50 ± 2.5, 50 ± 5, 50 ± 10; and,

a repeat at 20 ± 2.5 and 20± 10.

For each loading, periods of 7.5, 15, 100 and 200 seconds were tested in

sequence. The number of cycles in each condition varied with the period and

was equal to 100, 50, 10 and 5 cycles, respectively, for the above mentioned

periods. For each condition, measurements were taken at the last cycles.

6.2.2 Ropes

6.2.2.1 Stiffness

The stiffness of both ropes described above was evaluated under four

conditions:

(i) after a simulated installation and recovery at low load;

(ii) in a simulated quasi-static loading;

(iii) after "fatigue" testing; and,

(iv) after creep testing.

Samples similar to those use for strength measurements were used. For the

same reasons described in the previous section both ropes were tested

without their covers.

The same terminations were also used.

The same servo-hydraulic testing machine, 250 kN load cell and LVDT were

used. Extension was measured by an extensometer attached to the rope

sample through its knife edged arms pulled against the rope by rubber bands

(Figure 4.22).

Stiffness measurements relating to samples in the simulated quasi-static cycle

103

and after "fatigue" in water, were made using the stroke signal from the built-in

LVDT. These had to be corrected to take into account rope movement inside

the socket. This was achieved by cross plotting stroke versus strain for the

same loading in the dry condition.

The test procedure for the measurements taken in the as installed condition

samples was preceded by an "installation cycle" (taken to 50% of UBL kept

for 30 minutes, unloaded to 5% of UBL, maintained for 30 minutes).

The machine was then operated in load control following a sine wave. The

following mean loads and load ranges, shown as percentages of UBL, were

assessed in sequence:

5± 2.5;

10 ± 2.5, 10± 5;

15

20

30

± 2.5,

± 2.5,

± 2.5,

15

20

30

± 5;

± 5,

± 5,

20

30

± 10,

± 10, 30 ± 15;

40

50

± 2.5,

± 2.5,

40

50

± 5,

± 5,

40± 10,

50 ± 10,

40

50

± 15;

± 15; and,

a repeat at 20 ± 10.

For each loading, periods of 7.5, 15, 100 and 200 seconds were tested in

sequence and the number of cycles at each of these periods was 100, 50, 10

and 5, respectively. The measurements were taken at the last cycles for each

condition.

Before the simulated quasi-static loading an "installation cycle" as described

above and a bedding in loading between 10% and 30% of BL for 1000 cycles

were undertaken. The simulated quasi-static loading started at a load level of

20% of UBL and consisted of:

(i) a 3 hours ramp up to 30% of UBL;

(ii) a 72 hours period at constant load;

(iii) a 6 hours ramp down to 10% of UBL;

(iv) another 72 hours at constant load; and,

(v) a 3 hours ramp up to 20% of UBL.

104

For the samples assessed after "fatigue" testing, stiffness was measured

immediately after fatigue cycling, with the ropes immersed in water. Mean and

load ranges, as percentages of UBL, were: 20 ± 10, 20 ± 5, 20 ± 2.5, 10 ± 5

and 10 ± 2.5, for both rope types. The Brascorda Parallel rope was

additionally evaluated at 5 ± 2.5, 30 ± 12.5, 30 ± 10 and 30 ± 5% of UBL At

20 ±10% of UBL samples were tested at 0.2 and 0.067 Hz (periods of 5 and

15 seconds). At the other loading regimes measurements were all made at

0.2 Hz. The number of cycles at each condition was 100 for the tests at 0.2 Hz

and 50 for those performed at 0.067 Hz.

Samples evaluated after creep, were transferred from the creep rigs (as

described below) to the servo-hydraulic testing machine, loaded to 30% of

UBL, for approximately 30 minutes and cycled at 20 ± 10% of UBL for 100

cycles at a frequency of 0.2 Hz. Measurements were then taken between

these same load limits (20 ± 10%), at 0.2 Hz and 0.067 Hz (5 and 15 seconds

periods).

6.2.2.2 Hysteresis

Measurements were performed on:

(i) a sample of the parallel sub-rope Superline similar to that used in

the stiffness testing; and,

(ii) a 700 mm long sample of a 13 mm diameter 6x19(12/6+6F/1) +

IWRC 7x7(6/1) right hand ordinary lay steel wire rope.

Testing was executed on the 250 kN Dartec servo-hydraulic testing machine.

In the fibre rope test simultaneous readings were taken of: load range,

obtained from the 250 kN load cell, cyclic stroke, measured with the built-in

LVDT of the testing machine, and elongation range, measured over a gauge

length of 90 mm with the extensometer already described.

The steel wire rope sample was assembled in the test frame via a very

compliant arrangement and so stroke measurements were meaningless for

hysteresis purposes. In this case only load and strain measurements were

taken simultaneously.

105

Data corresponding to a single cycle was gathered by the computer that

controls the testing machine, using software developed by the manufacturer.

In each cycle a minimum of 1300 data points (load, stroke, and strain, or load

and strain only) was used.

The area (AU) within the load (y) versus elongation (x) and the load (y) versus

stroke (x) loop was calculated by a separate specially written programme that

scans the data points once in sequence and calculates:

AU = Ei ((x44 . y) - (xi . y io)) /2.

The reference input energy (U) was calculated as:

U = ( (xt-rac xnt) • (Yaw Yrril)) / 8;

where (X rroc , ym3x) and (xni, , yriiI ) are the extremes of the loop.

The fibre rope was conditioned for approximately 1 hour at 20% of the UBL

and then cycled between 10% and 30% of the UBL at 0.1333 Hz. Hysteresis

was measured after: 100, 300 and 1000 cycles.

For the wire rope sample, the data was collected at the beginning of a

bending-tension fatigue test (Ridge (1992)). The rope was kept at 34% of its

UBL for ca. 5 minutes and then cycled at 20 ±14% of its UBL at 0.25 Hz.

Measurements were taken after approximately 100 cycles.

6.3 Creep and Environmentally Assisted Degradation

6.3.1 Yarn

As already explained, the yarn tested was a single yarn removed from a

twisted AKZO yarn, Diolen 855TN. Yarns were terminated using the procedure

described on the section 6.1.1. In this case an additional 5 mm hole was

drilled through each termination, on its longitudinal axis, 10 mm away from the

edge opposite to the gauge length. The samples were hung and loaded

through these holes.

106

6.3.1.1 Creep

Since the only available creep data for the yarn tested was limited to periods

of 2 * 105 seconds(ENKA (1985,3), it was decided to run 'a small number of

tests to evaluate its behaviour up to 7.776 * 10 8 seconds (3 months). For this

purpose two types of tests were run: (i) one week, and (ii) 3 months long.

One week tests were run on the same testing machine used for yarn stiffness

testing, with the same grips and on samples of the same length (370 mm).

The testing procedure was as follows:

(i) install sample in the testing machine;

(ii) apply a pre-load of 0.5 N (ASTM (1985, ref. 58) and measure the

distance between tabs;

(iii) increase load up to 30% of YBL at a constant crosshead speed of

100% of the gauge length per minute ( typical loading time is 2

seconds ); and,

(iv) cycle between loads limits of 30% of YBL ± 0.023% ( ± 0.02 N),

with a variable crosshead speed (starting at 50 mm/minute but

quickly collapsing to 0.05 mm/minute).

Elongation was measured in two ways: by direct stroke reading on the

machine panel (encoder connected to the screw drive) and by a comparator

dial gauge installed between the crosshead and the columns. The resolution

on the panel reading was 0.01 mm and on the clock reading was

0.00254 mm.

A single three months test was done on a 1050 mm long sample. Terminations

were again acrylic tabs glued with epoxy resin. The sample was loaded with a

dead weight of 30% of YBL. A 897.5 mm gauge length was marked on the

sample with a fine black thread. The initial gauge length was measured at a

load of 0.5 N. The elongation was measured with a stainless steel rule with a

resolution of 0.5 mm.

In addition to these tests an insight on the creep rates up to one year was

obtained by measuring the distance between tabs in the yarn samples hung in

air for environmental degradation assessment. This was done with a vernier

107

with a resolution of 0.05 mm.

6.3.1.2 Environmental Assisted Degradation

A complete test facility was developed to allow the long time tensioning of a

large number of yarn samples, under controlled environmental conditions.

Four 200 litre polypropylene tanks were set to run at constant temperatures of:

4, 20, 30 and 40°C. The tanks were externally insulated and provided with

expanded polystyrene covers. These tanks were filled with substitute ocean

water according to ASTM D 1141-75 (1975). Inside each of these tanks an

additional 25 litre glass tank was installed. These were filled with deionised

water (DIW). Figure 6.6 shows a general view of the apparatus with the covers

removed to show the internal details.

For each tank a thermocouple and a heating or a cooling system were

connected to a central controller. Thermocouples were connected to a four

channel digital data acquisition and conditioning system (IMS Electronics,

model CM1600), which in turn was controlled by a BBC microcomputer. A

simple on-off control programme, scanning the four channels in sequence,

was implemented. It provided quite good response since the heating and

cooling elements were selected with a power well matched to the respective

thermal load. A back up bimetallic thermostat was installed on each tank after

a computer failure caused the 40°C tank to overheat.

The tanks operating at 20 and 30°C had one 300 W immersion heater each,

while the 40°C tank had two similar heaters. To avoid corrosion and

encrustation, these heaters were installed inside small glass tanks filled with

deionised water. A 120 W refrigeration unit (taken from a domestic refrigerator)

was used on the 4°C tank. To avoid excessive switching on and off of the

compressor, when the temperature was very close to the set point, a dual set

point system was implemented to control this channel.

Samples were hung from steel bars running across the tops of the tanks and

tensioned by polyester bottles filled with lead shot.

Samples tested in air were simply hung to a bar fixed to a wall, and tensioned

108

by similar weights. Temperature in the basement room where these samples

were tested varied between extremes of 16°C and 24°C over the full 12 month

duration of the tests.

At the end of the exposure, samples were unloaded, soaked in deionised

water for at least 15 minutes and tensile tested to assess their retained

strength. This was done in the same Instron test machine and with the same

procedure as described in Section 6.1.1. Results from samples showing

filament breaks in the region glued with epoxy resin or at the rubber-epoxy

interface have not been included in the analysis.

It was found that some of the yarns samples that had been in artificial sea

water at 20°C and 30°C had developed quite hard fine scale deposits. These

samples had to be left in a 0.1N solution of hydrochloric acid for 2 hours to

dissolve the deposits. This procedure was considered necessary to minimise

the mechanical interaction between the deposits and the yarn filaments. A

batch of tests verified that the immersion for 2 hours in the washing solution

was harmless to the yarn.

6.3.2 Ropes

Both Superline an Brascorda model ropes, described in Section 6.1.2, were

evaluated for their long term elongation and retained strength in substitute sea

water (ASTM D 1141-75 (1975)). Elongation and environmentally assisted

degradation were investigated using the same samples. In order to make this

evaluation in sea water, priority was given to the assessment of

environmentally assisted degradation over precise elongation measurements.

Rope terminations were painted with a marine epoxy paint and were provided

with zinc anodes. A polyethylene bag was installed between the terminations

and filled with substitute sea water.

The minimum number of tests, the loads and the time scales involved,

precluded the use of dead weights or a sophisticated tensile testing machine.

A design was therefore developed to build 4 low cost constant tensioning

machines with a capacity of 18 kN.

109

Two machines were used for testing one sample of each rope for one year.

The two remaining machines were used in sequence for tests running for: 1, 3

and 6 months.

The machine developed is shown in Figure 6.7. The rope sample is attached

between the lower frame and the upper arm by means of articulated holders.

A constant force pneumatic actuator (Firestone model 1T15M-6), fitted

between the frame and the arm, provides the loading. Each actuator was fed

from the building compressed air supply by a two stage precision regulator

(SMC Pneumatics model IR200-02). Between the actuator pedestal and the

upper arm four long screws can be used to either cope with unexpected

sample elongations or to install a load cell to check the actuator force.

Two methods were used to adjust the set point of the pressure regulators:

(i) a compression load cell, giving an indirect reading of rope tension

via actuator force; and,

(ii) a tension load cell mounted in place of the rope sample.

The compression load cell had to be short in order not to increase the size

and affect the design of the the machine, and it also had to provide bending

stiffness to avoid instability of the actuator. Since a commercial cell could not

be found a slotted hollow cylindrical load cell, based on beam shear was

design and used interchangeably on all machines. Figure 6.8 shows a

schematic drawing of the compression load cell.

Due to the imprecision resulting from these indirect measurements, a tension

load cell (Maywood Instruments Ltd. model 8402) was installed in the place of

the rope sample, for a finer adjustment of the pressure regulators before the 6

months tests.

The main advantages of the testing machines used are:

(i) possibility to transfer the sample directly to the servo-hydraulic test

machine, without need to re-terminate;

(ii) compactness;

(iii) low cost ( approximately £600.00 on material ); and,

(iv) simplicity and robustness.

110

The main drawbacks are:

(i) when operated with a plastic water jacket it is difficult to get

elongation measurements over a gauge length free from the

terminations;

(ii) over a range of sample lengths of 550 to 850 mm, at constant

pressure, a load variation of 86 N ( 0.5% ) was measured;

(iii) the machine relies on a very small but constant supply of

compressed air;

Extension was measured in two ways:

(i) with a steel rule (0.5 mm resolution) on a gauge length of typically

600 mm length, marked with a pen on the sample; and,

(ii) by measuring the distance between the socket holders with the

same steel rule.

Measurements on the gauge length were only possible at the start and at the

end of each test. These measurements were used to calculate an equivalent

gauge length to be used with the elongation readings taken on the socket

holders.

After the constant loading period, samples were taken to the servo-hydraulic

test machine to determine their retained strength.

Testing procedure was as follows:

(i) install sample on creep testing machine;

(ii) mark gauge length with pen;

(iii) measure distance between socket holders (D1);

(iv) measure initial position of resin cones (CI);

(v) with the regulator already adjusted, load sample by opening air

supply to the actuator (approximate loading time = 2 minutes);

(vi) measure simultaneously free gauge length, distance between

socket holders (D 2), and position of resin cones (C2);

(vii) calculate corrected distance between holders (Do) as:

D0 = D 1 + ( C2- C1);

(viii) calculate effective gauge length (EGL) to be used with distance

between holders as:

111

EGL= ( D2 - Do ) / e

where e is the strain measured on the free gauge length;

(ix) fill plastic bag with substitute sea water;

(x) measure elongation regularly (at approximately equal log time

intervals) until the end of constant load period;

(xi) drain water and remove plastic jacket;

(xii) simultaneously measure free gauge length and distance between

socket holders (D3);

(xiii) recalculate effective Gauge length as:

EGL= ( D3 - Do ) /e;

(xiv) unload sample and transfer it to the servo-hydraulic testing

machine;

(xv) make stiffness measurements as described in Section 6.2.2.1;

and,

(xvi) load to failure at a speed of 0.7 mm/s.

6.4 "Fatigue"

Long term cyclic behaviour of the model ropes was evaluated by loading three

samples of each model rope between 20 ± 10% of UBL in flowing tap water

for 1 million cycles.

After cycling, stiffness was evaluated under the loading conditions described

in section 6.2.2.1.

Residual strength measurements were performed for two samples of each

rope construction. Instead of subjecting to strength testing the remaining

samples were examined in detail, some yarns and filaments being removed

for microscopic examination.

Test samples were of the same length and with identical terminations as in the

other rope tests (see Section 6.1.2).

All testing was undertaken on the Dartec servo-hydraulic testing machine

already described. Elongation was measured from the stroke reading from the

112

actuator mounted LVDT.

The lower termination was fitted with an external grooved ring. An

environmental chamber, sealing on the grove by means of an 0-ring and open

at the top was used for the testing with the sample immersed. Tap water was

fed to the chamber just above the 0-ring and run off from above the upper end

of the rope free length. A fairly small water flow was used, just enough to keep

the outlet water cold.

Figure 6.9 shows a photograph of a sample on the test frame with the

environmental chamber. The hose connections are not shown.

Since the "fatigue" tests were to be performed with the samples immersed, it

would not be possible (with the instruments available) to measure strain

during the test. Therefore, to be able to obtain measurements of stiffness

during the fatigue tests, it was decided to use a correlation between stroke

and strain. Before the actual "fatigue" tests were performed, one sample from

each rope type was used to plot a stroke x strain graph (measured with the

extensometer previously described) at 20±10% of UBL and a frequency of 1.3

±0.1 Hz. A linear relation was obtained between actuator stroke and strain.

The test procedure for the actual cyclic tests was as follows:

(i) install chamber over the sample;

(ii) install sample on the test frame;

(iii) apply an "installation cycle" to 50% of UBL for 30 minutes and then

unload to 10% of UBL;

(iv) cycle between 10 and 30% of UBL for 1 million cycles at a

frequency of 1.3 ±0.1 Hz;

(v) measure stiffness as described in section 6.2.2.1;

(vi) unload sample and change mode to stroke control; and,

(vii) load sample to failure at a rate of 0.7 mm/s.

113

11I1

!

1

( )i

1i1i

r.. ) ii

i

i

1III

i!

Figure 6.8 - 2.5 kN compresion load cell.

7. MATERIAL PROPERTIES: RESULTS

7.1 Strength

7.1.1 Yarn

Table 7.1 summarises the relevant results obtained in testing yarn strength.

Results are presented in terms of the yarn breaking loads measured, as well

as tensile strength (in GPa) and specific strength (in N/tex). Due to the

statistical variation of yarn strength, direct comparison tests were used as

much as possible. A single parameter was varied at a time and trials were run

picking one sample from each group alternately.

The first series of tests show the influence of adding twist to the yarn,when

testing with rubber lined flat jaws. The difference in favour of tests on twisted

yarn is significant at a level of 0.5°/0 for a one taiied lest ail comparisons are

for "one tailed tests" unless noted).

Series two shows the difference between yarn with and without marine finish,

when tested with rubber lined flat jaws. Results for the yarns without finish

were better at a level of significance of 1%.

Series three is a repeat of series 2 with all samples without marine finish

tested first, and the samples with marine finish tested last. In this case the

significance of the results is better than 0.5%.

The difference between results from series 2 and 3 comes from the fact that,

on series 2, residual lubricant from the samples with marine finish is left on the

rubber lining, lowering the results of the samples without marine finish. It also

suggests that it could be possible to obtain higher results for the yarn with

finish by improving the gripping method.

Series four shows the results for yarns without marine finish, terminated

between acrylic tabs, with epoxy glue and nitrile rubber compound. No twist

was added for testing. A comparison with series one shows that the yarn

terminated with acrylic tabs without twist had intermediate results between the

yarn tested with twist and without twist in rubber lined flat jaws. However the

114

differences are relatively small and of low significance.

Series five shows results for yarns with marine finish, terminated with acrylic

tabs with the same procedure described for series four. Again no twist was

added. The mean value obtained was higher than the means obtained in

series two and three for the same yarn, with twist, tested with the rubber lined

flat jaws. The significance of this comparison is very poor though.

Results of series 4 and 5 were considered good enough to support the

selection of the terminating procedure between acrylic tabs, with epoxy glue

and nitrile rubber compound as the standard for all subsequent tensile and

environmental degradation tests.

Based in the results obtained from the Diolen 855TN yarn in series 2, 3 and 5

a breaking load of 87.0 N was taken as the reference value (YBL) for the

definition of loads for the environmental assisted degradation tests.

After the completion of these degradation tests, an additional series of

strength measurements was undertaken (series 8). Twenty samples were

terminated with the standard procedure and distributed at random in four

groups. Ten samples were tested the day after they have been manufactured:

half dry and the others after immersion in deionised water for approximately

30 minutes. The remaining ten samples were kept for 3 months under a

minimal tensile load (between 0.01 and 0.05N): 5 in air and 5 in deionised

water. The samples were kept in a room without humidity control and where

the temperature was 18± 2 0C. The samples that were kept dry were immersed

in deionised water for 15 minutes before breaking.

These tests were intended to provide a confirmation of the reference breaking

load value of 87.0 N for samples taken from the yarn bobbin at a completely

different position from the previous series. The tests were also devised to

investigate apparent anomalies in the results obtained for the long term air

samples that will be discussed in section 7.3.

Test results are shown as series 8 in Table 7.1. The 5 breaking tests

conducted on dry yarn gave a somewhat low average breaking load but the

mean of all 20 tests was 86.8 N and the mean of all wet tests in yarns that had

115

been kept dry for 1 day and 3 months was 87.8 N. The average of the samples

that stayed in air for 3 months and then tested wet was a bit high at 89.2 N. It is

also worth noting the high scatter in the yarns that were kept for 3 months in

DIW, but it was observed that a lot of algae had grown in these samples. In

general terms the results confirmed the use of 87.0 N as the reference

breaking load (YBL).

In order to evaluate rope conversion efficiency, as defined below, 18 samples

were selected at random from a disassembled Superline rope, and another

12 samples from a disassembled Brascorda Parallel rope. These were tested,

with added twist, using the rubber lined flat grips. Results of these tests are

summarised as series 6 and 7 respectively in Table 7.1.

7.1.2 Ropes

7.1.2.1 Superline

Five samples from the length of rope supplied were tested by the

manufacturer before shipping. Free sample length was 2000 mm and testing

speed was approximately 400 mm/minute. Wedge type jaws, lined with lead

foil were used. A single test was performed with the cover intact, and broke

free of the jaws. Four test were carried out with the cover cut at the centre of

the gauge length. Only one of those broke away from the grips.

The results of these tests are shown in Table 7.2, together with a guaranteed

minimum breaking load (59.7 kN), based on the manufacturer's catalogue.

The latter was calculated by reducing the catalogue breaking load (68.7 kN)

of a slightly bigger (16 mm external diameter, 184000 tex) rope in proportion

to the linear mass of the rope tested (160000 tex). Since the rope maker

calculates the guaranteed minimum breaking load as 90% of the average

breaking load (Banfield (1989)), the average breaking load for the rope tested

in this study, with jacket would be 66.3 kN (i.e. (68.7.160000) / (184000.0.9)).

It is interesting to note that, although the braided jacket accounts for 38% of

the rope weight and certainly contributes to improve load sharing between

sub-ropes, its removal has reduced rope breaking load by an average of

116

17.5%.

Several tensile tests were performed during termination development with

results always above 49.4 kN. After completion of termination development 3

tests were carried out. Results of these tests are shown in Table 7.2. Failure

mode was by successive rupture of individual sub-ropes inside the resin at the

transition between the cylindrical and the conical regions. Tests were stopped

after a few breaks and a visual inspection of the unbroken sub-ropes has

always revealed a substantial number of broken fibres distributed throughout

the sample length.

