DNV Freespands

7/27/2019 DNV Freespands

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DETNORSKE VERITAS

RECOMMENDED PRACTICE

DNV-RP-F105

FREE SPANNING P IPELINES

MARCH 2002


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FOREWORD

DET 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.

DNV Offshore Codes consist of a three level hierarchy of documents:

Offshore Service Specifications. Provide principles and procedures of DNV classification, certification, verification andconsultancy services.

Offshore Standards. Provide technical provisions and acceptance criteria for general use by the offshore industry as well asthe technical basis for DNV offshore services. Recommended Practices. Provide proven technology and sound engineering practice as well as guidance for the higher

level Offshore Service Specifications and Offshore Standards.

DNV Offshore Codes are offered within the following areas:

A) Qualification, Quality and Safety Methodology

B) Materials Technology

C) Structures

D) Systems

E) Special Facilities

F) Pipelines and Risers

G) Asset Operation

Comments may be sent by e-mail to [email protected] subscription orders or information about subscription terms, please use [email protected] information about DNV services, research and publications can be found at http://www.dnv.com, or can be obtained fromDNV, Veritasveien 1, N-1322 Hvik, Norway; Tel +47 67 57 99 00, Fax +47 67 57 99 11.

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Recommended Practice DNV-RP-F105, March 2002

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DETNORSKE VERITAS

CONTENTS

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

1.1 Introduction.......................................................4

1.2 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 ..............................10

2.4 Fatigue Criterion.............................................112.5 ULS Criterion .................................................122.6 Safety Factors .................................................13

3 Environmental Conditions ........................................153.1 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 ........................................................... 20

4.2 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.................................................... 296.1 General ........................................................... 296.2 Morphological classification .......................... 296.3 Structural modelling ....................................... 296.4 Functional Loads ............................................ 30

6.5 Static analysis................................................. 306.6 Eigen-value analysis.......................................316.7 Added Mass.................................................... 316.8 Approximate response quantities.................... 31

7 Pipe-soil interaction................................................... 347.1 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-line

Vortex 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 this

document.


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DETNORSKE 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

a

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)

Main

Com

onents

KeyParameters

DesignCriteria&Mainresults

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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DETNORSKE VERITAS

-2

-1

0

1

2

3

4

5

6

time

FlowVelocity(U

c+U

w)

current dominated flow

wave dominated flow a=0.8

a=0.0

a=0.5

Figure 1-2 Flow regimes

1.6.2 Oscillatory flow due to waves is stochastic in

nature, 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 Modelis 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 Modelis a model where the structural

response 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 factor FM 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

ak parameter for rain-flow counting factora 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 constantbk 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 damage

Ds 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 strength

fs vortex shedding frequency (Strouhalfrequency) =

D

US t

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(w) 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 number kc 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

r

zp

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 n

ni 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 parameterNg soil bearing capacity parameterpe external pressure

pi internal pressurePi probability of occurrence for ith stress cycleq deflection load per unit length

PE Euler load = (1+CSF)p2EI/Leff2

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

spreadingRv vertical soil reactionRIq reduction factor from turbulence and flow

directionRk reduction factor from damping

Re Reynolds number D=n

UD

s spreading parameter S stress range, i.e. double stress amplitudeSsw stress at intersection between two SN-curvesSeff effective axial forceShh wave spectral densitySSS stress spectraSUU wave velocity spectra at pipe levelsu undrained shear strength, cohesive soilsSt Strouhal numbert pipe wall thickness or time

Texposure 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 = DfUU

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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DETNORSKE VERITAS

1.10.2 Greek

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

ae temperature expansion coefficient

b Weibull shape parameter and relative soilstiffness parameterD/D relative trench depthDpi internal pressure difference relative to layingDT temperature difference relative to laying or

storm duration pipe deflection band-width parameterG gamma functiong peak-enhancement factor for JONSWAP

spectrum or Weibull location parametergsoil total unit weight of soilgsoil submerged unit weight of soil

gwater unit weight of watergs safety factor on stress amplitudegf safety factor on natural frequencygcr safety factor for cross-flow screening criteriongin safety factor for in-line screening criteriongk safety factor on stability parametergon safety factor on onset value for VRkRFC rainflow counting factork curvaturel1 mode shape factorlmax equivalent stress factorh usage factor

m mean valuema axial friction coefficientmL lateral friction coefficient Poisson's ratio

or kinematic viscosity (1.510-6 [m2/s]f mode shapeF() cumulative normal distribution functionj() normal distribution functionjs angle of friction, cohesionless soilsyk,CM correction factor for CM due to pipe rough-

