dnv rp f105

DET NORSKE VERITAS

RECOMMENDED PRACTICEDNV-RP-F105

FREE SPANNING PIPELINES

MARCH 2002

DNV-RP-F105.qxd 03-05-02 13:00 Page 2

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FOREWORDDET NORSKE VERITAS (DNV) is an autonomous and independent foundation with the objectives of safeguarding life,property and the environment, at sea and onshore. DNV undertakes classification, certification, and other verification andconsultancy services relating to quality of ships, offshore units and installations, and onshore industries worldwide, and carriesout research in relation to these functions.

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DNV Offshore Codes are offered within the following areas:A) Qualification, Quality and Safety MethodologyB) Materials TechnologyC) StructuresD) SystemsE) Special FacilitiesF) Pipelines and RisersG) Asset Operation

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Recommended Practice DNV-RP-F105, March 2002

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DET NORSKE VERITAS

CONTENTS

1 General .........................................................................4

1.1 Introduction.......................................................41.2 Objective...........................................................41.3 Scope and Application ......................................41.4 Safety philosophy .............................................51.5 Free Span Response Classification ...................61.6 Flow regimes.....................................................61.7 Relationship to other Rules...............................71.8 Definitions ........................................................71.9 Abbreviations....................................................71.10 Symbols ............................................................7

2 Design Criteria ...........................................................10

2.1 General............................................................102.2 Temporal classification...................................102.3 Screening Fatigue Criteria ..............................102.4 Fatigue Criterion .............................................112.5 ULS Criterion .................................................122.6 Safety Factors .................................................13

3 Environmental Conditions ........................................15

3.1 General............................................................153.2 Current conditions...........................................153.3 Short-term wave conditions ............................163.4 Reduction functions ........................................183.5 Long-term environmental modelling ..............183.6 Return Period Values ......................................19

4 Response Models........................................................ 20

4.1 General ........................................................... 204.2 Marginal Fatigue Life Capacity...................... 204.3 In-line Response Model.................................. 214.4 Cross-flow Response Model........................... 22

5 Force Model ............................................................... 25

5.1 General ........................................................... 255.2 FD solution for In-line direction..................... 255.3 Simplified Fatigue Assessment ...................... 265.4 Force Coefficients .......................................... 26

6 Structural Analysis.................................................... 29

6.1 General ........................................................... 296.2 Morphological classification .......................... 296.3 Structural modelling ....................................... 296.4 Functional Loads ............................................ 306.5 Static analysis ................................................. 306.6 Eigen-value analysis ....................................... 316.7 Added Mass.................................................... 316.8 Approximate response quantities.................... 31

7 Pipe-soil interaction................................................... 34

7.1 General ........................................................... 347.2 Modelling of pipe-soil interaction .................. 347.3 Approximate Soil Stiffness............................. 357.4 Artificial supports........................................... 38

8 References .................................................................. 39


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1 General

1.1 Introduction

1.1.1 The present document considers free spanningpipelines subjected to combined wave and current loading.The premises for the document are based on technical de-velopment within pipeline free span technology in recentR&D projects, as well as design experience from recentand ongoing projects, i.e. DNV Guideline 14, see Mrk & Fyrileiv (1998) The sections regarding Geotechnical Conditions and

part of the hydrodynamic model are based on the re-search performed in the GUDESP project, see Tura etal., (1994).

The sections regarding Free Span Analysis and in-lineVortex Induced Vibrations (VIV) fatigue analyses arebased on the published results from the MULTISPANproject, see Mrk et al., (1997).

Numerical study based on CFD simulations for vibra-tions of a pipeline in the vicinity of a trench, per-formed by Statoil, DHI & DNV, see Hansen et al,2001.

Further, recent R&D and design experience e.g. fromsgard Transport, ZEEPIPE, TOGI and TROLL OILpipeline projects are implemented, see Fyrileiv &Mrk (1998).

The basic principles applied in this document are inagreement with most recognised rules and reflect state-of-the-art industry practice and latest research.

This document includes a brief introduction of the basichydrodynamic phenomena, principles and parameters. Fora thorough introduction see e.g. Sumer & Fredse, (1997)and Blevins (1994).

1.2 Objective

1.2.1 The objective of this document is to provide ra-tional design criteria and guidance for assessment of pipe-line free spans subjected to combined wave and currentloading.

1.3 Scope and Application

1.3.1 Detailed design criteria are specified for UltimateLimit State (ULS) and Fatigue Limit State (FLS) due to in-line and cross-flow Vortex Induced Vibrations (VIV) anddirect wave loading.

The following topics are considered: methodologies for free span analysis; requirements for structural modelling; geotechnical conditions ; environmental conditions & loads; requirements for fatigue analysis; response and direct wave force analysis models; and

acceptance criteria.

1.3.2 Free spans can be caused by: seabed unevenness change of seabed topology (e.g. scouring, sand waves) artificial supports/rock berms etc.

1.3.3 The following environmental flow conditions aredescribed in this document: steady flow due to current; oscillatory flow due to waves; and combined flow due to current and waves.

The flow regimes are discussed in section 1.6.

1.3.4 There are no limitations to span length and spangap with respect to application of this RecommendedPractice.

The basic cross-flow VIV Response model is, however,based on single mode response.

In case several potential vibration modes can become ac-tive at a given flow velocity, the mode associated with thelargest contribution to the fatigue damage shall be applied.Unless otherwise documented the damage contribution forany modes should relate to the same critical (weld) loca-tion.

1.3.5 The free span analysis may be based on approxi-mate response expressions or a refined FE approach de-pending on the free span classification, see section 6.2.

The following cases are considered: single spans spans interacting with adjacent/side spans.The stress ranges and natural frequencies should normallybe obtained from an FE-approach. Requirements to thestructural modelling and free span analyses are given insection 6.

1.3.6 The following models are considered: Response Models (RM) Force Models (FM)An amplitude response model is applicable when thevibration of the free span is dominated by vortex inducedresonance phenomena. A force model may be used whenthe free span response can be found through application ofcalibrated hydrodynamic loads. The selection of anappropriate model may be based on the prevailing flowregimes, see section 1.6.

1.3.7 The fatigue criterion is limited to stress cycleswithin the elastic range. Low cycle fatigue due to elasto-plastic behaviour is considered outside the scope of thisdocument.


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DET NORSKE VERITAS

1.3.8 Fatigue loads due to trawl interaction, cyclicloads during installation or pressure variations are not con-sidered herein but must be considered as a part of the inte-grated fatigue damage assessment.

1.3.9 The main aspects of a free span assessment to-gether with key parameters and main results are illustratedin the figure below.

Environmentaldescription

ch. 3

Project data

Current statistics

Current profile

Wave statistics

Wave spectrum

Directionality

Turbulence

Wave & currentReturn periodvalues

Wave & currentlong-termdescription

Screening

Fatigue

ULS

Wave & currentReturn periodvalues

Structuralresponse

ch. 6 & 7

Pipe data

Seabed & pipe profile

Soil data

Lay tension

Operational conditions

Natural Frequency

Natural FrequencyStress amplitude

Natural FrequencyStress rangesStatic Bending

Response modelForce model

ch. 4 & 5

VR

KC

Damping

Free span parameters

Stress rangesNo of cycles

Extreme stresses

Acceptancecriteria

ch. 2

Safety class

Safety factors

SN curve

OK / not OK(span length)

OK / not OK(fatigue life)

OK / not OK(local buckling)

Mai

nC

ompo

nent

sK

ey P

aram

eter

sD

esig

n C

rite

ria

& M

ain

resu

lts

Figure 1-1 Overview of main components in a Free Span Assessment

1.4 Safety philosophy

1.4.1 The safety philosophy adopted herein complieswith section 2 in DNV-OS-F101.

1.4.2 The reliability of the pipeline against fatigue fail-ure is ensured by use of a Load and Resistance FactorsDesign Format (LRFD). For the in-line VIV acceptance criterion, the set of

safety factors is calibrated to acceptable target reli-ability levels using reliability-based methods.

For all other acceptance criteria, the recommendedsafety factors are based on engineering judgement inorder to obtain a safety level equivalent to modern in-dustry practice.


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1.5 Free Span Response Classification

1.5.1 An overview of typical free span characteristics isgiven in the table below as a function of the free span

length. The ranges indicated for the normalised free spanlength in terms of (L/D) are tentative and given for illus-tration only.

