OTC 7145

Impact of Coupled Analysis on GlobalDeep Water TLP’s

Performance

Sid Sircar, PMB Engineering Inc.; J,W. Kleinhans, BP Exploration Inc.PMB Engineering Inc.

Copyright 1993, Offshore Technology Conference

This paper wee presented at the 25th Annual OTC in Houston, Texas, U. S.A.,3-6 May 1993.

of

and Jitendra Prasad,

This peper was selected for presentation by the OTC Progrem Committee following review of information contained in an ebstract submitted by the author(s). Contents of the paper,as presented, hsve not been reviewed by the Offshore Technology Conference and are subject to correction by the author(s). The material, es presented, does not neceeserily reflecteny position of the Offshore Technofegy Conference or ite officers. Permissionto copy is restricted to an abstrsct of not more than 300 words. I)lustratlonsmay not be copied. The sbstractshould oentaln censplcuous acknowledgment of where and by whom the paper is presented,

ABSTRACT

This paper presents the results and conclusionsof a study whose objective was to determinewhether a “linear spring” analysis approach canadequately predict the global performancebehavior of a relatively large TLP in 3,000 ft ofwater for a typical Gulf of Mexico (GOM) site.“Coupled” and “linear spring” analyses of theTLP were performed using random timesimulation techniques in extreme, reducect-extreme and normal environments, with theTLP in the intact, one-compartment damagedand one-tendon removed conditions.

The results presented in this paper show that“coupled” analysis does not have significant

impact on the prediction of the total designresponses of the TLP. It however significantlyimpacts the prediction of the dynamic part ofdesign responses. k is further demonstratedthat for such TLPs, high-frequency resonantresponse of the tendons could significantlyimpact the strength and fatigue design of thesetendons.

References and figures at end of paper

103

lNTRODUCTIO~

Conventional approach to global analysis ofTension Leg Platforms (TLP) includes modelingthe tendons as simplified “linear springs”, i.e.,as straight rods having only axial stiffness. Itis also assumed that these tendons do notattract any hydrodynamic loads and have noinertia. This approach to TLP design is basedon the offshore industry’s past experience withdesign, operation and performance of TLPs inwater depths less than 2,000 ft (see reference1). More complex analytical studies and modeltest experience on these past projects haveconfirmed the validity of using the “linearspring” approach. One such complex analyticaltechnique is where the global analysis isperformed using a “coupled analysis” techniquein which each tendon is inodeled as a series ofbeam elements having axial and bendingstiffness and which are exposed tohydrodynamic loads and also have inertia.

In water depths 3,000 ft and more, limitedexperience exists in analyzing and modeltesting TLPs, Hence, it is not certain if thesimplified “linear spring” approach wouldproduce acceptable global analysis results ofsuch a TLP. API RP 2T (see reference 2) andother codes discuss this issue but do notprovide any clear guidance as to when“coupled” analysis is more applicable. Pastpublications on this topic (e.g. see Reference 3)have compared analytical methods which were

different in other ways besides the tendon

2 “IMPACTOFCOUPLEDANALYSISON GLOBALPERFORMANCEOF DEEPWATERTLP’S”OTC7145

mathematical model, This has resulted in notknowing with certainty whether the differencesbetween the responses predicted by these twomethods are significant enough to impact thedesign of one or more components of a TLP.

A study was initiated to determine whetherglobal analysis results of a 3,000 ft waterdepth TLP, using a “coupled analysis”technique would confirm “linear spring”analysis’ results. The focus of this study wasto investigate the differences in global analysisresults solely because of the differencesbetween the two types of tendon mathematicalmodels, as described above. To meet thisobjective, all other differences, such astimelfrequency-domain, wave theory,hydrodynamic theory, etc, were kept the samefor both analytical techniques. The results ofthis study are presented in this paper,

DESIGN BASIS

Studv Data

The overall TLP configuration used in this studyis shown in Figure 1. The principal dimensionsand major weight categories are summarized inTable 1. These particulars were developed inconjunction with non-site specific engineeringstudies as previously reported in Reference 4.To reduce the computational effort of thisstudy, all analysis were performed for the TLPwith no production or drilling risers installed.The total riser load shown in Table 1 wasreplaced with the same amount of ballast.