Results are also presented in terms of specific strength and ultimate tensile

stress. Specific strength is the more precise and effective way of comparing

rope strength since it relates to the actual amount of material in the rope and

hence rope cost. Since the measurement of the diameter is very imprecise

and the filling factor varies from one construction to another, the ultimate

tensile stress does not give a good indication of rope efficiency and should not

be used for comparison purposes. It is presented here because that is the way

strength has been considered for the mooring design calculations.

Taking into account: the short length of the sample, the pattern of damage on

the unbroken sub-ropes, the average breaking load of 57.2 kN (equal to 86%

of the average value calculated based in the manufacturer's catalogue, with

cover) and the reasonably low scatter obtained, the terminations were

considered satisfactory.

A value of 57.0 kN was used as reference for the definition of the loads

(abbreviated as RBL) for both the fatigue and the environmental assisted

degradation tests.

Referring to an average yarn breaking strength in the rope of 85.67 N (series 6

of yarn testing) the average strength conversion of the terminated rope was

found to be 79.5% and the tenacity conversion was 73.6%.

Figure 7.1 shows the load-elongation plot obtained during the installation

cycle performed on a model Superline. The average secant installation

modulus measured for these ropes was 2.89 GPa from the origin to the

117

rightmost point at maximum load. The corresponding elongation was 9.5%.

7.1.2.2 Brascorda Parallel

The amount of Brascorda Parallel rope available for testing was limited to 25

metres and so fewer samples were used for termination development and to

define the reference strength. Termination development was not very much

prejudiced by this limitation since rope material, diameter and number of

strands were very similar to the Superline.

Table 7.3 shows the results obtained once the terminations had been

considered satisfactory. In the first sample 9 out of the 34 strands were slack

and the maximum load obtained was 52.5 kN. Sample no. 2 broke clear of the

terminations at 58.7 kN. The average strength of the last two samples was

58.55 kN. Taking into account: the short length of the sample, the fact that a

clear failure was obtained and the availability of rope samples, the termination

method was considered acceptable.

A reference value, rounded to the nearest kN, of 59.0 kN (RBL), was selected

for the definition of the loading on both the fatigue and the environmental

degradation tests. This value represents a strength conversion of 75.6% in

relation to the yam results from series 7 and a tenacity conversion of 71.4%.

The specific strength corresponding to the reference breaking load is

0.551 N/tex and the tensile strength, based on the enclosed area for a

diameter of 11.5 mm, is 0.568 GPa.

A load-elongation graph for an "installation" cycle is shown in Figure 7.2. The

average secant modulus at maximum elongation was 3.56 GPa,

corresponding to an elongation of 8.0%.

7.2. Stiffness and Hysteresis

7.2.1 Yarn Stiffness

Results obtained following the sequence of increasing mean tension,

118

increasing tension range and increasing cycling period (see Section 6.2.1)

are presented in Table 7.4. For reasons already discussed (Section 4.2) the

specific modulus (in Nitex or N/(g/km)) has been used. Although not directly

useful, the Young's modulus (in GPa) based on the actual cross-section of the

filaments in the yarn can be obtained by multiplying the specific modulus by

the density of the material (in 9/cm3). To obtain EA (the product of the apparent

Young's modulus by the cross sectional area), in N, specific modulus should

be multiplied by the linear mass of the yarn (in tex).

Due to the non-linear viscoelastic behaviour of the material tested, the

stiffness is a function of the loading history. Therefore, results obtained are not

exactly the ones that are applicable to the material in service. For example,

the stiffness at 10 ± 5% of YBL after a preceding loading at an average of 30%

of YBL is higher than after a preceding average of 5% of YBL.

Since measurements were taken at increasing mean loads over an extended

period of time (typically 2 days), and in the real application, mean load would

go up and down at quite a low frequency, a method was devised to to even out

the effect of the measurement procedure. Using the results obtained for

specific modulus as dependent variable and taking mean load, load range

and the logarithm of the cycling period as independent variables a linear

regression was performed.

The equation obtained was:

SM = 13.411 + 0.178. Lm - 0.176. La -0.384 . Log T, (1)

where: SM = specific modulus (in N/tex);

Lm= mean load (in % of the yarn reference breaking load);

La = load amplitude (in % of YBL); and,

T = period (in seconds).

The significance of the regression analysis was verified by calculating the F

statistic from the data (Miller et al. (1990, ref. book). The F statistic value of this

analysis was 275.4. The critical value of F for this regression is 7.82 at a 0.1%

level of significance, corresponding to a numerator degree of freedom of 2, i.e.

119

the number of independent variables minus one, and a denominator degree

of freedom of 59, because 60 measurements were performed. Since the value

obtained from the data is larger than the critical value the regression is

significant at a level of better than 0.1%.

Table 7.4 also shows the the fitted values for each case, as calculated by the

regression equation. It should be noted that by using the logarithm of the

period the fit obtained is remarkably good. As confirmation of the quality of the

regression and of the assumption of normal distribution associated with the F

statistic test, Figure 7.3 shows the residues (as percentage of predicted value)

plotted against the predicted values as a narrow horizontal band distribution.

7.2.2 Rope Stiffness

7.2.2.1 Superline

Results of the stiffness measurements after an "installation" cycle,

representing the as installed condition, are presented in Table 7.5 both in the

form of specific modulus and as an apparent Young's modulus based in the

circumscribed area of the rope core. For the latter a diameter of 11.5 mm was

assumed.

The measurements were taken with increasing mean loads, load ranges and

periods. In service conditions these parameters would vary slowly over the

range investigated. Under these circumstances the stiffness observed will not

be quite the same as the values measured for two reasons:

(i) the viscoelastic behaviour of the material; and,

(ii) the constructional set of the rope structure.

In order to obtain values that more closely approximate reality, the same

procedure used on the yarn measurements was employed with the rope data.

The regression equation obtained for the specific modulus (SM) was:

SM = 10.409 + 0.152. Lm - 0.194. La - 0.427. Log T.

The F statistic value for this regression is 2113.9 and the critical value of F for

120

a 0.1% level of significance is 7.57, verifying the significance of the

regression. The fitted values obtained using the equation above are also

shown in Table 7.5. Figure 7.4 is a plot of the residuals of the regression

versus the fitted values and shows an horizontal band without apparent

spurious effects.

The apparent Young's modulus (in Pa) can be obtained by multiplying the

specific modulus (in N/tex) by the linear mass of the rope core (in tex) and

dividing the result by the circumscribed area of the rope core (in m2).

A load elongation plot for a sample undergoing a simulated quasi-static

reversal of loading over a period of one week is shown in Figure 7.5. The

initial mean load was 11.4 kN (20% of RBL), from which over a 3 hours ramp

load increased to 17.1 kN (30% of RBL) which was kept constant for 72 hours.

Load was then lowered to 5.7 kN (10% of RBL) at a constant rate in 6 hours

and kept at this level for a further 72 hours. Finally the load was ramped up to

11.4 kN in 3 hours.

The extreme elongations were divided by the effective gauge length to obtain

the strain limits. The apparent Young's modulus, referred to a core diameter of

11.5 mm, was calculated as 7.32 kN/mm 2. The corresponding specific

modulus is 7.64 N/(g.km), or N/tex, for a linear mass of the rope core equal to

99.5 g/m (99500 tex).

Results for stiffness measurements after "fatigue" of 1 million cycles at

20 ± 10% of the rope average breaking load in running tap water and at an

average frequency of 1.17 Hz, are shown in Table 7.6. The results are

tabulated in the order in which they were obtained. Again specific stiffness

was used for its convenience when scaling up.

Table 7.6 also shows the values of specific stiffness obtained from the fitted

curve for the as installed condition, as well as the ratio to the after "fatigue"

values.

This ratio is slightly greater than one for the same conditions in which the rope

was cycled. As soon as a different cycling condition is imposed the stiffness

falls to a level marginally below the value indicated by the regression

121

equation for the as installed condition.

Stiffness measurements after creep are shown in Table 7.7 together with the

as installed condition fitted data for the same loading condition, as well as the

ratio between the two. All results are somewhat lower than the fitted data for

the as installedcondition.

7.2.2.2 Brascorda Parallel

Results for the stiffness measurements in the as installed condition (Section

6.2.2.1) are presented in Table 7.8 as specific modulus as well as apparent

Young's modulus based in the circumscribed area of the rope core.

Based on the same argument as developed for the Superline, a regression

equation was fitted to the data obtained for specific modulus (SM) as a

function of mean load (Lm ), load amplitude (L.) and the logarithm of the

cycling period (T). The equation obtained was:

SM = 12.058 + 0.152 Lm - 0.201 La- 0.473 . Log T.

The F statistic value for this regression is 486.6 and the critical value of F for a

0.1% level of significance is 7.57. The fitted values obtained using the

equation above are also shown in Table 7.8. Figure 7.6 is a plot of the

residuals of the regression versus the fitted values, and shows an horizontal

band without apparent spurious effects.

Figure 7.7 shows a load elongation plot for a sample undergoing a simulated

quasi-static reversal of loading over a period of one week. The initial mean

load was 11.8 kN (20% of RBL), the upper load level was 17.7 kN and lower

level was 5.9 kN. The cycling followed a similar pattern to that used for the

Superline model rope.

The extreme elongations were divided by the effective gauge length to obtain

the strain limits. The apparent Young's modulus, referred to a core diameter of

11.5 mm, was calculated as 9.66 kN/mm 2. The specific modulus was

9.38 N/(g.km), or N/tex, for a linear mass of the rope core equal to 107.0 g/m

(107000 tex).

122

Stiffness after latigue n for 1 million cycles at 20 ± 10% of BL is shown in Table

7.9. Results are plotted as specific stiffness and results are tabulated in the

actual order used to take the measurements.

Regression values for the specific stiffness as installed is also shown with the

ratio between values after fatigue and as installed. After fatigue values are 4%

higher at the same loading used on the fatigue test, but for other conditions

the difference varies from 1% lower to 4% higher than the as installed figures.

Stiffness measurements after creep are shown in Table 7.7 (together with the

data for the Superline model rope). The results are about 5% lower than the

fitted data for the as installed condition.

7.2.3 Rope Hysteresis

Table 7.10 shows the results obtained for the model Superline PET rope and

for the small steel wire rope. The loss coefficient was used for presentation of

results to simplify comparison with data in the literature. For the fibre rope both

stroke and strain were measured allowing the calculation of hysteresis in the

rope alone or in the rope plus termination. This was not possible for the wire

rope (see Section 6.2.2.2).

Typical results for the fibre rope and the steel wire rope (excluding

terminations) were 0.03 and 0.06 respectively.

Although the measurements were taken under slightly different conditions, it is

clear that the energy absorbed by the fibre rope at wave frequency is not

greater than that absorbed by the wire rope. It is also interesting to note that,

when the energy absorbed in the terminations is accounted for, an increase of

up to 30% was observed.

123

7.3 Creep and Environmental Assisted Degradation

7.3.1 Yarn

7.3.1.1 Creep

The results of the short term test (1 week) are shown in Table 7.11. The

effective yarn length was taken as the distance between tabs at a loading of

0.5 N. The table shows the yarn strains based on the crosshead movement

measured by:

(i) the encoder in the testing machine; and,

(ii) an external dial gauge between the column and the crosshead.

The difference between the measurement methods is insignificant.

The strains measured in the dead weight tests are shown in Table 7.12.

Figure 7.8 shows the strains measured in both tests plotted on a logarithmic

time scale. The curves obtained are parallel and the strain measured for the

short term test is typically 5% higher than that of the test under dead weight.

This variation is compatible with the way the measurements were taken, i.e.:

(i) elongation measurements in the short term test incorporate a small

but unquantified amount of elongation in the tabs;

(ii) the yarn creep behaviour has a statistical variation; and,

(iii) none of the tests were done under temperature or humidity control.

It is interesting to note that even when plotted against Log (time) (BS 4618:

Section 1.1 (1970)) the strain rate is decreasing. A curve of the form y.a.xb

gives a very good fit to the data of each dataset. A regression of the short term

data produced the equation:

strain = 5.010. (Log time)0.0744,

which fitted the data with a (coefficient of correlation) 2 of 0.999.

In the same way a regression of the long term test data generated theequation:

124

strain = 4.740 . (Log time)0.0789,

which fitted the data with a (coefficient of correlation) 2 of 0.980.

Table 7.13 shows the strain rates per time decade between 10 3 and 107

seconds, calculated according to both equations. There is very little difference

between the creep rates which, after approximately 1 month, are already

down to about 0.07% per decade.

Although the samples used for the evaluation of strength degradation were

not intended for elongation measurements, the free distance between tabs

was measured in a number of samples at 20 and 30°C at regular intervals.

The initial gauge length could not be defined precisely because of the special

tabbing system and the short free length used.

The initial distance between tabs was 100 mm and the average initial distance

between the regions glued with epoxy resin was measured as 120 mm.

Table 7.14 shows total strain after 1 year based on a gauge length of 120 mm

and an initial distance between tab faces of 100 mm. It should be emphasised

that these values can only be seen as a rough estimate due to the nature of

the measurements taken. Nonetheless they provide an insight into the

behaviour of the material under constant load for up to 1 year.

7.3.1.2 Environmentally Assisted Degradation

A total of 142 yarn samples were tested under the conditions described in

Section 6.3.1.2 of which 101 gave results considered valid. Test results were

rejected due to :

(i) failure of filaments in the region were they were in contact with the

epoxy glue (16 rejects),

(ii) presence of salt crystals adhering to the yarn during testing (6

rejects);

(iii) overheating of the 40°C tank (13 rejects); and,

(iv) handling damage (5 rejects).

125

The results of the valid tests are shown in Tables 7.15, 7.16, 7.17, and 7.18, for

the temperatures of 4, 20, 30 and 40°C respectively.

Table 7.18 (40°C) also includes the results for the yarns that were in the tank

for which the control system failed, allowing the samples to overheat. These

are separately identified.

Considering that most of these samples were plastically deformed to the point

that the dead weights touched the bottom of the tank, it is thought that the

maximum temperature reached must have been close to, if not higher than,

the glass transition temperature, i.e. more than 70°C.

Tables 7.15, 7.16, 7.17, and 7.18 also show mean values and standard

deviation for all combinations of: environment, duration and loading.

The most consistent results were obtained for the samples staying in the 4°C

tank and for the samples tested in deionised water (DIW) at all temperatures.

Samples in sea water at 20, 30 and some at 40°C were found to have

developed a layer of crystals on the outside of the yarn. Although for most of

these samples the crystals were dissolved prior to the tensile test for

evaluation of residual strength, it is thought that these samples could have

been damaged by the crystals in the process of removing the constant load. It

should be noted that samples were washed in hydrochloric acid after removal

of the dead weights, and when unloading from 20% of YBL, the yarn

experiences a rapid recovery of at least 4% (40000 jig).

7.3.2 Ropes

7.3.2.1 Creep

Figure 7.9 shows the total strain measured in each of the four Superfine

samples plotted against a logarithmic time scale. Strains have been

measured in terms of the separation of the sockets using on effective gauge

length as defined in Section 6.3.2.

The curves obtained are basically parallel to each other. Within the

126

overlapping time period the 1 month (SUP1) and the 6 months (SUP4)

samples showed very similar strains. Results for the 12 months sample

(SUP2) were marginally lower than those of the 1 and 6 months tests. The

3 months sample (SUP3) showed strains typically 0.004% greater than the 1

and 6 months samples.

It should be noted that for samples SUP1, SUP2 and SUP3, the set point of

the pressure regulators was adjusted by measuring the compressive force

between the actuator and the rocking arm, while for SUP4 the adjustment was

based on a direct measurement of tension in a load cell installed in place of

the rope sample. After the tests of SUP3 and SUP2 were finished a direct

measurement of the tension load to which they had been subjected indicated

tensions of 17.9 kN (31.4% of RBL) and 17.4 kN (30.5% of RBL) respectively.

Considering the higher load indicated at the end of the test on the 3 month

sample (SUP3), the results of only the 1 month, the 6 month and the 12 month

tests have been replotted in Figure 7.10 on a Log (time) scale. The tendency

for decreasing creep rate with the logarithm of time is less clear than the

tendency found for the PET yarn, but it is still present. A linear regression of

strain versus Log (time) showed a poorer correlation than an equation of the

form y = a xb . The regression equation obtained was:

strain = 4.718. (Log time) 0 -205(1),

with a correlation coefficient squared of 0.915.

Figure 7.11 shows the strains measured in the four Brascorda Parallel

samples, using a logarithmic time scale. The results for all samples lie on a

very narrow band with a clear tendency for flattening with increasing time on a

logarithmic time scale.

It should be mentioned that for this rope a subsequent check of the creep

loads that had been applied to the 3 months and the 12 months samples,

showed that these were between 29.5 and 30.5% of the reference breaking

load (RBL).

Also shown in Figure 7.11 is a regression of the data for the four Brascorda

127

samples to a curve of the form y -- : : a. xb. The equation found was:

strain = 3.226. (Log time)0.303

(2),

and the coefficient of correlation squared was 0.976.

It may be noted that the results seem to conform better to a dual slope linear

relation with the slope transition around 500000 seconds, but the single

equation regression is conservative and more convenient.


The retained strength obtained from the Superline rope samples subjected to

long term constant loading is shown in Table 7.19.

All the results are a little below the average of the 3 reference results on

unloaded ropes (57.20 kN). However the average retained strength, 54.45 kN,

was not significantly lower at the 5% level. The lowest result was obtained

after 1 month under constant load. The retained strength measured after one

year was 97.6% of the average initial value.

Table 7.20 shows the retained strength of the 4 samples of BrascordaParallel rope. The average of the 4 results was marginally higher than the

average strength of the two new samples tested. As with the Superline

samples, the lowest result was obtained after 1 month exposure, down 5%

from the average new value. The strength measured for the one year sample

was 0.6% higher than the average new value.

7.4 "Fatigue"

Results for the retained strength of two samples of each model rope, after 1

million cycles at 20±10% of RBL, are shown in Table 7.21. Breaking load (in

kN), maximum specific stress (in N/tex) and ultimate tensile stress (in GPa)

are given. The average values of all these measurements of residual strength,

for each rope type, are also tabulated.

128

When tested to failure all samples showed the same pattern of behaviour, i.e.

sequential failure of independent sub-components (sub-ropes in the

Superline and strands in the Brascorda Parallel). All failures were associated

with the terminations. Most failures happened inside the resin at the transition

between the cylindrical and the conical sections of the socket. Some

components failed at the interface of the resin with the free rope length.

The examination of one sample of each rope after the cyclic loading indicated

that:

(i) the free length of the samples had a very small number of broken

fibres, estimated to be insignificant statistically;

(ii) in the Brascorda Parallel rope these few breaks were concentrated

on the external strands of the rope structure;

(iii) the fracture surfaces of the few damaged fibres found on the free

length of both samples showed that these fibres had been either

cut or mangled (Hearle et al. (1989), indicating that the damage

had happened before cycling;

(iv) no filament fatigue was observed (Hearle et al. (1989);

(v) both samples showed limited signs of degradation (broken fibres),

at the interface between the free rope length and the resin cone;

(vi) although the number of fibres broken at the termination interface

was not counted (because of the restricted access to this region), it

is estimated that something like 100 fibres were broken on each

termination of the Brascorda Parallel rope sample, and about 500

fibres were broken at the interface of each resin cone of the

Superline rope;

(vii) all broken fibres removed from the free length adjacent to the

termination in the Superline sample had fibrillated breaks.

Figures 7.12 and 7.13 illustrate the type of failures found at the termination

interface. The photographs were taken with the scanning electron microscope

at magnifications of 400 and 700 times respectively. Figure 7.12 shows the

fibrillar nature of the fracture. The view captured in Figure 7.13 highlights the

morphology of the fracture process and the shear stresses present in the wear

mechanism (Hearle et al. (1989)).

129

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kN

Break Specific Strength

N/tex (N/(q/km))

Tensile Strength

GPa

Catalogue intact 59.7 - 0.3732 0.3415

1 intact 68.95 clear 0.4309 0.4035

2 cut 53.41 jaw 0.5368 0.51423 cut 55.60 clear 0.5588 0.53534 cut 59.78 jaw 0.6008 0.57555 cut 58.79 jaw 0.5909 0.5660

Average 2 to 5 56.90 0.5718 0.5478Std. Dev. 2.93

6 removed 58.90 termination 0.5920 0.56717 removed 57.20 termination 0.5749 0.55078 removed 55.50 termination 0.5578 0.5343

Average 6 to 8 57.20 0.5749 0.5507Std. Dev.

removed

1.70

Reference removed 57 0.5729 0.5488

Table 7.2 - Tensile test results of the Superline model rope "as new".

Sample Jacket Breaking Load

kN

Break Specific Strength

N/tex (Nl(g/km))

Tensile strength

GPa

1* cut 52.50 termination 0.4907 0.50542 cut 58.70 clear 0.5486 0.56513 cut 58.40 termination 0.5458 0.5622

Average 2-3 58.55 0.5472 0.5637Std. Dev. 0.21

Reference cut 59.00 0.5514 0.5680

' some strands longer than the others

Table 7.3 - Tensile test results of the Brascorda Parallel model rope "as new".