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

in trenchyproxi,CM reduction factor for CM due to seabed prox-imity

yk,CD correction factor for CD due to pipe rough-ness

ytrench,CD correction factor for CD due to effect of pipein trench

yA,CD amplification factor for CD due to cross-flowvibrations

yproxi,CD reduction factor for CD due to seabed prox-imity

yproxi,onset correction factor for onset cross-flow due toseabed proximity

ymass,onset correction factor for onset cross-flow due tospecific mass of the pipeya,onset correction factor for onset cross-flow due to

waves

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

ya,in correction factor for onset cross-flow due toseabed proximity

r density of water

rs/r specific mass ratio between the pipe mass (notincluding added mass) and the displaced wa-ter.

s stress, spectral width parameter or standarddeviation

sc standard deviation of current velocity fluctua-tions

su standard deviation of wave induced flow ve-locity

sdyn dynamic stresssl longitudinal stresssN static axial stresssstat static stress

ss effective soil stress or standard deviation ofwave induced stress amplitude

qrel relative angle between flow and pipeline di-rection

q flow directionzT total modal damping ratiozsoil soil modal damping ratiozstr structural modal damping ratiozh hydrodynamic modal damping ratiow0 angular natural frequencyw angular wave frequencywp angular spectral peak wave frequency

tmax 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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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 freespan.

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, gap

ratio, 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 in

excess 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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DETNORSKE VERITAS

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

a

g

-

>

gIL

ILonset,R

year100,c

f

IL,0

250

D/L1

DV

Uf

Where

gf Safety factor on the natural frequency, see2.6

gIL Screening factor for inline, see 2.6

a

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

DVUUf g

+>g

Where

gCF 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 not

required 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:

h Tlife Texposure

where h 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 SiS 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+ 10

No of cycles, N

StressRange,

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 of

a scatter diagram in terms of (Hs, Tp, q) times theprobability of occurrence for the individual sea state.

In each sea-state (Hs, Tp, q) is transformed into (Uw,Tu, qw) 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 T

CF,RM

,Tp,Hs

,Tp,HsCFlife

H TIL,FM

,Tp,HsIL,RM,Tp,Hs

,Tp,HsILlife

-

=

-

=

qq

q

qqq

q

Whereq,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, q)

IL,RM,Tp,HsT q

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

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

IL,FM,Tp,HsT q

Marginal fatigue capacity against directwave actions in a single sea-state char-acterised by (Hs, Tp, q) 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 dynamic

bending 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:

tDI2M

sdynE

-

s=


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DETNORSKE VERITAS

Where

sdyn Dynamic stress given belowI Moment of inertia

Ds Outer diameter of steel pipe

t Wall thickness

2.5.4 The dynamic stress, sdyn, is taken as:

CFdyn

max,FMCF

ILCFILdyn

S2

1flowcross

S;A

AS5.0;Smax

2

1linein

=s-

=s-

Where

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

SFM,max Maximum stress range due to direct wave

loading (force model) , see section 5AIL In-line unit deflection stress amplitude due to

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

to VIV, see section 6.8.4The 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 sFM,max from direct

wave loading may be calculated using a design stormapproach using:

sFM,max= kp ss

where kp is the peak factor given by:

( )( )Tfln2

577.0Tfln2k

v

vpD

+D=

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

ss 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 s+ss=s

Where

sN Static axial stress from true wall axial force,Ntrgiven by: sN = Ntr/As

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

lateral directions.sdyn 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

gIL 1.15g

CF1.3

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:

( )h

gggg=

a

)(P.),,(SfTD

monkfsv

osureexpfat

gf, gon, gkand gs 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 individual

safety classes.

Table 2-2 Safety factors for fatigue

Safety ClassSafety Factor

Low Normal High

h 1.0 0.5 0.25gs 1.05

1) (1.0)

gf 1.201) (1.15)

gk 1.30gon 1.10

1) This safety factor is intended to be used in design when detaileddata about span length, gap etc is not known. If a span is assessed

in-service with updated and measured span data, the safety factor inbrackets may be used.


