probabilistic methods for planning inspection for fatigue cracks in offshore structures

8/19/2019 Probabilistic Methods for Planning Inspection for Fatigue Cracks in Offshore Structures

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RECOMMENDED PRACTICE

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DNVGL-RP-C210 Edition November 2015

Probabilistic methods for planning ofinspection for fatigue cracks in offshorestructures



© DNV GL AS November 2015

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FOREWORDDNV GL recommended practices contain sound engineering practice and guidance.



Recommended practice, DNVGL-RP-C210 – Edition November 2015

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C h a n g e s

–

c u r r e n tCHANGES – CURRENT

GeneralThis document supersedes DNVGL-RP-0001, May 2015.

Text affected by the main changes in this edition is highlighted in red colour. However, if the changes

On 12 September 2013, DNV and GL merged to form DNV GL Group. On 25 November 2013 Det NorskeVeritas AS became the 100% shareholder of Germanischer Lloyd SE, the parent company of the GL Group,and on 27 November 2013 Det Norske Veritas AS, company registration number 945 748 931, changed itsname to DNV GL AS. For further information, see www.dnvgl.com. Any reference in this document to “DetNorske Veritas AS”, “Det Norske Veritas”, “DNV”, “GL”, “Germanischer Lloyd SE”, “GL Group” or any otherlegal entity name or trading name presently owned by the DNV GL Group shall therefore also be considereda reference to “DNV GL AS”.

On 12 September 2013, DNV and GL merged to form DNV GL Group. On 25 November 2013 Det NorskeVeritas AS became the 100% shareholder of Germanischer Lloyd SE, the parent company of the GL Group,and on 27 November 2013 Det Norske Veritas AS, company registration number 945 748 931, changed itsname to DNV GL AS. For further information, see www.dnvgl.com. Any reference in this document to “DetNorske Veritas AS”, “Det Norske Veritas”, “DNV”, “GL”, “Germanischer Lloyd SE”, “GL Group” or any otherlegal entity name or trading name presently owned by the DNV GL Group shall therefore also be considereda reference to “DNV GL AS”.

involve a whole chapter, section or sub-section, normally only the title will be in red colour.

Main changesThe document code has been changed from DNVGL-RP-0001 to DNVGL-RP-C210.

AcknowledgementsThis recommended practice has been developed based on reports developed in a joint industry project onuse of probabilistic methods for planning of inspection for fatigue cracks in offshore structures sponsoredby Aker Offshore Partner, BP, ConocoPhillips, Dolphin Drilling, ExxonMobil, Statoil ASA, PSA, and TalismanEnergy Norge AS. The support from these companies is acknowledged. Furthermore, the support byProfessor Torgeir Moan NTNU during the work is acknowledged.

In addition to the above stated main changes, editorial corrections may have been made.

Editorial corrections




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C o n t e n t s

CONTENTS

CHANGES – CURRENT .................................................................................................. 3

Sec.1 Introduction.................................................................................................. 8

1.1 Purpose................................................................................................8

1.2 Scope...................................................................................................8

1.3 Validity of recommended practice ........................................................9

1.4 Abbreviations and definitions ............................................................10

1.4.1 Abbreviations ...........................................................................101.4.2 Definitions ...............................................................................11

Sec.2 Standards and reference documents ........................................................... 13

Sec.3 Inspection planning for fatigue cracks ........................................................ 14

3.1 General ..............................................................................................14

3.2 Analysis tools.....................................................................................16

Sec.4 Overview of analyses for planning inspection for fatigue cracks based onprobabilistic methods.................................................................................. 19

Sec.5 Fatigue analysis based on S-N data............................................................. 22

5.1 General ..............................................................................................22

5.2 Fatigue damage accumulation from more than one analysis model ...23

5.2.1 General ...................................................................................235.2.2 Mathematical model for probabilistic analysis with models with

different fatigue damage rates....................................................245.2.3 Example of analysis ..................................................................25

5.3 Jacket structures ...............................................................................27

5.4 Semisubmersibles..............................................................................27

5.5 Floating production vessels................................................................27

5.6 Long term dynamic loading................................................................27

Sec.6 Fatigue analysis based on fracture mechanics ............................................ 29