L/D Response description

L/D


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DET NORSKE VERITAS

-2

-1

0

1

2

3

4

5

6

time

Flo

w V

elo

city

(Uc+

Uw)

current dominated flow

wave dominated flow

Figure 1-2 Flow regimes

1.6.2 Oscillatory flow due to waves is stochastic innature, and a random sequence of wave heights and asso-ciated wave periods generates a random sequence of nearseabed horizontal oscillations. For VIV analyses, the sig-nificant velocity amplitude, Uw, is assumed to represent asingle sea-state. This is likely to be a conservative ap-proximation.

1.7 Relationship to other Rules

1.7.1 This document formally supports and complieswith the DNV Offshore Standard Submarine PipelineSystems, DNV-OS-F101, 2000 and is considered to be asupplement to relevant National Rules and Regulations.

1.7.2 This document is supported by other DNV off-shore codes as follows: Recommended Practice DNV-RP-C203 Fatigue

Strength Analysis of Offshore Steel Structures Offshore Standard DNV-OS-F201 Dynamic Risers Classification Note No. 30.5 Environmental Condi-

tions and Environmental Loads, 2000.

In case of discrepancies between the recommendations,this Document supersedes the Recommended Practice andClassification Notes listed above.

1.8 Definitions

1.8.1 Effective Span Length is the length of an idealisedfixed-fixed span having the same structural response interms of natural frequencies as the real free span supportedon soil.

1.8.2 Force Model is in this document a model wherethe environmental load is based on Morisons force ex-pression.

1.8.3 Gap is defined as the distance between the pipeand the seabed. The gap used in design, as a single repre-sentative value, must be characteristic for the free spanThe gap may be calculated as the average value over thecentral third of the span.

1.8.4 Marginal Fatigue Capacity is defined as the fa-tigue capacity (life) with respect to one seastate defined byits significant wave height, peak period and direction.

1.8.5 Response Model is a model where the structuralresponse due to VIV is determined by hydrodynamicalparameters.

1.8.6 Span Length is defined as the length where acontinuous gap exists, i.e. as the visual span length.

1.9 Abbreviations

CSF concrete stiffness factorFM force modelLRFD load and resistance factors design formatOCR over-consolidation ratio (only clays)RM response model (VIV)RD response domainRPV return period valuesTD time domainULS ulitmate limit stateVIV vortex induced vibrations

1.10 Symbols

1.10.1 Latin

a

parameter for rain-flow counting factor

a characteristic fatigue strength constant

Ae external cross-section areaAi internal cross-section (bore) areaAIL inline unit amplitude stress (stress induced by

a pipe (vibration mode) deflection equal to anouter diameter D)

ACF cross-flow unit amplitude stressAs pipe steel cross section area(AY/D) normalised in-line VIV amplitude(AZ/D) normalised cross-flow VIV amplitudeB chord corresponding to pipe embedment

equal to v or linearisation constantb

parameter for rainflow counting factorCa added mass coefficient (CM-1)CD drag coefficientCM the inertia coefficientCL coefficient for lateral soil stiffnessCV coefficient for vertical soil stiffnessCT constant for long-term wave period distribu-

tionC1-6 Boundary condition coefficientsc(s) soil damping per unit lengthD pipe outer diameter (including any coating)Dfat deterministic fatigue damageDs outer steel diameterE Young's modulusEI bending stiffnessE seabed gapes void ratio


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(e/D) seabed gap ratiof0 in-line (f0,in) or cross-flow (f0,cr) natural fre-

quency (determined at no flow around thepipe)

fsn concrete construction strengthfs vortex shedding frequency (Strouhal

frequency) =D

USt

FL lateral pipe-soil contact forceFV vertical pipe-soil contact forcefv dominating vibration frequencyfw wave frequencyF() distribution functiong gravitygc correction function due to steady currentgD drag force termgI inertia force termG shear modulus of soil or incomplete comple-

mentary Gamma functionG() frequency transfer function from wave eleva-

tion to flow velocityHeff effective lay tensionHS significant wave heighth water depth, i.e. distance from the mean sea

level to the pipeI moment of inertiaIc turbulence intensity over 30 minutesip plasticity index, cohesive soilsk Wave numberkc soil parameter or empirical constant for con-

crete stiffeningkp peak factorks soil coefficientkw normalisation constantK soil stiffnessKL lateral (horizontal) dynamic soil stiffnessKV vertical dynamic soil stiffness(k/D) pipe roughness

KC Keulegan Carpenter number = Df

U

w

w

KSstability parameter =

2

Te

D

m4

K0 coefficient of earth pressure at restk1 soil stiffnessk2 soil stiffnessL free span length, (apparent, visual)La length of adjacent spanLeff effective span lengthLs span length with vortex shedding loadsLsh length of span shoulderme effective mass per unit lengthm fatigue exponentm(s) mass per unit length including structural

mass, added mass and mass of internal fluidMn spectral moments of order nni number of stress cycles for stress block iN number of independent events in a return

periodNi number of cycles to failure for stress block i

Ntr true steel wall axial forceNc soil bearing capacity parameterNq soil bearing capacity parameterN

soil bearing capacity parameter

pe external pressurepi internal pressurePi probability of occurrence for ith stress cycleq deflection load per unit length

PE Euler load = (1+CSF)2EI/Leff

2

Ra axial soil reactionRc current reduction factorRD reduction factor from wave direction and

spreadingRv vertical soil reactionRI reduction factor from turbulence and flow

directionRk reduction factor from damping

Re Reynolds number D=

UD

s spreading parameterS stress range, i.e. double stress amplitudeSsw stress at intersection between two SN-curvesSeff effective axial forceS

wave spectral densitySSS stress spectraSUU wave velocity spectra at pipe levelsu undrained shear strength, cohesive soilsSt Strouhal numbert pipe wall thickness or timeTexposure load exposure timeTlife fatigue design life capacityTp peak periodTu mean zero up-crossing period of oscillating

flowTw wave periodU current velocityUc current velocity normal to the pipeUs significant wave velocityUw significant wave induced flow velocity normal

to the pipe, corrected for wave direction andspreading

v vertical soil settlement (pipe embedment)

VR reduced velocity = Df

UU

0

wc

w wave energy spreading functiony lateral pipe displacementz height above seabed or in-line pipe displace-

mentzD height to the mid pipezm macro roughness parameterz0 sea-bottom roughnesszr reference (measurement) height


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DET NORSKE VERITAS

1.10.2 Greek

current flow velocity ratio, generalised Phil-lips constant or Weibull scale parameter

e temperature expansion coefficient

Weibull shape parameter and relative soilstiffness parameter

/D relative trench depthpi internal pressure difference relative to layingT temperature difference relative to laying or

storm duration pipe deflection band-width parameter gamma function

peak-enhancement factor for JONSWAPspectrum or Weibull location parameter

soil total unit weight of soilsoil submerged unit weight of soilwater unit weight of waters safety factor on stress amplitudef safety factor on natural frequencycr safety factor for cross-flow screening criterionin safety factor for in-line screening criterionk safety factor on stability parameteron safety factor on onset value for VRRFC rainflow counting factor

curvature

1 mode shape factor

max equivalent stress factor

usage factor

mean valuea axial friction coefficientL lateral friction coefficient Poisson's ratio

or kinematic viscosity 1.510-6 [m2/s] mode shape() cumulative normal distribution function() normal distribution functions angle of friction, cohesionless soilsk,CM correction factor for CM due to pipe rough-

nesstrench,CM correction factor for CM due to effect of pipe

in trenchproxi,CM reduction factor for CM due to seabed prox-

imityk,CD correction factor for CD due to pipe rough-

nesstrench,CD correction factor for CD due to effect of pipe

in trenchA,CD amplification factor for CD due to cross-flow

vibrationsproxi,CD reduction factor for CD due to seabed prox-

imityproxi,onset correction factor for onset cross-flow due to

seabed proximitymass,onset correction factor for onset cross-flow due to

specific mass of the pipe,onset correction factor for onset cross-flow due to

waves

trench,onset reduction factor for onset cross-flow due tothe effect of a trench

,in correction factor for onset cross-flow due to

seabed proximity density of waters/ specific mass ratio between the pipe mass (not

including added mass) and the displaced wa-ter.

stress, spectral width parameter or standarddeviation

c standard deviation of current velocity fluctua-tions

u standard deviation of wave induced flow ve-locity

dyn dynamic stressl longitudinal stressN static axial stressstat static stresss effective soil stress or standard deviation of

wave induced stress amplituderel relative angle between flow and pipeline di-

rection flow direction

total modal damping ratiosoil soil modal damping ratiostr structural modal damping ratioh hydrodynamic modal damping ratio0 angular natural frequency

angular wave frequencyp angular spectral peak wave frequencymax soil shear strength

1.10.3 Subscripts

IL in-lineCF cross-flowonset onset of VIV100year 100 year return period value1year 1 year return period value


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Page 10

2 Design Criteria

2.1 General

2.1.1 For all temporary and permanent free spans a freespan assessment addressing the integrity with respect tofatigue and local buckling (ULS) shall be performed.

