OPT98 Fatigue Design-DNV-Guideline-Free Spanning Pipelines

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OPT'98Offshore Pipeline TechnologyOslo, 23-2-' February, 1998

FATIGUE DESIGN ACCORDING TO THE DNV GUIDELINEFOR FREE SPANNING PIPELINES

Kim J. Mark &Olav FyrileivDet Norske Veritas

ABSTRACTAn official DNV GUIDELINE (draft version) for free spanning pipelines has been issued inDecember 1997. The premises are based on the technical development within pipeline freespan technology in recent design and R&D projects performed by Danish HydraulicInstitute, Snamprogetti SpA and Det Norske Veritas.

The objective of the Guideline is to provide rational design criteria and guidance on fatiguedesign methods for free spans subjected to combined wave and current loading.This paper will give a brief introduction to the guideline with emphasis on the safetyphilosophy and relation to DNV Rules for Submarine Pipelines Systems. In particular thepaper provides an introduction to the detailed fatigue design criteria related to combinedin-line VIV and direct wave loading. Further a response model and acceptance criterion forcross-flow Vortex Induced Vibrations (VIV) will be presented.

An example on the use of the guideline will be given.

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INTRODUCTION

Free spans often become a problem in pipeline design and operation due to unevenseabed or seabed scouring effects. The costs related to seabed correction and spanintervention is often considerable. On the other hand the potential cost related to a fatiguefailure of the pipeline are enormous. However, free spans are normally designed applyingunduly conservative concepts and often very simple analytical tools.Therefore, a free span strategy that ensures an acceptable safety level at a minimum ofcosts is needed. Such a strategy must include accurate calculation methods and state-of-art acceptance criteria. In particular, analysis tools and empirical models calibrated againsttest data !o predict fr~e span vibration of. pipes exposed to various flow conditions have

'. .~received increased attention in recent years.A new DNV Guideline for free spanning pipelines has been issued recently. The objectiveof the Guideline is to provide rational state-of-the-art design criteria and guidance onfatigue design methods for free spans subjected to combined wave and current loading.The premises for the Guideline are based on the technical development within pipeline freespan technology in recent R&D projects as well as design experience from recent andongoing projects, see e.g. (Tura et ai, 1994) and (Merk et ai, 1997).The safety philosophy adopted applies the concept of safety classes and is in fullcompliance with the DNV Rules for Submarine Pipeline Systems, (DNV, 1996). The basicprinciples are in agreement with most recognised rules and reflect state-of-the-art industrypractice and latest research.

Detailed design criteria are specified for fatigue analyses due to in-line and cross-flowVortex Induced Vibrations (VIV). The following topics are considered Methodologies for free span analysis Requirements to structural modelling Geotechnical conditions covering cohesive soils (clay) and Cohesionless soils (sand) Environmental conditions & loads Recommendations for fatigue analysis Response and direct wave force analysis models

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Acceptance criteriaThe objective of this paper is to give an introduction to the detailed fatigue design criteriarelated to combined in-line VIV and direct wave loading. The design procedure will beillustrated by an example. A more detailed discussion of the technical background anddesign principles reflected in the Guideline may be found in M0rk et aI., 1998.

DESIGN PHILOSOPHY

Acceptance Criteria:

The fatigue damage assessment is to be based on the accumulation law by Palmgren-Miner:

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The reliability of the pipeline against fatigue loads is ensured by use of the safety classconcept The safety class concept accounts for the failure consequences and is adopted inthe DNV'96 Rules for Submarine Pipeline Systems.The following safety factor format are used:

YI,Yk and Y5denote partial safety factors for the natural frequency, damping (stabilityparameter) and stress range, respectively. The set of partial safety factors to be appliedare specified in the table below for the individual safety classes:

Safety Class Low Normal High

Tj 0.6

YI 1.3

Yk 1.3

Y5 1.05 1.30 1.55

In addition, a reduction factor \.(JR=0.9may be multiplied to Y5if the free span is well defined,e.g. with well defined boundary conditions, where the free span length and consequentlythe natural frequency is insensitive to changes in the functional loads.

Recent industry practice imply Tjold=0.1in case of no access and Tjold=0.3in case of accesscombined with Yf=Yk=Ys=1.0using somewhat different response models e.g. as reflected in(DNV'81). Usually the case TJold=0.3s not allowed for submarine pipelines in practice ..