6.1 Introduction.......................................................................................29

6.2 Example of crack growth analysis......................................................32

6.3 Fracture mechanics models for surface cracks at weld toes...............34

6.4 Alternative methods for derivation of geometry functions .................41

6.5 Geometry functions for plated structures with longer attachments ...416.6 Hot spot stress in plated structures derived from finite element

analysis..............................................................................................43

6.7 Simple tubular joints..........................................................................44

6.8 Stiffened tubular joints ......................................................................46

Sec.7 Assessment of probability of fatigue failure ................................................ 47

7.1 General ..............................................................................................47

7.2 Failure probability at design stage.....................................................48

7.2.1 General ...................................................................................487.2.2 Accumulated and annual failure probability...................................50

7.2.3 Time-limited failure probability ...................................................517.2.4 Probability of being exceeded .....................................................51




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C o n t e n t s7.3 Implementation of monitoring results ...............................................52

7.4 Inspection planning and inspection programme ................................52

7.5 Inspection updating...........................................................................52

7.6 Description of probabilistic fatigue analysis models ..........................53

7.7 Description of probabilistic crack growth analysis .............................54

7.8 Formulation of inspection updating....................................................55

7.9 Change in damage rate over service life ............................................57

7.10 Effect of correlation ...........................................................................57

7.11 Residual strength of the structure or system effects with a fatiguecrack present ....................................................................................57

Sec.8 Target reliability.......................................................................................... 58

8.1 General ..............................................................................................58

8.2 Calculated probabilities of fatigue failure...........................................58

8.3 Target probability of failure for different design fatigue factors ........60

8.4 Target probability of failure as function of consequence of a fatiguefailure ................................................................................................608.4.1 General ...................................................................................608.4.2 Consequence of fatigue crack in a jacket structure ........................618.4.3 Consequence of fatigue crack in a floating production vessel...........62

Sec.9 Calibration of fracture mechanics models to test data................................. 64

9.1 General ..............................................................................................64

9.2 Performed calibration for as-welded details ......................................64

9.3 Performed calibration for ground details ...........................................64

Sec.10 Assessment of input parameters to probabilistic analysis .......................... 65

10.1 Uncertainty modelling........................................................................65

10.2 Fatigue damage accumulation model.................................................66

10.3 Cycle rate...........................................................................................66

10.4 Fabrication tolerances........................................................................66

10.5 Residual stress and mean stress........................................................6610.5.1 General ...................................................................................6610.5.2 Shake-down of residual stresses and proposed assessment

procedure ................................................................................6710.5.3 Mean stress reduction factor.......................................................69

10.6 Stress concentration factors for tubular joints...................................70

10.7 Calculation of hot spot stress.............................................................70

10.8 S-N data.............................................................................................7010.9 Critical crack size in real structure as compared with failure

criterion in S-N curve used for design ................................................71

10.10 Stress magnification at welds and geometry functions ......................71

10.11 Crack growth parameters...................................................................71

10.12 Threshold value in fracture mechanics versus S-N curve ...................73

10.13 Crack initiation...................................................................................73

10.14 Effect of weld improvements on crack initiation ................................73

10.15 Effect of corrosion..............................................................................73

10.16 Fatigue loading ..................................................................................7310.16.1 General ...................................................................................73

10.16.2 Jackets....................................................................................7310.16.3 Semisubmersibles.....................................................................74




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C o n t e n t s10.16.4 Floating production vessels ........................................................75

Sec.11 Probability of detection............................................................................... 76

11.1 Inspection reliability for relevant inspection methods ......................7611.1.1 Flooded member detection.........................................................76

11.1.2 Leakage detection.....................................................................7611.1.3 Probability of detection curves for eddy current, magnetic particleinspection and alternating current field measurement ....................76

11.2 Ultrasonic testing...............................................................................79

11.3 Visual inspection................................................................................79

11.4 Methodology to provide reliable probability of detection curves forother inspection methods ..................................................................80