Mean Load% of YBL

Load Amplitude'% of YBL

Periods

Specific ModulusN/tex

Fitted ValueN/tex

ResidualN/tex

5 2.5 7.5 13.57 13.52 0.045 2.5 15 13.48 13.41 0.07

• .5 2.5 100 13.34 13.09 0.25

5 2.5 200 13.24 12.98 0.27

15 2.5 7.5 15.63 15.30 0.33

15 2.5 15 15.72 15.19 0.53

15 2.5 100 15.52 14.87 0.65

15 2.5 200 14.95 14.76 0.20

15 5 7.5 15.16 14.86 0.29

15 5 15 14.78 14.75 0.04

15 5 100 15.06 14.43 0.62

15 5 200 14.92 14.32 0.60

20 2.5 7.5 15.80 16.19 -0.39

20 2.5 15 15.26 16.08 -0.81

20 2.5 100 15.48 15.76 -0.28

20 2.5 200 15.4-8 15.64 -0.16

20 5 7.5 15.78 15.75 0.02

20 5 15 15.40 15.64 -0.24

20 5 100 15.02 15.32 -0.30

20 5 200 14.88 15.21 -0.32

20 10 7.5 13.70 14.87 -1.18

20 10 15 13.91 14.76 -0.85

20 10 100 13.62 14.44 -0.82

20 10 200 13.40 14.33 -0.93

30 2.5 7.5 17.47 17.97 -0.50

30 2.5 15 17.49 17.85 -0.37

30 2.5 100 17.09 17.54 -0.44

30 2.5 200 17.09 17.42 -0.33

30 5 7.5 17.35 17.53 -0.18

30 5 15 17.40 17.41 -0.01

30 5 100 17.09 17.10 0.00

30 5 200 17.09 16.98 0.11

30 10 7.5 16.05 16.65 -0.60

30 10 15 16.34 16.54 -0.19

30 10 100 15.93 16.22 -0.29

30,

10 200 15.78 16.11 -0.33

40 2.5 7.5 20.40 19.75 0.65

40 2.5 15 20.21 19.63 0.58

40 2.5 100 20.01 19.32 0.70

40 2.5 200 19.54 19.20 0.34

40 5 7.5 20.51 19.31 1.2040 5 15 20.57 19.19 1.3740 5 100 19.77 18.88 0.89

40 5 200 19.54 18.76 0.7740 10 7.5 19.83 18.43 1.4040 10 15 19.63 18.31 1.3240 10 100 18.86 18.00 0.86

40 10 200 18.65 17.88 0.7650 2.5 7.5 20.31 21.52 -1.2150 2.5 15 20.70 21.41 -0.7150 2.5 100 20.01 21.09 -1.0850 2.5 200 20.01 20.98 -0.9750 5 7.5 20.91 21.09 -0.1850 5 15 20.70 20.97 -0.2750 5 100 20.51 20.65 -0.1450 5 200 20.26 20.54 -0.2850 10 7.5 20.07 20.21 -0.1450 10 15 20.10 20.09 0.0150 10 100 19.54 19.78 -0.2450 10 200 19.54 19.66 -0.12

Table 7.4 - Dynamic yarn stiffness for increasing: mean tension, tension

range and frequency. Results obtained from regression also

shown.

Mean Load% B. L.

Load Amplitude% B.L

Periods

Young's ModulusGPa

Specific ModulusWiex

Fitted Spec. Mod.WIez

ResidualNam

5 2.5 7.5 9.48 9.89 10.31 -0.425 2.5 15 9.45 9.89 10.18 -0295 2.5 100 9.26 9.67 9.83 -0.165 2.5 200 9.23 9.64 9.70 -0.06

10 2.5 7.5 10.77 1127 11.07 0.2010 2.5 15 10.54 11.03 10.94 0.0910 2.5 100 10.39 10.87 10.59 0.2910 2.5 200 10.24 10.71 10.46 0.2510 5 7.5 10.02 10.48 10.59 -0.1010 5 15 9.99 10.46 10.46 0.0110 5 100 9.67 10.12 10.10 0.0210 5 200 9.51 9.95 9.98 -0.0215 2.5 7.5 11.15 11.66 11.83 -0.1715 2.5 15 10.86 11.35 11.70 -0.3515 2.5 100 10.82 11.31 11.35 -0.0315 2.5 200 10.60 11.35 11.22 0.1415 5 7.5 10.95 11.44 11.34 0.1015 5 15 10.84 11.33 11.22 0.1215 5 100 10.56 11.04 10.86 0.1815 5 200 10.46 10.94 10.73 0.2120 2.5 7.5 11.93 12.47 12.59 -0.1220 2.5 15 11.82 12.34 12.46 -0.1220 2.5 100 11.56 12.09 12.11 -0.0220 2.5 200 11.56 11.68 11.98 -0.3020 5 7.5 11.78 12.32 12.10 0.2220 5 15 11.62 12.15 11.97 0.1820 5 100 11.27 11.78 11.62 0.1620 5 200 11.16 11.67 11.49 0.1720 10 7.5 10.27 10.74 11.14 -0.3920 10 15 10.18 10.64 11.01 -0.3720 10 100 9.86 10.31 10.65 -0.3520 10 200 9.72 10.16 10.53 -0.3630 2.5 7.5 13.50 14.09 14.11 -0.0230 2.5 15 13.31 13.90 ' 13.98 -0.0830 2.5 100 13.00 13.58 13.62 -0.0530 2.5 200 13.00 13.58 13.50 0.0830 5 7.5 13.20 13.78 13.62 0.1630 s 15 13.04 13.62 13.49 0.1230 5 100 12.95 13.52 13.14 0.3830 5 200 12.80 13.37 13.01 0.3530 10 7.5 12.53 13.08 12.65 0.4330 10 15 12.34 12.88 12.52 0.3630 10 100 11.83 12.35 12.17 0.1830 10 200 11.58 12.09 12.04 0.0430 15 7.5 10.99 11.63 11.69 -0.0630 15 15 10.70 11.47 11.56 -0.0930 15 100 10.60 11.07 11.20 -0.1430 15 200 10.50 10.96 11.08 -0.1240 2.5 7.5 14.87 15.52 15.62 -0.1040 2.5 15 14.67 15.31 15.49 -0.1940 2.5 100 14.24 14.87 15.14 -0.2840 2.5 200 14.24 14.87 15.01 -0.1540 5 7.5 14.67 15.31 15.14 0.1740 5 15 14.61 15.26 15.01 0.2540 5 100 14.32 14.95 14.66 0.3040 5 200 14.15 14.50 14.53 -0.03ao 10 7.5 13.87 14.48 14.17 0.3140 10 15 13.79 14.39 14.04 • 0.3540 10 100 13.32 13.91 13.69 0.2240 10 200 13.24 13.82 13.56 0.2640 15 7.5 12.80 1326 13.20 0.0540 15 15 12.61 13.17 13.07 0.0940 15 100 12.26 12.80 12.72 0.0840 15 200 12.08 12.61 12.59 0.0250 2.5 7.5 16.24 16.95 17.14 -0.1950 2.5 15 16.08 16.78 17.01 -0.2450 2.5 100 15.60 16.30 16.66 -0.3650 2.5 200 15.60 16.30 16.53 -0.2350 5 7.5 15.97 16.67 16.66 0.0250 5 15 15.74 16.43 16.53 -0.1050 5 100 15.43 16.10 16.18 -0.0750 5 200 15.43 16.10 16.05 0.0650 10 7.5 15.29 15.96 15.69 0.2750 10 15 15.14 15.80 15.56 0.2450 10 100 14.85 15.51 15.21 0.3050 10 200 14.44 15.08 15.08 0.0050 15 7.5 13.81 14.60 14.72 -0.1250 15 15 13.63 14.23 14.59 -0.3650 15 100 13.24 13.82 14.24 -0.4250 15 200 13.14 13.71 14.11 -0.40

Table 7.5 - Dynamic stiffness of the Superline mode( ropes for increasing:

mean tension, tension range and frequency. Results obtained

from regression also shown.

Mean Load Load Amplitude Frequency Spec. Modulus Regression ValueNitex

Measured/Regession'Ye B.L. % B.L. Hz N/tex

20 10 0.067 11.65 11.01 1.05820 10 0.2 11.84 11.22 1.05620 5 0.2 12.46 12.18 1.02320 2.5 0.2 12.52 12.67 0.98810 5 0.2 10.13 10.67 0.94910 2.5 0.2 10.50 11.15 0.941

Table 7.6 - Influence of long term "fatigue" cycling in the dynamic stiffness of

the Superline model ropes.

Rope Mean Load% B.L.

Load Amplitude% B.L.

FrequencyHz

Spec. ModulusN/tex

Fitted ValueN/tex

Measured/Fitted

Superline 20 10 0.2 10.39 11.22 0.926Superline 20 10 0.067 10.34 11.01 0.939

Brasc. Parallel 20 10 0.2 12.04 12.76 0.944Brasc. Parallel 20 10 0.067 11.94 12.54 0.952Brasc. Parallel 20 10 0.01 11.37 12.15 0.935

Table 7.7 - Dynamic stiffness of the Superline and Brascorda Parallel model

ropes after long term exposure to a constant load of 30% of UBL.

Mean Load Load Amplitude Period Young's Modulus Specific Modulus Fined value Residual

% B. L. % B.L. s GPa N/Tex N/Tex N/Tex

5 2.5 7.5 11.97 11.64 11.90 -0.265 2.5 15 11.85 11.53 11.76 -0.23

5 2.5 100 11.58 11.26 11.37 -0.11

5 2.5 200 11.39 11.08 11.23 -0.1410 2.5 7.5 12.02 12.47 12.66 -0.2010 2.5 15 12.73 12.39 12.52 -0.1410 2.5 100 12.63 12.29 12.13 0.1610 2.5 200 12.39 12.05 11.99 0.0610 5 7.5 12.74 12.39 12.16 0.2310 5 15 12.47 12.13 , 12.02 0.1110 5 100 12.09 11.76 11.63 0.1310 5 200 11.99 11.66 11.49 0.1815 2.5 7.5 14.01 13.63 13.42 0.2015 2.5 15 13.92 13.54 13.28 0.2615 2.5 100 13.51 13.14 12.89 0.2515 2.5 200 13.60 13.23 12.75 0.4815 5 7.5 13.62 13.25 12.92 0.3315 5 15 13.60 13.23 12.78 0.4515 5 100 13.40 13.03 12.39 0.6415 5 200 13.27 12.91 1225 0.6620 2.5 7.5 13.87 13.49 14.18 -0.6920 2.5 15 13.78 13.40 14.04 -0.6420 2.5 100 13.47 13.10 13.65 -0.5520 2.5 200 13.42 13.05 13.51 -0.4520 s 7.5 13.83 13.45 13.68 -0.2320 s 15 13.64 13.27 13.54 -0.2720 5 100 13.27 12.91 13.15 -0.2420 5 200 13.17 12.81 13.01 -0.2020 10 7.5 12.61 12.27 12.68 -0.4120 10 15 12.42 12.08 12.54 0.4620 10 100 11.96 11.63 12.15 -0.5120 10 200 11.71 11.39 12.01 -0.6130 2.5 7.5 15.85 15.42 15.70 -0.2830 2.5 15 15.80 15.37 15.56 0.1930 2.5 100 15.35 14.93 15.17 -0.2530 2.5 200 15.35 14.93 15.03 -0.1030 5 7.5 15.77 15.34 15.20 0.1430 5 15 15.54 15.12 15.06 0.0630 5 100 15.09 14.68 14.67 0.0130 5 200 15.12 14.70 14.53 0.1830 10 7.5 14.82 14.41 14.20 0.21ao 10 15 14.47 14.07 14.06 0.0130 10 100 13.90 13.52 13.67 -0.1530 10 200 13.68 13.30 13.53 -0.2230 15 7.5 13.01 12.66 13.20 -0.5430 15 15 12.90 12.54 13.06 -0.5130 15 100 12.60 12.26 12.67 -0.4130 15 200 12.45 12.11 12.52 -0.41ao 2.5 7.5 18.20 17.70 17.23 0.47ao 2.5 15 18.02 17.52 17.08 0.4440 2.5 100 17.60 17.12 16.69 0.4340 2.5 200 17.49 17.01 16.55 0.4640 5 7.5 17.93 17.44 16.72 0.7140 5 15 17.84 17.35 16.58 0.7740 5 100 17.51 17.03 16.19 0.8440 5 200 17.60 17.12 16.05 1.07

40 10 7.5 17.21 16.74 15.72 1.0240 10 15 17.01 16.54 15.58 0.96ao 10 100 16.67 16.21 15.19 1.0240 10 200 16.41 15.96 15.05 0.9140 15 7.5 15.94 15.51 14.72 0.7940 15 15 15.42 15.00 14.58 0.4240 15 100 14.83 14.43 14.19 0.2440 15 200 14.42 14.03 14.04 -0.0150 2.5 7.5 18.58 18.07 18.75 -0.6850 2.5 15 18.52 18.01 18.60 -0.5950 2.5 100 17.90 17.41 1821 -0.8150 2.5 200 17.90 17.41 18.07 -0.66so 5 7.5 18.26 17.76 18.24 -0.4850 5 15 18.23 17.73 18.10 -0.3750 5 100 17.87 17.38 17.71 -0.3450 5 200 17.90 17.41 17.57 -0.1650 10 7.5 17.81 17.32 17.24 0.0850 10 15 17.45 16.98 17.10 -0.1250 10 100 16.87 16.40 16.71 -0.3050 10 200 16.63 16.17 16.57 -0.40so 15 7.5 16.53 16.08 16.24 -0.1650 15 15 16.35 15.90 16.10 -0.20

50 15 100 15.80 15.37 15.71 -0.34

50 15 200 15.67 15.24 15.57 -0.32

Table 7.8 - Dynamic stiffness of the Brascorda Parallel model ropes for

increasing: mean tension, tension range and frequency. Results

obtained from regression also shown.

Mean Load% B.L.

Load Amplitude'2/0 B.L.

FrequencyHz

Spec. ModulusN/tex

Fitted ValueNitex

Measured/Fitted

20 10 0.067 13.08 12.54 1.04320 10 0.2 13.29 12.76 1.04120 5 0.2 13.89 13.76 1.01020 2.5 0.2 13.92 14.26 0.97610 5 0.2 12.06 12.24 0.98510 2.5 0.2 12.61 12.74 0.9905 2.5 0.2 11.48 11.98 0.959

30 12.5 0.2 13.50 13.78 0.97930 10 0.2 14.05 14.28 0.98430 5 0.2 15.44 15.28 1.010

Table 7.9 - Influence of long term "fatigue" cycling in the dynamic stiffness of

the Brascorda Parallel model ropes.

Rope Loading% of UBL

No. of Cycles Loss CoefficientAU/2nU (stroke)

Loss CoefficientAU/2nU (elongation)

0.0376PET Superline 20%±10% 100 0.0383PET Superline 20%±10% 300 0.0380 0.0283PET Superline 20%±10% 1000 0.0339 0.0265

steel wire rope 20%±14% 100 - 0.0616

Table 7.10 - Hysteretic damping results for the Superline model rope and a

13 mm diameter six strand steel wire rope (with steel core).

Time Strain (Instron) Strain (clock)s

0 0.00 0.003.6 4.76 -5.6 4.89 -11.6 5.03 -38.6 5.18 -121 5.29 -284 5.35 -592 5.41 -1182 5.45 5.452382 5.49 5.494782 5.53 5.5310782 5.56 5.5721282 5.59 5.6050982 5.62 5.6385182 5.65 5.65151182 5.67 5.68258882 5.69 5.70318282 5.68 5.69403782 5.69 5.70490182 5.69 5.70512682 5.69 5.70574782 5.70 5.71

Table 7.11 - Creep strain results for a one week test on Diolen 855TN yam in

the lnstron universal testing machine at 30% of YBL.

TIME STRAINS 0/0

0 0.00220 5.07775 5.131495 5.183415 5.246295 5.2415295 5.3523095 5.3530295 5.3581295 5.35167095 5.40254695 5.40627295 5.40

3975295 5.527859695 5.57

Table 7.12 - Creep strain results for a three month dead weight test on Diolen

855TN yarn at 30% of YBL.

Strain Rate (%/decade)Dead WeightDecade Instron

10"3 to 1044 0.118 0.11910 1.'4 to 10 1'5 0.093 0.09410"5 to 10"6 0.077 0.07810 1'6 to 10"7 0.066 0.067

Table 7.13- Strain rate (in percent per time decade) observed in the two

types of creep tests performed.

Temperature°C

Load°/0 YBL

Strainok

Std. Dev. of Strain°h.

2020 3.92 0.1830 5.47 0.1840 6.58 0.36

3020 4.40 0.1930 6.11 0.1540 7.38 0.13

Table 7.14 - Estimated strains after one year in the yarn samples used in the

combined creep-environmentally assisted degradation tests.

IDENTIFICATION AMBIENT DURATION LOAD (%BL)20.00

BREAKING LOAD84.50_

11 DIW 12.0012 DIW 1.00 20.00 90.00

1111 DIW 12.00 40.00 84.501112 DIW 1.00 40.00 86.50IV1 SW 12.00 20.00 82.501V2 SW 12.00 20.00 86.501V3 SW 12.00 20.00 . 84.50IV4 SW 3.00 20.00 90.50IV5 SW 1.00 20.00 84.50V1 SW 12.00 30.00 86.50V2 SW 12.00 30.00 89.00V3 SW 12.00 30.00 86.00V4 SW 1.00 30.00 83.00V5 SW 3.00 30.00 83.50VI 1 SW 12.00 40.00 83.50V12 SW 12.00 40.00 87.00VI4 SW 3.00 40.00 82.00VI5 SW 1.00 40.00 85.50

19 DIW 1.00 20.00 84.001119 DIW 1.00 40.00 83.00

1V21 SW 1.00 20.00 85.50V21 SW 1.00 30.00 87.00V120 SW 1.00 40.00 83.50113 DIW 3.00 20.00 87.00

11113 DIW 3.00 40.00 86.501V25 SW 3.00 20.00 88.00V25 SW 3.00 30.00 88.00V124 SW 3.00 40.00 89.50

20% DIW 86.38 20% 86.142.75 2.54

30% 86.142.21

40% 85.140% DIW 85.13 2.3

1.71 MTH 85.26

2.173 MTH 86.88

20% SW 86 2.882.63 1 YEAR 85.45

1.91

DIW 85.7530% SW 86.58 2.22

2.06 SW 85.82.43

40% SW 85.17 ALL SAMPLES 85.792.75 2.33

Table 7.15- Results of the combined creep-environmentally assisted

degradation tests on yarn samples at 4°C.

IDENTIFICATION AMBIENT DURATION LOAD (%BL) BREAKING LOAD13 DIW 12 20 • as

1114 DIW 1 40 84.51V6 SW 12 20 82IV8 SW 12 20 78

IV10 SW 1 20 83V6 SW 12 30 78V7 SW 12 30 80.5V8 SW 12 30 82.5V10 SW 1 30 80V16 SW 12 40 84.5VI8 SW 12 40 84.5

V110 SW 1 40 84.511110 DIW 1 40 84IV22 SW 1 20 83V22 SW 1 30 81VII1 AIR 1 20 82V112 AIR 2 20 88V113 AIR 3 20 83VII6 AIR 12 20 84.5VllIl AIR 1 30 86.5VIII2 AIR 2 30 88VIII3 AIR 3 30 86VIII4 AIR 12 30 78.5VIII5 AIR 12 30 79VIII6 AIR 12 30 821X1 AIR 1 40 801X2 AIR 2 40 83IX3 AIR 3 40 81.5IX4 AIR 12 40 73IX5 AIR 12 40 83114 01W 3 20 87.5

11114 DIW 3 40 89IV26 SW 3 20 84.5V26 SW 3 30 85.5VI25 SW 3 40 86.5V1117 AIR 1 30 84.5IX7 AIR 1 40 85

L20% DIW 86.75 20% 84

1.06 2.6330% 82.46

40% DIW 85.83 3.332.75 40% 83.31

3.79

20% AIR 84.672.09 1 MTH 83.17

2.062 MTH 86.33

30% AIR 83.5 2.893.74 3 MTH 85.44

2.411 YEAR 81.66 .

40% AIR 80.92 3.584.22

DIW 86.220% SW 82.1 2.08

2.46 AIR 83.053.65

SW 82.5330% SW 81.25 2.6

2.54

40% SW 85 ALL SAMPLES 83.261 3.26

Table 7.16 - Results of the combined creep-environmentally assisted


IDENTIFICATION AMBIENT DURATION LOAD (%BL) BREAKING LOAD15 DIW 12 20.00 77.0016 01W 1 20.00 83.00

1115 D1W 12 40.00 , 82.00IV12 SW 12 20.00 82.00IV13 SW 12 20.00 83.00IV15 SW 1 20.00 79.50V11 SW 12 30.00 84.50V12 SW 12 30.00 84.50V15 SW 1 30.00 80.50VI11 SW 12 40.00 83.50VI12 SW 12 40.00 84.50VI13 SW 12 40.00 86.00VI15 SW 1 40.00 84.50

111 DIW 1 20.00 83.5011111 01W 1 40.00 79.00

, IV23 SW 1 20.00 85.00V23 SW 1 30.00 82.00VI22 SW 1 40.00 84.50115 DIW 3 20.00 86.50

11115 DIW 3 40.00 87.50V27 SW 3 30.00 89.00VI26 SW 3 40.00 87.00

20% DIW 82.5 20% 83.443.98 3.01

30% 84.13.23

40% 84.2840% DIW 82.83 2.61

4.311 MTH 82.38

2.263 MTH 87.5

20% SW 82.38 1.082.29 1 YEAR 83

2.6

DIW 82.6430% SW 84.1 3.76

3.23 SW 842.42

40% SW 85 ALL SAMPLES 83.571.26 2.89



IDENTIFICATION AMBIENT DURATION LOAD (%BL) BREAKING LOAD18 DIW 1 20 87

1117 * 01W 3.6 40 851118 DIW 1 40 85

IV16 * SW 3.6 20 81IV17 * SW 3.6 20

_

83.5IV20 SW 3 20 86

r V16* SW 3.6 30 83.5vii* SW 3.6 30 84.5V18* SW 3.6 30 84V19 SW 1 30 86.5V20 SW 3 30 89.5

V116 ' SW 3.6 40 83V117* SW 3.6 40 85VI18 SW 3 40 85VI19 SW 1 40 84112 DIW 1 20 87

11112 DIW 1 40 83IV24 SW 1 20 88.5V24 SW 1 30 87.5VI23 SW 1 40 84116* DIW 1.4 20 83

11116 * DIW 1.4 40 83IV28 * SW 1.4 20 84.5V28* SW 1.4

_30 81

V127* SW 1.4 40 79

20% DIW 87 S 20% 87.130 1.03

, 30% 87.831.53

40% 84.240% DIW 84 0.84

1.41

1 MTH 85.831.89

20% SW 87.25 3 MTH 86.831.77 2.36

DIW 85.530% SW 87.83 1.91

1.53 SW 86.382.03

40% SW 84.33 ALL SAMPLES 86.080.58 1.95

*yarn sample accidentally overheated



SAMPLE JACKET BREAKING LOADkN

BREAK

AVERAGE B. L. NEW removed 57.20 (1.70) "

REFERENCE NEW removed 57.00

1 MONTH CREEP removed 50.76 termination3 MONTH CREEP removed 56.75 termination

6 MONTHS CREEP removed 54.50 termination12 MONTHS CREEP removed 55.80 termination

AVERAGE CREEP removed 54.45 (2.63)

( ) = standard deviation


degradation tests on the Superline model rope samples.