Detailed studies have revealed that existing practice, although acceptable on averageprovides design with very varying reliability levels dependent on the stability parameter,natural frequency, stress amplitudes, etc.

The design format specified herein appties a set of 4 safety factors in order to control thesedominant uncertainty sources rather than one usage factor, 11.Due to this, the proposeddesign format is more flexible and provides design with a more uniform reliability levels

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. compared to industry practice. On average the difference in the resulting safety level is)minor when applying appropriate response models for the "old" industry practice and theapproach proposed herein.Note that the present format does not explicitly distinguish between access and no accessbut rather implicitly through the use of a safety class philosophy.For the in-line VIV acceptance criterion the above set of safety factors have beencalibrated to specified target reliability levels in compliance with the safety requirements inDNV'96 using a reliability based approach, see M0rk et a/., 1997. The safety factors 11andY s are considered to be valid in general while appropriate values for Y f and Y k should beevaluated on a case to case basis for the remaining criteria.

LOADING PHENOl\IENA

An assessment of a free spanning pipeline should consider the following loadingphenomena: Vortex Induced Vibrations Direct wave loads Sea-bed proximity EffectsAn amplitude response model may be applied when the vibrations of the free span aredominated by vortex induced resonance phenomena, while a force mode! may be usedwhen the free span response can be found through application of calibrated hydrodynamicloads. The selection of an appropriate model may be based on the prevailing flow regimes.In principle, force models may be used for both vortex induced and direct wave and currentdominated loads provided that appropriate formulations of force models exist and reliableand consistent data are available for calibration.

Vortex Induced Vibrations:

Vortex induced vibrations are mainly controlled by the following parameters:

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The reduced velocity, VR ,(5)

Here given in the general case with combined current and wave induced flow velocity. fo isthe natural frequency for a given vibration mode, 0 is the pipe diameter, Uc is the currentvelocity and Uw is the wave induced velocity (amplitude) at the pipe level.

(6)

The Keulegan-Carpenter number, KC :

where fw is the wave frequency ..For regular wave motion the vortex shedding frequency willbe a multiple of the wave frequency. In irregular wave motion, vortex flow regimes undergosubstantial changes and the resonance between wave frequency and vortex frequency isnot fully developed. The current flow velocity ratio, a :

(7)

Note that a=O correspond to pure oscillatory flow due to waves and a=1 correspond to pure(steady) current flow. Thus, amay be applied to classify the flow.

Response amplitudes are affected by damping. The damping is most often reflected by the(modal) stability parameter:

(8)

p is the water density, me is the effective mass including structural mass, added mass andmass of internal fluid. t : r is the total modal damping ratio at a given vibration modecomprising structural damping, soil damping and hydrodynamic damping, i.e. drag dampingoutside the lock-in region for the pipe.

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Direct wave loading:

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)The in-line force per unit length of a pipe free span is normally determined using theMorison's equation where the drag and inertia coefficient is given by:

CD = CD(R~,KC,Ct,(e/O)~(k!R},(ZIDC~I= C~JR", KC, o, (e l D), (k I D

(9)

R, is the Reynolds number, (e/O) is the gap ratio, (kiD) is the pipe roughness and (ZlO) isthe cross-flow vibration amplitude.

Sea-bed Proximity:

The presence of a fixed boundary near the pipe (for e/D


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The local fatigue design checks are to be performed at all free spanning pipe sectionsaccounting for damage contributions from all potential vibration modes related to the actualand neighbouring spans.Acceptance Criteria:When several potential vibration modes may become active simultaneously at a givencurrent velocity the mode associated with the largest contribution to the fatigue damagemust be applied, i.e., mexti; S'"). Formally, the fatigue damage criteria may be assessednumerically as

T -' ..D = ~ . J ' max(f . s(o)m )dF . (0) ~T lfa t C 0 v 0(10)

A is a vector of environmental parameters. In the response model approach it contains thenon-dimensional hydrodynamic (environmental) parameters: A=[VR KC alT. S(A) is thestress range for a given outcome of A and FA (A) is a long term probability distribution(vector-) function for AFor practical applications the fatigue damage contribution may be evaluated independentlyfor each sea-state (i.e. each cell in a scatter diagram in terms of Hs. T, and 8w) and thefollowing approximate fatigue damage criterion apply:

T~e I pr(.)f m a x (f v S ( V ; ; a ;K C r ) d F u c s TlH. Tp.ew I)

(II)

Pr(.) is the probability of occurrence for the given sea-state in terms of the significant waveheight H s . the spectral peak period Tp and wave direction 8w. fv is the dominating vibrationfrequency and dFu c denote the long term distribution function for the current velocity.In the analyses VR , KC, and a, are replaced by "significant" substitutes defined as:

Uc+U: (12)y' = foDKC U := fw D

~-- . - .. --- U;+U: - - - ---------- -.a =frP

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An asterisk * indicate that the wave induced flow velocity Uw is represented by the significant flow velocity,U : . Further, U ;, is a "significant" current velocity to be taken as:U: = E[UJ(I+2CoV) (13)

E[UcJis the mean value and CoV is the Coefficient of Variation of the long-term currentvelocity.

This implies that: KC* and u* are assumed constant in each sea-state while V; will vary due to thevariability in the current velocity .

The sea state is assumed to be represented by the significant short-term flowinducedvelocity amplitude normal to the pipe Uw* and mean zero upcrossing period Tu, i.e. by atrain of regular wave induced flow velocities with amplitudes equal to U.... and period Tu .The effect of irregularity may reduce the number of large amplitudes and may beaccounted for if proper documented .

The current and wave induced flow components are assumed to be co-linear andindependent, i.e. the current velocity U, taken from the long-term current velocitydistribution is added to Uw * in each sea-state.

The response quantities (i.e. natural frequency, mode shape and unit stress range) to beapplied in the fatigue analyses are normally evaluated from a non-linear FE-analysesconducted over an appropriate stretch of the pipeline. However, approximate analyticalresponse quantities are available and may be used provided that conservativeassumptions are applied and a sensitivity study is performed in order to quantify thecriticality of the assumptions.

CROSS-FLOW FATIGUESeveral analytical force models for cross-flow have been proposed and calibrated usingexperimental data. Work by Bearman (1984), Verley (1982), and Sarpkaya (1977) havefocused on VIV in steady current or in regular wave conditions. More recently gene,'almethods formulated for application on pipeline free spans have been pUbh; ; .hrJd.

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Pantazopoulos (1993), covering the complex pipeline response behaviour in combinedoscillatory and steady flow conditions. )However, generally applicable force models do not exist and a n empirical response modelreflecting observed pipeline response in a variety of flow conditions is at present superior.A short introduction is presented in the following.The response models discussed herein are empirical models providing the maximumsteady state amplitude response as a function of the basic hydrodynamic and structuralparameters. The response models are in agreement with the generally accepted concept ofvortex induced vibrations.The characteristic vortex shedding induced stress range S due to a combined current andwave flow is calculated by the cross-flow Response Model:

(14)

S F E is the unit stress amplitude (stress due to a unit diameter mode shape deflection). R k isa reduction factor due to damping and K s is the stability parameter. Y f ,Y k and Y 5 are safetyfactors defined previously. The characteristic (maximum) amplitude response fy(VR,KC,a)in combined current and wave flow have been derived based on available experimentallaboratory test data and a limited amount of full-scale test, see Figure 1.

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The fatigue criterion specified in this section applies to current dominated situations, i.e.) normally for a>O.8.

The in-line response of a pipeline span in current dominated conditions for 1.0


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iI0.02 +:': .i

0.00 + - 1 _ _ -j-__ ---f-'-------L-__,--...___---L.-t-..L..---+-----i----+---'-.L..+_.___..._--t------j

~=t~~~----.; ; ; .. . ..... ---- ----- - - _ . . _ - - - - - - - - - - - _ ... .

o .ZO T - - - _ . . . . - - - -i

0.18 t . . .,;;... '016 Li I:E 0.14.j.. .! I :~

0121 1 ' " : 1 ' " ~~P~~~/l~ ij 0.10 I . . . . + . . ; . . . . . . K ; : : : : : : .I C ::

~ 0.08 t : - - ; : . .~ 0.06 f r :-- ---:; ; I : .o 0.04 t . . . . . . . .....~.........- - - i . . . . . . . . . . .