2.1.2 Vibrations due to vortex shedding and directwave loads are acceptable provided the fatigue and ULScriteria specified herein is fulfilled.

2.1.3 In case several potential vibration modes can be-come active at a given flow velocity, the mode associatedwith the largest contribution to the fatigue damage shall beapplied. Unless otherwise documented the damage contri-bution for any modes should relate to the same critical(weld) location.

2.1.4 The following functional requirements apply: The aim of fatigue design is to ensure an adequate

safety against fatigue failure within the design life ofthe pipeline.

The fatigue analysis should cover a period which isrepresentative for the free span exposure period.

All stress fluctuations imposed during the entire de-sign life of the pipeline capable of causing fatiguedamage shall be accounted for.

The local fatigue design checks are to be performed atall free spanning pipe sections accounting for damagecontributions from all potential vibration modes re-lated to the actual and neighbouring spans.

Start

Free Span Data &Characteristics

OK

Screening Fatigue

ULS Check

Stop

Span interventionDetailed analysis

not OK

not OK

OK

OK

not OK

Figure 2-1 Flow chart over design checks for a free

span.

2.1.5 Figure 2-1 gives an overview of the required de-sign checks for a free span.

2.2 Temporal classification

2.2.1 The temporal criterion categorises the free spanas being caused due to scour or seabed unevenness, i.e. Scour induced free spans are caused by seabed erosion

or bed-form activities. The free span scenarios (spanlength, gap ratio etc.) may change with time.

Unevenness induced free spans are caused by an ir-regular seabed profile. Normally the free span sce-nario is time invariant unless operational parameterssuch as pressure and temperature change significantly.

2.2.2 In the case of scour induced spans, where no de-tailed information is available on the maximum expectedspan length, gap ratio and exposure time, the followingapply: Where uniform conditions exist and no large-scale

mobile bed-forms are present the maximum spanlength may be taken as the length resulting in a stati-cally mid span deflection equal to one external di-ameter (including any coating).

The exposure time may be taken as the remainingoperational lifetime or the time duration until possibleintervention works will take place. All previous dam-age accumulation must be included.

2.2.3 Additional information (e.g. free span length, gapratio, natural frequencies) from surveys combined with aninspection strategy may be used to qualify scour inducedfree spans. These aspects are not covered in this document.Guidance may be found in Mrk et al., (1999) and Fyrileivet al., (2000).

2.3 Screening Fatigue Criteria

2.3.1 The screening criteria proposed herein apply tofatigue caused by Vortex Induced Vibrations (VIV) anddirect wave loading in combined current and wave loadingconditions. The screening criteria have been calibratedagainst full fatigue analyses to provide a fatigue life inexcess of 50 years. The criteria apply to spans with a re-sponse dominated by the 1st symmetric mode (one halfwave) and should preferably be applied for screeninganalyses only and, if violated, more detailed fatigue analy-ses should be performed. The ULS criterion in 2.5 mustalways be checked.

2.3.2 The screening criteria proposed herein are basedon the assumption that the current velocity may be repre-sented by a 3-parameter Weibull distribution. If this is notthe case, e.g. for bi-modal current distributions, care mustbe taken and the applicability of these screening criteriachecked by full fatigue calculations.


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DET NORSKE VERITAS

2.3.3 The in-line natural frequency f0,IL must fulfil:

ILIL

onset,R

year100,c

f

IL,0

250

D/L1

DV

Uf

Where

f Safety factor on the natural frequency, see2.6

IL Screening factor for inline, see 2.6

Current flow ratio=

6.0;UU

Umax

year100,cyear1,w

year100,c

D Outer pipe diameter incl. coatingL Free span lengthUc,100year 100 year return period value for the cur-

rent velocity at the pipe level, see 3Uw,1year Significant 1 year return period value for

the wave induced flow velocity at the pipelevel corresponding to the annual signifi-cant wave height Hs,1year, see 3

ILonset,RV

In-line onset value for the reduced veloc-ity, see 4.

If the above criterion is violated, then a full in-line VIVfatigue analysis is required.

2.3.4 The cross-flow natural frequency f0,CF must fulfil:

CFCFonset,R

year1,wyear100,c

f

CF,0

DV

UUf

Where

CF Screening factor for cross-flow, see 2.6CF

onset,RVCross-flow onset value for the reducedvelocity, see 4

If the above criterion is violated, then a full in-line andcross-flow VIV fatigue analysis is required.

2.3.5 Fatigue analysis due to direct wave action is notrequired provided:

3

2

UU

U

year100,cyear1,w

year100,c

and the above screening criteria for in-line VIV is ful-filled. If this criterion is violated, then a full fatigue analy-ses due to in-line VIV and direct wave action is required

2.4 Fatigue Criterion

2.4.1 The fatigue criterion can be formulated as:

Tlife Texposure

where is the allowable fatigue damage ratio, Tlife thefatigue design life capacity and Texposure the life or loadexposure time.

2.4.2 The fatigue damage assessment is based on theaccumulation law by Palmgren-Miner:

i

ifat

N

nD

Where

Dfat Accumulated fatigue damage.ni Total number of stress cycles corresponding to

(mid-wall) stress range SiN Number of cycles to failure at stress range Si Implies summation over all stress fluctuations

in the design life

2.4.3 The number of cycles to failure at stress range Sis defined by the SN curve of the form:

swm

swm

SSSa

SSSaN

22

11

Where

m1, m2 Fatigue exponents (the inverse slope of the bi-linear S-N curve)

21a,a Characteristic fatigue strength constant de-

fined as the mean-minus-two-standard-deviation curve

Ssw Stress at intersection of the two SN-curvesgiven by:

1

sw1

m

Nlogalog

sw 10S

Where Nsw is the number of cycles for which change inslope appear. LogNsw is typically 6 7.

1

10

100

1000

1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09 1.E+10No of cycles, N

Stre

ss R

ange

, S

NSW

SSW

(a1;m1)

(a2;m2)

Figure 2-2 Typical two-slope SN curve.


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Page 12

2.4.4 The SN-curves may be determined from: Dedicated laboratory test data, Accepted fracture mechanics theory, or DNV-RP-C203 Fatigue Strength Analysis of Off-

shore Steel Structures.The SN-curve must be applicable for the material,construction detail, location of the intial defect (crackinitiation point) and corrosive environment. The basicprinciples in DNV-RP-C203 apply.

2.4.5 The fatigue life capacity, Tlife, can be formallyexpressed as:

a

PSf

1T

imiv

life

Where

Pi Probability of occurrence for the ith stresscycle

2.4.6 The concept adopted for the fatigue analysis ap-plies to both response models and force models. The stressranges to be used may be determined by: a response model, see section 4 a force model, see section 5.

2.4.7 The following approach is recommended: The fatigue damage is evaluated independently in

each sea-state, i.e., the fatigue damage in each cell ofa scatter diagram in terms of (Hs, Tp, ) times theprobability of occurrence for the individual sea state.

In each sea-state (Hs, Tp, ) is transformed into (Uw,Tu, w) at the pipe level as described in section 3.3.

The sea state is represented by a significant short-termflow induced velocity amplitude Uw with mean zeroup-crossing period Tu, i.e. by a train of regular waveinduced flow velocities with amplitudes equal to Uwand period Tu. The effect of irregularity will reducethe number of large amplitudes. Irregularity may beaccounted for provided it is properly documented.

Integration over the long-term current velocity distri-bution for the combined wave and current flow is per-formed in each sea-state.

2.4.8 The total fatigue life capacity in the in-line andcross-flow direction is established by integrating over allsea-states, i.e.

1

T

PT

1

T;Tmin

PT

S P

S P

H TCF,RM,Tp,Hs

,Tp,HsCFlife

H TIL,FM

,Tp,HsIL,RM,Tp,Hs

,Tp,HsILlife

Where ,T,H PS

P is the probability of occurrence of each

individual sea-state, e.g. the probability of occurrence re-flected by the cell in a scatter diagram. The in-line fatiguelife capacity is conservatively taken as the minimum ca-pacity (i.e., maximum damage) from VIV (RM) or directwave loads (FM) in each sea state.

The fatigue life is the minimum of the in-line and thecross-flow fatigue lives.