Env ironmental Criteria

The environmental criteria used in this study,defining the design wave statistics, windspeeds, current profiles and tides are shown inTable 2. To ensure that the theoreticallygenerated random wave elevation included themaximum wave, stochastic maximum waveheights were defined for the 100-year, 10-yearand 1-year return period storms.

~~f

Design load cases for this study were identified

based on a combination of past TLP designexperience and the design practicerecommended in API RP 2T. These design loadcases are shown in Table 3. For each loadcase, the TLP condition and the correspondingenvironmental criteria were selected to produceconservative estimates of maximum andminimum tendon tensions, maximum vesseloffset, minimum airgap and maximum tendonstress interaction ratio.

OBAL ANAL YSIS METHODOLOGY

Qmw ter Proaram Des criDtioq

All analytical work in this study were performedusing a Joint Industry developed computerprogram. It is a general purpose, non-linear,time-domain, dynamic analysis programdeveloped specifically for the design andanalysis of TLPs, semi-submersibles, CompliantTowers, fixed structures, etc. (see Reference5).

comDuter Model

The TLP configuration has port/starboardsymmetry in head, beam and quartering seas.All analysis were performed in quartering seassince this heading is expected to produce themost conservative results. To take advantageof the symmetry, only half the TLP about thequartering axis was modeled, In this model theX-axis is located at the center of the TLP andruns parallel to the quartering environmentalheading. Surge is defined as motions along theX-axis and pitch as rotations about a horizontalaxis perpendicular to the X-axis (see Figure 2).To take further advantage of the symmetry, allout-of-plane Degrees Of Freedom (DOF) wereconstrained, i.e. only surge, heave and pitchDOF were released. In the upstream anddownstream columns, only half the column andhalf the number of tendons were modeled, Forthe midstream column, the complete columnand all tendons were modeled, This symmetricmodel significantly reduced computer run timeswithout having to compromise on any of theanalyses results.

The hull structure was modeled with a series of

104

OTC7145 S. SIRCAR,J. W. KLEINHANS,AND J. PRASAD3

tubular beam elements as shown in Figure 2.The columns which are cut in half, weremodelled to represent one half the volume ofthe full column. Each pontoon was modeledwith tubular beam elements having differentcross section areas to represent the pontoonflare at the pontoon-to-column connection.The mass of the hull was modeled as lumpedmasses distributed to produce the correct totalmass and radii of gyration. Weights were alsosimilarly modeled as lumped weights.

The tendons at each column were representedby a single equivalent tendon consisting of:

● 28 tubular beam elements of equal 100ft lengths and one beam element 84 filong for the “coupled analysis” case.These elements have axial as well asbending stiffness. They attractpotential and viscous hydrodynamicforces and have inertia.

● One tubular weightless rod element2,884 ft long for the “linear spring”case. These elements have axialstiffness only. They do not attractpotential or viscous hydrodynamicforces and have no inertia.

The axial stiffness of the tendons was modeledto match the physical structure. The horizontalstiffness of the tendons is derived from thegeometric stiffness resulting from the axial loadin the tendons. For the tendons the programcomputes buoyancy and mass per unit length.For the TLP model where tendons are modeledas beam elements, the program computeshydrodynamic loads for these elements basedon user-defined inertia, added mass and dragcoefficients.