- - - - . . . . - - - - . _ - - - - - - - . . , ... )0.0 0.5 1.0 1.5 2. 0 2.5 3.0 3.5 4.0 4.5 5. 0

Reduced Velocity VR

Figure 2: Characteristic In-line VIV Amplitudes.

IN-LINE FORCE MODEL

The fatigue analyses for the force model in wave dominated conditions is based on thePalmgren-Miners rule in the following form, see e.g. (Madsen e t e t.; 1986):

T,. (fi ) mD = ~ . f .2 2 c .Y . K . I'(I +m/ 2) < '11fat C v S S RFC I (18)Where as is the standard deviation of wave induced stress amplitude and KRFC is a rainflow counting factor, given by (Wirshing & Light, 1980)

KRFC = a + (1- a)(1- e)b (19)a and b are constants and e is a spectral band width parameter. The rain flow countingfactor, KRFC, accounts for the exact" wide-banded damage, i.e. correcting the implicitnarrow-banded Rayleigh assumption for the stress amplitudes to provide results similar tothose arising from a state-of-the-art time domain rain flow counting technique.

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{he marginal fatigue life due to direct wave actions becomes:T~( = ~C

Iof,,",.Tp.9w' (2.J2.. O 's' Y s)m . fv ' KRFc' rn + m/2)(20)

In the Guideline both time domain or frequency domain solutions are allowed. A timedomain solution may account for all significant non-linearity's (e.g. in Morison's formula)but is generally very time-consuming if a large number of sea-states are to be analysed.For fatigue analysis a frequency domain solution (if thoroughly verified) is more tractablesince it facilitates a very large number of sea-states to be analysed at a small fraction ofthe time required for a time domain solution.

Below, the fundamental definitions and concepts for the stochastic response of pipeline) free spans will be derived (i.e., cs , fv and KRFC in a given sea-state). The derivation is inprinciple straightforward and additional guidance may be found in numerous textbooks onstochastic vibration theory.

Let the dh response spectral moment be given by::.c

A n = f r o n S R R ( c o ) d r oo

(21)

SRR(ro ) is the one-sided response (i.e. stress) spectral density function. The followingdefinitions apply:

The standard deviation of the response amplitude as:(22)

The characteristic vibration frequency of the response, fv. is taken equal to the mean up-crossing frequency:

(23)

The bandwidth parameter s:(24)

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In the following a frequency domain approach is applied in the assessment of the one-sided response spectral density function, SRR(W). \,I

Response Analvses of Pipeline Free Spans:

A given response quantity R(x,t) may be described using a modal analyses approach, i.e.:N

R(x, t) =L\If;(x)q;(t);=1

(25)

N is the number of significant mode shapes and \ I f ; ( ~ ) is a versatile form function definedas:

( (26)for displacementsfor bending momentsfor stress amplitudes

Where


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Assuming that u > - > - z where U is the instantaneous (time dependent) flow velocity and z(x)is the pipe in-line displacement Co is the drag coefficient and CM is the inertia coefficient.Note.that a hydrodynamic (qrC2_g)j~mping term appears explicitly.

Linearization of Morison's equation:

The main obstacle in using Morison's equation is the non-linearity induced by the dragterm. As a result of this, the response process will not be Gaussian even if the flow isGaussian. In order to perform a stochastic analysis within the context of linear vibrationtheory (i.e. to facilitate a frequency domain solution) it is inevitable to perform alinearization of the drag term.The non-linear drag term in eq. (29) are replaced by linear substitutes:

(30)

The deterministic coefficient a and b in the equivalent linear expansion is to be determinedfrom an accepted optimality criterion.b is a hydrodynamic damping terms normally to be taken as twice the expected value ofIU(x,t)l. Simple calculations leads to, see e.g. Madsen et al., 1986:

b(x) = .,f8j;,CJu(x) (31)Where CJu(x)is the standard deviation of the flow velocity at location x.The commonly used optimality criterion is the least mean square criterion, i.e.

E~ U I U" 1 (32)a(x) = [ ' JU~It is, however, recognised that eq. (32) underestimates the flow energy and may be undulyun-conservative in case of large flow velocities. An improvement may be obtained if theoptimality criterion is based on conservation of the variance from the original to theIinearized form, i.e.

