John F. Flory, Tension Technology International, Inc.Stephen P. Banfield, Tension Technology International, Ltd.David J. Petruska, BP America, Inc.

Copyright 2004, Offshore Technology Conference

This paper was prepared for presentation at the 2004 Offshore Technology Conference held inHouston, Texas U.S.A., 3–6 May 2004.

This paper was selected for presentation by the OTC Program Committee following review ofinformation contained in an abstract submitted by the author(s). Contents of the paper, aspresented, have not been reviewed by the Offshore Technology Conference and are subject tocorrection by the author(s). The material, as presented, does not necessarily reflect any positionof the Offshore Technology Conference or its officers. Electronic reproduction, distribution, orstorage of any part of this paper for commercial purposes without the written consent of theOffshore Technology Conference is prohibited. Permission to reproduce in print is restricted toan abstract of not more than 300 words; illustrations may not be copied. The abstract mustcontain conspicuous acknowledgment of where and by whom the paper was presented.

AbstractThis paper explains and defines the synthetic fiber rope

stretch and stiffness change-in-length properties which areimportant for deepwater platform mooring system design.It introduces the concept of accumulated elastic stretch,which causes temporary stretching and stiffening of therope during tension cycling. It proposes how these proper-ties can be determined by rope testing and by computermodeling. It proposes how the change-in-length propertiesshould be used in mooring system design and analysis.

BackgroundThe offshore industry and the fiber rope manufacturers

have now had some experience in using fiber ropes indeepwater platform moorings. Petrobras pioneered this inthe mid 1990s. In the late 1990s several class societies 1

2 3 and then API 4 published guidelines for fiber ropedeepwater moorings. Tension Technology Internationalwith others also published fiber rope design guidelines.5

Those guidelines were based on what was then perceivedto be the best design methods and the best test methodsfor the rope properties needed to carry out those methods.

Since those guides were published, several fiber ropemooring systems – Mad Dog 6 7 and Red Hawk – havebeen designed for the Gulf of Mexico. A number of largefiber ropes have been tested and analyzed for use in thoseand other projects. Also, findings are now available fromseveral significant fiber rope research programs whichwere conducted while and after those guides were written.

INTRODUCTIONThe unique stretch and stiffness characteristics of

synthetic fiber ropes are important in the design andanalysis of deepwater platform mooring systems.

Mooring system designers are experienced in designingwith wire rope and chain catenary mooring lines. Thestiffness characteristics of wire rope and chain are essen-tially linear. These components do not experience perma-nent stretch until high tension. With these components, theprincipal mooring system restoring force is produced by thecatenary effect.

As mooring water depths increase, there are incentivesfor using fiber ropes, as discussed in other papers. Butwith fiber rope, the principal mooring system restoring forceis produced by the tension vs. stretch (stiffness) character-istics of the rope instead of by the catenary effect. Mooringsystem designers are still trying to understand the uniquestretch and stiffness characteristics of fiber ropes and toincorporate them into traditional mooring design proce-dures.

The stretch and stiffness characteristics of typicalsynthetic fiber ropes are time dependent and non-linear.Fiber ropes experience both elastic and permanent stretch.Conflicting and confusing terminologies are sometimesused. Some important rope properties have only recentlybeen adequately understood and explained.

Here the term stretch refers to any change in rope lengthwhich is produced by tension. Stiffness is the relationshipbetween stretch and applied tension. Other terminology isintroduced in the text and summarized in Nomenclature atthe end of this paper.

The paper is divided into four parts:! Part 1 uses a spring-and-dashpot analog model to

describe the principal synthetic fiber rope stretch andstiffness characteristics.

! Part 2 illustrates some of these characteristics withresults from several large rope test programs.

! Part 3 discusses how these characteristics should beused in a deepwater platform mooring analysis .

! Part 4 describes how these characteristics might bedetermined through rope testing and through com-puter modeling of the rope.

Fiber Rope Deepwater Mooring Lines

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Defining, Measuring, and Calculating the Properties of

2 OTC 16151

Spring A

Spring C

Dashpot B

Dashpot D

Ratchet E

Figure 1 Analog Model of Viscoelastic Synthetic Fiber Rope Figure 2 Stiffness, Tension vs. Stretch of Synthetic Fiber Rope

Part 1: FIBER ROPE STRETCH ANDSTIFFNESS CHARACTERISTICS

Analog Model of Fiber RopeSynthetic fiber ropes are made of polymer fibers which

are viscoelastic materials. Thus the change-in-lengthcharacteristics of these ropes are similarly viscoelastic,meaning that deformation is a function of both the appliedload and the rate of application.

Figure 1 illustrates a mechanical analog model of atypical synthetic fiber rope. It consists of a spring A and adashpot (damper) B in series with a parallel combination ofa spring C and a dashpot D and also in series with aratchet E. When tension is applied to this system, the totalstretch comprises the stretch in the spring A, in the dashpotB, in the parallel combination C and D, and in the ratchet E.

The spring-dashpot analog model is used here todescribe the change-in-length properties of typical syntheticfiber rope. It is oversimplified. Simple springs and dash-pots do not adequately represent the complicated nonlinearand time dependent properties of a fiber rope. The modelis not intended to substitute for rope testing or rope com-puter modeling.

Figure 2 is a graph of tension vs. stretch based on thismodel with linear springs. The effect of ratchet E, whichrepresents non-recoverable constructional stretch of therope, is not shown in this figure.

As tension is applied to the system, spring A stretchesimmediately in proportion to the tension. Dashpot B movesslowly while and after tension is applied. Stretch acrossthe parallel combination of spring C and dashpot D must beequal. Dashpot D moves slowly while and after tension isapplied, and spring C stretches with it. Thus the immediatestretch of spring A is followed by the slower stretch of theother elements B, C, and D.

As tension is reduced, spring A contracts immediatelywhile and after tension is reduced, spring C contracts at aslower rate because it is retarded by dashpot D. DashpotB remains stretched after tension is reduced.

Rope Constructional StretchThe stretch and stiffness phenomena of the rope,

discussed later, depend on the properties of the syntheticfibers from which the rope is made. The manner in whichthe rope is made also influences its stretch. We willdiscuss this constructional stretch first.

The rope is made of individual fibers which are twisted

into yarns. The yarns are twisted into strands. And thestrands are laid or braided to form the rope. The structureof a new rope is relatively loose and uncompressed.

When the rope is first tensioned, the various yarns andstrands compact and realign, and the lay length of theyarns and strands in the laid or braided rope increases.These actions cause the rope length to increase. Thisprocess is sometimes called bedding in. We call thislength increase constructional stretch.