For the TLP model where tendons are modelledas “linear springs”, no hydrodynamiccoefficients were specified, In this model, one-third of the tendon’s mass was lumped at thetop node of each tendon to represent thetendon’s mass contribution,

Hvd odvr namic Model

Hydrodynamic loads on all elements were

105

generated using Morison’s equation, The dragand inertia coefficients used are shown below:

Element “Coupled” “Linear Spring”Cd CM Cd CM

Columns 0.7 2.0 0.7Pentat Midapan

2.01.75 2.2 1.75 2.2

pent. near COL 1.8 1.gTandons

1.8 1.91.4 2.0 0.0 0.0

The main objective of this study was todetermine whether the “coupled analysis”approach results in significantly different globalresponse behavior of the study TLP as

compared to the “linear spring” ana[YSiSpredictions. This necessitate using the samehydrodynamic forces for the two differentglobal analyses, In other words the objectivesof the study could be met irrespective of whichhydrodynamic theory was used. It is for thisreason that the computationally more efficientMorison’s equation (see Reference 6) wasselected for hydrodynamic load generationinstead of the more time consuming first-order,three dimensional, diffraction theory (seeReference 7).

Since the pontoons of this TLP configurationhave varying cross section area and shapealong their lengths between the columns, theywere modeled with two different memberproperties representing more closely the actualconfiguration.

Wind. Current And Wave Induce d Forces

In this study the wind, current and the variouscomponents of wave induced forces wereobtained from a combination of directcomputations by the program or defined by theuser in the program. The following tableidentifies the sources of origin of these forces:

Based on past model test experience of TLPs,the potential component of low-frequencyoffset was estimated to be +/-1 O ft for allcombinations of TLP and environmentalconditions, This estimate is reasonable if it isadded directly to the wave-induced offset ascalculated by the program. For the maximumoffset, maximum tension and maximum tendonstress ratio design cases, it is conservatively

4

as

“IMPACT OF COUPLED ANALYSIS ON GLOBAL PERFORMANCE OF DEEP WATER TLP’S”OTC 7145 I

Fbrce Co~onent Rogrern userDefinedvalue

Mean IMnd Force x

Maan Currant Fbrca x

Mean Wave Drift Force

-R2tantial Component x-Viscous Cotnponant x

Wava-fraquancy Force

-Fbtentkl Co~onent x-V13cousComponent x

Low-frequancy t%rce

-R2tentisi Co~onant x-VkOUs Component x

med that this low-frequency offset adds tothe total offset, However, for the minimumtension design case it is assumed that the low-frequency offset subtracts from the totaloffset.

The assumption of 10 ft low-frequency offsetfor all environmental conditions is consistentwith the fact that wave drift force is directlyproportional to the square of the wave heightand inversely proportional to the square of thewave period,

Wave Kine*

All analysis performed in this study were basedon random wave simulation in time-domain.“Wheeler Stretching” (see Reference 8) wasused to define the water particle kinematics.Since Morison’s equation was used for

computing wave loads, all loads werecomputed in a consistent manner up to theinstantaneous wave elevation. Conversely,even if second-order diffraction theory (seeReference 9) was used, all first-order and mostsecond-order potential forces, would becomputed only up to the still water line.

Figure 3 show the time history of waveelevations and its spectral representation forthe 100-year storm condition.

A time step of 0.5 seconds was adopted for allruns. This time step modeled wave componentswith periods as low as 3 seconds adequately,and provided reasonably good resolution for thewave spectral peak period of about 16seconds. Several computer test runs weremade with 0,2 second time step to confirmthese assumptions.

“LINEAR SPRINGW ANALYSIS RESULTS

Maxim urn Offse t Desian Case

Global analysis results for the maximum offsetdesign case (defined in Table 3) is summarizedin Table 4. The variation of surge offset withtime is shown in Figure 4. The maximumdynamic offset of 41 ft includes both wave-frequency and low-frequency components andincludes both potential and viscouscontributions, Minimum airgap correspondingto this maximum offset position is 7,5 ft,measured to the underside of the ModuleSupport Frame (MSF). In this calculation it isassumed that the maximum wave crest heightis 41 ft (57% of the maximum design waveheight). The maximum angle made by theupstream and the downstream tendons (at thetop and bottom of the tendons) to the verticalis 6.84 degrees, The “linear spring” TLP modelassumes that the tendons remain straight at alltimes, This results in the tendon angle beingthe same at the top and the bottom of thetendons,