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a(x) = -(33)

The linearization schemes introduced above are commonly used in offshore applicationsand are often considered acceptable in load calculations for ULS design checks.For fatigue analyses, however, a more appropriate optimality criterion may be based onconservation of the damage from the original to the linearized form, i.e. E[(U(x,t)IU(x,t)l)ml =E[(a(x)U(x,t))m], where m is the fatigue exponent. This leads to

(34)

Assuming that the flow velocity is zero mean normally distributed imply the followingresults:

Linearization Method a{x)/ cru(x)

Least Mean Square .J87lt~1.60

Conservation of Drag Force Variance, .J3~1.73Conservation of Damage Contribution ~2.11

Frequency Domain Analysis:

The standard deviation for a given response quantity crR(X)may be obtained from the\Niener-Khintchine relations (for a one-sided spectrum):

'"cr;(x) = fSRR(X,ro)droo

(35)

SRR(X,ro)s the one-sided response spectrum:N N~RRx, ill) = L L \ jJ j (x ) \ jJ j(x) SQiQJ (0));=1 j=1

(36)

S Q i Q j ( C O ) is the cross spectral density for the modal co-ordinate process:

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(37)

Hlw) is the jth rnodalfrequencyresponse function andSFiFj(W)is the cross soeetral-oensityfor the modal loading:

L LS F ; F / W ) = f f < P i ( x , ) < p j ( X 1) S P ; P j (o, X " X 2) d x , d X 2o 0 (38)

SPiPj(W,Xl,X2)is the cross spectral density for the linearized Morison load. If it isconservatively assumed that the load is invariant within each individual free spanSPiPj(W,Xl,X2)ecomes

(39)

Suu(W)is the wave induced flow velocity spectrum at pipe level given by:(40)

S ' 1 ' 1 ( W ) is the directional short-crested wave spectrum and G 2(w ) is a frequency transferfunction from sea surface elevation to wave induced flow velocities at pipe level.

Assuming separated eigenmodes the response spectral density is now given by:(41)

Where(42)

is an equivalent unit stress amplitude and RD is a factor accounting for the wave spreading.Wi=27tfi and ~i is the modal frequency and total modal damping ratio from structural, soiland hydrodynamic damping, respectively

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In the fatigue analysis the location associated with the largest (stress) response should beconsidered. Hence, A = m a x ( ~ A ( X ) J should be applied.max s L I L . . . . . ,x s \. ,= ,

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The nth response spectral moment A n to be used in the evaluation of as, fv and KRFC is noweasily obtained.

Verification of frequency domain solution:

The frequency domain fatigue analyses have been verified against a corresponding timedomain solution. In the time domain solution the fatigue damage have been assessedusing a Rain Flow Counting technique applying 6 hours of simulated stress response froma free span subjected to the non-linear Morison's load.It is concluded that the frequency domain.solution performs extremely well with a differenceless than 3% for both an typical average and extreme North sea-state condition. This isvery good since the frequency domain approach is close to 1000 times faster. It is notedthat the positive comparison only applies for moderate to deep water. The conclusion doesnot hold in general.

EXAMPLEIntroduction:

The new DNV Guideline has been applied in a free span assessment of the Zeepipe IIApipeline operated by Statoil. In the following a few of the important observations arediscussed. For details, see Fyrileiv & Merk, 1998.The Zeepipe IIA pipeline is a part of the Zeepipe system that transports gas from the Trollfield after being processed at the onshore plant at Kollsnes to the European continent.Zeepipe IIA is a 300 km long pipeline running from Kollsnes to Sieipner in the Norwegiansector of the North Sea.During the 1997 survey a large number of spans was observed whereas 36 spans exceedthe maximum allowable span length established in the original design. The original freespan design allowed in-line VIV but a no vibration criterion for cross-flow (onset-criteria)imposing rather strict criteria on the maximum span length. Thus, a reassessment was

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\performed to see if intervention was necessary due to recent technical development and)state-of-the-art models reflected in the new DNV guidelineAn example of measured pipe configuration from the ROV and GEOPIG surveys is shownin Figure 3.