14/39


Page 14

Comments:

h apply to both Response Model and Force Model gs is to be multiplied to the stress (S gS) gfapplies to the natural frequency (fo/gf)

gon applies to onset values for in-line and cross-flowVIV (VR,on/gon) gkapplies to the stability parameter (KS/gk) For ULS, the calculation of load effects is to be per-

formed without safety factors (gS = gf= gk= gon = 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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DETNORSKE 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 isuniformly 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 in

the horizontal direction. an Inner Zone where the mean current velocity and

turbulence 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 be

made 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:


16/39


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

s

=

where sc 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 Shh(w) i.e. thepower 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:

ws

w-w-

--hh g

ww

-wa=w

2

p

p5.0exp

4

p

52 )(4

5expg)(S

where

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


17/39


Page 17

DETNORSKE VERITAS

Tp Peak period.wp =2p/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

g-w

=a

The spectral width parameter is given by

ww

=selse09.0

if07.0 p

The peak-enhancement factor is given by:

S

p

H

T;

51

56.3)15.175.5exp(

6.35

=j

j


18/39


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

Bandwidthpara

meter,e g=1.0g=5.0

Tn=(h/g)0.5

Figure 3-4 Bandwidth parameter for flow velocity at

pipe level, e

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 q=

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

3.4.2 In case of combined wave and current flow the

seabed 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.

p

p-

bb-qb=2/

2/rel

2D d)(sin)(wR

where qrel 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:

+G

+G

p=

p


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Page 19

DETNORSKE 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 (a, b and g).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 be

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

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

A scatter diagram in terms of Hs, Tp, q

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

A histogram in terms of (Hs, q) versus probability ofoccurrence

The fatigue analysis is based on the discrete events forHs in the histogram. The corresponding peak period isassumed on the versatile form

( ) TsTp HCTa

=

Where 6 CT 8 and 0.3 aT 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 (a, b and g). 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:

( )( ) g+a= b/1c Nlnx

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

( )

( )

( )

3

HH

3s

HH2s

HHs

S

S

S

S

S

S

PH

PH

PH

s

m-

=d

m-=s

=m

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 =qq=

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


20/39


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, a Turbulence intensity, Ic, see 3.2.11. Flow angle, relative to the pipe, qrel 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

+

=a

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

2Te

S

D

m4K

r

zp=

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

4.1.8 The total modal damping ratio, zT, comprises structural damping, zstr, see section 6.3.10 soil damping, zsoil, For screening purposes zsoil = 0.01

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

in region, the hydrodynamic modal damping ratio zh isnormally to be taken as zero, i.e. zh = 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, q) is defined by, see section 2.4:

( )

q

=

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.


21/39


Page 21

DETNORSKE VERITAS

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

q

=

0Uc

m

CF

ILCFILv

IL,RM

,Tp,Hs

dFa

A

A

2

S;Smaxf

1

T

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 natural

vibration 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, qrelrelative 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 gy= a

Where

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

ya,IL Correction factor for current flow ratio ags 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 ofVRand 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

InlineVIVAmplitude(A

y/D) Ksd=0.00

Reduced Velocity VRd (=V R/gf)

Riq,1 = 1.0

Riq,2 = 1.0

gon = 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

g=

g=

where gfand gkare 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

q

q

-=

-=

g


22/39


Page 22

InlineVIVAm

plitude

D

AY

Reduced Velocity

D

A;V

1,YIL1,R

D

A;V

2,YIL2,R

( )0;V ILend,R( )0;V ILonset,R

Figure 4-2 Response Model generation principle.

4.3.7 The reductions RIq,1(Ic,qrel) and RIq,2(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

-

-=

-

q-

pp-=

qq

qq

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

Riq,2all angles

Riq,1 qrel=30o

Riq,1qrel=0o

Riq,1qrel=45o

Riq,1qrel=60o

Figure 4-3 Reduction function wrt turbulence intensity

and flow angle

4.3.8 ya,IL is a reduction function to account for re-duced in-line VIV in wave dominated conditions:

>a


23/39


Page 23

DETNORSKE VERITAS

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

( )

=

a-+

a

=

=

-=

=g

yyyy= a

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

f

p

f

Cross-FlowVIVAmplitude

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 a, whereas the maximum amplitudeis a function ofa and KC.