Maximum Tendon Tension Desian Case

Global analysis results for the maximum tendontension design case (defined in Table 3) aresummarized in Table 5, The tension results arefor the upstream tendons and are per TLPcolumn. The maximum tide condition is used(as compared to the minimum tide condition)since it produces maximum tendon tension dueto the increase in water elevation resulting inincreased hull buoyancy, Figure 5 shows amagnified view of the upstream tendon tension

106

OTC 7145 S. SIRCAR,J. W. KLEINHANS,AND J. PRASAD5

time history for this 100-year storm case.Evidence of “springing” contribution due tosecond-order viscous forces can be seen in thisfigure. The total dynamic tension of 3,194 S.Tons shown above includes wave-frequency,low-frequency and high-frequency componentsof tension response. Wave-frequency and low-frequency computations include both thepotential and viscous force contributions.High-frequency tension response includes onlyViSCOUS fOrCe contribution since thecomputation of second-order potential forceswas outside the scope of this study.

Minimum airgap calculation results show thatthe minimum Airgap corresponding to thisoffset position is 2,2 ft. For this particular TLPwith a specified maximum tide of 6 ft,minimum airgap is obtained for the maximumtendon tension design case instead of themaximum offset design case.

Minimum Tendon Tension De sifm Cas~

Global analysis results for the minimum tendontension design case (defined in Table 3) aresummarized in Table 6. The tension results arefor the downstream tendons and are per TLPcolumn. The minimum tide condition is used(aS compared to the maximum tide condition)since it produces minimum tension due to thedecrease in water elevation resulting in reducedhull buoyancy. Figure 6 shows a magnifiedview of the downstream tendon tension timehistory for this 10-year storm case with onedownstream compartment flooded. Evidenceof significant “springing” contribution due tosecond-order viscous forces can be seen in thisfigure. The total dynamic tension of 1,027 S,Tons shown above includes wave-frequency,low-frequency and high-frequency componentsof tension response.

The minimum tension of 297 S.Tons (percolumn) is at the bottom of the tendons.

M im Tn r~as~

Global analysis results for the maximum tendonstress ratio design case (defined in Table 3) issummarized in Table 7. This design case has

one upstream tendon removed and is exposed

to 1-year storm condition. Figure 7 shows amagnified view of the upstream tendon tension(per column) time history for this design case.The results in Table 7 are for one tendon andthe results in the Figure 7 are per column.Maximum tide condition (as compared tominimum tide condition) is used since it

produces maximum tension stress ratio due tothe increase in water elevation resulting inincreased hull buoyancy. It can be seen fromthis figure that “springing” contribution todynamic tension, due to second-order viscousforces, is almost as significant as wave-frequency contribution.

#~uLT~

For the “coupled” analysis, the “linear spring”computer model was modified by replacingeach single tubular rod element tendon with astring of 28 beam elements having axial andbending stiffness, All other aspects of theanalysis was kept the same.

Global analysis results for the maximum offset,maximum tension and minimum airgap,minimum tension and maximum tension stressratio design cases are summarized in Tables 4,5, 6 and 7 respectively. Time history of offsetand tendon tensions for these four designcases are shown in Figures 4, 5, 6 and 7respectively. All discussions regarding theresults presented in the previous section areequally applicable for these “coupled” analysisresults and hence will not be repeated.

cOMPARISON OF RESULTS

QZ!QGl!