11.5 Inspection methods for jackets..........................................................81

11.6 Inspection methods for floating structures........................................81

11.7 Effect of measurements on action effects ..........................................82

Sec.12 Validation of results.................................................................................... 83

Sec.13 Inspection planning .................................................................................... 84

Sec.14 Reporting of inspection results ................................................................... 84

Sec.15 Examples of inspection planning for fatigue cracks..................................... 84

15.1 General ..............................................................................................84

15.2 Example of analysis of a welded doubling plate .................................86

15.2.1 Example detail..........................................................................8615.2.2 Analysis steps and assessment ...................................................8615.2.3 Analysis that accounts for grinding after 15 years in service ...........8915.2.4 Analysis when grinding is performed before installation..................90

15.3 Example of analysis of a butt weld between stub and brace in jacket

structure............................................................................................9115.3.1 Example detail..........................................................................9115.3.2 Analysis steps and assessment ...................................................9115.3.3 Probability of the fatigue crack being larger than a given size .........9315.3.4 Design point values of stochastic variables ...................................9415.3.5 Influence of inspections on stochastic variables.............................9715.3.6 Analysis when cracks are found during inspection........................ 101

15.4 Topside support of floating production storage and offloading ........10515.4.1 Example detail........................................................................ 10515.4.2 Analysis steps and assessment ................................................. 10615.4.3 Inspection plan after relocating floating production storage and

offloading .............................................................................. 108

Sec.16 References ................................................................................................ 110

App. A Fatigue analysis of jackets ........................................................................ 114

A.1 Introduction...................................................................................... 114

A.2 Robustness........................................................................................ 114

A.3 Environmental data ........................................................................... 115

A.4 Basis for selection of fatigue analysis method................................... 115

A.5 Platform modelling............................................................................ 118

A.6 Basic criteria and analysis assumptions ............................................ 128

A.7 Deterministic discrete wave fatigue analysis..................................... 134

A.8 Fatigue caused by local hydrodynamic loads..................................... 135A.9 Fatigue analysis due to transport ...................................................... 137




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C o n t e n t sA.10 Fatigue analysis methodology for pile driving ................................... 137

A.11 Fatigue of grouted pile/sleeve connections subjected to alternatingloading ............................................................................................. 142

A.12 Stress concentration factors.............................................................. 142

A.13 Tubular joints welded from one side ................................................. 147A.14 Finite element analysis...................................................................... 148

A.15 S-N data and selection of S-N curve .................................................. 149

A.16 Fatigue damage and design fatigue factors....................................... 149

A.17 Verification and quality assurance..................................................... 150

App. B Fatigue analysis of semisubmersibles ....................................................... 151

B.1 Introduction...................................................................................... 151

B.2 Environmental conditions.................................................................. 153

B.3 Fatigue analyses methods for semi-submersibles ............................. 156

B.4 Hydrodynamic analysis model ........................................................... 159

B.5 Structural analysis model.................................................................. 162

B.6 Actions and response calculation ..................................................... 173

B.7 Documentation and verification of analyses...................................... 175

App. C Fatigue analysis of floating production storage and offloading ................. 178

C.1 Introduction...................................................................................... 178

C.2 Basis for the analysis ........................................................................ 178

C.3 Environmental conditions.................................................................. 180

C.4 Fatigue analyses methods for floating production storage andoffloading.......................................................................................... 180

C.5 Hydrodynamic load and motion analysis ........................................... 188C.6 Modelling principles for finite element models .................................. 197

C.7 Documentation and verification of analyses...................................... 202

C.8 Summary of analysis methods for floating production storage andoffloading.......................................................................................... 208

App. D Background and commentary.................................................................... 215

D.1 Introduction...................................................................................... 215

D.2 Geometry function for weld toes at cruciform joints ......................... 215

D.3 Critical crack size and failure criterion in S-N curve and criticality ofactual details..................................................................................... 238

D.4 Probabilistic fatigue analysis............................................................. 241

D.5 Assessment of input parameters to probabilistic analysis ................. 244

D.6 Calibration of fracture mechanics models to S-N data ....................... 246

CHANGES – HISTORIC.............................................................................................. 263




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SECTION 1 INTRODUCTION

1.1 PurposeThe purpose of this recommended practice (RP) is to provide guidelines for use of probabilistic methods for

inspection planning of fatigue cracks in jacket structures, semisubmersibles and floating production vessels.This also includes guidelines for fatigue analysis of these structures as required for probabilistic analysis.The presented analysis methodology is rather general and it may be used also for inspection planning ofother structures subjected to significant dynamic loading such as jackups.