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


24/39


Page 24

VRbetween 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 be

accounted 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.


25/39


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DETNORSKE 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-empiricalcorrection 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 sU 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,q) 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

gs=

k

k=c

+c+

+

k

=

-

-

-

q

WheresS 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 j =

-j-

x

1t dtte is the

Complementary incomplete Gamma function

)x,(G 2 j = -j-

x

0

1t dtte is the

Incomplete Gamma functiongs Safety factor on stress range, see 2.6

5.2.3 The standard deviation of the wave induced stress

amplitude sS is given by the square root of the spectralmoment of the 0th order defined by 5.2.6.

0S M=s

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

p

M0 and M2 is defined by 5.2.6.

5.2.5 The rain flow counting correction factor, kRFC,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 factorkRFC is given by:

323.2m587.1b

m033.0926.0awhere

)1)(a1(a)m( bRFC

-=

-=

e--+=k

k

k

kk

k


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The bandwidth parametere is defined by:

40

22

MM

M1-=e

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

5.2.6 The nth response spectral moment is given by:

www=0

SSn

n d)(SM

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

(

( )20T22202e

2max

22I22D22DSS

)2()(m

)(S)(GggbR)(S

wwz+w-w

l

www+=w hh

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(w) Frequency transfer function; see 3.3

Shh Single-sided wave elevation spectrum; see 3.3w0 = 2pf0/gf is the angular natural frequencyzT 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 lmaxis an equivalent stress factor given by:

( )( )

fl

-+=l

2

12

L1

smax

xmax

2

EtDCSF1

f1(x)) 1st mode shapeE Youngs modulus

CSF Concrete stiffness factor; see 6.3.5Ds Outer steel pipe diametert Pipe wall thicknessL Length of mode shapel1 Mode shape weighting factor given by:

f

f

=lL

0

2

1

L

01

1

dx)x(

dx)x(

l1 is typically in the order of 1.3

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

1IL

maxD

Al=l

where AIL is given by 6.8.4.

5.2.8 The linearisation constant b is given by:

)U

(g11.2bu

ccu

s

s=

where Uc is the mean current and su=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:

( ) ( )

( )

-

-

p

-

j=F

=j

F+jp=

x

x21

2

1

c

dx)x()x(

ex

;2

1xxx2)x(g

2

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

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

1U

c0e

Duh

U

Cgfm

g

2

1l

s

p=z

s

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,q) may be estimated as follows: (cf. 2.4.5)

umFM

,T,H TSaT PS-

q=

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 &&&&& r

p-+--=


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DETNORSKE VERITAS

where

r Water densityD Outer pipe diameter U Instantaneous (time dependent) flow ve-

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

24

CDrp

is the inertia force term

5.4.2 The added mass term in the Morison equation

zD4

C 2a &&rp 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, a; the gap ratio, (e/D); the trench depth, (D/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 yyyy=

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

( )

a+

a+a-=

5.0KC

545.0

5.0KC

519.0

C 0,Df

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

DragCoefficientC

D

0.1

0.1

0.1

0.1

CD,A

CD,trench

CD,proxi

CD,k

=y

=y

=y

=y

a0.00.10.20.30.40.5

Figure 5-1 Drag coefficient CD versus KC and a

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 yproxi,CD

is a correction factor accounting for theseabed proximity:

( )

1 is rarely assumed.

7.1.3 The parameters listed above should preferably beobtained by means of geotechnical tests on undisturbedsoil samples and be representative for the particular geo-

graphical location of the pipeline. In lieu of detailed in-formation, the values given in Table 7-1 and Table 7-2may be used.