A comparison of global analysis results usingthe “linear spring” and “coupled analysis”approach is presented in this section. Theparameters compared are maximum designoffset, minimum airgap, maximum angle madeby the tendon to the vertical, maximum designtension, minimum design tension and maximumtendon stress interaction ratio, All resultspresented under the column “Difference” inTables 4 through 7, are in comparison to the“linear spring” results,

107

6 “IMPACT OF COUPLED ANALYSIS ON GLOBAL PERFORMANCE OF DEEP WATER TLP’S”OTC 7145

MJ!dtxi

Table 4 shows a comparison of maximumoffset results. It may be noted that eventhough a large difference exists in theprediction of the dynamic offset, the “coupledanalysis” approach prediction of maximumdesign offset is only 5,5% greater than the“linear spring” approach. Minimum airgapresults for this design case show that the“coupled analysis” approach predicts 2,4 ft lessairgap than the “linear spring” approach. Thisis primarily due to the difference in setdowncaused by the difference in maximum designoffset. This difference though small, couldimpact the feasibility of a selectedconfiguration.

Table 4 also shows that the difference in theresults of tendon top angle is negligible (1.8%).However the difference in the prediction of thetendon bottom angle is quite significant(35.8%). This could impact the design of thefoundation templates.

These results indicate that when computingmaximum offset, minimum airgap and tendonangle it may not be conservative to use the“linear spring” approach.

M im.-Q

A comparison of maximum tendon tensionresults presented in Table 5 show that the“coupled analysis” approach predicts 20.2%more mean tension and 51.4% less dynamictension. However, the difference in theprediction of maximum design tension is only4.1 %. This indicates that the “linear spring”approach produces conservative maximumtension. Similar to the maximum offset designcase, Table 5 shows that the “coupledanalysis” approach predicts 2.1 ft less airgapthan the “linear spring” approach.

~inimum Tendon Tens[~.

A comparison of minimum tendon tensionresults presented in Table 6 shows that the“coupled analysis” approach predicts 11 .6%less mean tension and 22.1 % less dynamic

108

tension. This results in a difference in theprediction of minimum design tension of 73 S.tons indicating that it is conservative to use the“linear spring” approach.

Ma ximum Tendon Stress RatiQ

Similar to the maximum tendon tension designcase, maximum tendon stress ratio resultspresented in Table 7 show that the “coupledanalysis” approach predicts 22.8% more meantension and 33,8% less dynamic tension.However the difference in the prediction ofmaximum tendon stress ratio is only 4.9%. Forthis design case results indicate that it is

unconservative to use the “linear ‘sp&9;approach.

N4 PACT ON DESIGN

To determine whether the results presentedabove impacts the design of any of thecomponents of the study TLP, a comparison ofthe overall design values was made and aresummarized in Table 8. The following areobserved from this table:

1. “Linear spring” approach under-predictsmaximum design offset by about 5.5%,As a result, minimum airgap is alsounder-predicted by about 2.1 ft. If“linear spring” analysis is used, this

discrepancy can be rectified byincluding a 5% to 6% margin in themaximum design offset calculations,

2. “Linear spring” approach under-predictsmaximum tendon top angle by 1.8%(O. 12 deg). It under-predicts maximumtendon bottom angle by 35,8% (2.45deg). This, however, is not consideredto be a problem since as part ofconventional tendon design procedure,it is common practice to perform abeam element analysis of a “stand-alone” tendon. Such an analysisproduces the correct tendon top andbottom angles. It should be noted thatthese more realistic tendon anglesshould be used to develop the inplacefoundation template design loads and

OTC 7145 S. SIRCAR, J. W. KLEINHANS, AND J. PRASAD7

3,

tendon top and bottom connectordesign.

“Linear spring” approach over-predictsmaximum tendon tension by 4.1% ofmaximum design tension. Minimumtendon tension is also over-predicted by1.8% of tendon pretension. Theseresults indicate that the “Linear spring”approach results in a conservativeselection of tendon pretension.