The constructional stretch is represented in Figure 1 bya ratcheting device E which increases in length the firsttime tension is applied. This ratcheting effect takes placeon the first several tension cycles. It is not time dependentlike the dashpot effect. Unlike the spring effect, theratcheting effect is permanent and remains even aftertension is removed.

The constructional stretch can be reversed if tension iscompletely removed and the rope is then flexed so that itsstructure can become limp and uncompacted again.

This constructional stretch ratcheting effect depends onthe applied tension. A given amount of ratcheting occurswhen a given tension is first applied, and more might occurduring several more cycles to that same tension. No moreratcheting occurs while the rope is held at that tension or iscycled again to that tension. But if a higher tension is thenapplied, additional ratcheting can take place.

Once this ratcheting constructional stretch occurs, itremains, even after tension is reduced or removed. Thusit is similar to the permanent stretch discussed later. Butunlike permanent stretch, under constant tension construc-tional stretch does not increase with time.

Permanent StretchDashpot B does not contract as tension is reduced, even

after a long time. We call this stretch which does notcontract permanent stretch.

Permanent stretch is a function of applied tension and of

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time at tension. It is rapid at first, but the rate of permanentstretch decreases over time. Permanent stretch of a fiberrope usually follows a pattern such that the amount ofstretch which takes place in one minute is doubled in 10minutes, is tripled in 100 minutes, etc.

Permanent stretch can usually be plotted as a straightline against time on a semi-log graph. This permanentstretch can then be represented by an equation of the formS = Ln (t / A) where S is stretch, t is time at applied tension,and A is the slope of the permanent stretch line on a semi-log graph.

When permanent stretch is measured under constanttension in a rope test, the measurement includes construc-tional stretch and elastic stretch. These together are calledcreep. When such stretch is plotted on a semi-log graph,the early measurements might not fit a straight line. In thatcase, the straight line should be fitted only to the latermeasurements.

Polyester, aramid and LCAP (liquid-crystal aromaticpolyester) have similar linear logarithmic creep character-istics. Aramid and LCAP have very low creep rates.HMPE (high-modulus polyethylene) is an exception, in thatits creep rate typically plots as a straight line on a normaltime scale instead of on a logarithmic time scale. HMPEyarn can creep to failure at high or even moderate constanttension, depending on temperature.

Elastic Stretch Elastic stretch is that stretch which takes place while

tension is applied and maintained on the system but whichcan be recovered through contraction after tension isreduced or removed. It is comprised of the stretch ofspring A, which takes place immediately, and that of springC, which is delayed by the retarding effect of dashpot Dand takes place over time.

The stretch which takes place while tension is beingapplied is here called immediate elastic stretch. Thestretch which takes place after tension is applied but whichis not permanent stretch is here called delayed elasticstretch. Elastic stretch is the combination of immediateelastic stretch and delayed elastic stretch.

The stretch which takes place in spring C and dashpotD while tension is being applied contributes to immediateelastic stretch. This effect is shown in Figure 2 by the solidcurved line. If tension were applied instantaneously,dashpot D would not have time to respond, and only springA would stretch as shown by the dashed straight line.(Some permanent stretch also occurs while tension isbeing applied at a slow rate.)

Delayed elastic stretch continues to increase whentension is maintained on the rope, but at a decreasing rate,essentially logarithmically as described above. Delayedstretch is the combination of this delayed elastic stretchand the permanent stretch which occurs while tension ismaintained on the rope.

Elastic Contraction Elastic contraction, sometimes called recovery, is that

stretch which is recovered after tension is reduced. It iscomprised of the contraction of spring A and that ofspring C.

Spring A returns to its original length immediately aftertension is removed. As tension is reduced, spring Ccontracts and compresses dashpot D. We call the combi-nation of these effects immediate elastic contraction, thatcontraction which takes place as tension is reduced.

After tension is removed, spring C continues to contractand thus compress dashpot D until they recover to theiroriginal untensioned length. We call this contraction whichtakes place over time delayed elastic contraction.

The rate of delayed elastic contraction is at first rapidand decreases with time, essentially logarithmically. Fullcontraction might take a very long time.

Immediate elastic contraction and delayed elasticcontraction together comprise elastic contraction.

Static Stiffness CurveThe stiffness curve is a plot of tension vs. rope stretch.

Here we call it a curve to avoid confusion with the termmooring line. For simplicity, we will illustrate linear springsin the examples, although nonlinear springs would betterdepict the characteristics of some fiber ropes, such aspolyester.

Again referring to the above model, when tension isapplied at a relatively slow rate, dashpot D can stretch atessentially the rate of tension application, allowing springC to stretch almost as much as it would if unimpeded bythat dashpot. In this case, the stiffness curve is essentiallythe same as that of springs A and C acting in series, asshown in Figure 3.

We call this the static stiffness curve. It is the stiffnessmeasured when tension is applied slowly. Static stiffnessis sometimes ambiguously called “quasi-static stiffness”:In material science and applied mechanics, “quasi-static”means without stress-wave inertia effects.

The static stiffness curve can depend on the previousload history of the rope. If the rope was maintained attension for some time before tension increases, dashpot Dand spring C will already be partially stretched. If tensionwas recently removed from the rope, spring C and dashpotD might not yet have completely contracted. In either case,the static stiffness curve will be steeper because thepartially stretched dashpot D will move slower and alsobecause of nonlinear spring effects.

Dynamic Stiffness CurveReferring again to the above model, when tension is

applied at a relatively fast rate, dashpot D does not havetime to respond, and spring C stretches very little. In thiscase, the system stiffness is essentially only that of springA acting alone. It is steeper than the static stiffness curve,as shown in Figure 3.

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Figure 3 Idealized, Linear Static and Dynamic Stiffnesses

Figure 4 Accumulated Elastic Stretch

Figure 5 Typical Polyester Yarn Creep Data

We call this the dynamic stiffness curve. It is thestiffness measured when tension is applied rapidly.

Accumulated Elastic StretchIf a synthetic fiber rope, as represented in the above

model, is cycled only once and then allowed to contract, itwill soon return to essentially its original length, retainingonly permanent stretch. This behavior was discussedabove as elastic stretch and contraction.

But if the rope is rapidly and continuously cycled, dash-pot D doesn’t have sufficient time to contract, and somestretch remains in spring C. Because the rope does nothave time to contract after each cycle, it temporarilybecomes longer. This effect is shown in Figure 4.

By this process, elastic stretch accumulates duringtension cycles. We call this accumulated elastic stretch.The accumulated elastic stretch is retained until cyclingstops, but it contracts quickly after cycling stops.