Optimal allocation of inspection effort for the considered offshore structures with respect to fatigue cracksis aimed for.

Due to the nature of the fatigue phenomena minor changes in basic assumptions can have significantinfluence on the predicted crack growth rates. Calculated fatigue lives are sensitive to input parametersusing standard design analysis procedures. Calculated probabilities of fatigue failure using probabilisticmethods are even more sensitive to the methodology and to the input parameters to the analyses. It is thusimportant to provide as accurate fatigue analysis of the considered structures as possible before the

probabilistic analyses are performed.For design purpose it is appropriate to use conservative values for parameters required for the analyses.However, for planning inspection for fatigue cracks in offshore structures it is important to use relevant(expected or best estimate) values and associated uncertainties in order to predict accurate results thatallow the inspections to be directed to hot spot areas where the fatigue cracks are most likely to occur first.Thus, it is important to base planning of in-service inspection of offshore structures on fatigue analysis thathas been performed in a consistent way. By “consistent” is understood that all joints or potential hot spotsare analysed based on a similar methodology such that any inherent “conservatism” in the analysismethodology is similar for the different hot spots. Use of inconsistent assumptions in analyses may directinspection to areas with long fatigue lives and one might thus get a false impression of the reliability of thestructure with respect to fatigue.

Design of offshore structures with respect to fatigue is normally based on S-N data (test data) derived from

constant amplitude testing. In-service inspection for fatigue is normally performed in order to assure thatpossible cracks in the structure, which may have been present from the initial delivery or have arisen at alater stage during the service life, do not exceed a critical size.

For the S-N fatigue approach, the inspection results cannot be used directly to update the estimated fatiguereliability, as no direct relationship between the crack size and the damage accumulation in the S-Napproach is available. A calibration of the S-N fatigue approach to a fracture mechanics fatigue approach istherefore required. The resulting amount of required in-service inspection is dependent on how thiscalibration is performed. Therefore, an analysis methodology with calibrated initial defects is presented inthis document to make inspection planning less time consuming and less complex for the engineers.

The reliability of a non-destructive examination is described by the ability to detect an existing crack as afunction of the crack size and by the uncertainty associated with the sizing of an identified crack. Regardless

of the inspection outcome (detection or no detection of a crack at the considered hot spot), each inspectionprovides information additional to that available at the design stage. Thus, this information can be utilisedto update the estimated fatigue reliability.

1.2 ScopeThis RP is assumed to be used together with other DNV Offshore Standards (OS) or NORSOK N standardsas listed in /1/ to /6/ or other recognised standards. It is assumed that this RP will be used together withDNVGL-RP-0005 Fatigue Design of Offshore Structures. This RP is intended to give sufficient guidance tothe user on how to establish a sound basis for probabilistic in service inspection planning for fatigue cracks.This basis should as a minimum include advice on:

— Fatigue analysis methods for jacket structures, semisubmersibles and floating production vessels

(FPSOs).— Effect of methodology/refinement used in fatigue analysis with respect to calculated fatigue life.




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— Basic distributions of parameters required for calculation of stochastic properties for load effects andcapacity.

— Derivation of target reliability level in relation to consequence of a fatigue failure.

— Methodology for probabilistic analyses for planning inspection for fatigue cracks. Required theory toexplain the methodology should be provided in order that users of the document can easier understandthe use of the standard and significance of input parameters to the analysis.

The document may be used for planning inspection for fatigue cracks in new built and existing structuresand also for analysis of lifetime extension of platforms.