4. “Linear spring” approach under-predictsmaximum tendon stress interactionratio by 4.9%. This is not consideredto be a problem since as part ofconventional tendon design procedure,it is common practice to perform abeam element analysis of a “stand-alone” tendon, Such an analysis willproduce the correct tendon stress ratio.

lMP CT OA F TENDON “SPRINGING”

Dynamic tendon tension variation at highfrequency is a resonant response of the TLP inheave, pitch and roll DOF. These responses areproduced as a result of second-order potentialand viscous exciting forces. As mentionedearlier, only the viscous part of these forceswere included in the mathematical formulationsin this study.

Past experience with advanced analyticaltechniques have shown that higher the contentof shorter waves in a seastate, greater is thepossibility of “springing” contribution to totaldynamic tension, In other words a 1-yearstorm is expected to show a highercontribution from “springing” as compared to a100-year storm. Results presented in Figures5, 6 and 7 confirm this observation, Theseresults show that tension contribution from“springing” is significant for the 1-year storm,moderate for the 10-year storm and minimal forthe 100-year storm.

For this particular study TLP, the 1-year stormcombined with one-tendon removed load case,

produced the highest tendon stress ratio, From

this it can be concluded that for this TLP

“springing” impacts tendon strength design,Although fatigue analysis was not performed aspart of this study, from the above observation,it can be concluded that “springing” isexpected to significantly shorten the fatigue lifeof the tendons.

SUMMA RY AND CONCLUSION~

Global analysis results performed as part of thisstudy showed the following:

● “Linear spring” approach to globalanalysis for the study TLP in 3,000 ftof water, produces reasonable results.

● Using this analysis approach, themaximum and minimum design tendontension estimates appear to beconservative.

● Using the “Linear spring” approach,estimates of maximum offset andminimum airgap is determined not to beconservative. However, this can beresolved by allowing for an offsetmargin of about 5%. If a “coupledanalysis” approach is used, this marginwould not be required,

● “Linear spring” analysis under-predictsmaximum tendon angle at the top andat the bottom.

● This analysis approach under-predictsmaximum tendon stress interactionratio. This is not considered to be aproblem since as part of conventionaltendon design procedure, it is commonpractice to perform a beam elementanalysis of a “stand-alone” tendon.Such an analysis will produce thecorrect tendon angles and stress ratios.

c Resonant response i.e. “springing” ofthe tendons, impacts both tendonstrength and fatigue life.

● “Springing” contribution to totaldynamic tension is found to besignificant for a 1-year storm and less

significant for a 100-year storm

109

-

8 “IMPACT OF COUPLED ANALYSIS ON GLOBAL PERFORMANCE OF DEEP WATER TLP’S”OTC 7145

environment.

ACKNOWLEDGMENT

This work was commissioned by BP ExplorationInc. The authors would like to thank BPExploration for their support of this work andfor permission to publish these results.

BEFERENCE~

1.

2,

3.

4.

5.

6.

7.

8,

9.

Sircar S., Rager B.L., Praught M. W.,and Adams C. J,, ‘A Consistent Methodfor Motions, Strength and FatigueAnalysis of TLP’s”, Proceedings of 7thOMAE Conference, 1988.

API RP 2T, Recommended Practice forPlanning, Designing and ConstructingTension Leg Platforms,

Davies K, B. and Mungall J. C. H,,“Methods for Coupled Analysis ofTLPs”, OTC 6567, 1991.

Rajabi F, D,, Kleinhans J. W., “A newapproach for TLP Installation in the Gulfof Mexico”, OTC 6900, 1992.

SEASTAR User’s Manual, PMBEngineering, 1986.

Morrison J. R., O’Brien, M. P., Johnson,J,W. and Shaaf, S, A,, “The ForcesExerted by Surface Waves on Piles”,Petroleum Transactions, ASME Vol.189, 1950, pp. 149-154.

Garrison, C.J., “Hydrodynamics of largeDisplacement Fixed and Floating

Structures in Waves”, Report No, 80-102, December 1980, C.J. Garrison &Assoc.