On a graph of tension vs. stretch during tension cycling,accumulated elastic stretch is evident as the space be-tween curves on progressive loading cycles at the meanload. The limited data now available indicate that the rateat which elastic stretch is accumulated on each cycle israpid at first but decreases with cycles until a “steady state”stretch is reached. This is analogous to dashpot D bottom-ing out.

After cycling stops and the mean cyclic tension ismaintained on the rope, it can contract normally. Accumu-lated elastic stretch will essentially completely disappearover time, typically within an hour.

After this contraction takes place, it appears that therope has no memory of prior cycling. And when the ropeis then cycled again, the rate at which accumulated elasticstretch develops appears to be the same as that during theprevious cycling.

Part 2: EXAMPLES FROM TEST RESULTS

Part 1 described the change-in-length characteristics offiber ropes by analogy to a spring-dashpot model. ThisPart provides illustrations of these characteristics takenfrom actual test results.

Creep-Time Plotted on Semi-Log GraphFigure 5 shows creep data for a typical polyester yarn

from the Fibre Tethers 2000 study.8 Yarns were tested withhanging weights to apply constant tensions of 15%, 30%and 60% of break strength. Creep stretch data were takenfor about a half million minutes (almost a year). This creepcomprises both permanent and elastic stretch, as it ispractically impossible to measure the two separately.

The data are plotted on a semi-log plot, as discussedabove. Excluding the very early points, the data plot as astraight line against log time, even out to a half millioncycles. This is represented by the combination of the solid

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Figure 6 Example of Accumulated Elastic Stretch Test Data Figure 7 Tension-Stretch Graph, Polyester Rope Test

and the long-dashed lines. The line has been extended asa short-dashed line out to ten million cycles (approximatelytwenty years).

The interception of each line with the ordinate at oneminute represents initial elastic stretch at the appliedtension, along with initial permanent stretch and construc-tional stretch. These creep data represent yarn instead ofrope. Creep rate data for ropes reported by Petruskaagree closely with these yarn data. 6

The creep rates of different polyester yarns may differ.And the rope creep rate may depend on constructiondetails, especially lay length. Thus the data reported hereshould not be taken as representative “generic” data andused for design purposes.

Creep tests on polyester ropes lasting more than a yearindicate that creep essentially becomes stable, that is itfalls below the straight semilog line trend. Further researchis needed to confirm this effect for various ropes before itcan be relied upon in design analysis.

Tension-Stretch Curve, Accumulated Elastic StretchFigure 6 is a tension vs. stretch plot taken during a large

polyester rope test program.9 It is a good example ofaccumulated elastic stretch. This rope was cycled anumber of times about a relatively low mean tension, andthen about progressively higher mean tensions.

This graph exhibits accumulated elastic stretch while therope was being cycled at constant amplitude. Stretch tookplace during this cycling. The slope of the dynamicstiffness curve increased, but at decreasing rates. Whilebeing loaded to a higher tension, the curve initially contin-ued up the dynamic stiffness curve and then returned to thestatic stiffness curve.

Tension was then decreased in steps, pausing forcycling at each progressively lower mean tension.

As tension decreased, some accumulated elastic stretchwas contracted. And some contraction occurred evenduring this cycling, because the rope had previously beentensioned and cycled at a much higher tension. Finally, therope contracted to essentially its original length aftertension was removed.

Tension-Stretch Curve, Static and Dynamic StiffnessFigure 7 shows tension vs. stretch curves plotted from

data recorded during cyclic tension test conducted on alarge 2,000,000 lb (8900 kN) break strength polyester rope.This rope was cyclic tensioned about different meantensions to various amplitudes representing installation,installed, and storm conditions.10

Curve 1, the first application of a relatively low tension,follows the initial static tension curve. A substantial amountof constructional stretch occurred early in this stroke, butthe curve also represents both permanent stretch andelastic stretch.

Curve 3 is cycling up to that low installation tension,representing dynamic stretch. Curve 5 is first tensioning upto a higher tension at 50% of break strength after a fewlower tension cycles. Note that the slope of this curvefollows essentially the dynamic stiffness curve up to theprevious peak tension and then tends to follow an exten-sion of the earlier static stiffness curve.

Curve 7 is cycling up to the previous low installationtension. Note that this curve essentially follows the slopeof the previous dynamic stiffness curve. That completedthe installation phase of of this test. It was followed byseveral series of tension cycles, which are discussed later.

After many such cycles, cycling was then done to astorm tension. Curve 14 is the dynamic stiffness for thatseries of cycles.

The cyclic tension was then reduced to that of some ofthe preceding cycle series. Curve 17 is the dynamicstiffness during that series of cycles. Some of the accumu-lated elastic stretch had been dissipated.

Finally, cycling was then done to a higher storm tension.Curve 19 is the dynamic stiffness during that series ofcycles.Stretch-Time Plot

Figure 8 is a plot of maximum stretch vs. time takenduring the test described above. Beginning with series 8,the rope was cycled at constant stretch amplitude whilemaintaining constant mean tension. The rope was held atmean tension for a brief period between each series

6 OTC 16151

Figure 8, Stretch-Time Graph, Polyester Rope Figure 9, Stiffness-Time Graph, Polyester Rope Test

The installation process was simulated by several seriesof tests over a period of thirteen hours. Several tensioncycles were applied to 50 percent of break strength inseries 5. But apparently these were not sufficient toremove all constructional stretch from the rope.

Series 8 is the first cycling after the installation process.This was followed by series 9 at a lower mean tension,then by series 10 at the higher mean tension of series 8,then by series 11 at the lower mean, and then by anotherseries 12 at the higher mean. The stretch amplitude wasthe same in all of these series.

Stretch increased at the start of series 8 due to removalof more constructional stretch. It then reached a “steadystate” stretch. The increase in stretch above that at meancyclic tension is accumulated elastic stretch.

Series 10 and 12 were repeats of series 8, at the sametension mean and amplitude. The stretch in these repeatseries was the same as in series 8, except the “steady-state” stretch was reached immediately because the ropehad previously been cycled at this mean tension. Likewise,the stretch in the repeating series 9 and 11 is essentiallythe same.

Series 13 was run at the same mean tension as series9 and 11 but at a much higher stretch amplitude. Thishigher stretch amplitude produced the higher maximumstretch recorded in series 13. By the end of series 13,approximately twenty thousand cycles had been applied.

Series 14 represents a storm simulation at a highermean tension. Loading to this higher tension caused morestretch. Some of this might have been additional “bedding-in” constructional stretch but most of this was the develop-ment of accumulated elastic stretch.

This storm simulation was followed by series 15 cyclingbetween 10% and 30% of break strength. Series 19 wasanother storm simulation to a higher tension. This againcaused more stretch.