SAMPLE JACKET BREAKING LOADkN

BREAK

AVERAGE B. L. NEW removed 58.55 (0.21),

REFERENCE NEW removed 59.00

1 MONTH CREEP removed 56.10 termination

3 MONTH CREEP removed 60.00 termination

6 MONTHS CREEP removed 60.00 termination

12 MONTHS CREEP removed 58.90 termination

AVERAGE CREEP 58.75 (1.84)

Q == standard deviation


degradation tests on the Brascorda Parallel model rope samples.

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MilliiiiiPlidlird '11111116Elongation (mm)

Figure 7.1 - Typical load-elongation plot for the installation cycle in a

Superline sample.

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Load (kN)

Elongation (mm)

Figure 7.2 - Typical load-elongation plot for the installation cycle in a

Brascorda Parallel sample.

lesiduals

0eP

0' %00 •

% 0 0• di

.7- ',° % 00

0 44-6-0

00 .00 % 6

a

r13--- c-T2T-4'.:

0

00 0

000

o 0AP a, 0

Cb

oo

0

0

o

o v

10 12 14 16 1

0.6

0.4

0.2

-0.2

-0.4

-0.6

10RESIDUES (%)

••••• ••1

0•5 a 0 0 T.

0

000 00 0000?

5 oo0

0

-1012 14 16 18 20 22

FITTED VALUES

Figure 7.3 - Distribution of residues of the yarn stiffness regression.

SPECIFIC MODULUS

Figure 7.4 - Distribution of residues of the Superfine stiffness regression.

/

Et esiduals

. •04

os

ib, is• i

p• • i, - •----t-------IP--°• c:0 •d'q, i s t.el f a ce ie03

•

•0I-- 0

0

12 14 16 18

1.5

1

0.5

o

-0.5

17.1

,Load (kN)

zz/

Z

5.7

LElongation (mm) 682

Figure 7.5 - Load elongation plot for a Superfine undergoing a simulatedquasi-static loading cycle.

55.4

SPECIFIC MODULUS

Figure 7.6 - D'stribution of residues of the Brascorda Parallel stiffness

regression.

17.7

Load (kN)

5.9

)

V 1 11 15.4111 • • 1-1,71 • • • •-••• 9• • • —.--1-1—ra 1

1 0 4 1 0 5• , • • .6171

1 0 6

43.4

Elongation (mm) 53.0

Figure 7.7 - Load elongation plot for a Superline undergoing a simulated

quasi-static loading cycle.

8 -

7 -

6 -

--. 5 _e.... .c 4 -

IT! .CI)3 -

0

a aCI

13 13 13 01:1 (ICI CI 011333

CI •• •

0 •0 0• ••• • •• • • • •

2 -ti lnstion

• deadweight

0 • . ..•...,10 0 101

• V V •••••

1 0 7

Time (s)

Figure 7.8 - Creep strain in Diolen 855TN yarn at 30% of YBL.

o 1 Month

• 3 Mordhs

+ 6 Months

• 12 Months

0 1 11 0 1 1 0 2 1 0 3 1 0 4 1 0 5 1 0 6 1 0 7 1 0 8

Time (s)

1 1

3 6• I •

7I • I

4 5

Log time (s)

Figure 7.9 - Creep strain in the four samples of Superfine nominally at 30% of

UBL.

Strain

(%)

8 —-

7 --

6 -

5 -

4 _

3 -

2 -

1 -

e0 00 0

y = 4.7183 *

00

x^0.20544

°

R A2 = 0.915

+

o 1 Maith

+ 6 Months

• 12 Months

o2 8

Figure 7.10 - Creep strain in the three samples of Superline actually at 30%

of UBL.

0 t • I • I 1 12 3 4 5

Log time (s)

876

• 1 Morth

+ 3 Months

• 6 Months

o 12 Months

Figure 7.11 - Creep strain in the four samples of Brascorda Parallel at 30% of

UBL.

8 MATERIAL PROPERTIES : DISCUSSION

8.1 Strength

8.1.1 Yarn

The tensile strength measured during this test programme for the single yarn

Diolen 855T as supplied by the manufacturer varied between 1.15 and

1.17 GPa depending on the termination method, with standard deviation

generally below 0.013 GPA for the yarn tested with twist. This strength is

situated in the upper half of the range mentioned by the major manufacturers,

showing that a yarn strength of 1.15 GPa is a realistic value for good quality

"high tenacity" polyester yam.

From the two model ropes tested in this programme, the rope with more

manufacturing operations (Superline) was made of yarn of the same make

and grade of yarn, supplied by AKZO already twisted in bundles of 20 yarns

with additional finish (Diolen 855TN). Most testing concerning yarn

degradation was performed on yarn originally purchased by the rope

manufacturer, with this finish on, from the same batch used to make the model

rope. To reduce scatter one yarn from the 20 yarn assembly was selected for

the bulk of the testing programme. The average breaking strength of this

particular yarn was found to be 1.093 GPa and the standard deviation

0.029 GPa.

The yarn removed from the rope, assembled in 3 sequential twisting

operations, showed an average breaking load of 1.075 GPa, i.e. 92% of the

maximum strength measured, with a standard deviation of 0.025 GPa.

Considering that:

(i) most of this strength reduction was already evident in the yarn

tested after the first twist operation (94%); and,

(ii) full size mooring ropes will typically have one additional twisting

operation;

it can be considered that polyester yarns in a properly made full size mooring

rope of the same construction should retain strengths of at least 1.05 GPa,

130

corresponding to 90% of the original yarn strength.

Ropes made of PET yarns in two other constructions, parallel yarn and

parallel strand, were also found to be attractive options for substitution of all

steel mooring lines. These constructions are simpler than the parallel sub-

rope and as such are not expected to suffer degree of yarn damage during the

manufacturing process as that observed in the Superline. Measurements in

the parallel strand rope made by Brascorda support this conclusion, i.e. yarn

removed from the rope averaged 94.4% of the strength quoted by the yarn

manufacturer.

Full size steel wire mooring ropes (70 mm to 127 mm diameter) are usually

made of wires with nominal tensile strengths in the range of 1.57 to 1.77 GPa.

The average strength of wires from each of these grades can be expected to

be about 10% higher than the nominal figure. Assuming that no damage is

impaired to the wires in making a steel wire rope, the yarns in a good quality

low twist construction PET rope will have a tensile strength typically between

54% and 61% of the strength of wires in a steel wire rope.

The tensile strength of the material used to make mooring chain used for

mooring offshore platforms is either 0.69 GPa or 0.86 GPa minimum tensile

strength (Andreassen (1991)), somewhat below the polyester yarn.

The large advantage to be gained by changing to tethers based on polyester

fibres starts to became apparent when strength is considered on a weight

basis. High tenacity PET yarn in a rope has a specific strength of at least

0.76 N/tex, i.e. 0.76 MN/(kg/m), while the wire in a steel wire rope will not

exceed 0.23 MN/(kg/m) and the steel in a mooring chain will not be higher

than 0.11 MN/(kg/m). These differences correspond to weight reductions by a

factor of 3.3 and 6.9 respectively, for the same strength.

For mooring applications strength is best analysed in terms of the immersed

weight (apparent weight) of the mooring component. In this case, the strength

of the PET yarn in the rope will be ca. 0.28 MN/(N/m) (2.76 MN/(kgf/m)) while

steel wire will only give 0.027 MN/(N/m) (0.26 MN/(kgf/m)). This means, 10

times more apparent weight for the same strength! The efficiency of the steel

in the chain in these terms will be much worse at 0.013 MN/(N/m)

131

(0.13 MN/(kgf/m)).

These results, referring to actual measurements of strength from yam removed

from two ropes, give a taste of the potential weight advantages to be had by

replacing part of the steel components in a deep water spread mooring

system with ropes made of polyester yarns assembled in low twist

constructions.

The minimum tensile strength of the core, based in the actual fibre cross-

sectional area, given by Linear Composites Ltd. (1983) for their PET parallel

yam rope, Parafil, is 0.617 GPa. This corresponds to 59% of the minimum yarn

tensile strength identified in this study, i.e. 1.05 GPa. The average value

obtained by Crawford & McTernan (1988) for a 10 tonne PET Parafil was

0.783 GPa. The later result would be consistent with the 84% strength

efficiency calculated by Burgoyne & Flory (1990) for a high modulus aramid

parallel yarn rope and a termination efficiency of around 90%. In terms of the

enclosed area of the core, the tensile strength quoted by LCL becomes

0.432 GPa and the measurements by Crawford & McTernan (1988) average

0.548 GPa.

Considering that: the average breaking strength of small steel wire ropes is

typically 10 to 15% higher than the minimum breaking load quoted by the

manufacturer (Chaplin (1992)) and that the tensile strength given by British

Ropes (1988, ref. blue strand catalogue) for a 12 mm diameter 6x36 +IWRC

rope using grade 1770 kN/mm2 wire is 0.802 GPa, the tensile strength

measured by Crawford & McTernan is between 60 and 62% of the actual

strength of a six strand wire rope of similar breaking load. It is also interesting

to note that based on these results and the tensile strength measured for PET

yam in the present study (1.15 GPa new), it is possible to conclude that, on the

basis of enclosed area, small size (100 kN MBL) parallel yarn Parafil PET

ropes convert yarn strength into rope strength with an efficiency similar if not

better than 6x36 +IWRC six strand wire ropes convert the wire strength.

There is no data available in the literature concerning actual test data for

larger diameter PET Parafil ropes, but from the yarn results now obtained and

the tests performed by Crawford & McTernan, it seems that the tensile strength

132

quoted by Linear Composites is conservative, provided terminations of similar

efficiency are used. This can only be proved in full size testing.

8.1.2 Ropes

Two model ropes of approximately 60 kN breaking load have been tested in

this work. The tensile strength of both ropes, tested without their covers, was

found to be very similar both in terms of weight per unit length and in terms of

the enclosed area. The average strength obtained for the Superline parallel

sub-rope construction was 0.575 N/tex (N/(g/km)) or 0.551 GPa. For the

. Brascorda Parallel parallel strand rope the strength was 0.547 N/tex

(N/(g/km)) or 0.564 GPa.

On a basis of fibre cross-sectional area, tensile strengths were 0.794 GPa and

0.755 GPa respectively. The later results are quite similar to the 0.783 GPa

measured by Crawford & McTernan (1988) for a 10 tonne PET Parafil, the

difference between the 3 ropes being not more than 5%. This is a remarkable

coincidence, since not even the yarn used to make the ropes is from the same

manufacturer or batch.

Although the parallel yarn rope could potentially be stronger than the parallel

strand which in its turn could be stronger than the parallel sub-rope, not all

potential strength is realised due to: variation in yarn strength, variable yarn

slack, load sharing between yarns increasing with complexity of construction,

and termination efficiency.

Based in the results obtained there is no reason to prefer any of the

constructions on the basis of the average strength.

Dividing the specific strength of each rope by the average specific strength of

the yarns in the rope we obtain the tenacity conversion efficiency which tells

us, in absolute terms how well the construction converts the strength of the

fibre. The measured efficiency of the model Superfine was 73.8% and the

efficiency of the model Brascorda Parallel was 70.9%. These results are

numerically equal to the rope tensile strength (based in the fibre cross-

sectional area) divided by the yarn tensile strength on the same area basis.

133

The tensile strength of the Superline based on the enclosed area was 59.8%

of the strength reported by Ridge (1992) for a 122.5 kN breaking load 6x19 +

IWRC steel wire rope (see Section 6.2.2 for detailed description). The strength

of the Brascorda Parallel rope on the same basis was 61.1% of the wire rope.

This small wire rope has a linear mass of 0.673 kg/m and is made of nominally

1.77 GPa wires. If we assume the average strength of these wires to be 10%

up from the minimum (Chaplin (1992)), we can calculate the tenacityconversion efficiency of this rope as approximately 74%. It is interesting to

note that the efficiency measured for the fibre ropes tested (73.8% and 70.9%)

is very similar to that estimated for this wire rope.

The comparison between the specific strength of the fibre ropes tested, with

steel wire ropes in dry conditions or under immersion, gives results very much

like the ones obtained for PET yarn and steel wire. Typically, compared on a

weight basis, the fibre ropes are 3 times stronger than the wire rope dry and

10 times stronger for the same apparent weight in water.

The number of tensile tests carried out on the model ropes was limited, so the

calculated variation shown in Tables 7.2 and 7.3 should be taken as an

indication rather than definitive. The coefficient of variation found for the

Superline was 0.0297 (3 tests) and for the Brascorda Parallel it was 0.0036

(2 tests).

Calculating the coefficient of variation of all tensile tests including the results

after creep and "fatigue" gives a conservative idea of the strength variation of

these ropes. Results obtained for the Superline and for the parallel strand

ropes are 0.0450 with 9 tests and 0.0434 with 8 tests respectively.

Unpublished results for a 100 m length of 19 mm diameter 6x19 Seale +

IWRC steel wire rope (Tantrun & Chaplin (1984)) show a coefficient of

variation of 0.00231 for four clear breaks in samples taken at random over the

length. Results for three breaking load tests on a 19 mm Lang's lay rope, with

two of the failures at the termination, showed a coefficient of variation of

0.0546. In a series of 4 tests on a 50 m length of 13 mm diameter 6x19 Filler +

IWRC steel wire rope, all with clear failures, Ridge (1992) found strengths

within a coefficient of variation of 0.00376.

134

From the results presented, it seems clear that the variation observed in

values of the breaking strength, measured for both model fibre ropes, is

compatible with the termination failures obtained. With termination failures,

one would expect to find a skewed distribution of breaking strengths, however

the limited dataset available did not show skew, and was not large enough to

suggest the use of a particular statistical distribution. Assuming a normal

distribution, 95% confidence limits for all Superline ropes (9) and Brascorda

Parallel ropes (8) would typically be set at ±3.5%. Therefore it is not

unreasonable to expect ( but still to be explicitly proven) that these ropes have

a similar strength variation to steel wire ropes.

The average tensile strength measured for the core only of the Superline

model rope (0.551 GPa) is 6% bigger than the strength reported by Karnoski &

Liu (1988) for a 53 mm diameter 1157 kN breaking load Superline with

braided jacket. Since the tensile stresses in the jacket are substantially lower

than in the core, the difference in core strength between the two ropes is

smaller than 6%.

Considering that a factor of 20 in breaking load exists between these ropes,

and very little change in ultimate tensile stress was observed, it is thought that

a sensible way to estimate the average tensile strength of ropes, with breaking

loads between 3000 kN and 6000 kN, is to put a penalty of 10% on the

average strength obtained for the model rope, i.e. to assume an average

strength of 0.496 GPa. Based on the scatter measured in this study, it is

considered that a sensible minimum strength to be used for design purposes,

with PET Superline ropes is 0.446 GPa, i.e. 90% of 0.496 GPa.

Using the same procedure for the Brascorda Parallel, parallel strand rope, it is

assumed that such ropes, in a size compatible with a mooring application, will

have an average tensile strength of 0.507 GPa and for design purposes a

strength of 0.457 GPa should be used.

If the same procedure is applied to the data obtained by Crawford & McTernan

(1988) for a 128 kN PET parallel yarn Parafil, the average tensile strength of

large PET Parafil ropes would be estimated as 0.493 GPa and the strength to

be used for design would be 0.444 GPa. This is only 2.8% greater than the

135

0.432 GPa quoted by Linear Composites Ltd. (1983).

It should be noted that using this procedure to obtain the strength of scaled up

Parafil and Brascorda Parallel ropes has no experimental support. Test on a

larger scale are needed to confirm these assumptions. For the time being it

seems unrealistic to consider that any of these 3 ropes has a tensile strength

greater than the others, and it is therefore thought reasonable to consider that

large ropes of any of these constructions have a minimum breaking strength of

0.44 GPa.

Elongation during installation

Elongation measured for the model Superline in the "installation" cycle

averaged 8.6%. This result is lower than the elongation of 11.3% observed in

H&T Marlow (1985) for a single loading to 50% of the breaking load in a new

rope. This is not unexpected since the model rope, like ropes for spread

mooring systems, have been manufactured with lower twist angles than

standard products.

Based on this figure it is thought safe to use an upper steel component

between the fibre rope and the fairlead with an initial length of 13% (1.5 x

8.6%) of the length of fibre rope, plus the take-up due to the change in

geometry in the lower component catenary, plus an a fixed length to account

for rope movement during anchor bedding in.

The elongation measured for the Brascorda Parallel model rope during the

installation cycle was 8.0%. Using a similar reasoning as for the Superline, it

is considered that a safe initial length for the upper component would be 12%

(1.5 x 8.0%) of the fibre rope length plus the same allowances described for

the Superline.

8.2 Stiffness and Hysteresis

8.2.1 Yarn Stiffness

The dynamic modulus measured for PET yarn at the lowest mean stress,

0.055 GPa, at the lowest frequency investigated in this study (0.005 Hz) was

136

18.27 GPa and the value indicated by the regression equation developed is

17.91 GPa. The static modulus reported by Hadley et al. (1969) for highly

drawn PET filament at very low mean and range of stresses was ca. 18 GPa.

Considering that Hadley's paper gives no indication of the precise stresses

used and that characteristics of the polymer, such as molecular weight,

distribution are certainly different from the material tested in this study, we can

consider the agreement between the results good.

Results reported by Van Der Meer (1970) for another PET yarn tested at 10 Hz

at varying mean stresses are in quite good agreement with the values now

measured. For example, at a mean stress of 0.22 GPa and for a frequency of

10 Hz the regression equation obtained in this study (note the extrapolation)

indicates a modulus of 23.1 GPa, while the value measured by Van Der Meer

was ca. 25 GPa.

Rim & Nelson (1991) cycling a PET tire yarn at 10 Hz between fixed strain

limits corresponding to ca. 1.25% and 3.75% of the breaking load measured a

modulus of 12.3 GPa while the regression equation now obtained indicates a

value of 13.4 GPa. The difference is acceptable since the yarn tested is not

exactly the same and the equation is being used as an extrapolation from

experimental data.

Due to variable yarn slack in the rope, the dynamic modulus of parallel yarn

ropes should fall slightly below the dynamic modulus of its constituent yarns,

for the same average stress condition in the filaments.

For the Parafil rope tested by Crawford & McTernan (1988) average tensile

strength was 75% of the yarn strength (on a fibre area basis): So when the

stress in the rope is say 20% of its breaking strength, the average stress in the

yarns is 0.75 x 20% of their breaking strength. The same factor applies to the

stress amplitude. Rewriting the yarn stiffness regression equation

(Section 7.2.1, equation (1)) taking this into account, we get an expression for

the maximum specific modulus of a PET Parafil having no yarn slack:

SM = 13.41 + 0.75. (0.1778. Lm- 0.1756. La) - 0.3835. Log T

where:

137

SM = specific modulus (in N/tex);

Lm = mean load (in % of the ultimate breaking load of the rope);

La = load amplitude (in % of UBL); and,

T = period (in seconds).

Incorporating the filling factor of 70% given by the manufacturer and taking

into account the material density we can obtain an estimate for the Young's

modulus of PET Parafil (Er) based on the enclosed area of the core as:

Er= (13.41 + 0.75. (0.1778. L m- 0.1756. La) - 0.3835. Log T) . 0.966

This equation produces values for modulus between those obtained for the

parallel strand rope (with a single twist operation) and the values measured

for PET yarn, and can be used as a sensible approximation in the absence of

experimental results for PET Parafil ropes. The results so obtained probably

overestimate the modulus, since yarn slack is not taken into account, and

should give conservative results when calculating wave frequency line

tensions.

8.2.2 Rope Stiffness

8.2.2.1 Wave Frequency and Low Frequency

"As Installed"

Results obtained for both model ropes, in the "as installed" condition, showed

clearly that dynamic modulus is a function of the previous history of loading

seen by the rope. A multivariate linear regression of the data obtained was

performed for each rope, to even out the influence of the particular loading

history used in the measurements, with time being considered on a

logarithmic scale. The equations obtained (one for each rope, below referred

to as "the regression equations") were statistically very significant (better than

99.9%). Significance obtained as measured by the F-statistic parameter was

better than obtained by Bitting (1980), who had incorporated quadratic

elements in his analysis. In agreement with Bitting (1980), the regression

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equations indicate that, over the range of parameters investigated, the

stronger influence is caused by the mean load, followed by the load range

(twice the load amplitude used in the regression equations). The influence of

frequency was much smaller, with typically less than 10% difference in

modulus between wave frequency and low frequency results.

Young's modulus obtained for the model Superline was ca. 3.3 times the

values observed by Bitting (1980) for double braided PET ropes of similar

size, cycled at wave frequency. The parallel strand rope results were ca. 4

times Bitting's values. Results reported by Toomey et al (1990), also for double

braided ropes, were higher than Bitting's results but still well below the values

obtained here. The model Superline was approximately 2.2 times as stiff as

Toomey's double braid. The Brascorda Parallel was ca. 2.6 times as stiff.

These results clearly demonstrate that, contrary to what was suggested by

Flory et al. (1988), rope structure is a dominant parameter on the dynamic

stiffness of worked fibre ropes.

Karnoski & Liu (1988) found a Young's modulus of 8.4 GPa for a 53 mm

diameter Superline, including the braided jacket, cycled between 8% and

50% of its breaking load with a 10 s period. Making some reasonable

assumptions about the jacket characteristics the calculated modulus for the

rope core would be 9.6 GPa. Using the regression equation for the model

Superline gives a Young's modulus of 10.3 GPa, a bit higher but still in quite

good agreement with Karnoski & Liu (1988).

The results obtained here for the Superline rope reinforce the warning about

the use of the model presented by Ractliffe & Parsey (1985) because of the

rather low values of Young's modulus that it can produce.

The modulus now measured for the Brascorda Parallel model rope was about

15% lower than measured for the 40 kN rope with the same construction,

tested in the "pilot study". This difference draws attention to the

approximations that are made when basing the stiffness on the enclosed area,

particularly of a small diameter rope. It is considered that more consistency

can be obtained if specific stiffness is used instead.

Bearing in mind the simplicity of the rope constructions, especially of the

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parallel strand rope, and the relatively low twist employed in their construction,

it is considered reasonable to model the equivalent stiffness of each rope in

terms of the yarn regression equation. The model used considered no

variation of rope diameter with load, each strand as a twisted yarn and, for the

Superline, approximated each 3-strand rope as a yarn made of three

filaments.