1.3 Validity of recommended practiceThe calculated inspection interval to a first inspection of a hot spot area is rather dependent on the accuracyof the performed fatigue analysis. Therefore, it is not meaningful to use probabilistic methods for planningthe time interval to a first inspection if a reliable fatigue analysis has not been performed. This requirementmay be relaxed for older structures where regular inspections have been performed. If reliable inspectionshave been performed, one may still use this RP to assess further need for inspections and inspectionintervals even if the calculated fatigue life for the considered detail is very uncertain. The reason for this isthat a fatigue life at weld toes is associated with a significant crack growth life as compared to crackinitiation time. Provided that a reliable inspection method is used and that a crack has not been detected,one can assess that a potential crack is smaller than a certain value and there is still a potential fatiguecrack growth life left before the crack has grown to a critical size.

The efficiency of the in-service inspection depends on the crack growth development at a considered hotspot. Therefore it is important to establish reliable geometry functions for calculation of crack growth basedon fracture mechanics analysis as these functions represents possible redistribution of stress flow at hotspots during crack growth. Longer inspection intervals can be used for details showing some redistributionof stress flow during crack growth as compared with that of small scale test specimens fatigue tested in thelaboratory. The actual crack growth behaviour can best be illustrated by a deterministic analysis that showscrack size as function of number of cycles or life time in service. Therefore, it is strongly recommended thatsuch crack growth analysis is performed in addition to the probabilistic analysis for the purpose of qualitycontrol.




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1.4 Abbreviations and definitions

1.4.1 Abbreviations

Term Description

ACFM alternating current field measurement

ACPD alternating current potential drop

ALS accidental limit state

AP aft perpendicular

CoV coefficient of variation

BL baseline

CP cathodic protection

CTOD crack tip opening displacement

CVI close visual inspection

DAF dynamic amplification factor

DFF design fatigue factorDOB degree of bending

EC eddy current

FE finite element

FLS fatigue limit state

FM fracture mechanics

FMD flooded member detection

FORM first order reliability methods

FP fore perpendicular

FPSO floating production storage and offloading

GVI general visual inspection

HIM hull integrity management systemHRI high resolution image

LAT lowest astronomical tide

LCF low cycle fatigue

LF low frequent

MWL mean water line

MPI magnetic particle inspection

NDE non-destructive examination

NDT non-destructive testing

PoD probability of detection

RAO response amplitude operator

RBI risk based inspection

This notation is frequently being used where inspection planning is based also onprobabilities of failures derived from probabilistic analysis. Otherwise this description isbeing used about probabilities derived from experience statistics. Risk based inspectionmay include gross errors which are difficult to include in a probabilistic analysis.

ROV remotely operated vehicle

RP recommended practice

RSF residual strength factor

RSR reserve strength ratio

SCF stress concentration factor

SCGL additional stress concentration factor due to longer attachment

Semi semi-submersible platform – two – or ring pontoon with and without bracings




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1.4.2 Definitions

SENB single edge notched bend test

SENT single edge notched tensile test

SRD soil resistance during driving

SWL still water levelTSS topside support structure

ULS ultimate limit state

UT ultrasonic testing

VIV vortex-induced-vibration response

WF wave frequent

Adi smallest detectable crackC crack growth parameterD accumulated fatigue damage; diameter of chordDcycle fatigue damage during one cycleF calculated fatigue lifeN number of cyclesK max maximum value of stress intensity factorK min minimum value of stress intensity factorK th threshold level for the stress intensity below that the crack is not propagating∆ K K max - K min

M k geometry function due to the weld notchM km geometry function due to the weld notch for membrane stressM kb geometry function due to the weld notch for bending stressM(t) limit state functionP(t) accumulated probability of fatigue failure at time t

∆P (t i ) annual probability of fatigue failure as difference between year i+1 and i∆S stress rangeT time periodT N year start of period N Y m geometry function for membrane loadingY b geometry function for bending moment∆ Miner sumΦ elliptic integral of the second kindθ angle to position in crack tip in semi-elliptic crack

a crack depth for surface cracks, parameter describing PoDa0 initial crack depthad detectable sizeb parameter describing PoDc half crack length for semi-elliptic surface crackc0 half initial crack lengthd diameter of braced i damage rate per year for period id N damage rate per year for period N

f correction factor f w finite-width correction functionh form parameter in the Weibull distributionm inverse negative slope of S-N curves