Note that the stretch was essentially the same each timethe same cycling regime was repeated, even though higheror lower mean tension was experienced between therepeats. At the start of each series, the correspondingstretch returned almost immediately. At the beginning ofseries 8, 14, and 19 the stretch slowly increased, due to

some additional constructional stretch and also due to thedevelopment of accumulated elastic stretch.

Stiffness-Time PlotFigure 9 is a plot of stiffness vs. time taken during this

test.11 The labeling is the same. Stiffness is plotted as Kr,which is EA divided by the mean break strength.

In series 8, conducted after the installation cycles, thestiffness increased rapidly and then reached a “steadystate”. Series 10 and 12 were repeats of series 8, at thesame mean tension. They followed the same generalstiffness pattern.

Intervening series 9 and 11 were conducted at a lowermean tension. Series 13 was conducted at the meantension as series 9 and 11, but at a greater stretch ampli-tude. The stiffness patterns during these series are essen-tially the same, even though the amplitude in series 13 wasgreater. The stiffness reduced during the intervening cyclicseries at a lower mean tension. But it returned to the samestiffness during the repeating series at the higher meantensions.

During the first storm simulation series, 14, the stiffnessrapidly increased. This illustrates further constructionalstretch and also the development of accumulated elasticstretch.

The next series, 15, was cycled at the same meantension as series 8, 10, and 12. During series 15 thestiffness followed the same pattern as those earlier series,even though the rope had been cycled at a much highertension before this series and even though the stretchamplitude in this series was much greater..

Series 16 and 17 were short series conducted at lowmean tensions. These lower tensions produced muchlower stiffnesses than in the previous high-tension series.

During the second storm simulation, 19, stiffnessessentially followed the same pattern as that measuredduring the first storm simulation.

Examination these and other similar polyester ropeconstant-stretch-amplitude test results, indicates that theaccumulated elastic stretch reaches a “steady state”condition. But the dynamic stiffness continues to increase

OTC 16151 7

oInstallation Tension

Stretch

Tens

ion

Initial Static

Stiffness

Installed Stretch

Later Installed Stretch

o

o1 2

34o

Maximum Installation Stretch

Delayed Contraction

Construction, Permanent and Elastic

Stretch

Post

Instal

lation

Contr

actio

n Stiff

ness

Installed Tension

Immediate Installation Stretch

Figure 10 Installation Procedure Analysis Method

at a decreasing rate, apparently plotting as a straight lineagainst number of cycles.

Part 3: USE OF FIBER ROPE PROPERTIES IN MOORING SYSTEM DESIGN ANALYSIS

The design analysis of a deepwater mooring involvesthree principal tasks(1) Determining the necessary rope length.(2) Determining the maximum offset of the platform

during storm conditions, even after many years ofservice.

(3) Determining the peak (and trough) tensions duringstorm conditions.

Installation and Installed Stretch AnalysisDuring the installation process, the rope is usually

pretensioned to a load much higher than the intendedinstalled tension and is held or cycled near that tension forsome time. The purpose is to test the mooring system andsometimes to set the anchors. At the completion of thisprocess, rope tension is then reduced to the installedtension.

We call the mooring line stretch which takes place duringthis installation process the installation stretch. We call thestretch immediately after tension is reduced to installedtension the installed stretch.

Several factors are of concern during and immediatelyafter installation:! Sufficient rope length must be provided so that, at the

start of installation, the total length of the untensionedrope and other mooring system components canreach from the anchor to the vessel fairlead.

! Sufficient take-up capability must be provided so that,as stretch takes place during installation the upperend of the rope does not approach the fairlead.

! Sufficient chain must be provided at the anchor endso that, immediately after the installation process, thelower end of the rope (before contraction) does nottouch the sea floor.

Figure 10 shows our recommended method for analyz-ing installation and installed stretch. Linear stiffnesscharacteristics are represented here for simplicity.1, Apply installation tension to the initial static stiffness

curve to determine immediate installation stretch.2, Add the construction stretch, permanent stretch, and

elastic stretch expected during the installation processto the immediate installation stretch to determine themaximum installation stretch.

3, Fit the post-installation contraction curve through thepoint of maximum installation stretch. Apply theinstalled tension to this curve to determine the imme-diate installed stretch.

4. Subtract the expected delayed contraction from theimmediate installed stretch to determine the later

installed stretch.Installed stretch consists of constructional stretch,

permanent stretch, and elastic stretch. Provided thatsufficient tension is applied for sufficient time, almost allthe constructional stretch is taken out of the rope during theinstallation process. And about half of the permanentstretch takes place during the installation process, asexplained later,.

Considerable elastic stretch takes place during the longtime at high tension in the installation process. Aftertension is reduced to installed tension, some of the elasticstretch experienced at the higher tension will contract, butthis contraction does not take place immediately. Whendetermining the immediate installed stretch for use inchecking if the rope will touch the sea floor, this delayedelastic contraction should be excluded.

After completion of installation, as the rope is maintainedat installed tension, some permanent extension will con-tinue to take place. Also, delayed contraction will continueto take place.

For synthetic fibers (other than HMPE), these twoprocesses will probably essentially offset each other ifsufficient tension has been applied for sufficient time duringthe installation process. Thus for such cases, we believethat permanent stretch after installation can be ignored insubsequent analyses.

The installation stretch and installed stretch can bedetermined by applying the highest installation tension andthe installed tension to a prototype rope (or subrope) in atest lab, as discussed further in Part 4.

Mooring System Service Analysis MethodsIn analyzing the mooring system for service and storm

conditions, the following factors are of principal concern:

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Figure 11 Present Mooring System Analysis Method Figure 12 Recommended Mooring System Analysis Method

! The maximum platform offset does not exceed thelimitations of riser length.

! The maximum mooring line tension is not excessive.! The minimum mooring line tension does not permit

the rope to touch the sea floor (and does not permitaxial compression fatigue in aramid ropes).

! The tension range between trough and peak does notinduce cyclic tension fatigue, either in the rope or inother components of the mooring system.

Present Analysis ProcedureA mooring analysis procedure which is now commonly

used is illustrated in Figure 11. Primes are assigned to thestep numbers to distinguish them from the procedure whichis recommended next.5'. Apply installed tension to static stiffness curve to

determine installed stretch.6'. Add service life permanent stretch.7'. Using the static stiffness curve to represent mooring

lines, analyze the platform mooring system to deter-mine the mean drift position in steady storm condi-tions. From this mean drift position, determine thestretch increase (or decrease) in each mooring line.

Add (or subtract) this storm drift stretch to the respec-tive mooring line to determine mean storm stretch (a).This also determines the mean storm tension (b).