As explained in Appendix 3, under these assumptions, the equivalent specific

stiffness of the Superline parallel sub-rope construction (Es p) can be

approximated by:

E= E. cos2 a. cos2 [3,

and the equivalent specific stiffness of the Brascorda Parallel rope (Em) can

be approximated by:

EEp= E. cos2a,

where:

Ey is the specific modulus of the yarn, from Section 7.2.1 equation (1);

a is the helix angle of the outermost yarns in the strand; and,

(3 is the helix angle of the strands.

The values of mean load and load range to be used in Section 7.2.1

equation (1) to obtain Ey can be obtained by using equation (16) and (13) from

Appendix 3, respectively for the Superline and the Brascorda Parallel ropes.

Figure 8.1 is a plot of the specific modulus obtained using this model versus

specific modulus measured for both ropes (actually the values interpreted via

the rope regression equations). The assumptions made are such that results

are always conservative. Better results are obtained for the parallel strand

rope that has the simplest geometry.

Modelled results converge to the measured results for the high values of

specific modulus which correspond to high mean loads and small load

ranges. Global Maritime Ltd. (1989,1) calculated typical mean loads in

mooring lines under extreme conditions between 35% and 45 To of the

minimum rope breaking load. The amplitudes of line tension were calculated

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to be between 15% (500 m water depth, North Sea) and 2% of MBL (2000 m,

Campos Basin). In this range of conditions, modelled results for the Superline

are between 5% and 18% greater than the measured modulus. For the

Brascorda Parallel the model overestimates the modulus by between 1% and

11°A.

In the absence of test data for a particular parallel sub-rope or parallel strand

rope, conservative stiffness data in the "as installed" condition can be

obtained from the yarn data given a knowledge of: rope construction

geometry, average breaking load and mass per unit length.

"After Fatigue"

Results of wave frequency modulus measured after fatigue cycling showed

that there is a limited amount of stiffening (about 6%) associated with long

term cycling at a constant load level. It was also observed that, as soon as the

conditions were changed, stiffness converged very quickly to the values

obtainable from the regression equations for the "as installed" condition.

Considering that long term cycling under constant loading conditions is

completely artificial as far as the real application is concerned, it can be

concluded that no stiffening should be considered in association with fatigue

loading.

"After Creep"

Wave frequency modulus values at 20 ± 10% of UBL, after creep testing at

30% of UBL, were found to be 4 to 7% lower than those indicated by the

regression equations for the as installed condition. Two alternative

explanations can be suggested for these results:

(i) either any stiffening that might have happened during the creep test

has disappeared in removing the rope from the creep testing

machine and taking it to the servo-hydraulic tester; or,

(ii) because the rope has been under a constant load of 30% of BL it

has set at this mean load and upon cycling at a lower mean load

behave in a more compliant manner.

The second explanation is more likely to be the principal cause of the lower

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modulus measured after creep since it agrees with the findings in the after

fatigue condition, where for example, coming from a loading at 20 ± 10% of

UBL, to cycling at 10 ± 5% of UBL produced a stiffness lower than the fitted

data for the as installed condition.

For the amount of variation measured after creep and considering the

discussion above, it can be concluded that, for design purposes, there is no

need to correct the values for stiffness obtained in the as installedcondition for

the effect of long term constant loads.

8.2.2.2 Quasi-static

A simulated quasi-static load cycle was defined in terms of a typical reversal of

load between 10% and 30% of UBL taking place over a period of one week

with 3 days plateaux at both load extremes. Stiffness was measured as the

secant modulus between the extreme elongation data points. The values

obtained provide a realistic assessment of the apparent quasi-static modulus

shown by these rope constructions in a spread mooring application. This

experimental approach bunches together the time dependent a load

dependent behaviour of the tether (material plus construction). An analytical

modelling of this behaviour was out of the scope of this study but should be

considered for further work. There are no results for similar conditions

available in the literature for comparison purposes.

Results obtained for the two ropes were 7.32 GPa and 9.66 GPa for the

Superline and the Brascorda Parallel respectively These are about half the

values obtained for typical wave frequency storm conditions. It is strongly

suggested that these figures are taken into account when verifying the offset

performance of any mooring system incorporating these materials.

Table 8.1 shows selected values for Young's modulus and specific modulus of

both ropes for typical: "installation", quasi-static, wave and low frequency

regimes. Bearing in mind that the "installation" condition is only relevant to

size the upper steel component, the range of modulus to be taken into account

in a mooring analysis would be from 9.66 GPa to 19.16 GPa for a Brascorda

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Parallel parallel strand rope and from 7.32 GPa to 16.29 GPa for a Superline

parallel sub-rope construction. This subject is discussed in more detail in

Chapter 9.

8.2.3 Hysteresis

Figure 8.2 shows the damping measured for the PET Superline in terms of

the loss coefficient as a function of the number of cycles performed at 20 ±

10% of UBL. A tendency for a constant or almost constant loss coefficient after

about 300 cycles was observed. A similar levelling off has been reported by

Parsey (1983) for eight strand plaited polyester ropes and by Kenney (1983)

for polyester yarn. The loss factor obtained, 0.03, is typically 5 times lower

than reported by Parsey for 8 strand ropes. This difference seems plausible,

since the rope tested here has a much simpler construction and is much less

compliant. The results obtained in this study are in agreement with the

preliminary measurements taken in the preparatory work, reported in

Section 4.6.9, for a 9.5 mm diameter parallel strand rope. The later is a slightly

stiffer construction, in a smaller diameter, which gave a loss factor of

approximately 0.02.

The results obtained for both the model Superline now tested, and the 9.5 mm

diameter parallel strand rope previously tested are within the range of loss

factors reported by Van Der Meer (1970), 0.013 to 0.035, and Rim & Nelson

(1991), 0.02 to 0.03, for polyester yarns. This shows that, at least for small

ropes, the hysteretic damping observed in low twist almost parallel

constructions is mainly due to material damping.

The increased damping observed when using stroke as a measurement of

displacement (Table 7.10) is compatible with the small test piece size but also

provides a warning about the increased friction present at the cylindrical

section of the socket, where minor abrasion damage was observed after the 1

million cycle "fatigue" tests.

The hysteretic damping of the steel wire rope was only measured once at 100

cycles indicating a loss coefficient of 0.0616. According to Casey (1988) the

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loss factor of steel wire ropes under cyclic tension levels off in a similar way as

reported for PET ropes (Parsey (1983)). Stabilised levels between 40 and

70% of the hysteresis measured in the first few cycles are reported by Casey

(1988).

Although there might be a scaling up effect in the hysteresis of parallel strand

and parallel sub-rope PET fibre ropes, the value of loss coefficient measured

for the small wire rope, 0.0616, being about twice of the value measured for

the Superline model rope, practically rules out any worries that tether

"internal" damping would be high enough to be of significance when

compared with hydrodynamic damping, in systems incorporating a catenary in

the lower steel tether component.

Another concern inherent to fibre ropes is overheating of the rope core due to

hysteresis. Considering that the rope is immersed in water, its surface will

loose heat by convection to the water at a rate, q, given by Holman (1987):

q = h . A . (Tw - T.,) (1),

where:

q = heat transfer rate per unit length of rope;

h = convection heat transfer coefficient;

A = external area per unit length of rope;

Tw = temperature of the rope wall; and,

Tc.= is the water temperature remote from the rope.

The temperature in the centre of the rope (To), in its turn, can be estimated by

its difference to the rope wall temperature (Tw) which is given by Holman

(1987):

To - Tw = (el . R2) / (4. k) (2);

where:

q = heat generated by unit volume;

R = radius of the rope; and,

k = thermal conductivity.

Considering the almost straight line obtained in the loading portion of the

cyclic tension versus strain plot for both model ropes, di can be calculated as:

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Ci.(tanD.7c/2 ).(Aa.e/2). 1/T (3);

where:

tanD = loss coefficient;

Au= cyclic stress range;

e = strain range; and,

T = cyclic period.

Using: a loss coefficient of 0.03 (as measured for the Superline model rope), a

typical storm RMS stress range of 10.7% of the minimum breaking strength

(Global Maritime Ltd. (1989,1)) with MBL taken as 0.445 GPa (Section 8.1.2),

a strain range of 0.375% as measured for the Superline when cycled between

45 and 55% of UBL, and a period of 17 s, equation (3) gives:

4 . 247.5 W/m3(4).

A rope with a breaking load of about 5000 kN will typically have a radius (R) of

72,5 mm (including an allowance for a cover). For such a rope, the heat

transfer rate per unit length would be:

q . 4.09 W/m (5)-

Using the lowest value of heat transfer coefficient measured by Li et al (1990),

i.e. h = 1000 W/m.°C (to be conservative), an external area per unit length of

rope (A) of 0.456 m 2/m, and (5) in (1), we get:

;- T., = 0.009°C,

confirming Li's conclusion that the wall temperature of the rope can be taken

as the water temperature.

To estimate To - T w we will use the thermal conductivity (k) of 0.17 W/m.°C

measured by Parsey (1983) for a dry PET yarn. This assumption is

conservative for a rope that has not got a water tight jacket or is flooded.

Substituting q from (5), k as above and R (72,5 mm) in (2) we find:

To - Tw = 1.9°C.

Therefore we can conclude that the Superline parallel sub-rope will not suffer

145

excessive heating of the core under the worst storm conditions envisaged.-

Considering the hysteresis results previously obtained for the Brascorda

Parallel rope, and the absence of twisted structure in the Parafil parallel yarn

ropes it can safely be concluded that these ropes will operate at even lower

core temperatures, and will have an internal damping less significant in terms

of the hydrodynamic line damping, than the Superline ropes.

8.3 Creep and Environmental Assisted degradation

8.3.1 Yarn

8.3.1.1 Creep

Creep results obtained in both the one week and the three months tests

confirmed the trend reported by ENKA (1985,3), Tabor & Wagenmakers

(1991) and Oudet & Bunsell (1987) of decreasing strain rate with the logarithm

of time, which was not observed by E. I. du Pont de Nemours & Co. (1987).

The strain measured in the short term test, performed in the universal testing

machine was typically 5% higher than under the dead weight for the same

elapsed time. This difference is compatible with the test methods used,

especially if we consider how the gauge length was measured. It should be

kept in mind that the accuracy of the 3 month test is better than the 1 week test

since the former has a properly defined gauge length. The reason for

performing the short term test, was to be able to investigate the variation in

strain rate during the initial phase of loading when optical measurements are

too slow to be meaningful.

Figure 8.3 shows the results obtained at a dead weight loading of 30% of YBL,

together with data obtained by ENKA (1985,3) at 20 and 30% of YBL. The

agreement is surprisingly good, if we consider that the yarn tested in this

investigation has been manufactured at least 5 years later than that tested by

ENKA. It is also worth noting the agreement obtained on the creep rates. For

example between 103 and 104 s ENKA reported a strain of 0.13% while 0.12%

has now been measured.

146

Using the data available for the polyester yarn it is possible to estimate the

elongation under constant load of a PET parallel yarn Parafil rope.

Considering that the average strain in the yarns of a Parafil rope is the same

as the strain in the rope, rope failure could happen by phenomena happening

in the terminations or by imbalances in the strength or in the slack of the yarns

in the rope. If we assume the average rope strength to be 0.783 GPa (as

measured by Crawford & McTernan (1988)) and the yarn strength to be 1.10

GPa, as typically found in this study, the average tensile stress in the yarns of

a PET Parafil rope would be about 71% of the rope stress (based on the

actual cross-sectional area of fibre).

Rope elongation will be the sum of average yarn elongation plus an increase

in length due to variable yarn slack in the rope. Considering that Parafil ropes

are also manufactured from quite stiff fibres, such as high modulus aramids,

with an average failure strain of only 2.5%, it is clear that the manufacturing

process cannot allow large yarn slacks to develop, otherwise the behaviour of

such rope would be disappointing, which is not the case ( Linear Composites

Ltd. (undated). Under these circumstances it is reasonable to assume that

average yarn slack does not exceed 1%.

So an estimate of the total creep elongation on a Parafil rope can be obtained

by adding 1%. i.e. 10000 liz to the yarn elongation under creep at a tensile

stress equal to the rope stress. Expressed as a percentage of YBL, the yarn

stress will correspond to 71% of the tensile stress in the rope, expressed as a

percentage of the ultimate breaking load of the rope.

For example, creep elongation of a PET Parafil rope at a load corresponding

to 30% of its breaking strength will be approximately 1% plus the yarn strain at

a stress of 21.3% of the average yarn breaking strength. Interpolating from

ENKA data at 20% and 30%, total strain in the Parafil rope at 10 4 seconds for

example would be about 4.8% (and of course not less than the yarn strain at

21.3% of YBL, i.e. 3.8%).

The creep rates measured in this study for a load of 30% of YBL for periods of

time longer than 1 day (see Table 7.13) are lower (as low as half, after 1

month) than the creep rate reported for a 3 tonne Parafil loaded at 40% of its

147

nominal breaking load. However the precision of the results presented by

Linear Composites Ltd. (1983) is such that it is not possible to draw any further

conclusion from the values quoted.


The quantitative assessment of yarn degradation due to hydrolysis proved

more difficult than originally thought. The main problem encountered in this

task was to obtain relevant data from tests performed for a relatively short

period of time (one year) on a variable that changes very slowly with time, in

comparison with the statistical variation in the measured values.

An additional difficulty observed was the growth of crystals on the exposed

surface of the yarn samples in artificial sea water at all temperatures but 4°C.

This is similar to what is observed on fixed sea structures (Chandler (1985)).

As observed in a yarn where crystals have been mechanically removed, the

filaments that where positioned out of the yarn periphery where found to have

an insignificant amount of crystals. Although crystal growth presented a

problem in the test programme, it made clear that maintaining a minimum

tension in the rope would probably be extremely beneficial, minimising crystal

growth inside the rope structure.

Dissolution of the crystals by a mild acid solution, after the constant load was

removed and before performing the break load test, was only a partial solution

to the problem of yarn damage induced by the crystals. Since they adhere to

the yarn when stretched by between 3.5% and 7%, and since upon load

removal about half of this strain was recovered almost immediately, some

damage must have been inflicted on the yarn before the crystals were

dissolved.

Mechanical measurements of elongation made on some yarn samples,

although carefully executed, introduced damage in the filaments resulting in

poor retained strength.

This was observed mostly in yarns which were kept under load in air. An

additional series of tests was performed, without measuring yarn elongation,

148

and no strength reduction was observed. Since the first series did not show

any influence of creep load, the second series was kept under a very small

constant load.

A series of statistical analyses was performed on the data obtained. For each

temperature, the correlation between breaking load and: creep load, time

under load and ambient, was investigated. Statistical significance was set at a

95% level for a two-tailled distribution. The main findings of these analyses

are listed below:

(i) Data from samples at 4°C showed very low negative correlation

between breaking load and both creep load and time under load.

The correlation between breaking load and the ambient (deionised

or sea water) was null. After one year the average retained

strength was 1% lower than the average strength of the new

samples tested wet (shown in Table 7.1, series 8, line 2). This

difference was not significant at a 95% level.

(ii) Considering all samples kept at 20°C together, a significant

negative correlation was found between breaking load and time

under load. This correlation becomes non significant when the

samples in air are removed from the dataset. Since the elongation

of the air samples was measured more often than any other

samples, it is suspected that they had been accidentally damaged.

(iii) An additional set of 5 samples was kept in air for 3 months, without

being measured. The average retained strength of these samples

(Table 7.1, series 8, line 3) was significantly higher (3.4%) than

when new (Table 7.1, series 8, line 2). Results presented in

Table 7.1 , series 8, line 2, were taken as the reference for all

further comparisons in this chapter (5 tests, 86.3 N average

breaking load and standard deviation of 1.75N).

(iv) A single sample broke clear of the terminations after 1 year in DIW

at a load of 86 N. This result does not indicate a signcant

degradation.

(v) Samples that stayed in artificial seawater for 1 year at 20°C and

149

30°C had average breaking loads of 81.8N and 84.0N,

significantly lower than the reference dataset. Considering the

level of crystalline precipitation on these samples, and the fact that

the available literature (McMahon et al (1959) and ICI (undated))

reports that hydrolytic degradation increases exponentially with

temperature, it is concluded that the strength degradation

observed was certainly not caused by hydrolysis but probably due

to damage inflicted by the crystals during yarn unloading.

(vi) Samples at 30°C in DIW showed quite low retained strength

(average breaking load of 82.6 N, 96% of the average breaking

load), especially the two samples that were loaded for one year

(with breaking loads of 77 and 82 N). It is thought that the low

values obtained are due to mechanical damage when measuring

elongation. This DIW tank also showed algae growth. This was

observed when removing the samples, which were slippery, and

verified with the optical microscope.

(vii) Samples in the 40°C tank that overheated (13 samples) were

plastically elongated by up to 30 mm, and drawing only stopped

when the dead weights touched the bottom of the tank. Even under

these extremely severe conditions, the average retained strength

was 83.69N, i.e. a significant reduction of 3% when compared with

the reference data base.

(viii) Three samples remained for 3 months in the 40°C tank and were

removed for assessment of residual strength before the tank

overheated. The average retained strength of these samples was

86.83N, 0.6% higher than the average of the reference dataset.

In a final attempt to identify and quantify any degradation effect due to

hydrolysis the data obtained for samples in deionised and sea water was

analysed separately. At a level of significance of 5% no correlation was found

in either dataset between retained strength and: temperature, creep load or

time under load.

Since no deleterious influence of sea water, as opposed to deionised water,

150

was found in the tests conducted at 4°C (where no crystal growth was

observed) it is recommended that further testing for assessment of the

hydrolysis of PET fibres, to be used for ropes operated permanently

submerged in sea water, should be conducted in deionised water. For long

term testing, consideration should be given to using some form of algae killing

product provided that it is harmless to the fibre, or to running the tests in the

dark. From the great quantity of algae found on the 3 month retest samples in

DIW, where plenty of light was available, compared with the much smaller

amount found in the 1 year test, where lighting conditions were substantially

reduced by the tank cover, it seems that light control can be an effective way of

avoiding algae growth.

Comparing the results now obtained with predictions based on equations (5)

and (6) in Section 4.4 (deduced from McMahon et at (1959), and from ICI

(undated), respectively), it is apparent that the ICI (undated) recommendations

are too conservative.

For example, samples kept at 40°C for 3 months showed a marginal gain in

strength of 0.6% over the reference dataset, which is well within one standard

deviation. The equation derived from McMahon et at (1959) predicts a

strength loss of 0.12% and is clearly compatible with the data measured,

considering that their results are for a PET yarn produced around 1958.

It should be noted that the yarn tested in this study has an average molecular

weight of 17000, higher than the yarn tested by McMahon et al (1959) at

15600. Furthermore high tenacity yarns currently in production have higher

proportions of crystalline phase than the early, but never the less high quality,

yarn tested by McMahon et al. From these differences it would be expected

that, if there was any difference in sensitivity to hydrolysis, the yarn now tested

would perform better than the material tested by McMahon et al.

However the predicted strength loss using ICI recommendation would be

2.3%, which seems very unlikely even considering the scatter in the results

now obtained.

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8.3.2 Rope

8.3.2.1 Creep

Results obtained for 7 of the 8 rope creep tests executed were very consistent.

Due to an imprecision in load measurement the 3 month Superline sample

was loaded at 31.4% of UBL instead of 30% of UBL. Resulting from this error,

strain on this sample over the measurement time was typically 400011E higher

than the average of the other 3 samples. The strain observed in this test has

not been taken into account in the following discussion.

Figure 8.4 shows the strain data obtained for the seven consistent rope tests.

The strain is already 5.5% for the parallel sub-rope construction, after the first

100 seconds, while for the parallel strand rope it is only c.a. 4%. This

difference is maintained almost at the same level to the end of the tests with a

strain after one year of 7.1% for the Superline and 5.8% for the Brascorda

Parallel. This difference is due to the higher initial constructional

accommodation afforded by the Superline rope, that has one more twist

operation and higher twist angles. Twist migration and lateral contraction are

the major accommodation mechanisms.

In addition, we can observe a pronounced tendency for reduction in strain

rate, mainly in the Brascorda Parallel rope samples, at about 10 6 s (12 days).

Initial differences in slack between the strands, clearly observed in the

samples, are thought to be the reason for this behaviour. This is considered to

be a manufacturing problem that could be overcome by a better tension

control in the strands during rope making. A less likely, but possible,

explanation for the tendency of lowering strain rates would be a prolonged

bedding in of the terminations.

This observation highlights the advantage of using PET fibre over stiffer

materials such as aramids. The former can easily cope with construction

imbalances of the order of 1% without any significant problem. Such a

difference would have serious consequences for aramid, because of its low

failure strain.

152

For comparison with published data, we can consider typical creep rates (after

equalisation of constructional imbalances) to be about 0.25% and 0.20% per

decade for the parallel sub-rope and the parallel strand ropes respectively.

These rates are 2.8 and 2.2 times the rate reported by Linear Composites Ltd.

(1983) for a similar sized PET parallel lay rope at 40% of UBL.

These results are compatible since: the ropes tested here are more compliant

due to the constructional twist, and the loading used was lower than that used

by Linear Composites Ltd. (1983). As already mentioned PET fibres show

decreasing creep rates with load, for tensions between 15% and 50% of UBL.

Strain rates now measured for the Superline and the Brascorda Parallel ropes

are respectively 2.0 and 1.6 times the rates reported by Lewis (1982) for a

Kevlar 29 aramid wire rope construction tested at 40% of UBL. The

construction of this aramid rope has a similar compliance to that of the ropes

tested here. The lower creep rate observed by Lewis is explained by the

difference in creep rate between aramid and PET fibres and by the smaller

diameter (6.35 mm) of the aramid rope.

In view of the tendency for strain rates reducing with load discussed above,

the regression equations (1) and (2) from Section 7.3.2.1 (seen in Figure 8.4)

for both model ropes will provide conservative results for moderate

extrapolations. Considering the behaviour observed for PET yarns subjected

to loads of up to 40% of YBL for up to one year at 30°C it seems unlikely that,

at a load level of 30% of UBL, strain rates in these ropes could pick up for at

least another decade, i.e. 10 years. It should be noted that BS 4618 (1970)

states that the extrapolation of creep data should not exceed one time decade.

Although the ropes tested were meant to model larger ropes, it is considered

that, until data on full size mooring ropes is available, a safe approach would

be to allow for a 10% greater strain in these, full size ropes, than measured in

the model ropes. Table 8.2 shows suggested creep strains to be used in the

design of mooring systems incorporating parallel sub-rope (Superline), and

parallel strand (Brascorda Parallel) ropes. Also included are suggested creep

strains for a parallel yarn (Parafil) rope, based on the PET yarn creep data

obtained, and considering an average yarn slack of 1%.