Crack growth parameter or crack growth exponent based on fracture mechanics.n0 total number of load cycles during the considered time period

P f annual annual probability of failureP SYS probability of a failure given that the considered element has failed

Term Description




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q scale parameter in the Weibull distributions1 stress range at transition from one part of the S-N curve to the other partt ini crack initiation time

X 0 distribution parameter (= 50% median value for the PoD)

α membrane to total stress ratio β ratio brace diameter over chord diameterσ hot spot hot spot stressσ b bending stressσ m membrane stressσ mean mean stressσ j standard deviation of the stress response process in short-term condition j

∆σ stress range




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SECTION 2 STANDARDS AND REFERENCE DOCUMENTS

It is assumed that this document is used together with NORSOK N-003 Action and action effects regardingload calculations if not recommended otherwise in the present document. Alternatively it can be usedtogether with other standards such as DNV-OS-C101 and DNV-RP-C205.

Furthermore it is assumed that this standard is used together with NORSOK N-004 Design of SteelStructures which refers to DNVGL-RP-0005 Fatigue design of offshore steel structures for assessment offatigue capacity.

However, the referred documents are mainly intended to be used for design. Thus, for inspection planningother considerations are also relevant as described in [1.1]. Reference is made to App.A, App.B and App.C for additional information regarding fatigue analysis of jacket structures, semisubmersibles and floatingproduction vessels for the purpose of inspection planning.

A number of references to relevant literature have been included in [15.1]. Reference is also made to DNV-RP-G101 which is related to risk based inspection of topside structures. Even if much of the content isdifferent in these documents, they largely present the same basic philosophy for planning in-serviceinspection. This document also gives some definition of terminology frequently used in planning in-serviceinspection.




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SECTION 3 INSPECTION PLANNING FOR FATIGUE CRACKS

3.1 GeneralDegradations of offshore structure are caused by corrosion and fatigue crack growth. The effect of corrosion

is designed for by corrosion allowance or a protection system, which makes the corrosion developmentgradual and rather easy to control. The fatigue crack growth can be more critical because cracks can resultin a sudden rupture when subjected to large storm loads. Moreover, cracks are hard to detect because theyare small for a significant part of the crack growth time.

Defects much larger than those implicit in fatigue design curves are also of concern as observations of somecracks found during inspections can be attributed to such defects. Thus, these defects are understood to besignificantly larger than those included in a probabilistic fatigue analysis. Such large defects are alsosometimes denoted as gross errors.

Therefore the following safety principles should be implemented:

— design for adequate fatigue life including design fatigue factors (DFFs) and a sound corrosion protectionsystem

— design for robustness in relation to member failure

— plan inspection of the structure during fabrication as well as during the service life.

When inspections priorities are set, the potential of gross fabrication defects should also be considered.Since inspections after fabrication onshore can be performed at less cost and with higher reliability thanduring operation offshore, it is worthwhile to emphasise such inspections, at least for components whichare significant for the integrity of the structures.

Different inspection strategies may be relevant for different types of offshore structures. This is because theexisting structures possess different robustness with respect to fatigue cracking and because inspection,repair and failure costs vary significantly.

Jackets with four (4) or more legs are rather redundant structures when X-type bracing is used. The

consequence of a fatigue crack will still be dependent on position of crack and type of loading and possibilityfor redistribution of stresses during crack growth. For most hot spots there is a significant crack growthperiod before the integrity of the structure becomes a major concern. FMD can be used at these hot spotswhere potential fatigue cracks are likely to grow into air filled members.

The crack control in semi-submersibles with slender braces is based on a basic fatigue design criterion anddesign for the accidental limit state (ALS) as well as leak detection during operation. By ALS is understoodthat the structure shall be documented to be redundant in the accidental limit state condition.