8'. Using the dynamic stiffness curve to representmooring lines, analyze the platform mooring system todetermine the platform-motion-induced mooring linestretch amplitude (PA). Add (or subtract) the effect ofplatform amplitude to each mooring line’s mean stormstretch to determine the maximum storm stretch (a).Fit the dynamic stiffness curve through the point ofmean storm tension. Determine the maximum storm

tension from the point of maximum storm stretch on thisdynamic stiffness curve (b).

This may not be the best or even a reasonably accurateway of determining the parameters of concern: maximumoffset, maximum line tension, and minimum line tension.

Recommended Analysis ProcedureWe propose the following analysis procedure, as shown

in Figure 12.5. Apply installed tension to the installed static stiffness

curve to determine installed stretch.6. Using the installed static stiffness to represent

mooring lines, analyze the platform mooring system todetermine the mean drift position resulting fromsteady storm conditions. At this early mean driftposition, determine the stretch increase (or decrease)in each mooring line. Add (or subtract) this storm driftstretch to the respective mooring line to determinemean early storm stretch (a). This also determinesthe mean storm tension (b).

7. Add (or subtract) the storm elastic stretch (describedbelow) to the mean early storm stretch to determinethe mean late storm stretch.

8. Using the late storm dynamic stiffness curve, analyzethe platform system to determine the platform-motion-induced mooring line stretch amplitude (PA). Add (orsubtract) the effect of platform amplitude to eachmooring line’s mean late storm stretch to determinethe maximum storm stretch (a). Fit the dynamicstiffness curve through the point of mean stormtension. Determine the maximum storm tension fromthe point of maximum storm stretch on this dynamicstiffness curve (b).

OTC 16151 9

The storm elastic stretch consists of the additionalstretch which occurs when the rope is maintained at thestorm tension and also the accumulated elastic stretchwhich occurs when the rope is cycled for the duration of thestorm. Depending on the magnitude and duration of thestorm, this storm elastic stretch can be significant whenpredicting platform offset.

Note that this analysis should be done for each individualmooring line around the platform. When the platform issubjected to the storm waves, the platform storm driftdecreases tension in the lines opposite the storm. Thisdecreases the stiffness in these lines, as shown in runs 16and 17 of figure 9. The effect is beneficial, because theselines then exert less pull on that side of the platform. Butthe minimum storm tension in these lines might be aconcern, either to assure that the rope does not touch thesea floor or in the case of aramid, to assure that axialcompression fatigue does not occur.

The maximum rope storm offset is the difference be-tween the installed stretch and the maximum stretchinduced by the storm. This is the value of principal concernwhen predicting the maximum platform offset.

Service Life Permanent StretchThe principal difference between the present procedure

and the recommended procedure is that, instead of addinga service life permanent stretch to the installed stretch, astorm elastic stretch is added to the early mean stormstretch.

As mentioned above, we believe that any permanentstretch which takes place after the installation process isnegligible (except for HMPE ropes). This additionalpermanent stretch will essentially be counteracted by theelastic stretch which is recovered as the rope contractsafter completion of the installation process.

Creep data for a polyester yarn maintained at severalconstant tensions for almost a year were shown in Figure5. The solid portion of each creep line represents thetypical duration of the installation process, two days or2880 minutes, about 3.5 log cycles. The constructionalstretch and other initial stretch which occurs during the firstseveral minutes is represented by the intersection of thestraight line with the ordinate. Based on the slope of thestraight creep trend line, after this initial stretch takes place,about 0.6% additional stretch will take place during theinstallation process.

Twenty years of service life is essentially 10,000,000minutes, or seven log cycles. The total creep over this timeis about 1.2%. Thus about half of this creep takes placeduring the installation process.

We recommend that the installed stretch be defined andmeasured immediately after reducing to the installedtension, instead of waiting until all contraction takes place.This measurement will include some elastic stretch whichhas not yet contracted. That contraction will probablyessentially offset any creep which might take place over the

service life of the mooring. An exception is the case ofHMPE rope, where continued creep should be carefullyevaluated.

Storm Elastic StretchBased on recent experience from cyclic tension testing,

we believe that the effect of accumulated elastic stretchunder storm conditions can be significant.

Figure 6 showed the development of this accumulatedelastic stretch during cycling at several progressively highermean tensions during a polyester rope test. Duringconstant cycling at each mean tension, the rate of accumu-lation decreased, until it became almost negligible. Buteach time the tension level was increased, more elasticstretch accumulated.

Figure 8 showed this same phenomenon. Each time themean cyclic load was increased, this caused increasedstretch. Some of this was elastic stretch. But some of thiswas due to accumulated elastic stretch. This effect isespecially pronounced during the two storm simulations, 14and 19.

We recommend that accumulated elastic stretch beconsidered in the mooring system analysis We believethat accumulated elastic stretch while the rope is cycledunder storm conditions is more significant than creep whendetermining the maximum storm platform offset.

Early and Late Storm StiffnessesThe dynamic stiffness increases during cycling. This

phenomenon is shown in Figure 9. Each time mean cyclictension was increased, the stiffness was less at thebeginning of that set than at the end. The stiffness in-creased rapidly early in each of these sets, but the rate ofincrease decreased with numbers of cycles. This effectwas most pronounced during sets 8, 14, and 19.

The platform mooring system storm analysis taskinvolves cycling to a prescribed platform motion amplitude.As rope stiffness increases during constant amplitudecycling, the minimum tension decreases and the maximumtension increases. The greater dynamic stiffness later inthe storm will impose higher (and lower) tensions on themooring lines.

We recommend that the dynamic stiffness which isexpected late in a storm should be used when predictingthe minimum and maximum mooring line tensions.

Part 4: TESTING FIBER ROPE PROPERTIESFOR MOORING SYSTEM ANALYSIS

In order to perform a platform mooring analysis, asdescribed in the previous section, the following ropechange-in-length data will be required:• Initial Static Stiffness Curve (step 1)• Construction, Permanent, and Elastic Stretch (for

duration of installation process) (step 2)

10 OTC 16151

• Post Installation Contraction Stiffness Curve (step 3)• Delayed Contraction (step 4)• Static Stiffness (steps 5 and 6)• Elastic Stretch (for duration of storm) (step 7)• Dynamic Stiffness (representative of late storm) (step 8)

Determining Rope Performance Through PrototypeTesting

The change-in-length properties are usually determinedthrough prototype rope testing. Only a few test machinesare capable of performing such testing of large, long ropes.The testing is time consuming and expensive. The testspecimens are also expensive.