153

To give a better illustration of the significance of these results, the actual rope

elongation was calculated for a 2500 m Superline at an average tension of

30% of UBL, as might be used for a mooring in 1000 m water depth. In the first

hour, stretch would be about 170 m most of which (c.a. 130 m) would take

place in the first minute.

During the rest of the first 24 hours, elongation would increase by about 13 m.

At the end of the first month another 10 m of stretch would have occurred, an

additional 6 m by the end of the first year and a further 5 m over the next 9

years.

The mooring system concept on which most attention has been focused

incorporates a substantial amount of chain as the lower component. Fibre

rope elongation will be absorbed by the combined mooring line as a decrease

in the length of chain lifted off the seafloor and as tension reduction of the line.

As a guide for operational procedures, a sensible maximum pretension loss

due to creep between retensionings would be 5% of the UBL. At a typical

breaking load of 5000 kN and for mooring stiffness between 50 and 300

kN/m (Global Maritime Ltd. (1989,1)), retensioning would need to take place

after elongations varying between 0.8 and 5 m.

For a Superline in 2500 m of water depth at an average tension level of 30%

of UBL this would mean between 7 and 41 retensioning operations in 10

years after the first hour. If we assume a line stiffness of 145 kN/m 20

retensionings are going to be needed in ten years, then 7 would need to take

place in the first day, another 6 would be needed in the next 29 days, 4 would

be spread over the next 11 months, completing the first year and only 3 more

would have to be performed over the remaining 9 years.

The maximum strains for both ropes after 10 years at 30% of UBL, which is a

fairly high mean load, would be about 85% of the respective "installation"

strain. It is then concluded that, under normal pretensions, creep is not the

dominant parameter in defining the length of the upper steel component to

avoid the connection to the fibre rope reaching the fairlead.

If the actual installation procedure of the mooring line is similar to that

154

assumed, i.e after being at 50% of UBL for c.a. 30 minutes, the load is

released to 30% of UBL, the strain soon after the rope is relaxed to 30% of

UBL will already be about 7.6%, equivalent to an elapsed time of 1 month at

30% of UBL.

If after the installation procedure the mooring line is operated at 30% of its

ultimate breaking load, the rope will initially experience a slight rope recovery

followed by a slow creep tending to follow the creep strain curves observed.

Under these circumstances, 10 years after the operating pretension load was

reached, total strain would only be about 0.5% (in the example 12.5 m) for

both ropes, and retensioning would only be necessary a very few times during

the service life time of the rope (seven times for the example given above).

8.3.2.2 Environmental assisted degradation

The residual strength measured after one year at a constant load of 30% of

UBL was 97.6% of the average breaking load "as new" for the Superline and

100.6% for the Brascorda Parallel model ropes, when compared with the

average strength "as new". The average retained strength of the 4 Superline

samples after creep over periods from 1 month to 1 year was 95.2% and the

average retained strength of the corresponding Brascorda Parallel samples

was 100.3%, both compared with their respective average results "as new".

Figure 8.5 shows the retained breaking load of all samples tested plotted

versus time under constant load. The valid breaking load results for the as

new rope samples are also shown in Figure 8.5 at zero time.

The results for both ropes do not show any obvious apparent trend of a loss in

retained strength with time under load.

Taking into account that the strength degradation behaviour of polyester yarn

was found by McMahon et al (1959) and by ICI (undated) to be a linear

function of time, a linear regression of the results obtained was attempted.

Each rope construction was considered separately. The valid data for the

samples tested "as new" was also taken into account. A total of seven data

points was then available for the Superline and six results for the Brascorda

155

Parallel model rope. The regressions equations obtained are also shown in

figure 8.5.

The correlations obtained were very weak, which is justified by the small

amount of degradation expected in comparison with the typical scatter in

strength determinations for fibre ropes. The average strength degradation of

the parallel strand rope was marginally negative, as shown by the positive

slope of the regression equation, indicating a gain in strength with time under

load in water. For the parallel sub-rope construction, a very small tendency for

degradation was observed, as shown by the respective regression equation.

In an attempt to enhance our knowledge of the degradation process the data

for both ropes was analysed in combination. This was done by normalising

the breaking loads measured for each sample by the average new breaking

load of that rope type. Results are plotted in Figure 8.6 and a linear regression

of the data indicates again no correlation between time and retained strength.

However it is worth noting that the regression equations of both ropes, tested

wet, and the combined equation for the normalised data, indicate an average

breaking load slightly below the average of the new samples, tested dry. This

would mean an immediate negative influence of water immersion on rope

strength. Considering the results obtained in the yarn testing programme, the

relatively small number of tests now carried on in ropes, and the fact that this

effect has never been reported in the literature, it is thought that this indication

is most probably due to scatter in the test data.

The results obtained indicate that the loss in strength measured by Bitting

(1980), i.e. 10% per year for double braided PET ropes and 4.8% per year for

8 strand PET ropes, was not due to hydrolysis of the fibres.

The observations made in this testing programme, concerning the retained

strength of yarns and ropes after immersion for up to one year in artificial

seawater under various constant loads, do not contradict the result reported

by Linear Composites Ltd. (1983) of no strength loss on a parallel yarn

polyester rope (Parafil) recovered from the sea after 10 years.

Predictions based on McMahon et al. (1959) data and ICI (undated), for a

duration of ten years, assuming a water temperature of 20°C, would be of

156

strength losses of 0.63% and 19.2% respectively.

Having calculated the maximum increase in rope core temperature under

centenary storm conditions in the most severe location, and for the rope with

highest hysteresis, to be equal to 1.9°C (see Section 8.2.3), we can consider

that the rope temperature will be equal to the water temperature for the

purpose of estimating hydrolysis degradation. Typical maximum design

temperature for the North Sea is approximately 20°C and for Campos Basin it

is 27°C (Petrobras S.A. (1991)).

As far as mooring applications are concerned the results obtained in this work

in conjunction with published data show that environmentally assisted

degradation does not significantly reduce the breaking strength of the ropes

tested over a period of one year. The trends obtained suggest that an

assumption of a linear rate of 1% strength loss per year is safe for long term

installations. It is felt that applications with longer design life, say 25 years,

would grant additional testing to a duration of up to 5 years.

8.4 "Fatigue"

After 1 million cycles under conditions equivalent to a 3 hour storm that,

statistically, would happen once in 100 years in the West of Shetlands, the

average retained strength of the 2 samples of the model Superline, cycled for

1 million cycles at 20 ± 10% of its breaking load, was 97.9%.

Two samples of the Brascorda Parallel rope, after the same treatment,

retained 95.2% of their original average strength.

The average retained strength of both ropes after cycling is compatible with

the 93% residual strength measured by Karnoski & Liu (1988), after 2 million

cycles between 8 and 25% of UBL, on a 1157 kN breaking load PET

Superline.

Considering the results obtained by Karnoski & Liu (1988) for a 1000 kN

breaking load Kevlar 29 aramid Parafil, the present results indicate that PET

ropes of parallel sub-rope construction, using either resin socket or splice

terminations, behave better than parallel yarn aramid ropes terminated with

157

spike and cone fittings, under mean loads of about 20% of UBL and with load

amplitudes close to 10% of UBL. The retained strength measured in the

samples of the Brascorda Parallel model rope terminated with resin cast

sockets indicates that the "fatigue" behaviour of these ropes is similar to that of

the Superline rope when terminated in the same way. Since "fatigue" failure of

low twist fibre ropes is always associated with the terminations, comparisons

can only be made between terminated ropes, and should not be extrapolated

to ropes with different terminations.

Two termination methods are available for the Superline, parallel sub-rope

construction tested, splicing and the resin socketing. The splicing method

used by Marlow Ropes for its Superline, performed reliably, for the sort of

loading expected on a deep water spread mooring system, on the 1157 kN

rope tested by Karnoski & Liu (1988). According to the manufacturer the

splicing procedure can be scaled up to a rope with a breaking load around

5000 kN without loss in "fatigue" performance or reliability (Banfield (1989)). It

is considered that the behaviour of such a termination would need to be

proven in full size tests.

The resin socketing procedure used in this study proved very reliable and

gave quite consistent results both in simple tensile tests and in "fatigue"

loadings similar to the most severe that are likely to happen in deep water

spread mooring systems. No problem can be foreseen in scaling up the

termination method used here. However before a full size application of these

ropes is implemented it is considered that the termination method feasibility

and performance have to be proven at a very similar size to that of the

application envisaged.

Only one termination method has been tried on the Brascorda Parallel,

parallel strand, rope tested in the study, resin socketing. Using the method

developed in this study, the performance of these terminations, both in simple

tensile tests, and in "fatigue" tests at the relevant loadings, was consistent and

reliable, similar to the behaviour of parallel sub-rope construction. As far as

scaling up the termination, the same comments made for the parallel sub-rope

construction apply.

158

The examination of the fibres from selected regions of one sample of each

rope after "fatigue" cycling indicated that:

(i) filament fatigue is not a cause of concern at these load ranges;

(ii) yarn on yarn and inter-strand abrasion, in the rope free length, are

not significant degradation processes again at these load levels;

and,

(iii) the only degradation mechanism observed was fibre abrasion at

the ill defined interface between the resin and the fibres at the

termination.

Based in these findings it is thought that any future model development for

predicting cyclic degradation of these kind of ropes with potted termination

should be based on an abrasion mechanism.

These results and observations also show that at the load levels envisaged in

spread mooring systems, cyclic loading does not cause significant strength

degradation to these fibre ropes.

Considering that the hysteresis measured for the Superline model rope, at the

loading regime used for cycling, is within the range of reported hysteresis

values for similar PET yarns (Van der Meer (1970) and Rim & Nelson (1991)) it

can be concluded that inter-yarn and inter strand slip is very limited. Therefore

it is not a surprise that no signs of frictional degradation were found in the rope

free length. From this point of view, low twist fibre rope constructions are in a

favourable position in comparison with wire ropes, where for low mean loads

full-slip between wires occurs at fairly low load ranges (Hobbs & Raoof, 1985).

The scaling up of the two constructions studied, to breaking loads of the order

of 5000 kN, typically involves either an additional twist operation and or an

increase in strand diameter. If the same twist (lay length) was used in both

rope sizes the bigger rope would have higher compressive forces. Since the

model ropes had higher twist for better stiffness simulation it is thought that in

general, scaled up ropes should be no more sensitive to yarn on yarn

abrasion than the ropes tested.

In the process of scaling up, an additional variable may be introduced in the

form of imbalance in the rope construction. Although results reported by

159

Karnoski & Liu (1988) for a 1157 kN Superline corroborate the findings of the

present study at a scale of 20:1, it is still considered wise to confirm these

findings for a full size mooring component.

160

LOADING REGIME SUPERLINE MODULUS BRASCORDA PARALLEL MODULUSYOUNG'S

GPaSPECIFIC

N/tex (N/(q/km)YOUNG'S

GPaSPECIFIC

N/tex (N/(q/km)

"Instalation" 2.89 3.02 3.56 3.46

20±10% of UBL- quasi-static 7.32 7.64 9.66 9.38

10±5% of UBL-7.5s period 10.14 10.59 12.53 12.16

20±10% of UBL-15s period 10.55 11.01 12.92 12.54

40±10% of UBL-15s period 13.45 14.04 16.05 15.58

50±2.5% of UBL-15s period 16.29 17.01 19.16 18.6

50±15% of UBL-15s period 13.89 14:59 16.59 16.1

50±15% of UBL-100s period 13.64 14.24 16.18 15.71

Table 8.1 - Specific modulus and Young's modulus for selected cycling

conditions.

ELAPSED TIME PARALLEL SUB-ROPESUPERLINE

PARALLEL STRANDBRASCOR DA PARALLEL

PARALLEL YARNPARAFIL

1 hour 6.74 5.21 5.43

1 day 7.21 5.76 5.58

lmonth 7.6 6.23 5.71

1 year 7.85 6.54 5.78

10 years 8.06 6.79 5.84

20 years 8.11 6.86 5.86

Table 8.2 - Typical creep strains to be used in the design of mooring systems

incorporating PET fibre ropes.

• Brasoorda Parallel

0 Superfine

0.05

0.04 -

0.03 - N0.02 -

0.01 -

0.00 . • 111 1 . 11 I II V I • . I I

0

200 400 600 800 1 000

1200

Number of cycles

Io 10

20

Actual specific stiffness (N/tex)

Figure 8.1 - Comparison between the dynamic rope modulus derived from

simple structural model and measured values.

Figure 8.2 - Influence of the number of cycles on the hysteresis of the

Superline model rope.

•••n64, •••••

• parallel sub-tcpe

o paraJlel strand

• I3 4 5

Log time (s)

2 6 7 8

6

5 - 0

13 13 0 alo CI CI ri 1:1

El

4 -

30°/0• ENKA209/0YEL▪ ENKA30%YE3L

2

1

-I •100 1 0 1 1 0 2 1 0 3 1 0 4 1 0 5 1 0 6 1 0 7

Time (s)

Figure 8.3 - Creep of Diolen 855T (ENKA (1985,3)) and Diolen 855TN at 30% .

of YBL.

Figure 8.4 - Creep of Superline and Brascorda Parallel model ropes (7 tests).

60 -

•1I • 1

IEi0•

WB ••

70

Id-- D Brascorcia Parallela- • Superine•50 -

40 -

30 -

20 -

10 -

• i .- 1 0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3

Time (months)

• 1 ' 1 ' 1 1 ' 1 • 1 • I •I •1 •

Figure 8.5 - Residual breaking load of model ropes after creep-

environmentally assisted degradation exposure.

1.0

0.8

0.6B Brascada Parallel

• Supetine

0.4

0.2

0.0-1 0 1

' 1 ' 1-' 1 • 1 ' 1 1 • 1 I

2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3Time (months)

1 1 1 ' 1 ' 1

Figure 8.6 - Normalised retained strength of all model ropes after creep-

environmentally assisted degradation exposure.

9. CASE STUDIES

9.1. Background

This chapter is primarily intended to provide an indication of how the tether

properties obtained in the materials investigation can influence the design of

spread mooring systems incorporating light weight tethers, by comparison

with the results obtained in the "pilot study" (Global Maritime Ltd. (1989,1)).

The aim was to examine the conclusions previously obtained, upon

introduction of experimentally validated time scale dependent tether

properties. Through analysis of the case studies more precise guidance can

be given on the design of spread mooring systems incorporating LWM.

The work described was first used to obtain experience in the use of the

analysis methods, developing a feeling for the influence of the various

parameters involved. This led to the decision to add a further mooring concept

to those tried in the "pilot study", in the form a line composed of a short upper

steel component attached to a long polyester fibre rope and a piled anchor

capable of taking vertical loads.

Recapitulating the differences observed between the tether properties derived

in the literature review (Section 4.6), which were used in the analyses of the

pilot study, and the behaviour observed in Otis sta4, as discussed in

Chapter 8, the relevant areas of dissimilarity were found to be rope strength

and rope stiffness.

The rope strength measured for the model parallel sub-rope, Superline, was

0.551 GPa and the recommended tensile strength for design (Section 7.1.2)

was 0.464 GPa ( 0.9 2 x 0.551 ), based in the enclosed area of the rope core.

This is 55% higher than the value of 0.3 GPa used in the "pilot study". The

strength assumed for the parallel strand, Brascorda Parallel, in the "pilot

study" was very similar to what is now being proposed.

The issue of stiffness is more complicated, since in the pilot study a single

value for modulus has been used throughout the analysis for each rope

construction. The test programme showed that the apparent modulus of

161

polyester ropes, based in the enclosed area of the rope core, may vary by a

factor of 2.3 from quasi-static to extreme wave frequency conditions, with an

intermediate value for the resonant low frequency response.

For the Superline, for example, a Young's modulus of 5 GPa was used

previously, while typical quasi-static, low frequency and wave frequency

results now advocated are respectively 6.6, 12.3 and 16.0 GPa. These values

correspond to: 90% of the value measured in the 1 week simulated quasi-

static cycle, 90% of the result obtained at 50±15% of UBL at a frequency of

0.01 Hz and the full modulus measured at 50±2.5% of UBL at 0.067 Hz.

A parallel sub-rope construction using a standard modulus aramid, Kevlar 29

or Twaron 1000, was also investigated and for this rope a single value of

Young's modulus, 72 GPa, was used in all analyses. This is an estimated

value, which was obtained by multiplying the PET Superline wave frequency

modulus by the ratio of the modulus of the aramid yarn to the modulus of the

PET yarn (the yarn moduli quoted by the manufacturers being used). This

stiffness is substantially higher than assumed for any standard modulus

aramid rope in the pilot study. The tensile strength of this rope was estimated

in a similar way and considered to be 0.95 GPa.

The cases studied were also intended to investigate the influence of axial

tether stiffness on wave frequency tensions, which was somewhat

contradictory in the literature. Results presented by Larsen & Fylling (1982) for

wire rope mooring lines in up to 300 m of water showed a pseudo axial elastic

behaviour for the most relevant range of first order frequencies and

pretensions, with dynamic line tensions being very close to the product of the

top oscillation and the axial spring constant of the line. Similar maximum

tension behaviour was observed by Global Maritime (1989,1) for mooring

lines consisting of wire rope, wire rope and chain, and fibre rope and chain

combinations. However it was observed that the tensions did not derive from a

real "frozen catenary" behaviour of the mooring components.

Pollack & Hwang (1982) also found increasing wave frequency tensions with

line stiffness for a Kevlar 29 aramid and chain combination system. However

tensions were not directly proportional to axial line stiffness. First order wave

162

frequency tensions, calculated by GVA (1990) for a wire rope chain

combination mooring system in 1000 m of water, were about half or less than

would be predicted by the "frozen catenary" behaviour.

The major difference between the assumptions made by Pollack & Hwang

(1982) and GVA (1990) and those made by Larsen & Fylling (1982) and

Global Maritime (1989), seems to relate to the nature of the fairlead

movements. The former considered a combined horizontal and vertical motion

in the plane of the line, while the later assumed an exclusively horizontal

fairlead motion.

9.2 Design Cases and Methods

A floating production system (FPS) based on an Aker H3.2, 8 column semi-

submersible was selected for all the cases. This is a widely available vessel,

which is actually being used as an FPS by Petrobras in Campos Basin,

offshore Brazil.

Platform displacement was taken as 225000 kN, with an 18 m draft. An eight

line symmetric mooring pattern was used (45° angle between each iine). The

system was considered as operated passively, i.e. no slackening of the

leeward lines or load equalisation on the windward lines. This choice was due

to the fact that testing performed in this study suggested the possibility of

crystal nucleation inside the rope structure at minimal tensions, and no data is

available on the cyclic performance of fibre ropes in sea water at very low

minimum loads. However minor pretension adjustments are going to be

needed to cope with fibre rope creep, as discussed in section 8.3.

Three water depths: 500, 1000 and 2000 m in two locations: Campos Basin,

and West of Shetlands, offshore UK, were investigated. Table 9.1 summarises

the extreme (centenary) environmental data for both locations as used in the

present analyses. Campos Basin data was extracted from recent surveys

available (Petrobras (1989)), West of Shetlands data used is a combination of

data used in the pilot study (Global Maritime Ltd. (1989,1)) and DnV

POSMOOR (1989).

163

Current speed was assumed to vary linearly with depth and to be zero at the

bottom. Wind speed was taken as the hourly mean, 10 m above the still water

level. A Harris wind spectrum was assumed for the Campos Basin and a

Kaimal spectrum in the West of Shetlands. An ISSC wave spectrum was used

for Campos Basin and a JONSWAP spectrum applied in the West of

Shetlands.

The results of the pilot study (Global Maritime Ltd. (1989,1)) for a similar

vessel indicated the quartering seas to be the most severe angle of incidence

for the West of Shetlands and one of the most severe at Campos Basin (an

observation which coincides with Petrobrds experience for the Campos

Basin). Hence only the quartering seas condition was analysed.

Three line configurations were investigated for all conditions and locations:

(i) a short upper length of steel tether (either chain or wire rope), and a

polyester Superline (parallel sub-rope) rope attached to a pile;

(ii) a similar upper component, a polyester Superline (parallel sub-

rope) intermediate segment with a lower section of oil rig quality

(ORQ) chain leading to a drag embedment anchor; and,

(iii) a long six strand wire rope upper segment and an ORQ lower

component leading to an anchor.

In a similar way as was done in the 4"pilot study", the short upper length of

steel component was considered small enough not to be incorporated in the

line model.

For a water depth of 1000m in the West of Shetlands, a further case was

analysed, consisting of a Kevlar 29, standard modulus aramid Superline,

parallel sub-rope construction, in combination with ORQ chain and anchor.

The evaluation was based solely on performance under maximum design

condition for intact systems as defined on the draft standard API RP 2FP1

(1991). A maximum offset of 10% of the water depth was selected and, in

accordance with the draft API standard, a maximum tension of 60% of the

guaranteed minimum breaking load was the tensile strength design criterion.

A number of other conditions must be evaluated in an actual design, however

164

this condition was chosen since it gives a better insight on the differences in

system behaviour than the other design conditions. In particular it is

recognised that, for mooring lines having a lower chain component

(configurations (i) and (iii) above), the length of lower section is going to be

dictated by the "one line broken" (damaged survival) condition (see

Section 2.4.7) and will be longer than calculated here. If the amount of extra

chain needed by the fibre rope-chain system is greater than the extra chain

necessary in the wire rope-chain combination, the cost comparison would be

biased in favour of the systems with lower strength light weight tethers. A spot

check was performed in 1000 m in the West of Shetlands with one line

broken, to verify the amount of extra chain needed to avoid anchor uplift.

The analyses were performed using a deterministic mooring analysis

package, DMOOR (Noble Denton & Assoc. (1986)). Five modules of the

programme suite were used in the analyses. A brief description of each one of

them is given below. More detailed information can be obtained from Noble

Denton & Assoc. (1986).

Module 1, DETER, fixes most of the input data concerning the type of analysis

to be performed, environmental data and vessel characteristics, including

environmental load coefficients. It computes the mean static environmental

forces and the low frequency spectra of winds and waves.