Also for floating production vessels there is significant residual strength with respect to fatigue cracks whichnormally makes it possible to detect cracks using leak-before-break detection and by a close visualinspection (CVI). However, it is difficult to document acceptable crack length based on existing assessmentstandards which corresponds to that observed in sailing ships.

When planning inspection, it is important to assess the consequence of a potential fatigue crack at aconsidered hot spot. One may select different activities to achieve an optimal inspection plan. Engineeringassessment of the different methods and suitability of method for each hot spot should be assessed. Asketch to illustrate the assessment and development of an inspection plan for a detail is shown in Figure 3-1.

It may occur that cracks have been detected during former inspections, but have been assessed to notrequire a repair before another inspection is performed. If there are such cracks in the structure, one wouldstart out with this information as basis for another inspection planning.

All structural details should be evaluated in the development of an inspection plan. Each detail is consideredbased on calculated fatigue lives. In addition, the probability of a gross error related to load effect orcapacity should be kept in mind. The probability of such errors should also be considered when planninginspection for fatigue cracks. A general visual inspection (GVI) has traditionally been recommended for the

purpose of control of gross errors. A GVI may thus also have a positive effect on reliability with respect tofatigue even if the reliability of the inspection method is rather low until the cracks have grown large.




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Figure 3-1 Schematic development of inspection plan with respect to fatigue

Experience shows that gross errors are more likely for new types of details than if well proven design andfabrication methodologies are used. A new type of conductor support introduced in the 1990s is an exampleof this, where fatigue cracking occurred after short time in service. For such gross errors a GVI and leakagedetection is considered to be the most effective methodology.

Probabilistic analyses are performed for selected details to take into account the best estimate of long termloading and fatigue capacity.

The acceptance criterion is related to consequence of failure. Based on this it should be assessed if a detailedinspection by NDT is required or if it is sufficient with CVI, or NDE, for long calculated fatigue lives asindicated in Figure 3-1. Due to the redundancy of the considered structures it is assumed that NDT will onlybe required in special cases where the consequence of an error is large or catastrophic as indicated by thedotted line in Figure 3-1 for details with long calculated fatigue lives.

In fatigue assessment of an existing structure one will use the best available data and information about itsfatigue condition as derived from the fatigue analyses described in App.A, App.B and App.C. However, itshould also be realised that it is not practical to assess all details by probabilistic analysis, e.g. in a shipwhere longitudinals crosses transverse frames as it is not realistic to perform detailed inspection at allwelds. When assessing need for inspection of these areas, it should be remembered that the consequenceof a fatigue crack in longitudinals at transverse frames in the deck head in cargo tanks in FPSOs may belarger than for connections subjected to local bending moments as the plated deck structure are oftensubjected to large dynamic longitudinal membrane forces.

Due to the nature of fatigue and number of uncertain parameters involved, there will be uncertainty as towhen and where fatigue cracks will occur in a structure subjected to significant dynamic loading. The more

information that is available, the better it is for predicting future behaviour with respect to fatigue cracking.For example if stress measurements have been performed over a sufficient period together with measured




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environmental data, it may be possible to reduce the uncertainty related to the long term loadingsignificantly. When inspection of the as built structure is performed and is properly reported, it may bepossible to include fabrication quality in the assessment. If a low fabrication quality is detected, the fatiguecapacity may be downgraded for example by one or more S-N curves. This requires skilled surveyors andengineers. Good documentation in terms of photos is recommended as that can improve engineering

assessments in this respect. Also better guidelines on how to relate the level of fabrication quality to S-Ndata would be useful.

3.2 Analysis toolsWhen a defect or a crack is detected in a structure, the reason for this is asked. Quite often it is concludedthat the main reason for the crack is a poor fatigue detail. The reason for defects and cracks can be lessgood fabrication quality or it has simply not been analysed properly. If cracks are detected, moreinformation about the detail and the surrounding structure is achieved. This information can be used forfurther inspection planning. A similar assessment can also be made for details that have been inspectedwithout finding of any fatigue crack. This may be explained by a long calculated fatigue life. However, hotspots with very long fatigue lives would normally not be inspected. If the calculated fatigue life is short andfatigue crack might be expected, but is not detected, one may ask if the reason for not detecting a crack is:

— a better detailed design with a lower stress concentration for the considered detail than estimated,

— a higher S-N class than assumed,

— a dynamic loading lower than assumed at design stage,

— that one simply has to wait for another inspection period for more information about potential crackdevelopment.