'97 survey data

I.115.6.;-l -Seabedl-'15.8 G.116.0r '\

g .116.21 \.c ! ~'---"',a : 1~ i116.4 - t -I.1.16.6+i \ _ ~ i

i \\J'.116.8 r117.0 .j - .-i. -- - - ;204.2 204.25 . 204.3 204.35 204.4

-- Pipe bottom" ROV-Pipe bottom ..Geo

KP

Figure 3.: Measured pipe configuration

An interpretation of free span configurations in temporal conditions of scour induced freespans is in combination with life cycle fatigue analyses is very complex. For simplicity it ismerely assumed that the measured free spans are stationary.

In recent years an onset criterion for cross-flow VIV (sometimes also for in-line), imposing aconstraint on the reduced velocity, has often been applied in free span design.

This criterion is normally based on a few (maximum or significant) extreme flow conditions,_pipe ~~~~t~~ and na~ural frequency. An additional safety factor should thus provide asufficient safety margin against fatigue for a range of spans and environmental conditions.The motivation and argument is that fatigue failure occurs if cross-flow vibrations can exist

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for a short period of time. This may be true for relatively short spans subjected to purecurrent but do not hold in general for extreme wave conditions. The criticality of exceedingan onset criterion depends on the induced stress range as well as on the naturalfrequency. In addition, fatigue is a life-time process and is normally not governed byextreme environmental wave.

)

Hence, an onset criterion is in a narrow sense only rational for predefined free spanscenarios (span length 'and boundary conditions) and environments (location, water depthand combination of wave and current).A maximum allowable span length criterion often used in the industry implicitly assumesthat the span length control the natural frequency (and reduced velocity). This is only truefor short spans and the concept suffers from (at least) the same limitations as describedabove.

Analyses Procedure:

Refined FE-analyses are very time consuming and an approach with increased analysiscomplexity have been developed in order to perform an efficient screening of the surveyresults to identify spans, which may be critical. The following three level assessmentapproach are proposed:1. Simplified maximum span length criterion2. Fatigue criterion with simplified estimates of frequencies, mode shapes and stress

ranges3. Fatigue criterion with response quantities from a refined FE analysesThe level 1 maximum span length is derived from a full fatigue evaluation of a free span ina pre-defined environment (given long term distribution for wave and current and variouswater depths). The natural frequencies and associated mode shapes are based onestimates of a pipe with simplified support conditions. Spans with length shorter than thelevel 1 sQc:ln length are considerec as not critical due to the implicit conservatism whenestablishing these span lengths.

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The level2 criterion is similar to level 1 but consists of individual fatigue calculation based) on the measured span length, gap and water depth.-The third level consists of a refined FE analysis to establish natural frequencies and

associated mode shapes, and a fatigue analysis to calculate the fatigue lives due to in-lineand cross-flow vibrations.In Figure 4 the fatigue lives normalised with respect to the design life for in-line vibrationsare given for different span lengths and water depths, i.e. level 1 criterion. Further, 5 spansanalysed at level 3 are given for comparison. The fatigue analysis calculations isperformed by an EXCEL worksheet denoted FATFREEusing the Module facilities (VisualBasic).

0.10 '" ",,-"- .."- "- \\

_. _. d=80m...... d=1oo m

100.00

. . . . . . . . . . . . . . . . .... 119 m. . . .-, ." 1J!im: ! . . . . " .1 r'-.

:J " ...........& 1.00 t--___,..,...-------~...------:::...""--:::... ...._------------+: ; . . . . . . . . . . . . . .IL ...

~..I, 1000'0;. .c

. . . . . . . . . . . . . . . -," --d=120m_ - - d=140 m level 3 spans24 m

"', - - -,0.01 ~.--_.._---------,-----.-------'-'.___- __ ----___,--__+

30 35 40 45 50 55Span Length I 0

60 65 70 75 80

Figure 4.: Normalised fatigue life versus span length for level 1 and level 3 analysis

CONCLUSION

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A short introduction to the new DNV Guideline for free spanning pipeline has been given. )The Guideline has not yet been extensively applied in design. However, in developing andapplying the Guideline in practice the fQIJowjng observations and comments apply: Full fatigue analyses (true ULS) provides robust decision criteria. The result is not verysensitive to subjective assumptions such as boundary conditions or soil-pipe modelling. A maximum span length criterion is only appropriate for given pipe, loading and

environment. Onset criteria (SLS or ULS) is only appropriate in case the natural frequency is

insensitive to the structural modelling, e.g. for short, unevenness-induced spans incurrent dominant conditions.