The test specimen must be long enough to measure thechange-in-length properties with sufficient accuracy. Therelationship between specimen length and accuracy isdiscussed in the Cordage Institute Test Method.12 Thepossible effects of length imbalance in short rope speci-mens on strength were discussed by Flory.13

Because of the length limitations of available testmachines, it may be preferable either to test smaller scalerope specimens or, in the case of parallel structure ropes,to test individual subropes.

New Rope Break Strength TestBefore conducting the change-in-length tests, the new

wet break strength (NWBS) of the rope should be deter-mined. The test methods of the OCIMF SPM HawserGuidelines are recommended for this. The rope should betested with essentially the same terminations as will beused in actual installations. The rope should be precycledbefore break test to set the terminations and to bed in therope.

Other tests, such as fatigue tests and torque tests mightalso be carried out. These are beyond the scope of thispaper and these recommendations.

Initial Static Stretch Stiffness Curve TestData to plot the initial static stiffness curve can be

measured by tensioning a rope specimen up to the ex-pected installation tension at a slow rate.

Constructional, Permanent, and Elastic Stretch CreepTest

After bringing the rope up to installation tension, it maybe desirable to apply a few tension cycles to removeconstructional stretch. A long-term creep test should thenbegin.

A constant tension should be maintained on the ropeduring the creep test. It will be necessary to adjust theapplied tension to counteract the effect of increasingstretch.

Precise change-in-length measurements should berecorded frequently during the creep test, especially duringthe first few minutes. During the test, plot stretch dataagainst time on a semi-log graph in order to detect when

the curve begins to follow a straight line, which indicatesthat constructional stretch is essentially complete.

After the stretch data begins to plot as a straight line, itmay only be necessary to continue the test for three morelog cycles, for example, 4, 40, and 400 minutes (6.7 hours)in order to adequately establish the slope of the line. Thetest can then be stopped. But it should immediately befollowed by the post-installation contraction stiffness test,described next.

Although the installation process might involve loweringand cycling the tension, it is not necessary or desiralbe todo this in the creep test. Unless the test is conducted atconstant tension, the rate of creep cannot be determined,and it would then be necessary to conduct a test for thetotal duration of the installation process. The creep datataken at the maximum installation tension will be conserva-tive.

Plot a semilog graph of creep against time and developan equation for the rate of creep.

Post-Installation Contraction Stiffness and DelayedContraction Test

Immediately after completing the above “creep” test,tension should be reduced to the installed tension, whilerecording data for the post-installation contraction stiffnesscurve.

The installed tension should be maintained on the ropewhile the post installation contraction is measured. Thattest should be conducted much like the creep test de-scribed above. If the rope is maintained at a constantlength while conducting this test, the rope cannot contractand the tension will rise. It will be necessary to monitor andadjust tension to allow the rope to contract during this test.

As above, the change-in-length measurements shouldbe plotted on a semi-log graph against time. The data willprobably follow a straight line almost immediately, and thusit may only be necessary to carry this test for about anhour, e.g. 0.6, 6, and 60 minutes. This should be sufficientto derive an equation for long term contraction, especiallysince it is probably not necessary to calculate this withgreat accuracy during a mooring system analysis.

After completing this test, tension can be removed fromthe rope in preparation for the following tests.

Installed Static Stiffness Curve TestThe installed stiffness test should be carried out as soon

as practical after completing the above tests. The ropewould continue to contract. But this further contractionprobably has a negligible effect on the installed stiffnessmeasurement.

The installed static stiffness curve should be measuredwhile tensioning the rope specimen up to the expectedmean storm tension at a very slow rate without pause. Thetest can be carried out to a higher tension if desired. Or thedata can be extrapolated to a higher mean storm tension ifneeded later.

OTC 16151 11

Figure 13 Fibre Rope Modeller and Rope Test Results Compared

Accumulated Elastic Stretch at Storm Tension TestIn preparation for this testing, calculate the platform

motion amplitude. The rope stiffness for this calculationmight be estimated with sufficient accuracy from generaldata on installed (broken-in) static rope stiffness.

Calculate the stretch in the most highly loaded mooringline caused by that platform amplitude. Call this theplatform amplitude-Induced mooring line stretch. Calculatethe strain in the mooring line at this stretch. Then calculatethe test specimen stretch corresponding to that strain. Callthis the platform amplitude-Induced test stretch.

In this test, the rope should be cycled about the positionof storm mean tension through an amplitude plus/minus theplatform-motion-induced test stretch. Cycle at approxi-mately the same frequency as expected for platformresponse to the storm conditions.

On each cycle, measure the specimen stretch at thepeak, mean, and trough as accurately as possible. Plot thetotal stretch at mean tension on each cycle on a semi-logplot against number of cycles or against time. The in-crease in stretch above the stretch which was measured atthe storm mean tension is accumulated elastic stretch.

Experience indicates that accumulated elastic stretchincreases rapidly at the start of cycling to a higher meantension, but that it reaches a “steady state” within about100 cycles. But it will be necessary to continue this test inorder to determine the dynamic stiffness rate of change.

Dynamic Stiffness TestDuring the above storm tension test, calculate the slope

of the dynamic stiffness curve between the trough andpeak on each cycle. This is dynamic stiffness. Experiencehas shown that, unlike stretch, the dynamic stiffnesscontinues to increase with number of cycles, although at adecreasing rate.

Plot this dynamic stiffness slope against cycles on asemilog graph until enough data is taken to confidently plota straight line. Then use these data to derive an equationfor calculating the late storm dynamic stiffness after anyreasonable storm duration.

Calculating Rope Performance Through ComputerModeling

The change-in-length properties of large synthetic fiberropes can now be calculated using the Fibre Rope Modeller(FRM) computer program.14 FRM calculates the tension-stretch and torque-twist behavior of a rope using the basicfiber or yarn properties and the rope construction details.

The FRM program was specifically developed to modelsynthetic fiber ropes. It can model laid (helical), braided,and parallel-element rope constructions. In addition to thestress-strain and break strength (tenacity) characteristicsof the fiber or yarn, it accounts for hysteresis, abrasion,fatigue, and creep. In modeling the rope construction, itaccounts for the shape, packing and compaction ofstrands. It includes the effects of friction, which inhibits or

permits relative motion between strands other rope ele-ments. It accounts for changes in lay length brought aboutby compaction, movement, and stretch of elements.

In modeling the rope, FRM imposes a given stretch(extension) on the rope and calculates the correspondingstretch in strands and yarns. It then uses the properties ofthe yarn to calculate the tension resulting from that givenstretch. Because the program’s basic input is stretch, it iswell suited for calculating the tension which results from thestretch induced by a given platform amplitude motion, asdiscussed above.