Module 2, STEADY, requires additional input for the mooring line composition,

properties and pretensions. It performs a conventional quasi-static analysis

based on the catenary equations applied to all individual lines. Each line is

discretized in up to 100 finite difference points, the procedure handles,

amongst other things, elastic stretch and intermediate buoys. This module is

also used to perform a static combination to incorporate the low frequency

motions with the mean displacement and to incorporate the wave frequency

motions in a quasi-static analysis (API RP 2P (1987));

Module 3, WAVFRQ, requires the response amplitude operators (RAO) for the

environmental directions analysed as additional input. It computes the transfer

functions horizontally and vertically for the first order end motions of each

mooring line.

165

Module 4, LOWFRQ, receives additional input in the form of the added mass

and damping for each direction to be analysed. It performs a one degree of

freedom dynamic analysis of the moored vessel, using the directional stiffness

from Module 2, and outputs the second order RMS vessel motions.

Module 5, FREQ, performs a frequency domain analysis of individual mooring

lines, subjected to a mean end tension obtained from Module 2, and to a

spectrum of end motions calculated in Module 3. It is also based on the Finite

Difference Method and assumes a constant touch down point for the line. The

main output is the RMS tension at selected points of the line being analysed.

In general terms the analyses followed a frequency domain sequence

consisting of:

(i) quasi-static analysis under the mean environmental loads to

obtain the mean vessel offset and the mean tension in the most

loaded line, using Modules 1 and 2;

(ii) computation of spectra for the wave frequency vessel motions and

the tairlead motions, using Module 3;

(iii) dynamic analysis of the low frequency vessel motions about the

mean offset, using Module 4;

(iv) quasi-static analysis incorporating the low frequency motions,

taking into account the low frequency parameter which will

generate the worst combination of significant low frequency plus

maximum wave frequency, or maximum low frequency plus

significant wave frequency responses, using Module 2;

(v) dynamic analysis of the first order wave frequency line motions and

tensions, using Module 5; and,

(vi) combination of static, low and wave frequency tensions and offsets

for evaluation against the design criteria.

The tensile strength of the polyester rope was taken as 0.464 GPa. The

minimum breaking strength of the ORQ chain was taken from Ramnas (1990).

Wire rope strength was based in British Ropes (undated) minimum breaking

load values for "rig/barge mooring lines". The strength used for the Kevlar 29

Superline was 0.955 GPa.

166

Designs incorporating aramid fibre ropes or wire ropes in combination with

chain, were analysed using their single -characteristic value for Young's

modulus. These were taken as: 72, 67.7 and 112 GPa for the aramid

Superline, the wire rope and the chain respectively. A single pass through the

analysis sequence described above is needed for each verification.

For systems using the polyester Superline, in each part of the analysis, the

appropriate Young's modulus was used, i.e. 6.6, 12.3 and 16.0 GPa for quasi-

static, low frequency and wave frequency calculations respectively. In practice,

to cope with the characteristics of the software package, the values adopted

differed in one of the analysis steps. The following description of the

procedure adopted, based on the steps (i) to (vi) described above, should

clarify the subject.

The Young's modulus was set at the low frequency level (12.3 GPa) and steps

(i) to (iv) performed; the modulus was changed to the wave frequency level

(16.0 GPa) and steps (v) and (vi) carried on. The tensions obtained were

considered as the final tension results. The modulus was set at the quasi-

static level (6.6 GPa) and step (i) repeated. The maximum offset was

considered as the combination of the mean offset of the last run of step (i) with

the appropriate combination of the low frequency and wave frequency offsets

from the first pass in (ii) and (iii).

The sensitivity of the results to the number of elements used to describe each

line was assessed. Based in this sensitivity analysis, single component

systems (with piles) were modelled with 25 elements per line, and for two

component systems 35 elements per line were used. It was interesting to note

that the convergence was worse (but still acceptable) at 500 m than at

2000 m.

For each combination of: depth, environment and mooring configuration an

optimisation for minimum tether capital cost was performed. LWDESGN (see

Section 3.2) was not available during this part of the study, therefore no

automatic procedure was used in the optimisation process. However it was

found that, for each location and line composition, after a few trials, a good

feeling of the behaviour of the system was developed, and an optimum

167

configuration could be obtained in a sensible time.

For each combination of location, water depth, and line composition it is

estimated that between 5 and 10 analyses were needed to achieve a

reasonably optimised solution. Not all of these trials needed to include a run

of the line dynamics module (FREQ), which consumes approximately half of

the time required to perform the analysis. The average computer time for each

full analysis in a 16 MHz, IBM 386-SX PC with a mathematical co-processor,

was 30 minutes, for the systems containing the polyester fibre ropes, and 20

minutes, for the other mooring configurations.

In addition to these case studies two other sets of analyses were performed:

(i) a set of quasi-static analyses, mainly for the systems incorporating

the PET Superline fibre rope; and,

(ii) a series of 7 analyses with the final design selected for the aramid

Superline combination with chain, varying the fibre rope stiffness.

The quasi-static analyses (item (i) above) were performed in the Campos

Basin conditions for the systems with piles and for the PET fibre rope

configuration with chain and anchor. In the West of Shetlands, only the PET

rope-chain combination (all depths) and the wire rope chain system, in

1000 m, were quasi-staticaly analysed. The recommended wave frequency

Young's modulus of 16 GPa was generally used for the fibre rope. Some runs

were performed using the recommended quasi-static Superline modulus,

6.6 GPa.

The analyses for the system containing the aramid rope (item (ii) above) were

all performed in 1000 m in the West of Shetlands, using the frequency domain

procedure described.

9.3 Results

Tables 9.2 and 9.3 summarise the optimum line configurations and the results

obtained in the dynamic analyses for the different water depths in Campos

Basin and in the West of Shetlands, respectively.

For each component, diameter, length and minimum breaking load (MBL) are

168

presented. Also given are the mean tension, the root mean square (RMS) first

order and the RMS low frequency tensions calculated. "Maximum tension (API

RP 2FP1)" is either the significant low frequency tension plus the maximum

wave frequency tension or the maximum low frequency tension plus the

significant wave frequency tension, whichever is greater, added to the tension

corresponding to the mean environmental loads. Offsets are presented in a

similar manner as tensions (API RP 2FP1 (1991)).

The RMS "frozen catenary" tensions presented have been computed

considering: a fixed touch down point, the equivalent elastic stiffness of the

line components between the fairlead and this point, and the RMS wave

frequency offsets. These results are also presented as percentages of the

calculated maximum RMS wave frequency tension in the line, calculated by

the dynamic analysis.

The costs tabulated correspond to the capital cost of the tethers without

jackets, based on the cost per unit weight supplied by the manufacturers

(same figures as used in the "pilot study"). No cost penalty has been added to

account for the vertical force imposed by the mooring system on the vessel.

The cost of piled anchors or drag embedment anchors has not been

considered either. The vertical force on the vessel has been computed in the

equilibrium position without environmental loads.

The results of the quasi-static analyses are presented in Tables 9.4 and 9.5 for

the Campos Basin and the West of Shetlands respectively.

In Campos Basin the maximum tension according to API RP 2P (1987) was

found to be the mean tension plus the significant wave frequency component

plus the maximum low frequency tension. In the West of Shetlands the wave

frequency tension dominated the design. Maximum tensions are presented in

absolute values (kN) and also as percentages of the results obtained from the

dynamic analyses.

Offsets were calculated in a similar way and are also presented as

displacements from the unloaded vessel position (metres) and as fractions of

the values from the dynamic calculation.

169

To verify the differences in the amount of extra chain needed, in the damaged

survival condition, to avoid anchor uplift between systems with PET fibre ropes

and systems with wire ropes, a quasi-static comparison was performed in

1000 m in the West of Shetlands. The results indicated that an extra 260 m of

chain would be needed by the optimum PET rope-chain system and an extra

315 m would be necessary on the wire rope-chain configuration.

Table 9.6 shows the tension results obtained by varying the rope modulus,

with other quantities remaining constant, based on the optimum design for the

aramid Superline, in combination with chain, in 1000 m West of Shetlands.

The RMS wave frequency "frozen catenary" tensions have been calculated

based on the equivalent axial stiffness of the suspended line components, as

discussed above. They are also presented as percentages of the RMS wave

frequency tensions (in the segment with the highest load) obtained from the

dynamic analyses.

9.4 Discussion

A primary function of a spread mooring system is to resist the mean

environmental loads. Since these forces do not cancel out over a reasonable

period of time, the mooring system has to provide a direct reaction to them.

This has to be done by offsetting from the pretension equilibrium position.

First order vessel motions, including platform offset, are virtually unrestricted

by the mooring system. Line tensions associated with these motions are a

direct function of tether characteristics.

The mooring system stiffness, in conjunction with the vessel characteristics,

determine vessel response to second order environmental forces. Therefore

tensions and offsets associated with these motions will be a function of line

stiffness.

Considering that, for an intact system, only a fixed proportion of the MBL is

"available" for use (60% according to API RP 2FP1 (1991)), a clear measure of

the technical merit of different mooring systems is how much of this proportion

is used in reaction to the loads which are independent of the mooring system

170

characteristics, i.e. the mean environmental loads.

9.4.1 Dynamic Analyses

In order to assess how well the different mooring systems performed their

function, the three components of the line tensions were plotted for all cases

analysed in four graphs.

Figures 9.1 and 9.2 present the absolute values, in kN, of the components of

line tension calculated according to API RP 2FP1 (1991), for the Campos

Basin and the West of Shetlands respectively.

It can clearly be seen that the absolute value of the mean tensions developed

in the systems incorporating fibre ropes is always lower than that developed in

the all steel system, the difference increasing markedly with water depth. This

is basically due to the catenary sag originating from the higher immersed

weight of the the steel tethers. The tensile behaviour of the systems with piled

anchors was similar to the PET rope/chain systems in all conditions except in

500 m in the West of Shetlands, which was high due to excessive system

stiffness.

The difference in dynamic environmental loading between Campos Basin and

the West of Shetlands is striking. In Campos Basin the design is dear*

dominated by the mean loads, while in the West of Shetlands strong first order

wave frequency forces are present.

In the West of Shetlands maximum wave frequency tension amplitudes were

found be almost as high as the mean loads, especially in the all steel system

and in the PET rope with piled anchor in 500 m of water. Under these

conditions of fluctuating tension, the very low minimum loads are potentially

very dangerous for tethers susceptible to kinking and/or torsional instabilities.

Both the Kevlar 29 rope and the steel wire rope combination systems with

chain in 1000 m are also far from safe from near slack conditions associated

with storms. This situation cannot possibly happen in storms in Campos Basin.

There is very little difference in low frequency tension between the two

171

locations studied, at least in storm conditions. However, in Campos Basin, the

low frequency components appear in the API summation as their maximum

value, for systems incorporating PET ropes, due to the mild wave frequency

loading.

Figures 9.3 (for the Campos Basin cases) and 9.4 (West of Shetlands cases)

show the same tension components normalised using the appropriate rope

breaking load (MBL).

The first striking characteristic is the excellent match between the performance

of almost all mooring systems and the environmental loading observed in

Campos Basin (Figure 9.3). Mean tensions consistently above 45% of the

tethers MBL were obtained.

In the West of Shetlands (Figure 9.4) it is possible to see that the systems with

polyester ropes did a good job of attenuating the the first order wave

frequency components in all depths, except in 500 m. Considering that, in the

later case, the maximum offset of the cost optimised systems (5.5% of water

depth for the system with piles and 6.7% for the combined mooring) is still

well below the limit selected (10%), there is a clear indication that a fibre rope

with a lower dynamic stiffness, possibly half of the modulus of the PET ropes

now analysed, could perform better.

In all conditions, the systems incorporating PET fibre ropes performed more

efficiently than the all steel and the aramid rope chain systems, as confirmed

by the higher percentage of the breaking load "used" in reacting the mean

loads. The only exception was the PET rope-pile system in 500 m in the West

of Shetlands environment (which was much stiffer than needed). For example,

in the West of Shetlands, in 1000 m, the systems with PET rope use 39 to

40% of their strength to cope with the mean environmental load while both the

all steel and the system with the aramid rope only use 32% of their MBL to

cope with the mean load.

The behaviour of the system with the aramid rope was very similar to the wire

rope-chain system in 1000 m. This is not a surprise since both ropes have

approximately the same dynamic stiffness, the heavier weight of the steel rope

being compensated by the longer length of chain lifted off the sea bed, in the

172

system with the aramid rope. The shorter length of aramid rope compared with

the PET ropes at the same depth is an outcome of the cost optimisation.

The significant wave frequency tension ranges, presented as percentages of

rope MBL, are shown in Figure 9.5 for both locations. As already observed the

ranges measured in Campos Basin are between two and three times lower

than in the West of Shetlands. It is worth noting the much lower tension ranges

in the systems incorporating polyester fibre ropes, which varied between 33

and 68% of the ranges in the all steel systems. The West of Shetlands 500 m

condition is an exception, as already discussed.

Figure 9.5 also gives an insight into the likelihood of "fatigue" damage due to

first order wave frequency tensions. Considering that the highest significant

wave frequency range (except the 500 m West of Shetlands conditions)

observed was 16.4%, not forgetting that these are centenary conditions, it is

clear that ropes that are able to withstand 1 million cycles, at a tension range

of 20% of their actual breaking load, will not be affected by the cyclic loads

available at these frequencies.

Low frequency tension ranges (in proportion to the tether breaking load) are

lower for the wire rope/chain systems and higher for the piled systems in all

conditions, with the fibre rope/chain systems giving intermediate values. Low

frequency tensions were found to be higher than first order wave frequency

tensions in some cases incorporating PET fibre ropes in the Campos Basin.

However the highest significant tension range calculated was 13.2% of MBL.

Considering that the number of cycles involved in this oscillations is typically a

third to a tenth of the cycles associated with wave frequency tensions, "fatigue"

damage due to low frequency tensions is less likely than cyclic damage

caused by first order tensions. It should be noted that, for a real application,

although seemingly improbable, the possibility of higher low frequency

tensions occurring under other environmental conditions should be

investigated.

Due to the design constraint on the tension safety factors ("Maximum tension

on rope, % MBL" in Tables 9.2 and 9.3), the minimum breaking load of the

tether components is directly proportional the maximum tensions developed in

173

the mooring lines.

The minimum breaking load of the rope component for all the conditions

investigated is shown in Figure 9.6. Except for the anomalous results at 500 m

West of Shetlands, the required MBL for the systems incorporating PET fibre

ropes is always substantially lower than the corresponding wire rope-chain

system. This difference increases with water depth, being maximum in the

West of Shetlands, in 2000 m water depth where the MBL of the PET based

systems is only 56% of the MBL of the wire rope-chain alternative. The

difference is somewhat smaller in Campos Basin, where the ratio only

reaches a maximum of 69%, at the same water depth of 2000 m.

It is curious to see that in 2000 m the same optimum system was obtained for

the PET rope/pile configuration in both locations. The same rope was also

used in the PET rope/chain system, but the minimum chain needed in

Campos Basin was found to be slightly bigger due to its higher mean loads.

Although an effort was made to use the full offset allowable (10%) in all

conditions, it was not always possible to get a minimum cost solution

simultaneously with maximum offset. In such cases a bonus low offset was

obtained. As can be seen in Figure 9.7, this happened with the polyester

rope/pile systems in all conditions and to a lesser extent to most of the PET

rope/chain combination cases. It should be noted that the polyester rope/pile

systems achieved maximum offsets between 6 and 7.4% without

compromising cost. These lower offsets offer potential advantages if

consideration is given to the possibility of installing rigid risers.

Figure 9.8 shows the capital cost of the tether components in relation to the

cost of the wire rope/chain combination system, in each location and water

depth. To compensate for the minor differences in tension safety factors

obtained, costs have been normalised to a safety factor of 1.667 (60% of MBL

maximum tension). The polyester rope/chain systems are cheaper in all

conditions and locations, the advantage being greater in the West of

Shetlands, with a typical ratio of 0.85 of the cost of the all steel system, except

in 500 m. Polyester rope/pile systems work out even cheaper, with ratios

between 0.37 and 0.65. The system based on the aramid rope/chain

174

combination had the highest capital cost (1.56 times the all steel system). It is

worth noting that this is an optimum cost system which does not show the

station keeping potential of systems incorporating high modulus fibre ropes.

By increasing the length of aramid fibre rope (and obviously spending more

money), these systems can be designed to give maximum offsets as low as

3% in 1000 m water depth.

For both Polyester fibre rope and wire rope in combination with chain it is

considered that differences in installation costs would not be significant, since

PET ropes are inherently damage tolerant (due to the high failure strain of

polyester fibres) and both ropes would probably be similarly jacketed for use

in a floating production system. The comparison between the cost of piles and

anchors is not straightforward, therefore any cost comparison involving

systems with piled anchors should be judged in the light of this omission.

As can be seen in Tables 9.2 and 9.3, the total vertical force, imposed by the

mooring systems based on fibre ropes on the vessel, in the equilibrium

position without environmental loads, in 500 m of water, is half of the force

imposed by the all steel system. As the depth increases so does the difference

in loading. In 2000 m vertical loading caused by moorings with synthetic fibre

ropes will only be about 25% of the load in all steel systems. The additional

vertical force, for the all steel system in 2000 m in Campos Basin, corresponds

to 5% of the displacement of the vessel studied. This effect can be seen as a

bonus payload available at the platform or as a penalty cost for providing the

additional buoyancy required.

An assessment of the advantages in using systems with fibre ropes taking into

account the cost of additional buoyancy was undertaken. No attempt was

made to obtain optimum systems based on cost incorporating an addition for

buoyancy. It was assumed that to generate the corresponding buoyancy

additional load on the platform had to be backed up by one fifth of that weight

in structural steel work in the platform (Global Maritime Ltd. (1989,1)). The cost

of the fabricated structure was taken as US$6,400/tonne (Lim (1988) and

Global Maritime Ltd. (1989,1)). Figure 9.9 shows the results obtained by

adding the cost calculated in this basis to the total capital cost from Tables 9.2

and 9.3 and normalising by the cost of the wire rope/chain combination

175

system for each location and water depth. To compensate for the minor

differences in tension safety factors, costs extracted from tables 9.2 and 9.3

have been normalised to a safety factor of 1.667 (60% of MBL maximum

tension).

The advantage of the polyester Superline rope/chain combination over the all

steel systems considerable. In 1000 m in the West of Shetlands, for example,

the system based in the PET rope is costed at 70% of the estimated cost for

the wire rope chain system. In 2000 m the advantage is even greater. The

system based on the aramid rope comes out only 23% more expensive than

the all steel system, which is quite surprising. However this particular aramid

system does not offer any advantage over the steel system, other than

corrosion resistance, and has a number of draw backs such as: sensitivity to

accidental damage and unproven performance when cycled at very low

minimum loads.

To assess the performance of the "frozen catenary" assumption, in comparison

with the results of the dynamic analysis conducted, total tensions were

compared as predicted by both methods. Figure 9.10 shows the ratio of the

total tension for the "frozen catenary" assumption divided by the tension from

the dynamic analysis. This ratio corresponds to a safety factor associated with

the simplified assumption.

All results obtained show the "frozen catenary" assumption to be conservative.

Agreement with dynamic analysis is seen to be quite good for the systems

based in PET fibre ropes, being very good for the Campos Basin cases. This

is explained by the low proportion of the loading coming from the wave

frequency component. Results for the system containing wire ropes and

aramid ropes came out too conservative to be of practical use.

Figure 9.11 presents the RMS wave frequency tensions obtained in the

analyses in 1000 m West of Shetlands, for the Kevlar 29 aramid rope/chain

system, as functions of the modulus of the fibre rope (varied from about 14 to

100 GPa). There is a pronounced flattening of the graph for increasing

modulus, possibly indicating a substantial movement of the grounding chain.

These results agree with the trend reported by Pollack & Hwang (1982).

176

The equivalent "frozen catenary" tensions are also shown in Figure 9.11.

Agreement with the tensions obtained in the dynamic analysis is good at low

modulus, but poor at the actual range of modulus expected for aramid ropes.

The dynamic behaviour found in the case studies analysed and reported by

Pollack & Hwang (1982), do not agree with the results obtained by Larsen &

Fylling (1982) and Global Maritime Ltd. (1989,1) for ropes with modulus above

ca. 20 GPa. Within the scope of the current work it was not possible to

investigate this discrepancy any further. One possible cause is the fact that, in

the present analysis as well as in the Pollack & Hwang (1982) study, both

horizontal and vertical fairlead motions were considered simultaneously. Only

horizontal fairlead motions were taken into account in the two remaining

studies.

The results obtained from the analyses confirm the trends indicated by Global

Maritime Ltd. (1989,1) of:

(i) cost effectiveness of mooring systems incorporating low twist

polyester fibre ropes in combination with chain;

(ii) lower vertical vessel loads and wave frequency tensions for these

ropes in comparison with wire rope/chain systems;

(iii) systems based on PET fibre ropes with strength significantly lower

than all steel systems being able to achieve the same tension

safety factors;

(iv) small influence of low frequency tensions in extreme design

conditions;

(v) moderate success of a simplified procedure based in a quasi-static

analysis, with wave frequency tensions calculated via an axial

elastic stiffness assumption, in predicting extreme tensions in

systems incorporating PET ropes;

9.4.2 Quasi-Static Analyses

The total tensions obtained in the quasi-static analysis (Tables 9.4 and 9.5),

using the first order wave frequency modulus proposed for the PET ropes

177

(16 GPa) and a modulus of 67.7 GPa for the steel wire rope, have been

plotted in Figure 9.12 as a function of the values obtained in the dynamic

analysis. The greatest difference is found for the wire rope/chain system, with

its high dynamic tensions.

As expected from the low levels of wave frequency tensions, agreement is

quite good in Campos Basin, where the greatest difference between the

results of the two methods is 2%. These results are in agreement with the

results of the pilot study (Global Maritime Ltd. (1989,1)). It should be noted

that using a Young's modulus of 16 GPa in a quasi-static analysis results in

erroneously small offsets (up to 34% lower than actual values). However a

safe prediction of offset can easily be obtained by using the apparent quasi-

static modulus, 6.6 GPa, in the quasi-static analysis (see Tables 9.4 and 9.5).

In the West of Shetlands the performance of the quasi-static analysis improves

with water depth, errors below 10% resulting for water depths greater than

1000 m.

178

Location I Wind Speed

m/s

Current Speed

m/s

Sig. Wave Height

m

Peak Period

s

Campos Basin

West of Shetlands

33.7

41

1.5

0.91

7.64

17

13.1

17.8

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Water depth .