2.4.9 The following marginal fatigue life capacities areevaluated for (all) sea states characterised by (Hs, Tp, )

IL,RM,Tp,HsT

Marginal fatigue capacity against in-line VIV and cross-flow induced in-line motion in a single sea-state (Hs, Tp,) integrated over long term pdf for thecurrent, see section 4.2.2.

CF,RM,Tp,HsT

Marginal fatigue capacity againstcross-flow VIV in a sea-state (Hs, Tp, )integrated over long term pdf for thecurrent, see section 4.2.1.

IL,FM,Tp,HsT

Marginal fatigue capacity against directwave actions in a single sea-state char-acterised by (Hs, Tp, ) using meanvalue of current, see section 5.2.2.

2.4.10 Unless otherwise documented, the followingassumptions apply: The current and wave induced flow components at the

pipe level are statistically independent. The current and wave-induced flow are assumed co-

linear. This implies that the directional probability ofoccurrence data for either waves or current (the mostconservative with respect to fatigue damage) must beused for both waves and current.

2.5 ULS Criterion

2.5.1 For the local buckling check reference is made tothe combined loading load controlled condition criterionin DNV-OS-F101, section 5, D500. Static and dynamicbending moment, axial force and pressure shall be ac-counted for.

2.5.2 For extreme wave conditions, which can be as-sumed to cause large deformations on the shoulders, de-tailed analyses of the soil stiffness at the shoulders may berequired. In lieu of detailed documentation, the boundaryconditions for the free span should be assumed as pinned-pinned (only valid for the Force Model calculations).

2.5.3 The maximum dynamic bending moment due toVIV and/or direct wave action may be found from the dy-namic stresses:

tD

I2M

sdynE


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DET NORSKE VERITAS

Where

dyn Dynamic stress given belowI Moment of inertia

Ds Outer diameter of steel pipet Wall thickness

2.5.4 The dynamic stress, dyn, is taken as:

CFdyn

max,FMCF

ILCFILdyn

S2

1flowcross

S;A

AS5.0;Smax

2

1linein

Where

SIL In-line stress range, see section 4SCF Cross-flow stress range, see section 4

SFM,max Maximum stress range due to direct waveloading (force model) , see section 5

AIL In-line unit deflection stress amplitude due toVIV, see section 6.8.4

ACF Cross-flow unit deflection stress amplitude dueto VIV, see section 6.8.4

The unit deflection stress amplitude AIL and ACF may beevaluated using the following return period environmentalflow conditions:

year100,wyear10,cyear10,wyear100,cyear100

year10,wyear1,cyear1,wyear10,cyear10

year1,wyear1,cyear1

UU;UUmaxU

UU;UUmaxU

UUU

2.5.5 For the cross-flow direction, the stress simplystems from the VIV induced amplitude. For the in-linedirection, the dynamic stress range is taken as the maxi-mum of: The return period stress range, e.g. 100 year, for in-

line VIV, Sin, defined in section 4.3. The stress from 50% of the cross-flow induced VIV

motion. All parameters are defined in section 4.4.

2.5.6 The maximum dynamic stress FM,max from directwave loading may be calculated using a design stormapproach using:

FM,max= kp s

where kp is the peak factor given by:

Tfln2

577.0Tfln2k

v

vp

T is the storm duration equal to 3 hour and fv is given insection 5.2. kp may conservatively be taken equal to 4.

s is the standard deviation of the stress (amplitude) re-sponse calculated from a time domain or frequency do-main analysis, see section 5.

Alternatively a regular wave approach using Hmax may beapplied.

2.5.7 A simplified ULS screening may be performed interms of an equivalent stress check, ref. DNV-OS-F101,section 12, F1200.

2.5.8 The longitudinal stress is given by:

dynstaticNl

Where

N Static axial stress from true wall axial force,Ntr given by: N = Ntr/As

static Static bending stress from static bending mo-ment, see 6.8.6. Applies to both vertical andlateral directions.

dyn Dynamic bending stress, see 2.5.4. Applies toboth directions, in-line and cross-flow inde-pendently.

2.6 Safety Factors

2.6.1 The safety factors to be used with the screeningcriteria are listed below.

Table 2-1 Safety factors for screening criteria

IL 1.15

CF 1.3

2.6.2 Pipeline reliability against fatigue uses the safetyclass concept, which takes account of the failure conse-quences, see DNV-OS-F101, Section 2.The following safety factor format is used:

a

)(P.),,(SfTD

monkfsv

osureexpfat

f, on,k and s denote partial safety factors for the naturalfrequency, onset of VIV, stability parameter and stressrange respectively. The set of partial safety factor to beapplied are specified in the table below for the individualsafety classes.

Table 2-2 Safety factors for fatigue

Safety ClassSafety Factor

Low Normal High

1.0 0.5 0.25

s 1.051) (1.0)

f 1.201) (1.15)

k 1.30

on 1.101) This safety factor is intended to be used in design when detailed

data about span length, gap etc is not known. If a span is assessedin-service with updated and measured span data, the safety factor inbrackets may be used.


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Page 14

Comments:

apply to both Response Model and Force Model s is to be multiplied to the stress (S S) f applies to the natural frequency (fo/f) on applies to onset values for in-line and cross-flow

VIV (VR,on/on) k applies to the stability parameter (KS/k) For ULS, the calculation of load effects is to be per-

formed without safety factors (S = f = k = on = 1.0),see also section 2.6.3.

2.6.3 The reliability of the pipeline against local buck-ling (ULS criterion) is ensured by use of the safety classconcept as implemented by use of safety factors accordingto DNV-OS-F101, section 5 D500 alternatively section 12.


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DET NORSKE VERITAS

3 Environmental Conditions

3.1 General

3.1.1 The objective of the present section is to provideguidance on: the long term current velocity distribution, short-term and long-term description of wave induced

flow velocity amplitude and period of oscillating flowat the pipe level, and

return period values.

3.1.2 The environmental data to be used in the assess-ment of the long-term distributions shall be representativefor the particular geographical location of the pipeline freespan.

3.1.3 The flow conditions due to current and wave ac-tion at the pipe level govern the response of free spanningpipelines. The principles and methods as described inClassification Note CN 30.5 may be used in addition tothis document as a basis when establishing the environ-mental load conditions.

3.1.4 The environmental data must be collected fromperiods that are representative for the long-term variationof the wave and current climate, respectively. In case ofless reliable or limited number of wave and current data,the statistical uncertainty should be assessed and, if sig-nificant, included in the analysis.

3.1.5 Preferably, the environmental load conditionsshould be established near the pipeline using measurementdata of acceptable quality and duration. The wave and cur-rent characteristics must be transferred (extrapolated) tothe free span level and location using appropriate conser-vative assumptions.

3.1.6 The following environmental description may beapplied: Directional information, i.e., flow characteristic versus

sector probability; Omnidirectional statistics may be used if the flow is

uniformly distributed. If no such information is available, the flow should beassumed to act perpendicular to the axis of the pipeline atall times.

3.2 Current conditions

3.2.1 The steady current flow at the free span level maybe a compound of: tidal current; wind induced current; storm surge induced current, and density driven current.

When detailed field measurements are not available, thetidal, wind and storm surge driven current velocity com-ponents may be taken from Classification No. 30.5.

3.2.2 For water depths greater than 100 m, the oceancurrents can be characterised in terms of the driving andsteering agents: the driving agents are tidal forces, pressure gradients

due to surface elevation or density changes, wind andstorm surge forces.

the steering agents are topography and the rotation ofthe earth.

The modelling should account adequately for all agents.

3.2.3 The flow can be divided into two zones: an Outer Zone far from the seabed where the mean

current velocity and turbulence vary only slightly inthe horizontal direction.

an Inner Zone where the mean current velocity andturbulence show significant variations in the horizon-tal direction and the current speed and direction is afunction of the local sea bed geometry.

3.2.4 The outer zone is located approximately one localseabed form height above the seabed crest. In case of a flatseabed, the outer zone is located approximately at height(3600 z0) where z0 is the bottom roughness, see Table 3-1.

3.2.5 Current measurements (current meter) should bemade in the outer zone outside the boundary layer at alevel 1-2 seabed form heights above the crest. For large-scale currents, such as wind driven and tidal currents, thechoice of measurement positions may be based on thevariations in the bottom topography assuming that the cur-rent is geo-strophic, i.e., mainly running parallel to thelarge-scale bottom contours.

Over smooth hills, flow separation occurs when the hillslope exceeds about 20o. Current data from measurementsin the boundary layer over irregular bed forms are of littlepractical value when extrapolating current values to otherlocations.