Wheeler J, D,, “Method for CalculatingForces Produced by Irregular Waves”,Journal of Petroleum Technology,March 1970.

Williams, A. N., “Nonlinear DiffractionEffects on TLPs”, Tension Leg Platform

110

- A state of the Art Review, Edited bvZeki Demirbilek, 1988, ASCE Wave andWave Forces Committee.

I

I

DESCRIPTION VALUE

VESSEL CONFIGURATION

Deoksize(ftxft) 225 X2SSNo. of Columns &) 4Column Spaoing @) 210 x 210Column Diameter (ft) 88Column Height (ft) 185.5Pontoon Crose Seotion Shape ReotangloPontoon Width (ft) 32Pontoon Height (ft) 28.6Ckaft @) 116

Total No. of Tendon$ 16Tendon Length @) 2,878Tendon O,D. (in) 28Tendon W,T. (in) 1,4375Total Tendon Weight in Air (S.T.) 9,880Tendon Buoyancy (S.T,) 5,728

WEIGHT~

l-lullSteelWeight (S.T.) 18,220Deok Steel Weight (S.T.) 7,377Hull Syetems Weight (S.T.) 3,87813affaat(S,T.) 4,717Total Operating Payload (S.T.) 9,8s8Total F&or bad (S.T.) 7,852Total Tendon Tension (S.T.) 16,208

DISPiACEMENT (S,T.) 67,708

I

TABLE 2: ENVIRONMENTAL CRITERIA

DESCRIPTION 100 YEAR ~REDUCED NORWLUNIT

EDDY

STORM yoyME OPERATION CURRENTEVEN

Max. Wave Height FrASS. WaV8 Period

H I 48.9 30.0 30,0SEC , I 12.0 9.1 9.1

Spectrum

HsPM

FrTz ;.: [ z: ‘M ‘M160

SEC16.0

Duration~~s I 2:0 [ 4.4 g ::

Tide j

High w, r. t. MLWFf + &o \ + 1.0 + 3.5

Low w. r. t. MLW + 3,5Fr -2.0 / -1.0 -1.0 -1.0

IWind

(1/6 power Law, measured

@ +33 (F7J Abwe MLW)I1 ! i I

1- min. Avg, MPH 115.0 ~ 78.0 53.01 - hour Avg. MPH53.0

98.0

I67.o 45.0

5- sec. Gust 45.0MPH 129.0 68.0 59.0 59.0

Current ILinearly hterpola!ed

Surface

Elev. -1OU (,7)

Elev. -200 (~

Elev. 400 (r=7)

Elev. -1,000 (F7)

Bonom

IT/ SEC 4.3 3.3- / SEC 3.3 2.6fl / SEC 2.4 1.9~ j SEC 0.4 0.4F7 f SEC 0.2 0.2~ j SEC 0.1 0.1

2.7

2.2

1.7

0.7

0.3

0.1

6.0

5.8

3.5

2.0

1.0

0.2I I I I I

TABU 3: DESIGN LOAD CASES

Maximum Minimum Maximum Max TonrfonEnvironment & TLP Condition Torraiors Caso Tonaion Caao Offaat Caae Stroaa Ratio Caae

TLP Condition Intact One Compart. Intact One TandonDamage Ramowsd

No. of Riaara None None None None

Storm Return Period 100-yaar 1O-yaar 100-yaar 1-year

Wind Spaad 1-minute mean 1-hour meen 1-minute maan 1-minuta maan

Tida Lavel Max Tide Min Tide Min Tide Max Tida

Environment Heading Quart. Quart. Quart. Quart.

Low-frequancy Potential Wave Drift Offset +10’ -1o’ +10’ +10’

111

I

TAELS 4 MAX3MW OFFSET DESIGN CMS

IITEM DESCRIPTION

!