For a given applied tension, FRM uses an iterativeprocedure to calculate the resulting rope stretch. It cancalculate new rope strength. It can calculate the very long-time strength loss caused by internal abrasion, whichtesting has shown to be the principal cause of strengthreduction during cycling of polyester ropes.. .

Demonstration of Computer Program ResultsFigure 13 compares the results of cyclic testing of a

large subrope with modeling calculations for that samerope. The subrope was taken from a polyester rope whichhad been used for six months in an offshore mooring. This42 mm dia. subrope was twelve-strand braided construc-tion with a new break strength of 144,000 lb (642 kN).

The plot shows tension vs. time for 100 seconds. Notethat the ordinate (tension) begins at 100 kN instead of zero.The agreement between the measured and calculatedresults is very good. Because of dynamics and difficultieswith measuring actual rope tension, the calculated resultsmay be more accurate than the measured test results

Versatility of Rope Computer Modeling.A computer model for a general rope design, material

and construction can be developed and verified throughcomparisons with rope test data,. That rope model then bealtered to model other similar rope designs, for example bychanging strand size, lay length, or yarn properties.

12 OTC 16151

If a similar computer model has not already beenverified, it will be necessary to conduct a brief rope test, butthat verification test does not need to be as extensive orelaborate as the prototype rope test program describedabove.

The verified rope computer model can then be used topredict change-in-length characteristics for any othertension-time or stretch-time history. The program can alsobe used to analyze other similar ropes by inputing differentyarn properties or by changing design parameters such asnumbers of yarns and lay length. The characteristics ofother rope designs can then be predicted without having toconduct more testing.

Use of Rope Computer Model in Mooring AnalysisA verified rope computer model can easily calculate the

change-in-length properties needed to perform a mootingsystem design analysis. A rope test will only be necssaryif a computer model for a similar type of rope has notalready been validated. This requires only a short testwhich is not as complicated at the test procedure describedabove.

The rope computer program model can be run tosimulate any mooring situation. The model can be used tosimulate the entire sequence of installation tensions. It canbe used to investigate alternative sequences. It can beused to investigate other installed tensions. It can be usedto simulate the effects of various storm scenarios Thecomputer program can also be used to calculate the newand used strength characteristics of the rope. After themooring line is in service, it can be used to simulate theeffects of the normal and storm conditions actually experi-enced at the mooring location over time.

It will still probably be necessary to conduct a test on theactual rope, taken from early production. The actual ropeperformance would be compared with the performancecalculated by the computer program. This validationshould not require an elaborate rope test program. If theperformance of that production rope differ from the model,then the computer model can be adjusted accordingly andto then rerun to calculate the complete set of performancecharacteristics. These performance characteristics wouldthen be used to conduct a final mooring system analysis.

CONCLUSIONSAccumulated elastic stretch has a significant influence

on the dynamic stretch and stiffness characteristics ofpolyester ropes and probably other fiber ropes. Accumula-tive elastic stretch takes place whenever the rope is cycled.

Accumulated elastic stretch causes the rope to tempo-rarily become stiffer and to stretch more. It quickly accu-mulates whenever mean tension increases and thenreaches a “steady state”. It dissipates quickly when meantension decreases.

Dynamic stiffness increases during cycling whenevertension mean or amplitude increases. It increases quicklyat first, but unlike accumulated elastic stretch, dynamicstiffness continues to increase during cycling.

For the purposes of deepwater platform mooring systemoffset and maximum tension analyses, constructionalstretch (bedding in) is of little significance because most ofit takes place during the installation process.

For the purposes of deepwater platform mooring systemdesign, creep is of little significance (except in the case ofHMPE rope) because much of it takes place during theinstallation process.

Other than the effects of constructional stretch andcreep, the rope is not affected by its past loading history,After cycling at a high tension mean and amplitude andthen returning to a lower tension mean or amplitude, thestretch and stiffness characteristics of the rope quicklyreturn to those associated with that lower tension meanand amplitude. And the same is true after returning to ahigher tension mean and amplitude.

RECOMMENDATIONSThis paper makes recommendations on how to conduct

a mooring system analysis and on how to use a rope testprogram or a computer program to determine the change-in-length properties needed to carry out that analysis.

These recommendations are preliminary, based on theknowledge and experiences of the authors. They shouldnot be taken as firm and final recommendations.

The recommended mooring system design methodshould be evaluated by others experienced in this field, andfurther improvements should be made.

The recommended prototype rope test proceduresshould be tried to make sure that they are practical andpracticable. Det Norske Vereitas has proposed a project toaccomplish these goals.15

Computer modeling should be used along with ropetesting to predict rope properties. A rope computer modelcan be validated with a short test program. It can then useto predict rope properties for many other tension scenariosand for other similar rope designs..

The authors urge that these recommendations beconsidered when the several fiber rope deepwater mooringguidelines are reviewed and rewritten. Those guidelinesshould be reviewed and rewritten in the near future toincorporate present knowledge and experience.

OTC 16151 13

AcknowledgmentsThe authors acknowledge Mr. Neil Casey of the National

Engineering Laboratory for his work in conducting andanalyzing the rope tests. The authors acknowledge Prof.John Hearle, Dr. Chris Leech and Mr. Nick O’Hear ofTension Technology International and Mr. Vidor Ahjem ofDet Norske Veritas for their contributions to this paper.

NomenclatureThe following terminology is used in this paper and is

recommended for the testing and analysis of synthetic fiberropes used in deepwater mooring systems. This terminol-ogy does not necessarily correspond to terminology usedin other papers, guidelines, standards or texts. Unfortu-nately, there is not universal agreement on such terms.For example, elongation and extension have oppositemeanings in ISO and ASTM textile standards; see stretchand strain here. And some terms accepted by the textileindustry would cause confusion in the maritime industry;see recovery here. Accumulated Elastic Stretch, AES: Elastic stretch whichdevelops and does not immediately contract during cyclicloading.Constructional Stretch: Stretch which is caused bychanges in the alignment, compaction, and lay length of therope structure under tension and which does not normallycontract when tension is released. Sometimes called“bedding in”.Contract, Contraction: Shortening of the rope towards itsoriginal length after tension is relieved. (The term “recov-ery” is more generally used, but in the marine industriesthis term implies removing an object from the water.)Creep: The combination of permanent stretch and elasticstretch in a rope under tension.Delayed stretch: That stretch which takes place aftertension is being applied but while tension is maintained.Delayed elastic stretch: The elastic stretch which takesplace while tension is maintained.Delayed elastic contraction: The contraction which takesplace after tension is relieved.Dynamic Stiffness Curve: The plot of stretch vs. tensionwhen the rope is loaded at a relatively fast rate, for exam-ple at wave frequency.Elastic Contraction: The contraction which takes placewhile and after tension is relieved.Elastic Stretch: Stretch which takes place under tensionbut which is recovered after tension is diminished orrelieved.Immediate Elastic Contraction: The contraction whichoccurs while tension is being relieved.Immediate Elastic Stretch: The elastic stretch which takesplace while tension is increasing.