3.2.6 In the inner zone the current velocity profile isapproximately logarithmic in areas where flow separationdoes not occur:

)zln(zln

)zln(zln)z(UR)z(U

0r

0rc

where:

Rc reduction factor, see 3.4.1.z elevation above the seabedzr reference measurement height (in the outer zone)z0 bottom roughness parameter to be taken from

Table 3-1:


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Page 16

Table 3-1 Seabed roughness

Seabed Roughness z0 (m)

Silt 5 10-6

fine sand 1 10-5

Medium sand 4 10-5

coarse sand 1 10-4

Gravel 3 10-4

Pebble 2 10-3

Cobble 1 10-2

Boulder 4 10-2

3.2.7 If no detailed analyses are performed, the meancurrent values at the free span location may assume thevalues at the nearest suitable measurement point. The flow(and macro-roughness) is normally 3D and transformationof current characteristics should account for the local bot-tom topography e.g. guided by numerical simulations.

3.2.8 For conditions where the mean current is spreadover a small sector (e.g. tide-dominated current) and theflow condition can be assumed to be bi-dimensional, thefollowing model may be applied in transforming the meancurrent locally. It is assumed that the current velocity U(zr)in the outer zone is known, see Figure 3-1. The velocityprofile U(z*) at a location near the measuring point (withzr*>zr) may be approximated by:

)zln(zln

)zln(*zln)z(U*)z(U

m*r

mr

The macro-roughness parameter zm is given by:

)zln()zln(

zzz

z)zln()zln(

or

rrr

rrm

zm is to be taken less than 0.2.

z*z*r

zZr

Seabed profile

Iso-line for horisontalmean velocity

Outer Zone

Inner Zone

U0 Measuring Point

Figure 3-1 Definitions for 2D model

3.2.9 It is recommended to perform current measure-ments with 10 min or 30 min averages for use with FLS.

3.2.10 For ULS, 1 min average values should be applied.The 1 minute average values may be established from 10or 30 min average values as follows:

min30c

min10cmin1 UI3.21

UI9.11U

where Ic is the turbulence intensity defined below.

3.2.11 The turbulence intensity, Ic, is defined by:

c

cc

UI

where c is the standard deviation of the velocity fluctua-tions and Uc is the 10 min or 30 min average (mean) ve-locity (1 Hz sampling rate).

3.2.12 If no other information is available, the turbu-lence intensity should be taken as 5%. Experience indi-cates that the turbulence intensity for macro-roughnessareas is 20-40% higher than the intensity over a flat seabedwith the same small-scale seabed roughness. The turbu-lence intensities in a rough seabed area to be applied forin-line fatigue assessment may conservatively be taken astypical turbulence intensities over a flat bottom (at thesame height) with similar small-scale seabed roughness.

3.2.13 Detailed turbulence measurements, if deemedessential, should be made at 1 m and 3 m above the sea-bed. High frequency turbulence (with periods lower than 1minute) and low frequency turbulence must be distin-guished.

3.3 Short-term wave conditions

3.3.1 The wave induced oscillatory flow condition atthe free span level may be calculated using numerical oranalytical wave theories. The wave theory shall be capableof describing the conditions at the pipe location, includingeffects due to shallow water, if applicable. For most prac-tical cases, linear wave theory can be applied. Waveboundary layer effects can normally be neglected.

3.3.2 The short-term, stationary, irregular sea statesmay be described by a wave spectrum S

() i.e. the

power spectral density function of the sea surface eleva-tion. Wave spectra may be given in table form, as meas-ured spectra, or in an analytical form.

3.3.3 The JONSWAP or the Pierson-Moskowitz spec-trum is often appropriate. The spectral density function is:

2

p

p5.0exp

4

p

52 )(4

5expg)(S

where

=2/Tw is the angular wave frequency.Tw Wave period.


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Page 17

DET NORSKE VERITAS

Tp Peak period.p =2/Tp is the angular spectral peak frequencyg Acceleration of gravity

The Generalised Phillips constant is given by

)ln287.01(g

H

16

52

4p

2s

The spectral width parameter is given by

else09.0

if07.0 p

The peak-enhancement factor is given by:

S

p

H

T;

51

56.3)15.175.5exp(

6.35

where Hs is to be given in metres and Tp in seconds.

The Pierson-Moskowitz spectrum appears for = 1.0.

3.3.4 Both spectra are describing wind sea conditionsthat are reasonable for the most severe seastates. However,moderate and low sea states, not dominated by limitedfetch, are often composed of both wind-sea and swell. Atwo peak (bi-modal) spectrum should be considered toaccount for swell if considered important. Further detailsmay be found in Classification Note No. 30.5.

3.3.5 The wave induced velocity spectrum at the pipelevel SUU() may be obtained through a spectral transfor-mation of the waves at sea level using a first order wavetheory:

)(S)(G)(S 2UU

G2() is a frequency transfer function from sea surfaceelevation to wave induced flow velocities at pipe levelgiven by:

hksinh

)eD(kcosh)(G

Where h is the water depth and k is the wave number es-tablished by iteration from the transcendental equation:

hkcothg

hkh

2

3.3.6 The spectral moments of order n is defined as:

d)(SM0

UUn

n

The following spectrally derived parameters appear: Significant flow velocity amplitude at pipe level:

0S M2U

Mean zero up-crossing period of oscillating flow atpipe level:

2

0u

M

M2T

The bandwidth parameter

40

22

MM

M1

The velocity process is narrow-banded for 0 andbroad banded for 1 (in practice the process may beconsidered broad-banded for larger than 0.6).

US, Tu and may be taken from Figure 3-2 to Figure 3-4assuming linear wave theory.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Tn/Tp

UST

n/H

s

Tn=(h/g)0.5

Figure 3-2 Significant flow velocity amplitude at pipe

level, US

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Tn/Tp

Tu/T

p

Tn=(h/g)0.5

Figure 3-3 Mean zero up-crossing period of oscillating

flow at pipe level, Tu


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Page 18

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Tn/Tp

Ba

nd

wid

th p

ara

met

er,

Tn=(h/g)0.5

Figure 3-4 Bandwidth parameter for flow velocity at

pipe level,

3.4 Reduction functions

3.4.1 The mean current velocity over a pipe diameter(i.e. taken as current at e+D/2) apply. Introducing the ef-fect of directionality, Rc becomes:

)sin(R relc

where rel is the relative direction between the pipelinedirection and the current flow direction.

3.4.2 In case of combined wave and current flow theseabed roughness is increased from the non-linear interac-tion between wave and current flow. The modified veloc-ity profile and hereby-introduced reduction factor may betaken from DNV-RP-E305.

3.4.3 The effect of wave directionality and wavespreading is introduced in the form of a reduction factor onthe significant flow velocity, i.e. projection onto the ve-locity normal to the pipe and effect of wave spreading.

DSW RUU

The reduction factor is given by; see Figure 3-5.

2/

2/rel

2D d)(sin)(wR

where rel is the relative direction between the pipelinedirection and wave direction

3.4.4 The wave energy spreading (directional) functiongiven by a frequency independent cosine power functionis:

2

s

2

1

2

s1

1k;

else02

)(cosk)(w ws

w

is the gamma function; see 3.5.1 and s is a spreadingparameter, typically modelled as a function of the seastate. Normally s is taken as a real number, between 2and 8; 2 s 8. If no information is available, the mostconservative value in the range 2-8 shall be selected.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80 100 120 140 160 180Relative pipeline-wave direction, rel

Red

uctio

n fa

cto

r R D

s=2s=4s=6s=1000

sin(rel)

Figure 3-5 Reduction factor due to wave spreading and

directionality

3.5 Long-term environmental modelling

3.5.1 A 3-parameter Weibull distribution is often ap-propriate for modelling of the long-term statistics for thecurrent velocity Uc or significant wave height, Hs. TheWeibull distribution is given by:

xexp1)x(FX

where F() is the cumulative distribution function and isthe scale, is the shape and is the location parameter.Note that the Rayleigh distribution is obtained for =2 andan Exponential distribution for =1.

The Weibull distribution parameters are linked to the sta-tistical moments (: mean value; : standard deviation; :skewness) as follows:

33

2

112

21

113

31

11

21

11

is the Gamma function defined as

0

t1x dtet)x(

3.5.2 The directional (i.e. versus ) or omni-directionalcurrent data can be specified as follows: A Histogram in terms of (Uc, ) versus probability of

occurrence


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DET NORSKE VERITAS

The fatigue analysis is based on the discrete events inthe histogram. The corresponding Return Period Val-ues (RPV) are estimated from the corresponding ex-ceedance probability in the histogram or from a fittedpdf, see section 3.6.