Table 7-1 Typical geotechnical parameters for sand

Soil type js gsoil[kN/m3]

n es

Loose 28-30o 8.5-11.0 0.35 0.7-0.9Medium 30-36o 9.0-12.5 0.35 0.5-0.8

Dense 36-41o 10.0-13.5 0.35 0.4-0.6

Table 7-2 Typical geotechnical parameters for clay

Soil type su[kN/m2]

gsoil[kN/m3]

n es

Very soft 200 10-13 0.45 0.3-0.9

7.1.4 Uncertainties in the soil data should be consid-ered, e.g. by sensitivity analysis. These uncertainties mayarise from variations in the soil conditions along the pipe-line route and difficulties in determining reliable in-situsoil characteristics of the upper soil layer, which is the soil

of most importance for the pipeline. Soil data down to adepth equal to about 0.5-1.0 times the pipe diameter aremost important to consider in this context.

7.2 Modelling of pipe-soil interaction

7.2.1 The pipe-soil interaction is important in theevaluation of the static equilibrium configuration and thedynamic response of a free spanning pipeline. The fol-lowing functional requirements apply for the modelling ofsoil resistance: the seabed topography along the pipeline route must

be represented; the modelling of soil resistance must account for non-linear contact forces normal to the pipeline and liftoff;

the modelling of soil resistance must account forsliding in the axial direction. For force models thisalso applies in the lateral direction;

appropriate (different) short- and long-term charac-teristics for stiffness and damping shall be applied, i.e.static and dynamic stiffness and damping.

7.2.2 The seabed topography may be defined by a ver-tical profile along the pipeline route. The spacing of the

data points characterising the profile should relate to theactual roughness of the seabed.

7.2.3 The axial and lateral frictional coefficients be-tween the pipe and the seabed shall reflect the actual sea-bed condition, the roughness, the pipe, and the passive soilresistance.

7.2.4 The axial and lateral resistance is not always of apure frictional type. Rapid changes in vertical stresses are(in low-permeable soil) reacted by pore water and not by achange in effective contact stresses between the soil andthe pipe. In addition, the lateral resistance will have a con-tribution due to the penetration of the pipe into the soil,which needs be accounted for.


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DETNORSKE VERITAS

7.2.5 For sands with low content of fines, the frictionalcomponent of the axial and lateral resistance is propor-tional with the vertical force at any time. For clays, thefrictional component is proportional with the undrainedshear strength.

7.2.6 Where linear soil stiffness has to be defined forthe eigenvalue analysis, the soil stiffness should be se-lected considering the actual soil resistance and the am-plitude of the oscillations.

7.2.7 The soil stiffness for vertical loading should beevaluated differently for static and dynamic analyses. Thestatic soil response will be governed mainly by the maxi-mum reaction, including some cyclic effects. Dynamicstiffness will be characterised mainly by the unloading/re-loading situation.

7.2.8 The soil damping is generally dependent on thedynamic loads acting on the soil. Two different types ofsoil damping mechanisms can be distinguished: Material damping associated with hysteresis taking

place close to the yield zone in contact with the pipe. Radiation damping associated with propagation of

elastic waves through the yield zone.

7.2.9 The radiation damping may be evaluated fromavailable solutions for elastic soils using relevant soilmodulus reflecting the soil stress (or strain) levels. Theradiation damping depends highly on the frequency of theoscillations, and is more important for high frequency os-

cillations.

7.2.10 The modal soil damping ratio, zsoil, due to thesoil-pipe interaction may be determined by:

f

f

p=z

L

2L

2

0soil

ds)s()s(m

ds)s()s(c

f4

1

where the soil damping per unit length, c(s), may be de-fined on the basis of an energy balance between the maxi-mum elastic energy stored by the soil during an oscillationcycle and the energy dissipated by a viscous damper in the

same cycle.

Alternatively, the modal soil damping ratio, zsoil, may betaken from Table 7-3 or Table 7-4, in which L denotes thelength of the free span and D is the outer diameter of thepipeline. Interpolation is allowed.

Table 7-3 Modal soil damping ratios (in %) for sand.

Horizontal (in-line)direction

L/D

Vertical (cross-flow)direction

L/DSandtype

160 160

Loose 3.0 2.0 1.0 2.0 1.4 0.8Medium 1.5 1.5 1.5 1.2 1.0 0.8

Dense 1.5 1.5 1.5 1.2 1.0 0.8

Note that the sand type is identified by the value of thefriction angle js (Table 7-1), and the clay type is identifiedby the value of the undrained shear strength su (Table 7-2).

For pipes supported by rock, values for the modal soil

damping ratios may be taken as for dense sand.