Immediate Installation Stretch: That stretch which takesplace while the rope is being tensioned to installationtension.Immediate Installed Stretch: That stretch which remains inthe rope immediately after tension is reduced from installa-tion tension to installed tension.Immediate Stretch: That stretch which takes place whiletension is increasing.Initial Static Stiffness: The stiffness on the first tensioncycle.Installation Stretch: That stretch which takes place whilethe rope is maintained at maximum installation tension.Installation Tension: The maximum tension which is placedon the rope during the installation process. Installed Tension: That tension which is maintained on therope immediately after installation without the effects ofenvironmental forces applied to the platform.Installed Stretch: The stretch of the rope after the installa-tion process is completed and immediately after tension isreduced to installed tension.Later Installed Stretch: That stretch which remains in therope after it has contracted while being maintained at theinstalled tension after the installation process.Late Storm Dynamic Stiffness: The stiffness after the ropehas been cycled a number of times about the mean stormtension to the stretch produced by platform amplitude.Maximum Storm Stretch: The stretch produced by adding(or subtracting) the stretch produced in a particular mooringline by platform amplitude motion to the mean late stormstretch.Maximum Storm Tension: The tension produced bymaximum storm stretch, by following procedures describedin this paper.Mean Early Storm Stretch: The sum of installed stretch andstorm drift stretch, but excluding storm elastic stretch.Mean Late Storm Stretch: The sum of installed stretch,storm drift stretch, and storm elastic stretch.Offset: The movement of the platform induced by theenvironment from its normal position. Also the change inlength (stretch or contraction) produced in a particularmooring line by this platform offset.Permanent Stretch: Stretch which takes place undertension but which is not recovered after tension is relieved.Platform Amplitude: The amplitude of motion which theplatform experiences about its storm drift position due tothe storm environment.Platform Storm Drift: The mean offset of the platforminduced by the design storm environment. The designstorm environment might be either the effects of currenteddy or the combined effects of waves, wind and current.Platform-Motion-Induced Mooring Line Stretch Amplitude,PA: The stretch induced in a particular mooring line by theplatform motion caused by storm conditions.Platform-Motion-Induced Test Stretch Amplitude: Thestretch induced in the rope test specimen corresponding tothe greatest platform-motion-induced mooring line stretch

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1. .. "Certification of Synthetic Fibre Ropes for MooringSystems”, Bureau Veritas, Paris,1997

2. ..., "Standard for Certification of Offshore Mooring FibreRopes, Det Norske Veritas, Hovik, Norway, 1998

3. ...“Guidance Notes on the Application of Synthetic Ropes forOffshore Mooring”, American Bureau of Shipping, Houston,1999.

4. API, “Recommended Practice for Design, Manufacturing,Installation, and Maintenance of Synthetic Fiber Ropes forOffshore Mooring” RP 2SM, American Petroleum Institute,Washington, DC, 2001

5. ... “Deepwater Fiber Moorings, an Engineer's DesignGuide”, Nobel Denton Associates and Tension Technol-ogy International, London, 1999

6. Petrusaka, D.J., J.F. Geyer and A.Z. Ryan, “Mad Dog PolyesterMooring - Prototype Testing and Stiffness Model for Use inGlobal Performance Analysis”, OTC 16589, 2004 OffshoreTechnology Conference Proceedings, Offshore TechnologyConference, Richardson, TX, 2004

7. Petruska, D.J., J.F. Geyer, R.R.Ayers, and M.J. Craig, “MadDog Polyester Mooring – In Service Inspection and RopeManufacturing Quality Control”, OTC 16590, 2004 OffshoreTechnology Conference Proceedings, Offshore TechnologyConference, Richardson, TX, 2004

8. ... “High Technology Fibres for Deep Water Tethers and Moor-ings”, (Fibre Tethers 2000 JIP), Nobel Denton, National Engi-neering Laboratory, and Tension Technology International,London, 1995

9. Francois, M. and P. Davies, “Fibre Rope Deep Water Mooring:A Practical Model for the Analysis of Polyester MooringSystems”, Rio Oil and Gas Conference, IBP24700 (2000)

10. ..., “Testing and Optimisation of Full Scale Fibre FPS MooringLines” JIP Report, National Engineering Laboratory andTension Technology International, East Kilbride, UK, 1999

11. Casey, N.F. and S.J. Banfield, “Full-Scale Fiber DeepwaterMooring Ropes, Advancing the Knowledge of Spliced Sys-tems, OTC 14243, 2002 Offshore Technology ConferenceProceedings, Offshore Technology Conference, Richardson,TX, 2002.

12. Cordage Institute, “Test Methods for Fiber Ropes, Appendix A,Determining Change-In-Length Properties of Synthetic FiberRopes”, CI 1500, The Cordage Institute, Wayne, PA, 2002.

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15. ... “Improved Fiber-Mooring System Design Practices”,Joint Industry Project Proposal, Det Norske Veritas,Hovik, Norway, 2003

amplitude (using rope strain to relate relative specimenlength to length of actual mooring line).Post-Installation Contraction Curve: A plot of stretch vs.tension as tension is being reduced from the maximuminstallation tension after the installation process.Rope Storm Offset: The difference between the installedstretch and the stretch induced by the storm.Static Stiffness Curve: The plot of stretch vs. tension whenthe rope is loaded at a relatively slow rate, for examplewhen applying pretension during installation.Stretch: Change in length experienced by rope undertension. (The term “extension” is used by ASTM and someother American sources. The term “elongation” is used byISO and some other European sources. See also Strain.)Stiffness: The relationship between stretch and appliedtension.Storm Drift Stretch: The stretch induced in a mooring lineby the storm drift offset of the platform.Storm Elastic Stretch: The elastic stretch which occurswhen the rope is maintained at storm tension for the stormduration plus the accumulated elastic stretch which occurswhen the rope is cycled during the storm.Storm Offset: The offset of the platform which is inducedby the storm conditions.Strain: The ratio of change in length to original length. (Theterm “elongation” is used by ASTM and some otherAmerican sources. The term “extension” is used by ISOand some other European sources. See also Strain.)Tensioned Stretch: Stretch which takes place whiletension is applied and maintained. The sum of immediatestretch and delayed stretch.

References