A long term probability density function (pdf)

The corresponding Return Period Values for 1, 10 and100 year are established from section 3.6.

Based on Return Period Values

Distribution parameters for an assumed distributione.g. Weibull, are established using e.g. 3 equations(for 1, 10 and 100 year) with 3 unknowns (! and ).This is, in principle, always feasible but engineeringjudgement applied in defining return period values canlead to an unphysical underlying long-term pdf.

3.5.3 The wave climate at a given location may becharacterised by a series of short-term sea-states. Eachshort-term sea state may be characterised by Hs, Tp, and themain wave direction , measured relative to a given refer-ence direction

The directional (i.e. versus ) or omni-directional signifi-cant wave height may be specified as follows:

A scatter diagram in terms of Hs, Tp,

The fatigue analysis is based on the discrete sea-statesreflected in the individual cells in the scatter diagram.

A histogram in terms of (Hs, ) versus probability ofoccurrenceThe fatigue analysis is based on the discrete events forHs in the histogram. The corresponding peak period isassumed on the versatile form

T

sTp HCT

Where 6 CT 8 and 0.3 T 0.5 are location spe-cific

A long term probability density function (pdf)

The corresponding Return Period Values (RPV) for 1,10 and 100 year are established from section 3.6.

Based on Return Period Values

The corresponding Weibull distribution is establishedfrom 3.6.2 using 3 equations (xc for 1, 10 and 100year) with 3 unknowns (! and ). This is, in princi-ple, always feasible but engineering judgement ap-plied in defining return period values can correspondto an unphysical Weibull pdf.

3.6 Return Period Values

3.6.1 Return period values are to be used for ULS con-ditions. A Return Period Value (RPV) xc is defined as:

N

11)x(F c

where N is the number of independent events in the returnperiod (e.g. 100 year). For discrete directions, N may betaken as the total number of independent events times thesector probability.

The time between independent events depends on the envi-ronmental condition. For currents, this time is often takenas 24 hours, whereas the time between independent sea-states (described by Hs) normally may be taken as 3-6hours.

3.6.2 For a Weibull distributed variable the return pe-riod value is given by:

/1

c Nlnx

3.6.3 In case the statistic is given in terms of a scatterdiagram, a long term Weibull distribution !!" is es-tablished from 3.5.1 using statistical moments derived di-rectly from the scatter diagram as follows:

3

HH

3s

HH

2s

HHs

S

S

S

S

S

S

PH

PH

PH

Where PHs is the discrete occurrence probability. The sameprinciple apply for current histograms.

3.6.4 The return period value for to be used for direc-tional data is taken as the maximum projected flow veloc-ity, i.e.

)s,0(R/)s,(Rxmax relDi,relDi,cn..1i

where RD is a reduction factor defined by 3.4.3, rel,i isthe relative direction between the pipeline directionand the flow direction for direction i. For current flows>8.0 may be applied.


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Page 20

4 Response Models

4.1 General

4.1.1 Amplitude response models are empirical modelsproviding the maximum steady state VIV amplitude re-sponse as a function of the basic hydrodynamic and struc-tural parameters. The response models provided hereinhave been derived based on available experimental labo-ratory test data and a limited amount of full-scale tests forthe following flow conditions: In-line VIV in steady current and current dominated

conditions; Cross-flow VIV induced in-line motion; Cross-flow VIV in steady current and combined wave

and current conditions;The response models are in agreement with the generallyaccepted concept of VIV.

4.1.2 In the response models, in-line and cross-flowvibrations are considered separately. Damage contribu-tions from both first and second in-line instability regionsin current dominated conditions are implicit in the in-linemodel. Cross-flow induced additional in-line VIV result-ing in possible increased fatigue damage is consideredapproximately.

4.1.3 The amplitude response depends on a set of hy-drodynamic parameters constituting the link between theenvironmental data and the Response Models: Reduced velocity, VR Keulegan-Carpenter number, KC Current flow velocity ratio, Turbulence intensity, Ic, see 3.2.11. Flow angle, relative to the pipe, rel Stability parameter, KSNote that the Reynolds number, Re, is not explicit in theevaluation of response amplitudes.

4.1.4 The reduced velocity, VR, is in the general casewith combined current and wave induced flow, defined as:

Df

UUV

0

wcR

where

f0 Natural frequency for a given vibration modeUc Mean current velocity normal to the pipe; see

section 3.4.Uw Significant wave induced flow velocity; see

section 3.4.D Outer pipe diameter

4.1.5 The Keulegan-Carpenter number is defined as:

Df

UKC

w

w

where fw is the wave frequency.

4.1.6 The current flow velocity ratio is defined by:

wc

c

UU

U

4.1.7 The stability parameter, KS, representing thedamping for a given modal shape is given by:

2Te

SD

m4K

where: Water densityT Total modal damping ratiome Effective mass, see 6.8.3

4.1.8 The total modal damping ratio, T, comprises structural damping, str, see section 6.3.10 soil damping, soil, For screening purposes soil = 0.01

may be assumed. For details, see 7.2.10. hydrodynamic damping, h. For VIV within the lock-

in region, the hydrodynamic modal damping ratio h isnormally to be taken as zero, i.e. h = 0.00

4.2 Marginal Fatigue Life Capacity

4.2.1 For cross-flow VIV, the marginal fatigue capac-ity against VIV in a single sea-state characterised by (Hs,Tp, ) is defined by, see section 2.4:

0Uc

mCFv

CF,RM,Tp,Hs

dFa

Sf

1T

where

SCF Cross-flow stress range defined in 4.4fv Vibration frequency; see 4.2.3.

a Fatigue constant, depending on the relevantstress range, see 2.4.3

m Fatigue exponent, depending on the relevantstress range, see 2.4.3

The integral cudF(...) indicates integration over the long-

term distribution for the current velocity represented by aWeibull distribution, or histogram.


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Page 21

DET NORSKE VERITAS

4.2.2 For the in-line direction, the marginal fatiguecapacity against VIV in a single sea-state characterised by(Hs, Tp, ) is taken as:

0Uc

m

CF

ILCFILv

IL,RM,Tp,Hs

dFa

A

A

2

S;Smaxf

1T

where

SIL In-line stress range defined in 4.3AIL Stress due to unit diameter in-line mode shape

deflection;ACF Stress due to unit diameter cross-flow mode

shape deflection

The in-line stress range is taken as the maximum of:

The in-line VIV stress range Sin The in-line stress range corresponding to a figure 8 or

half-moon motion, i.e., stress induced by 50% of thecross-flow induced VIV amplitude.

4.2.3 The dominating vibration frequency, fv, is to betaken as: fv = f0,IL for in-line VIV fv = f0,CF for cross-flow VIV fv = 2f0,CF for cross-flow induced in-line motionwhere f0,il and f0,CF are the in-line and cross-flow naturalvibration frequencies.

4.3 In-line Response Model

4.3.1 The in-line response of a pipeline span in currentdominated conditions is associated with either alternatingor symmetric vortex shedding. Contributions from both thefirst in-line instability region and the second instabilityregion are included in the model.

4.3.2 The amplitude response depends mainly on thereduced velocity, VR, the stability parameter, KS, the tur-bulence intensity, Ic, and the flow angle, relrelative to thepipe. Further, mitigation effects from the seabed proxim-ity, (e/D) is conservatively not included.

4.3.3 The in-line VIV induced stress range SIL is cal-culated by the Response Model:

sIL,YILIL )D/A(A2S

Where

AIL Unit stress amplitude (stress due to unit di-ameter in-line mode shape deflection);

,IL Correction factor for current flow ratio s Safety factor to be multiplied on the stress

range

4.3.4 (Ay/D) is defined as the maximum in-line VIVresponse amplitude (normalised with D) as a function ofVR and KS, see Figure 4-1 for illustration. The corre-sponding standard deviation may be obtained as (AY/D)/#2.

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Inli

ne

VIV

Am

pli

tud

e (A

y/D

) Ksd=0.00

Reduced Velocity VRd (=V R/f)

Ri,1 = 1.0

Ri,2 = 1.0

on = 1.0

Ksd=1.50

Ksd=1.25

Ksd=1.00

Ksd=0.75

Ksd=0.50

Ksd=0.25

Figure 4-1 Illustration of the in-line VIV Response

Amplitude versus VRd and KSd.

4.3.5 In the evaluation of (AY/D) the design values forthe reduced velocity and stability parameter shall be ap-plied:

k

ssd

fRRd

KK

VV

where f and k are safety factors related to the natural fre-quency and damping respectively. In addition, an onsetsafety factor is needed, see section 2.6.