Table 7-4 Modal soil damping ratios (in %) for clay.

Horizontal (in-line) direction

L/D

Vertical (cross-flow) direction

L/DClay type

160 160

Very soft - Soft 3.0 2.0 1.0 3.0 2.0 1.0

Firm Stiff 2.0 1.4 0.8 1.2 1.0 0.8

Very stiff - Hard 1.4 1.0 0.6 0.7 0.6 0.5

7.3 Approximate Soil Stiffness

7.3.1 The following expressions may be used for thestatic vertical soil reaction per unit length as a function ofthe penetration, v:

Rv = gsoilb(Nqv+0.5Ngb) - sandy soilsRv = b(gsoilNqv+Ncsu) - clayey soils

Where

b Load distribution width:

>

-= 0.5Dfor vD

0.5Dfor vv)vD(2

D Outer pipe diameter (including any coat-ing)

gsoil Submerged unit weight of soil.su Undrained shear strength

The expressions for RV are based on bearing capacity for-mulas for ideal 2-D strip foundations. Note that if theseformulas are used to predict the expected penetration v fora given contact pressure RV, they may lead to underesti-mation of the true penetration due to effects of the pipelayprocess and erosion as well as possible 3-D effects on the

shoulder near the free span.

7.3.2 The bearing capacity factors Nc, Nq and Ng versusthe internal friction angle js may be calculated from thefollowing formulas:

sq

sqc

s2sq

tan)1N(5.1N

cot)1N(N

)2

45(tan)tanexp(N

j-=

j-=

j+jp=

g

For clayey soils the friction angle is set equal to 0, i.e. Nq= 1.0 and Nc = 5.14.


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1

10

100

0 10 20 30 40 50

j[degree]

Nc,

Nq

andN

Nc

Ng

Nq

Figure 7-1 Bearing capacity factors Nc, Nq and Ng ver-sus the internal friction angle js

7.3.3 The maximum static, axial soil reaction per unitlength may be taken as:

Ra = Rvma - sandy soilsRa = min{Rvma, btmax} - clayey soils

Where

Rv Vertical static soil reaction given by 7.3.1

ma Axial friction coefficientb Given in 7.3.1

kc =

+

-

200

3.1

2001

61.2

ppiiOCR

ip in %

tmax

Soil shear strength:

=

2

2 )1(5.0

--

b

Rks

vcu

7.3.4 The static vertical stiffness is a secant stiffnessrepresentative for penetration conditions such as duringinstallation and erosion and during development of freespans.

The static vertical stiffness KV,S is defined as KV,S=RV/v,where RV is the static vertical soil reaction per unit lengthof pipe and v is the vertical penetration of the pipe re-quired to mobilise this reaction. Unless effects of pipelayand erosion and 3-D shoulder effects are significant, the 2-D approach outlined in 7.3.1 can be used to predict v. Oth-erwise, or when no detailed information is available, thestatic stiffness value may be taken according to Table 7-7for sand and Table 7-8 for clay.

7.3.5 The vertical dynamic stiffness KV is defined asKV=DFV/DdV, where DFV is the incremental vertical forcebetween pipe and soil per unit length of pipe, and DdV is

the associated incremental vertical displacement of thepipe.

7.3.6 The lateral (horizontal) dynamic stiffness KL isdefined as KL=DFL/DdL, where DFL is the incremental

horizontal force between pipe and soil per unit length ofpipe, and DdL is the associated incremental horizontal dis-placement of the pipe.

7.3.7 For a detailed determination of KV, the followingexpression may be applied:

n-

=

1

G88.0Kv

which is based on elastic halfspace theory for a rectangularfoundation under assumption of a pipe length that equals10 times the contact width between pipe and soil. Pois-sons ratio n is given in Table 7-1 and Table 7-2.

7.3.8 For a detailed determination of KL, the followingexpression may be applied:

)1(G76.0KL n+=

which is based on elastic halfspace theory for a rectangularfoundation under assumption of a pipe length that equals10 times the contact width between pipe and soil. Pois-sons ratio n is given in Table 7-1 and Table 7-2.