Line configuration

m

-

500m

poly + chain

1000 m

poly + chain

1000 m

wire + chain

2000m

poly + chain

Chain diameter/length mm/m 100/400 84/600, 107/600 84/720

Rope diameter/length mm/m 145/1500 125/2500 122/1500 125/5000

Chain MBL kN 7600 5550 8560 5550

Rope MBL kN 7340 5460 8970 5460

Max. tension (API RP 2FP1)/E=16 GPa kN 3622 2829 3417 * 2899

Max. tension in rope/E=16 GPa % of dyn. 88 91 67 * 96

Max. offset (API RP 2FP1)/E=16 GPa m 25.8 49.7 97.9 * 86.1

Max. offset/E=16 GPa % of dyn. 77 72 100* 66

Max. offset (API RP 2FP1)/E=6.6 GPa m 34.6 70.5 - 135.9

Max. offset/E=6.6 GPa % of dyn. 103 102 - 104

' Young's modulus = 67 GPa

Table 9.5 - Maximum tensions and offsets obtained in the quasi-static analysis

of West of Shetlands cases. Offsets calculated assuming Young's

modulus of 16 and 6.6 GPa for the PET ropes are presented.

Young's modulus GPa 14.4 28.8 43.2 57.6 71.9,

86.5 100.9

Mean tension kN 2083 2101 2106 2109 2112 2115 2115

RMS low freq. tension kN 121 128 133 136 137 138 139

RMS wave freq. tension kN 166 266 329 371 400 421 437

Max. tension (API RP 2FP1) kN 2943 3347 3596 3762 3874 3957 4019

"Frozen catenary" tension kN 186 348 492 621 735 840 934

"Frozen catenary" tension % of actual 112 , 131 150 167 184 200 214

Table 9.6 - Tension components calculated by a frequency domain dynamic

analysis procedure and assuming a "frozen catenary" behaviour,

based on the Kevlar 29/chain configuration in the West of

Shetlands in 1000 m water depth.

5000

4000

3000

2000

1000

I, . , :. , . t , 6

y . , 6, .:: y a,,,.7-4G '

- AC /..a /,,, ' ./.... ' . ..... v. .,6.:./...... ......- =

a.

2

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a.

8

Ca a.

88

Ca

Tension(kN)

El mean tension

Ea lowfreq. tension

El wave freq. tension

5000

4000

1000

3000

Tension(kN)

2000

C.a_c_c

a)

I--alQ.

2

cco To

-co

E E

m mean tensim

bw freq. tension

El wave freq. tension

Figure 9.1 - Components of maximum tension according to API RP 2FP1(1991) for the Campos Basin cases.

Figure 9.2 - Components of maximum tension according to API RP 2FP1(1991) for the West of Shetlands cases.

60

50

40

Tension 30(%MBL)

20

10

(17;.ccs1

CY.

CO_c(.)CO

_c

-

a)

a.

a)

o.

a-

g)

60

50

40

Tension 30(% MBL)

20

10

a) c c a) c 0•

Ta.co

• Tipca •

i—_c

o_c

0

o

wo

w

a. .u. Q.; :2.

E E . I§ E E

to §§

§

EE

, §

To_c

N mean tension

N low freq. tension

im wave freq. tension

Figure 9.3 - Components of maximum tension, shown as percentages of

MBL, for the Campos Basin cases.

ineantensbn

• bw freq. tension

E3 wave freq, tension

Figure 9.4 - Components of maximum tension, shown as percentages of

MBL, for the West of Shetlands cases.

West of Shetlands

E. Carnpos Basin

a.

O.

c§

a)

a._c .2co.c0

a.

0as as.0 .0cs 01.-- Ew •0. 30E Ecoa§

-c7).

tr)

'E.

a_

00

CC-a

a.

—J 6000 -

•

co2

cc 4000 -

O West of Shetlands

O Campost3asin

-C

r-

36_

Figure 9.5 - Significant wave frequency tension range associated with

extreme environmental conditions.

Figure 9.6 - Minimum breaking load (MBL) required in the rope component.

Figure 9.7 - Maximum offset attained.

West of Shetlands

0 Carrpos Basin

Cost/all steelE3 West of Shetlands

Carpos Bash

co.c

In

.ca.

o_

.cC.

a_EY.

a)

a)

a.

a.

-c

(1)

(13

a

-c

8

16.

E•

tr)

cY.

Lc)

Figure 9.8 - Capital cost of the tether components, in relation to the capital

cost of the optimum all steel system in the same location.

To_c

Ta_c

Cost/all steel

C)

a.ct. CU

II0.

B West of Shetlands

O Canpos Basin

West of Shetlands

0 Campos Basin

3

co

CC

0

CEoc'7) cC

13

C73

0 a-

4Ci;

C.)

2

2

CCU

_c

c§8

CU

.61)

C)a_

n.

a.

o.

CU_c

a.

CU

Iiirt.

8

Ta.c

8

CU

I

CU_c

In

Figure 9.9 - Cost of tether options plus a cost penalty for buoyancy, in relation

to the cost of the corresponding optimum all steel systems.

Figure 9.10 - Performance of the "frozen catenary" assumption to account for

first order wave frequency tensions.

76

•

600 -c

F.! 400-

C)

200 -

•

0

•

Ej West of Shetlands

0 Campos E3asin

1.0

0.2

0.0

1000

•

•— 800 -z

•

O dynamb

• ftozen catenary

•20 40 60 80

100

1 20

Young's modulus (GPa)

Figure 9.11 - Influence of Young's modulus on the RMS wave frequency

tensions, based on the Kevlar 29/chain configuration in the West

of Shetlands in 1000 m water depth.

1.2

Figure 9.12 - Performance of the full quasi-static analysis procedure to

account for first order wave frequency tensions.

10. CONCLUSIONS AND RECOMMENDATIONS

10.1 Conclusions

This work has studied the use of light weight tethers in deepwater moorings.

Based on the results of a "pilot study", the behaviour of low twist construction

ropes, made from polyethylene terephthalate (polyester) fibres, has been

thoroughly investigated, under the relevant loadings and environmental

conditions. The properties obtained have been used to analyse selected

design cases for a deep water floating production system. The performance of

spread mooring concepts incorporating the ropes investigated was compared

with that of combined steel wire rope-chain moorings.

The conclusions of this study are given below:

1. Light weight ropes, using high strength polyester yarns in low twist

constructions based on current technology, provide practical cost

effective options for spread mooring systems for deep water platforms.

2. System configurations using a short length steel upper component and:

(i) a lower chain segment and a drag embedment anchor; or,

(ii) a short length of chain and a pile;

provided attractive solutions in terms of station keeping performance,

vertical loads on the vessel, minimum breaking load (MBL) and fatigue,

as well as cost.

3. It was found that a quantitative measure of the technical merit of different

systems could be obtained by calculating the proportion of the MBL used

in reacting the mean environmental forces.

4. Results of the case studies analysed, in line with results of the "pilot

study", showed that designing to the same offset and tensile safety factor

criteria the minimum breaking load necessary for the systems based on

PET fibre ropes is substantially lower than for the all steel systems. The

difference was found to be greater in the West of Shetlands than in

Campos Basin due to the higher wave frequency loads in the former

location. The difference generally increased with water depth due to the

179

greater immersed weight of the all steel system.

5. For the same tether safety factor, optimum cost systems based on

polyester ropes showed substantially lower dynamic loads than optimum

all steel systems. In particular first order wave frequency tensions on

these fibre ropes were much smaller, due to the low axial stiffness in

comparison with steel wire rope and chain. Therefore fatigue loading

was substantially reduced. The highest RMS wave frequency tension

range found for systems based on PET fibre ropes in all the case studies

analysed was 16.4% of MBL, except in 500 m in the West of Shetlands.

6. The results for the systems based on PET ropes in 500 m in the West of

Shetlands, indicated that the stiffness of the fibre ropes selected was too

high for the application. Ropes with more compliant constructions and/or

fibre could probably retain the same offset and safety factor criteria at a

lower cost, by attracting lower first order wave frequency loads.

7. For a water depth of 500 m in the West of Shetlands, all steel systems

were found to be in danger of being subjected to very low minimum

tensions. Even in 1000 m, a system based on a stiffer light weight fibre

(aramid) rope and an all steel system were both found to be far from safe

with respect to near slack conditions. This is potentially very dangerous

for tethers susceptible to kinking (aramid fibre ropes) or torsional

instabilities (steel wire ropes). Cyclic tensions with low minimum loads

were not predicted in the designs incorporating polyester fibre ropes, due

to the lower dynamic loads.

8. Low frequency tensions in the combined systems incorporating PET fibre

ropes were found to be of similar magnitude to those in the all steel

systems, however they represented a larger proportion of the MBL of the

tethers. This tendency was accentuated in the PET rope systems with

piles.

9. Based on prices obtained in 1989, the material cost of optimum

combined PET Superline rope-chain systems was found to be lower than

all steel systems in all conditions analysed, the advantage being greater

in the West of Shetlands.

180

10. A similar comparison incorporating a cost penalty for additional

buoyancy to react the vertical loads imposed by the tethers in the

platform, based on costs found in the literature, increased the advantage

of systems based on PET fibre ropes. Typical costs became 70% of that

of the corresponding all steel system.

11. Optimum cost systems based on a Superline aramid fibre rope in

combination with chain were found to be substantially more expensive

than the all steel option in 1000 m in the West of Shetlands. Also the

wave frequency tensions associated with storm conditions were of the

same proportion in relation to the MBL of the rope as in the equivalent

steel system.

12. Systems based on taut inclined PET Superline ropes connected to piles

showed a similar tension response as the PET rope-chain combination,

however a bonus low offset was obtained (at optimum cost). Although the

material cost was found to be much lower (typically 50%) than the all

steel system, a meaningful cost comparison can only be made if the

capital and installation cost of the systems are accounted for.

13. The assumption of a "frozen catenary" first order wave frequency

behaviour was found to be a convenient and reasonably accurate way of

computing the line tensions associated with these motions for systems

incorporating PET fibre ropes. However results obtained using the

"frozen catenary" assumption for all steel systems and combined systems

with aramid fibre ropes were found to be excessively conservative,

especially for the shallower water depths.

14. The performance of a quasi-static analysis procedure for systems based

on PET ropes in Campos Basin was very good. However the same was

not found either for the same systems in the West of Shetlands cases or

for the all steel systems in either location.

15. Based on the above results, the following recommendations are made

concerning analysis methods for systems incorporating fibre ropes:

(i) comparison of systems based on low twist PET fibre ropes in

benign environments such as Campos Basin can be performed

181

by means of a quasi-static analysis procedure;

(ii) comparison of systems based on low twist PET fibre ropes in

any location can be performed by means of a quasi-static

analysis procedure, accounting for the first order wave frequency

tensions by means of a "frozen catenary" assumption; and,

(iii) comparisons involving all steel systems and/or systems

incorporating high modulus light weight tethers should be

performed using a dynamic analysis procedure.

16. The specific tensile strengths obtained for the Superline and Brascorda

Parallel 60 kN model ropes were found to be 0.58 and 0.55 N/tex,

respectively, which is approximately 74% of the specific strength of the

yarns removed from these ropes. These results correspond to

approximate ultimate tensile stresses of 0.55 and 0.56 GPa (based on

the enclosed area of the rope core). Published results for a 1157 kN UBL

Superline rope agree well with the results of this study. The scatter

observed in the tensile test results was comparable with available data

for steel wire ropes including termination failures.

17. Rope axial stiffness was found to vary substantially according to whether

the tethers were loaded at first order wave frequency,low frequency or

statically. This behaviour should be taken into account in designing the

system.

18. Typical stiffness values obtained for the model ropes were 7.3, 13.6 and

16.3 GPa for the Superline and 9.7, 16.2 and 19.2 GPa for the Brascorda

Parallel at wave frequency, low frequency and quasi-static conditions

respectively. Values corresponding to 90% of the stiffness measured for

the model ropes at low frequency and for the quasi-static conditions, and

the full value measured at wave frequency were used in the case studies

and are advocated as reasonably safe assumptions for full size ropes.

19. A simple structural model was found to produce reasonably good

predictions for the dynamic stiffness of the Brascorda Parallel rope based

on the stiffness measurements for the polyester yarn. A similar model

gave passable results for the Superline rope. For both ropes predictions

182

were conservative. The quality of the prediction was found to improve for

loading conditions leading to high stiffness. For typical extreme loads,

stiffness predicted for the Brascorda Parallel overestimated the actual

modulus by between 1 and 11%. For the Superline the prediction was

out by between 5 and 18%.

20. It was found that the influence of long term constant load or long term

cycling between fixed load limits, on the low frequency or wave

frequency stiffness of low twist PET fibre ropes, is small and need not be

considered. Furthermore these conditions do not occur in practical

applications, due to the random nature of the tensions acting on the

mooring lines.

21. The hysteretic damping in the most compliant rope tested, the Superline,

was found to be similar to published data for polyester fibres, indicating

very little effect of constructional hysteresis. The loss coefficient

measured after 1000 cycles at 20±10% of UBL at 0.133 Hz, 0.0265, was

substantially lower than peak values reported in the literature for large

steel spiral strands, and also lower than values for a 13 mm diameter six

strand wire rope obtained here. Therefore it is thought that, as with wire

ropes, hydrodynamic damping will predominate over internal damping, in

the design of systems incorporating low twist PET fibre ropes. It was also

verified that the amount of heat generated by cycling would not be

sufficient to increase the temperature of the core, of a full size rope of the

constructions studied, by more than 1.9°C.

22. The elongation of the fibre rope during loading simulating installation

(50% of UBL for 30 minutes), was found to be the dominant parameter

controlling the minimum length of the upper steel component needed in

the concepts investigated here. Typical values for this elongation were

8.0 and 8.6% for the Brascorda Parallel and the Superline respectively.

23. PET yarn creep rates were confirmed to decrease with the logarithm of

time. The same trend was observed in the model ropes. Although creep

rates were similar for the two ropes tested, the total elongation of the

Superline, at 30% of UBL, was approximately 1.4% more than that of the

183

Brascorda Parallel.

24. Guidance on line retensioning due to creep is given in this study. If an

installation procedure similar to the one modelled is implemented,

retensioning of the mooring lines in 1000 m water depth is expected to

be needed between 5 and 10 times, for a period of operation of 10 years.

Most of the retensionings would have to take place at the beginning of

this period.

25. The tests performed to assess the combined effect of a sea water

environment and constant loads at levels likely to be found on a mooring

rope did not show a quantifiable reduction in yarn or rope samples, for

periods of up to one year. On the basis of the results obtained here and

from published data it is considered safe to assume a constant rate of

reduction in strength of 1% per year. This rate should not be used for

extrapolations beyond ten years.

26. Samples of both model ropes studied, cycled for 1 million cycles at

20±10% of UBL, showed no degradation in the rope free length and only

minor abrasion damage in the terminations. This result is corroborated by

limited published data for a 1157 kN Superline rope. Considering the

cyclic loads forecasted by the "pilot study" and the case studies

performed here, "fatigue" is not a problem for these ropes in the

application which has been addressed. The indications of abrasion

damage highlighted the need to validate terminations in full size tests.

10.2 Further Work

It is considered that short term work aimed at promoting the implementation of

mooring systems incorporating low twist polyester fibre ropes should be

directed to:

(i) full scale static and "fatigue" testing to validate termination design

and to confirm the stiffness characteristics relevant to design; and,

(ii) development of detailed installation procedures, having in mind the

danger of damage to fibre ropes when bearing against sharp

184

edges.

Necessary long term further work is seen to include:

(i) development of improved termination methods, possibly by

obtaining improved pressure distribution in resin sockets, to extract

more strength from low twist PET fibre ropes, and to reduce the

likelihood of "fatigue" damage associated with the terminations;

(ii) additional environmentally assisted degradation tests for periods of

up to five years to extend the safe operational life of PET fibre ropes

beyond ten years;

(iii) development of procedures for monitoring the in service

degradation of these ropes;

(iv) refinement of cost analysis and tools to do it, incorporating the

anchoring methods (including piling), the installation procedures

and the operational life of the mooring;

(v) an investigation of the use of low stiffness tethers in tension leg

platforms; and,

(vi) the performance of low twist polyester fibre ropes operating over a

fairlead and onto a winch drum.

Finally it is worth noting that a preliminary bending-tension (Chaplin (1986))

test was performed on a sample of the model Superline, cycled at 20±10% of

UBL at 0.19 Hz with an angle of wrap of 45° over a pulley with 240 mm

diameter and with a bending length of 30 mm. The test was stopped after

156600 cycles, approximately 2.5 times the expected life of a similar sized six-

strand wire rope (Ridge (1992)). Abrasion damage was found to be

concentrated in the rope cover and the residual strength was 53.2 kN (93% of

UBL).

185

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197

extension›—

198

forceenergy disipated per cycle AU

o characteristic elastic energyinput per cycle U

A

APPENDIX 1

Hysteresis Terminology

The definitions presented here are based on Lazan (1968), where a full

description of the terminology used in damping is given.

Hysteretic damping is measured in terms of the energy dissipated per cycle

divided by a measure of the energy input per cycle. Linear materials present

elliptical hysteresis loops, while non-linear materials generally exhibit pointed

loops.

The energy dissipated per cycle (AU) is easily and uniquely identifiable, i.e.

the area inside the hysteresis loop, however several different definitions of

energy input have been used to obtain a non-dimensional measure of

hysteresis.

The definition of energy input per cycle more commonly used for wire ropes

(characteristic elastic energy input per cycle, U) is schematically represented

below and is adopted here.

From this definition of characteristic energy input various expressions are

used for non-dimensionalising the measurement of hysteresis. The

expressions found in the literature relevant to ropes are:

(i) loss coefficient, loss factor or tan 5,

=tan 5 =AU/2nU ;

(ii) logarithmic decrement,

A = AU/2U ; and,

(iii) relative damping,

D rei = AU/4U.

It should be noted that tan 8, for linear materials, is the ratio between the loss

modulus and the storage modulus.

199

APPENDIX 2

References for strength and stiffness values shown in Table 3.3

The strength values given in Table 3.3 have been based on the following

sources:

polyester double braid - Crawford & McTernan (1983) and National

Coal Board (1979);

polyester Superline - Karnoski & Liu (1988);

polyester Parafil - Riewald (1979) and Hood (1978);

polyester parallel strand - test performed for the "pilot study";

Spectra 900 double braid - estimate based on the polyester double

braid and the fibre strength ratio;

Kevlar 29 wire rope - Riewald et al. (1986), Riewald (1979) and

Koralek & Barden (1987);

Kevlar 29 Parafil - Riewald (1979), Karnoski & Liu (1988), and Hood

(1978);

Kevlar 49 wire rope - Riewald et al. (1986), Riewald (1979) and

Koralek & Barden (1987);

Kevlar 49 Parafil - Riewald (1979), Karnoski & Liu (1988), and Hood

(1978);

wire rope spiral strand - British Ropes (1989); and,

wire rope 6x36 - British Ropes (1987).

Wave frequency stiffnesses shown in Table 3.3 were based on the following

sources :

polyester double braid - National Coal Board (1979);

polyester Superline - Taylor et al. (1987);

polyester Parafil - yarn stiffness x filling factor (Linear Composites

Ltd. (1983));

polyester parallel strand - tested performed in the "pilot study";

Spectra 900 double braid - estimate based on the polyester double

braid and the fibres stiffness ratio;

Kevlar 29 wire rope - Riewald et al. (1986);

200

(4).

(5),

• APPENDIX 3

Rope Stiffness Model

Brascorda Parallel

The model is based on a formulation presented by Hearle et al. (1969). The

following equations from the book have been used:

I (h + h . sec a)/ 2 (1),

= Ey cos20 (2),

Ey = E f cos2a (3),

where:

I = mean length of filaments in a length h of twisted yarn;

h = length of one turn of twist;

a = surface angle of twist;

Ct = filament strain;

Cy = yarn strain;

0 = helical angle of filament;

E = specific modulus of the yarn; and,

Ef = specific modulus of the filament.

Let us call 0 the helical angle of the filament with length i . Then:

0= arc cos —h

Substituting (1) and (4) into (2) and sympliflying we get:( 2 2

el =EY • 1+seca)

where Ei is the strain in the filaments having the mean stress.

Let af and ay be the specific stress in the filament with average length and in the

yarn respectivelly. By definition:

o= Ei ei and,

202

(7),

(8).

ay = Ey . Ey •

Since all the filaments have the same modulus we can use interchangeably Ef

and Ef. Therefore we can write (3) as:

E = Ef- cos2a. (6).Y

Multiplying equation (5) by equation (6) and simplifying we get:

4 Ev . = Ey . E„ . /

7 kl +cosa)2

and using the definitions of of and ay we get:

4

(31 = GY . (1+cosa)2

For a strand it is necessary to approximate and write:

4

o- = a . (9)-Y s (1+cosa)2

The regression equations are based on loads as percentages of UBL, and so we

need to obtain an expression of the percentage of the yarn breaking load (%YBL)

as a function of the percentage of the strand breaking load (%SBL), to be used

with the yarn siffness regression equation.

By definition:

FsF;as = wa and 5 = 11,—; (10),

.. s viy

where:

Fs . Force in the strand;

F- - Force in the yarn with average length;Y-Ws . linear mass of the strand; and,

WY =linear mass of the yarn.

However:

Fs . %SBL . SBL and F- . %YBL . YBLY

203

where SBL and YBL are the breaking loads of the strand and of the yarn

respectivelly.

Therefore equations (10) can be writen as:

(YoSBL.SBLand

a_ = 'YoYBLYBL(12).as — Y Wws Y

Substituting the expressions for as and 5 into equation (9) we obtain:

4 SBL W_c cNBL . , '2 c'kUBLs • YBL • W_Y (13).

ki +cosa)2 s

For a given mean load or load amplitude in the strands of a Brascorda Parallel

rope (%SBL), equation (13) can be used to obtain the corresponding yarn loads

L m and La (mean and amplitude). These should be fed into the regression

equation (Section 7.2.1 equation (1)) to obtain E.

The modulus of the strand can then be obtained as:

E = •E cos2 a (14).s y

Superline

The model for the Superline begins in the same way as for the Brascorda Parallel

but a further approximation is needed, which considers the strands in each sub-

rope to be similar to yarns. Using the same equations for this additional level of

geometry we get:

4 4 CY

Y = G

r .

(1+cosa)2" (1+cos [3)2

where:

a . helix angle of the outermost yarn in the strand;

13. helix angle of the strands in the sub-rope; and,

ar = specific stress in the rope.

(15),

204

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