4.3.6 The Response Model can be constructed from theco-ordinates in Figure 4-2:

2,Isd2,Y

2,Y1,I

sd1,Y

sd

sdsdILend,R

2,YILend,R

IL2,R

ILonset,R

1,YIL1,R

sdon

sdon

sd

sdon

ILonset,R

R8.1

K113.0

D

A

D

A;R

2.1

K118.0max

D

A

0.1Kfor7.3

0.1KforK8.05.4V

D

A2VV

VD

A10V

6.1Kfor2.2

6.1K4.0forK6.0

4.0Kfor0.1

V


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Page 22

Inli

ne

VIV

Am

pli

tud

e

D

AY

Reduced Velocity

D

A;V

1,YIL1,R

D

A;V

2,YIL2,R

0;V ILend,R 0;VIL

onset,R

Figure 4-2 Response Model generation principle.

4.3.7 The reductions RI(Ic,rel) and RI(Ic) accountsfor the effect of the turbulence intensity and angle of at-tack (in radians) for the flow, see Figure 4-3.

1R0

17.0

03.0I0.1R

1R003.0I22

1R

2,Ic

2,I

1,Icrel2

1,I

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Turbulence Intensity, Ic

Ri2

all angles

Ri1 rel

Ri1 rel

Ri1 rel

Ri1 rel

Figure 4-3 Reduction function wrt turbulence intensity

and flow angle

4.3.8 IL is a reduction function to account for re-

duced in-line VIV in wave dominated conditions:

8.0

8.0for0.1

5.0for3.0/)5.0(

5.0for0.0

IL,

Hence, in case of < 0.5 in-line VIV may be ignored.

4.4 Cross-flow Response Model

4.4.1 Cross-flow VIV are affected by several parame-ters, such as the reduced velocity VR, the Keulegan-Carpenter number, KC, the current flow velocity ratio, ,the stability parameter, KS, the seabed gap ratio, (e/D), theStrouhal number, St and the pipe roughness, (k/D), amongothers. Note that Reynolds number, Re, is not explicit inthe model.

4.4.2 For steady current dominated flow situations,onset of cross-flow VIV of significant amplitude occurstypically at a value of VR between 3.0 and 5.0, whereasmaximum vibration levels occurs at a value of VR between5 and 7. For pipes with low specific mass, wave dominatedflow situations or span scenarios with a low gap ratio,cross-flow vibration may be initiated for VR between 2 and3.

4.4.3 The cross-flow VIV induced stress range SCF dueto a combined current and wave flow is assessed using thefollowing Response Model:

skZCFCF R)D/A(A2S

Where

ACF Unit stress amplitude (stress due to unit di-ameter cross-flow mode shape deflection);

Rk Amplitude reduction factor due to damp-ing

s Safety factor to be multiplied on the stressrange

The cross-flow VIV amplitude (AZ/D) in combined currentand wave flow conditions may be taken from Figure 4-4.The figure provides characteristic maximum values. Thecorresponding standard deviation may be obtained as (AZ/D)/#2.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Cross

-Flo

w V

IVA

mp

litu

de (

AZ/D

)

cronset,RV

1.0

1.0

1.0

1.0

1.0

on

onset,

onsetmass,

onsettrench,

onsetproxi,

Reduced Velocity VR,d (=V R/f)

< 0.8 ; KC < 10

> 0.8 ; all KC

< 0.8 ; KC > 30

Figure 4-4 Basic Cross-Flow Response Model


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Page 23

DET NORSKE VERITAS

4.4.4 The amplitude response (AZ/D) as a function of and KC can be constructed from:

D

A

D

A

30KC9.0

30KC108.010KC01.07.0

10KC7.0

KCall8.03.1

D

A

16V

D

A

3.1

9VV

5V

3V

1,Z2,Z

1,Z

CFend,R

1,ZCFend,R

CF2,R

CF1,R

on

onset,trenchonset,onset,massonset,proxiCFonset,R

Cro

ss-F

low

VIV

Am

pli

tud

e

Reduced Velocity

D

A;V

2,ZCF2,R

D

A;V

1,ZCF1,R

1.0;VCFonset,R 0;V CFend,R

0.0;0.2

Figure 4-5 Response Model generation principle

4.4.5 The reduced onset velocity for cross-flow VIV,CF

onset,RV depends on the seabed proximity, trench geometry

and current flow ratio !whereas the maximum amplitudeis a function of and KC.

4.4.6 proxi,onset is a correction factor accounting for theseabed proximity:

else1

8.0D

efor)

D

e25.13(

4

1

onset,proxi

4.4.7 mass,onset is a correction factor accounting for thespecific mass (gravity) of the pipe:

else1

5.1for3

1

2

1 ssonset,mass

where s/is the specific mass.

4.4.8 ,onset is a correction factor accounting for the

current wave ratio:

else167.1

5.0for3

1onset,

4.4.9 trench,onset is a correction factor accounting for theeffect of a pipe located in/over a trench:

D5.01onset,trench

where /D denotes a relative trench depth given by:

1D

0where

D

ed25.1

D

The trench depth d is to be taken at a width equal to 3outer diameters. /D = 0 corresponds to a flat seabed or apipe located in excess of D/4 above the trench, i.e. the pipeis not affected by the presence of the trench, see Figure4-6. The restriction /D < 1.0 is applied in order to limitthe relative trench depth

d

D

e

3D

Figure 4-6 Definition of Trench Factor

4.4.10 The characteristic amplitude response for cross-flow VIV may be reduced due to the effect of damping.The reduction factor, Rk is given by:

4Kfor

4Kfor

K3.2

K15.01R

sd

sd5.1

sd

sdk

4.4.11 The normalised amplitude curves in Figure 4-4 toa large degree embody all available test result. In addition,the following comments apply: The response for small gap ratio (e/D


Page 24

VR between 2.5 and 3.0 occur at Tu/T0 2. Tu is thewave induced flow period at pipe level and T0 is thenatural period.

4.4.12 Potential vibrations at low KC numbers must beaccounted for and care should be observed in case:

9KC3and)1(3

KCVR

This corresponds to rare cases where Tu < 3T0. If violated,the criticality should be evaluated using an appropriateforce model.


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Page 25

DET NORSKE VERITAS

5 Force Model

5.1 General

5.1.1 In principle, force models may be used for bothvortex induced and direct wave and current dominatedloads if appropriate formulations of force models exist andreliable and consistent data are available for calibration.For cross-flow VIV, generally applicable force models donot exist and empirical response models presented in 4.4reflecting observed pipeline response in a variety of flowconditions is at present superior.

5.1.2 A force model based on the well-known Mori-sons equation for direct in-line loading is consideredherein. Both time domain (TD) and frequency domain(FD) solutions are allowed. A time domain solution mayaccount for all significant non-linearities but is in generalvery time consuming if a large number of sea-states are tobe analysed. For fatigue analyses, a frequency domainsolution (if thoroughly verified) is more tractable since itfacilitates analyses of a very large number of sea-states ata small fraction of the time required for a time domainsolution.

5.1.3 In this document, a complete FD approach forshort-term fatigue analyses is presented. Recommendedprocedures for state-of-the-art Time Domain (TD) short-term damage calculation may be found in DNV-OS-F201.A simplified assessment method is given in 5.3.

5.2 FD solution for In-line direction

5.2.1 The recommended FD solution for the short term-fatigue damage due to combined current and direct waveactions in a single sea-state is based on: Palmgren-Miner approach using SN-curves; linearisation scheme for drag term in the Morison

equation based on conservation of damage; effect of co-linear mean current included in linearisa-

tion term; narrow banded fatigue damage with semi-empirical

correction to account for wide-band characteristic;The formulation presented in this document has been suc-cessfully verified against comprehensive time domainsimulations using Rain flow Counting techniques, see e.g.Mrk &Fyrileiv, 1998. The formulation is based on thefollowing assumptions:

the main damage contribution comes from lowestnatural mode, i.e. the excitation frequency is far fromthe natural frequency for the higher order modes;

the effective mass, me, and standard deviation of theflow velocity U is invariant over the free span length,i.e. for span length less than the dominant wavelength.