7.3.9 For conditions with small-amplitude deforma-tions, the shear modulus for the soil can be taken as:

s+

-

s+

-

=

clayfor)OCR(e1

)e3(1300

sandfore1

)e3(2000

Gsk

ss

2s

ss

2s

[kN/m2]

where

ss Effective mean stress (in units of kPa), see7.3.10.

OCR Over-consolidation ratioes Void ratioks Coefficient, taken from Figure 7-2

0

0.1

0.2

0.3

0.4

0.5

0 20 40 60 80 100 120 140Plasticity index, ip

ks

Figure 7-2 ks versus plasticity index, ip


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DETNORSKE VERITAS

This expression for G, which gives lower-bound values forthe initial shear modulus, has been calibrated to measure-ments from free pipeline spans. It is based on an expres-sion for the initial shear modulus, formulated by Hardinand Drnevich (1970) and based on experimental results for

a broad range of soil types.

For extreme conditions, which can be assumed to causelarge deformations, considerably lower G values apply.

7.3.10 The effective mean stress, ss, in the soil at thespan supports may be calculated from the stress conditionsat a representative depth below the pipe. The representa-tive depth may be assumed equal to the contact width b,which is given in Section 7.3.1. The following formulamay then be applied:

)L2L1(

b3q'b)K1(

21

shsoil0S ++g+=s

in whichK0 Coefficient of earth pressure at rest, usu-

ally K0=0.5gsoil Submerged unit weight soil (kN/m

3)q Submerged weight of pipe per unit length

of pipe (kN/m)Lsh Span support length on one shoulder (for

transfer of one-half the weight of the freespan)

L Span length

Note that for pipes on clay, the clay will not be consoli-dated for the weight of the pipe in the temporary phaseimmediately after pipelay. For calculations for a pipe onclay in this phase, the formula forss reduces to

'b)K1(2

1soil0S g+=s

When detailed information does not exist and the topog-raphical conditions are not complex, the support lengthratio Lsh/L may be taken according to Table 7-5 for sandand according to Table 7-6 for clay.

Table 7-5 Support length ratio Lsh/L for sandSand type Lsh/L

Loose 0.3Medium 0.2Dense 0.1

Table 7-6 Support length ratio Lsh /L for clay

Clay type Lsh/LVery soft 0.5

Soft 0.4Firm 0.3Stiff 0.2

Very stiff 0.1Hard 0.07

7.3.11 The procedure in Sections 7.3.7-7.3.10 leads tovalues of the dynamic stiffness KV and KL, which can beconsidered as lower-bound values for initial small-strainstiffness at either end of the free span, but which are notadjusted for possible non-linear soil behaviour at larger

strains.

If there are indications that the values for KV and KLshould be different from those produced by this procedure,then the ratio between the assumed pipe length on theshoulder and the contact width may be adjusted from theadopted value of 10. Calculation of the effective meanstress ss from the stress conditions at a different represen-tative depth below the pipe than b may also be considered.Note that, in this context, it is acceptable to distinguishbetween representative depths for calculation of KV andfor calculation of KL.

7.3.12 When normal conditions prevail and when nodetailed analysis is carried out for determination of KV andKL for small-strain conditions, the values of these stiff-nesses in units of kN/m/m may be calculated in simplifiedmanner as (D is in units of metre):

D)3

1

3

2(CK sVV +

r

r=

D)3

1

3

2(CK sLL +

r

r=

in which the coefficients CV and CL are taken according to

Table 7-7 and Table 7-8. The soil type, which is used asentry to these tables, is identified by the value of the fric-tion angle js for sand (Table 7-1) and by the value of theundrained shear strength su for clay (Table 7-2).

Table 7-7 Dynamic stiffness factor and static stiffness

for pipe-soil interaction in sand.

Sand type CV(kN/m5/2)

CL(kN/m5/2)

KV,S(kN/m/m)

Loose 16000 12000 250Medium 22000 16500 530Dense 32000 24000 1350

Table 7-8 Dynamic stiffness factor and static stiffness

for pipe-soil interaction in clay with OCR=1.

Clay type CV(kN/m5/2)

CL(kN/m5/2)

KV,S(kN/m/m)

Very soft 1200 800 50-100Soft 2700 1800 160-260Firm 6000 4000 500-800Stiff 9000 6000 1000-1600

Very stiff 21000 14000 2000-3000Har

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