Refined FE modelling is recommended in general apart from screening analyses wheresimplified methods are tractable. )

Criticality assessment and sensitivity study to be performed on a span by span basis. Experienced people and engineering judgement should be employed.

REFERENCESBSI PD6493, Guidance on Methods for Assessing the Acceptability of Flaws in FusionWelded Structures, British Standard Code of Practice, 1991BS8010 - part 3, Pipelines Subsea - Design, Construction and Installation, BritishStandard Code of Practice, 1993Blevins, R.D., "Flow-Induced Vibrations", Krieger Publishing Company, Florida, 1994Bruschi, R. & Vitali, L., "Large-Amplitude Osciiiations of Geometrically Non-linear ElasticBeams Subjected to Hydrodynamic Excitation", JOMAE, Vol. 113, May, 1991.Bearman, P. W., Graham, J. M. R, Obasaju, E. D., "A Model Equation for the TransverseForces on Cylinders in Oscillatory Flows", Applied Ocean Research, Vol. 6, No.3, pp. 166-172,1984.

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DNV, "Rules for Submarine Pipeline Systems, Det Norske Veritas", 1981

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..\ DNV, "Rules for Submarine Pipeline Systems, Det Norske Veritas", 1996!

DNV Guidelines No. 14, "Free Spanning Pipelines", Draft for industry hearing, December1997.DNV CN. 30.2, "Fatigue Strength Analysis for Mobile Offshore Units", 1984.DNV CN 30.5, "Environmental Conditions and Environmental Loads", 1991.Fyrileiv, O. & M0rk, KJ. "Free Span Assessment of the Zeepipe IIA Pipeline", To bepresented at OMAE'98, Lisboa, July 6-9, 1998.

Jacobsen, V., 8ryndum, M., Nielsen, R. & Fines, S. "Cross-flow Vibrations of a Pipe Closeto a Rigid Boundary", J. of Energy Resources Technology, Vol. 106, 1984.Madsen, H., Krenk, S., & Lind, N., "Methods of Structural Safety", Prentice Hall, 1986Mark, KJ., Vitali, L. & Verley, R., " The MULTISPAN Project: Design Guideline for FreeSpanning Pipelines", Proc. of OMAE'97 conf., Yokohama, Japan, April 13-17, 1997M0rk, KJ. et a/ "An Introduction to DNV Guideline for Free Spanning Guideline", To bepresented at OMAE'98, Lisboa, July 6-9, 1998.Pantazopoulos, M. S., Crossley, C. W., Orgill, G. and Lambrakos, K F., "FourierMethodology for Pipeline Span Vortex-Induced Vibration Analysis in Combined Flow",Proc. of the 12th Int. OMAE Conf., Glasgow, U.K, 1983.

Sarpkaya, T., "In-Line and Transverse Forces on Cylinders Near a \lVall in Oscillatory Flowat High Reynolds Numbers", OTC #2898, Houston, pp. 161-166, 1977.Tura, F., Dumitrescu, A., Bryndum, M. B. & Smeed, P.F. "Guidelines for Free SpanningPipelines: The GUDESP Project", OMAE'94, Volume V, pp 247-256, Houston, 1994.Vandiver, J.K "Dimensionless Parameters Important to the prediction of Vortex-InducedVibration of Long Flexible Cylinders in Ocean Currents", Journal of Fluid and Structures,Vol. 7, pp.423-455, 1993.

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Verley, R, "A Simple Method of Vortex-Induced Forces In Waves and Oscillating ')Currents", Applied Ocean Research, Volume 4, No.2, 1982.Vitali, L, Verley, R, Merk, KJ., & Malacari, LE. liThe MULTISPAN Project: ResponseModels for Vortex-Induced Vibrations of Submarine Pipelines", OMAE'97, Yokahama,Japan, April 13-18, 1997.Wirshing, P.H. & Light, M.C., "Fatigue under Wide Band Random Stresses", J . of theStruct. Div., ASCM, Vol. 106, 1980, pp.1S93-1607.

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OPT98 Fatigue Design-DNV-Guideline-Free Spanning Pipelines

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