5.2.2 The short term fatigue capacity against directwave actions in a single sea-state characterised by (Hs, Tp,) is given in the following form:

ss

)mm(

2

1

1RFC

2RFC

12

sw22

2

sw11

1RFCv

m1FM

,T,H

22S

Sa

a

)m(

)m(

S

S,

2

m1G

S

S,

2

m1G

)m(f

SaT

12

1

PS

WhereS Standard deviation of stress amplitudefv Vibration frequency

21 a,aFatigue constant; see 2.4.3

m1 , m2 Fatigue exponent; see 2.4.3Ssw Stress range, for which change in slope oc-

curs; see 2.4.3

x,G1

x

1t dtte is the

Complementary incomplete Gamma function

)x,(G 2

x

0

1t dtte is the

Incomplete Gamma functions Safety factor on stress range, see 2.6

5.2.3 The standard deviation of the wave induced stressamplitude S is given by the square root of the spectralmoment of the 0th order defined by 5.2.6.

0S M

5.2.4 The characteristic vibration frequency of consid-ered pipe stress response, fv, is taken equal to the mean up-crossing frequency defined by:

0

2v

M

M

2

1f

M0 and M2 is defined by 5.2.6.

5.2.5 The rain flow counting correction factor, RFC,accounts for the exact wide-banded damage, i.e. cor-recting the implicit narrow-banded Rayleigh assumptionfor the stress amplitudes to provide results similar to thosearising from a state-of-the-art rain flow counting tech-nique. The Rain Flow Counting factor RFC is given by:

323.2m587.1b

m033.0926.0a

where

)1)(a1(a)m( bRFC


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Page 26

The bandwidth parameter is defined by:

40

22

MM

M1

The process (spectrum) is narrow-banded for 0 andbroad banded for 1 (in practice the process may beconsidered broad-banded for larger than 0.6).

5.2.6 The nth response spectral moment is given by:

0SS

nn d)(SM

Where SSS("is the one-sided stress response spectraldensity function given by:

2

0T222

02e

2max

22I

22D

22DSS

)2()(m

)(S)(GggbR)(S

WhereRD Factor accounting for the wave spreading and

direction; see 3.4.3.b Linearisation constant; see 5.2.8.gD Drag force term; see 5.4.1.gI Inertia force term; see 5.4.1.G() Frequency transfer function; see 3.3S

Single-sided wave elevation spectrum; see 3.3

0 = 2f0/f is the angular natural frequencyT Total damping ratio from

structural damping; see 6.3.10 soil damping; see 7.2.10. hydrodynamic damping; see 5.2.9.

me Effective mass per unit length incl. added mass;see 6.8.3

5.2.7 maxis an equivalent stress factor given by:

21

2

L1

smax

xmax

2

EtDCSF1

1(x)) 1st mode shapeE Youngs modulus

CSF Concrete stiffness factor; see 6.3.5Ds Outer steel pipe diametert Pipe wall thicknessL Length of mode shape

1 Mode shape weighting factor given by:

L

0

21

L

01

1

dx)x(

dx)x(

1 is typically in the order of 1.3

In lieu of more detailed data, max may be taken as:

1IL

maxD

A

where AIL is given by 6.8.4.

5.2.8 The linearisation constant b is given by:

)U

(g11.2bu

ccu

where Uc is the mean current and u=Uw/2 is the standarddeviation of the wave induced flow velocity. gc() is a cor-rection function accounting for the effect of a steady cur-rent given by:

x

x2

1

2

1

c

dx)x()x(

ex

;2

1xxx2)x(g

2

(x) is the Gaussian probability density function and (x)is the corresponding distribution function.

5.2.9 The (linearized) hydrodynamic damping ratio his given by:

1U

c0e

Duh

U

Cgfm

g

2

1

5.3 Simplified Fatigue Assessment

5.3.1 In situations where quasi-static stress responsecan be assumed (when the wave period is far larger thanthe natural vibration period of the span), a simplified fa-tigue assessment may be tractable rather than a completeTD or FD approach.

In such cases, the short term fatigue capacity against directwave actions in a single sea-state characterised by (Hs, Tp,) may be estimated as follows: (cf. 2.4.5)

umFM

,T,H TSaT PS

where S is the quasi-static stress range response from adirect regular wave load at pipe level using Morisonsequation. Tu is the mean zero upcrossing period in 3.3.6.

5.4 Force Coefficients

5.4.1 The force P(x,t) per unit length of a pipe free spanis represented by the Morisons equation. Assuming thatthe velocity of the structure is not negligible comparedwith the water particle velocity Morisons equation reads:

yD4

CUgyUyUg)t,x(P 2aID


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Page 27

DET NORSKE VERITAS

where

Water densityD Outer pipe diameterU Instantaneous (time dependent) flow ve-

locityy Pipe lateral displacementgD = 0.5DCD is the drag force termgI = M

24

CD

is the inertia force term

5.4.2 The added mass term in the Morison equation

zD4

C 2a is assumed implicit in the effective mass me, see

6.7.1.

5.4.3 The drag coefficient CD and inertia coefficient CMto be used in Morisons equation is a function of : the Keulegan Carpenter number, KC; the current flow ratio, $ the gap ratio, (e/D); the trench depth, (/D); Reynolds number, Re; the pipe roughness, (k/D);In addition also the cross-flow vibration level, (Az/D) in-fluences the drag coefficient. Note that the dependency ofthe Reynolds number is embedded in the cylinder rough-ness effect.

5.4.4 The drag coefficient CD is to be taken as

CD,ACD,trenchCD,proxiCD,k0,DD CC

5.4.5 CD,0 is the basic drag coefficient in oscillatoryflow for a free concrete coated pipe (KC>5):

5.0KC

545.0

5.0KC

519.0

C 0,D

For pure current CD,0 = 0.45 (i.e., for KC%).

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 5 10 15 20 25 30 35 40KC

Dra

g Co

effic

ient

CD

0.1

0.1

0.1

0.1

CD,A

CD,trench

CD,proxi

CD,k

Figure 5-1 Drag coefficient CD versus KC and

The drag load is often of small practical importance forsmall KC values and CD,0 may be interpolated for com-pleteness for KC < 5, see Figure 5-1.

5.4.6 proxi,CD is a correction factor accounting for theseabed proximity:

else1

8.0e/Dfor)D/e(51

5.09.0

CD,proxi

5.4.7 CD,k is a correction factor for the pipe rough-

ness.

D

kln05.025.1CD,k

In lieu of detailed documentation of the surface roughnessthe following values may be applied:

Pipe surface k [metres]

Steel, painted 10-6

Steel, un-coated (not rusted) 10-5

Concrete 1/300

Marine growth 1/200 1/20

5.4.8 trench,CD is a correction factor accounting for theeffect of a pipe in a trench:

D3

21CD,trench

/D is the relative trench depth given by 4.4.9.

5.4.9 A,CD is an amplification factor due to cross-flowvibrations, i.e., proportional to increased projected area tomean flow.

D

A21

yCD,A

5.4.10 The inertia coefficient CM is to be taken as:

CM,trenchCM,proxiCM,k0,MM CC

5.4.11 CM,0 is the basic inertia coefficient for a free con-crete coated pipe taken as, see Figure 5-2:

5.06.0

5.026.1)(f

5KC

)(f25)(fC 0,M


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Page 28

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 5 10 15 20 25 30 35 40KC

Iner

tia C

oef

ficie

nt C M

1.01.0

1.0

CMtrench,

CMproxi,

CMk,

Figure 5-2 Inertia coefficient CM versus KC and

5.4.12 CM,k is a correction factor accounting for the

pipe roughness.

CD,kCM,k 2

5.4.13 proxi,M is a correction factor accounting for theseabed proximity:

else1

8.0e/Dfor)D/e(51

8.084.0

M,proxi

5.4.14 trench,M is a correction factor accounting for theeffect of a pipe in a trench:

D3

11M,trench

/D is the relative trench depth given by 4.4.9


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Page 29

DET NORSKE VERITAS

6 Structural Analysis

6.1 General

6.1.1 The following tasks are normally required forassessment of free spans: structural modelling modelling of pipe-soil interaction load modelling a static analysis to obtain the static configuration of

the pipeline an eigenvalue analysis which provides natural fre-

quencies and corresponding modal shapes for the in-line and cross-flow vibrations of the free spans

a response analysis using a response model or a forcemodel in order to obtain the stress ranges from envi-ronmental actions.

6.2 Morphological classification

6.2.1 The objective of the morphological classificationis to define whether the free span is isolated or interacting.The morphological classification determines the degree ofcomplexity required of the free span analysis: two or more consecutive free spans are considered to

be isolated (i.e. single span) if the static and dynamicbehaviour are unaffected by neighbouring spans;

a sequence of free spans is interacting (i.e. multi-spanning) if the static and dynamic behaviour is af-fected by the pre

dnv rp f105

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