“LINEAR SUUN& “COUPLED● DIFFERENCERESULTS RESULTS n

MW’I Offnt 302 n 302 tt o%

Total Dynamic Off-t 41 ft Wft + 48.3 %

Max. Duign Off-t 343 it 362 fi + 6.6 %

Min. Airgap to MSF 7.6 ft 5.1 ft -2.4 ft

Max. Tandon TOP AWb 6.s4 dq. 6.96 &g. + 1.s%

Max. Tin-don Sottom hgh 6.S4 ckfj. 9.29 &g. + 36,S %

TASLS C: MWIMm TENsIoN DEsIGN CASE

ITEM DESCRIPTION “UNIX? SPRINO” “COUPLW” DIFFERENCERESULTS RESULTS

Mean T~”on + 1,324 ST + 1,170ST -11.s%

I‘ Total Dyrumic Tuwion -1,027 ST - Soo ST -22.1 %

Min. Tendon + 297 ST . a7n @’l- ,--- 1

TASLS 8: MA)OMUM TSNSION DSSIDN CASE

IITEM DESCRIPTION “LINEAR SPRIN& 9COUPLEO- DIFFERENCE

RESULTS RESULTS1

M,an Tbnoh 6,220 ST 7,477 ST + 20.2 %

Total %wllic Termkm 3,1 S4 ST 1,662 ST -61.4 %

M@x. Tumion 9,414 ST S,020 ST -4.1 %

Min. Akgap te MsF 2.2 n 0.1 ft -2.1 ft

TASL67: MAXIMW TENDON STRESS RATIO DESNIN CASS

ITEM DESCRIPTION ‘LINEAR SPRING” “COUPLED* DIFFERENCERESULTS RESULTS

Totsi Mebn Twmion 1,327 ST 1,630 ST + 22.s %

Total Dyrwnic T,mion 6s2 ST 3s5 ST - 33.s %

Mm. Tumica 1,90!3 ST 2,016 ST 6.6 %

Mu. Straaa Ratio 0.82 0.86 ST + 4.s %

T~LE S: IMPACT OF DLOBAL PERFORMANCE

ITEM DESCRIPTION ‘LINEAR SPRING- “COUPLEDANALYSIS DIFFERENcERESULTS RESULTS

Max. IMsign Offset 343 ft 362 tt + 6,6 %

MaN Tmd.m Top Anglc 6.S4 chg. 6.9S d~. + 1.8%

Max. Tmdon Sottcm AKIIe 6.S4 (k)& 8.29 (kg. + 36.s %

Min. Airgqj to MSF 2.2 ft 0.1 ft -2.1 ft

Max. Dasign Tension S,414 ST S,029 ST -4.1 %

Min. Dadgn Teruhn + 297 ST + 370 ST + 1.s%

Max. Daign StraOS R.tiO 0.s2‘b 0,S6 + 4,9 ?4

I

112

,,,,,, ,, ),,,,

00

I

‘. /“

E. ,...<,/,

x, .

/ .

\,. .

.-

It

v2‘a.00 80 16C 2$0 320 400 480 560Time (see) 640 720 800 88o

FIGURE 4: SURGE OFFSET TIM HISTORY

1

“LinearSpring”z62o 64o 660 66o 7@o 720 140m,.-..,. .— i 760

s “CoupledAnalysis”.660 680 700 720 740 760

Time (Se=)780 Eho

FIGURE 5: UPSTREAM TENDON TENSION IN 1W-YEAR STORM

114

—. . . .

I

I

I

I

d “Unear Spring”660 680 700 720 740 76o

Time (see)780 8bo

Iysis’

FIGURE & DOWNSTREAM TENDON TENSION IN 1O-YEAR STORM

115

! “Unear Spring”:860 880 900 92!? 940 96o 98o 1001Time (see)

e

“CoupledAnaiysis”:76o 78o 800 820 840

Time (see)860 880 900

FIGURE 7: MAXIMUM TENSION STRESS RATlO CASE

I

I

I

I