Two different tools can help the analyst to keep control on need for inspection:

1) fracture mechanics making it possible to establish crack growth curves

2) probabilistic analysis to include uncertainties in parameters used for calculation of fatigue damage andmaking it possible to link the probability of detecting fatigue cracks by a specified inspection to that of

estimating probability of a fatigue failure.

When planning inspection, it is often useful to consider a deterministic crack growth development beforeone go into a probabilistic analysis approach. The reason for this is that a deterministic analysis approachis easier to understand and it can more easily be related to actual physical behaviour than by probabilisticanalysis.

The crack growth in a detail is dependent on the stress distribution through the thickness of the plate.Furthermore it is dependent on the possibility for redistribution of stress flow during crack growth.

Different crack growth developments are shown in Figure 3-2. The crack growth may start out from similarcrack sizes, but then the crack growth behaviour can be rather different depending on the structural detailand type of loading. The crack growth curve in Figure 3-2 a) may be representative for simple tubular jointswith possibility of redistribution of stress flow during crack growth. This means that there is a significanttime interval from the crack can be detected until failure of the joint.

For higher loaded joints the hot spot areas may need to be ground to achieve sufficient fatigue life asindicated in Figure 3-2 b). This means that with higher hot spot stress range the crack will grow faster whenit is initiated and the time period available for detection of crack is reduced. This time interval is furtherreduced for elements subjected mainly to dynamic tensile stresses like that in tethers of a Tension LegPlatform as illustrated in Figure 3-2 c). This development is also similar to that observed in the AlexanderL.Kielland platform. Even higher dynamic stresses can occur in ground butt welds as indicated in Figure 3-2 d). It is seen that these different crack growth curves show a large difference with respect to crack growthperiod after a crack is so large that it can be detected.

To include the effect of uncertainty of an inspection, a description of probability of presence of a crack atthe hot spot is needed. A description of the uncertainty of an inspection is also needed. Finding or no finding

of a crack does not provide enough information for a direct updating of all parameters in a fatigue analysiswhere several parameters are uncertain and contribute to the probability of a fatigue crack. However, the




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event of not finding a crack can be formulated as a limit state function as a probability of not finding a crack.This function can in principle be fulfilled by a number of combinations of the different parameters involved.The most likely of these combinations is the most interesting one. The parameter values for this most likelycombination can be determined based on first order reliability methods (FORM). These parameters for thiscombination can also be defined as “design values” of the parameters. These parameters need not

necessarily be the physically correct values, but are considered to be the best values an engineer candetermine based on available information.




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Figure 3-2 Schematic crack growth curves for different as-welded and ground details

a.

b.

c.

d.

00

Service life (years)

C r a c k d e p t h ( m m )

Maximum allowable size

Detectable size

td tT

T

00




Detectable size

td tT

T

Weld is groundWeld is ground

00




Detectable size

td tT

T

00




Detectable size

td tT

T

00




Detectable size

td tT

T

00




Detectable size

td tT

T

Weld is groundWeld is ground




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SECTION 4 OVERVIEW OF ANALYSES FOR PLANNINGINSPECTION FOR FATIGUE CRACKS BASED ON PROBABILISTICMETHODS

There are many aspects to consider when performing analysis for planning of inspection for fatigue cracksbased on probabilistic methods. Also the required technology covers a rather broad area from detailedfatigue analysis and crack growth analysis based on fracture mechanics to that of rather advanced statisticalanalysis taking the results from former inspections into the methodology. In addition to this also the morepractical issues related to actual inspections of structures above and below water need to be remembered.Therefore, the following section is written as guidance for the different steps to be performed. More detailedinformation is presented in the different sections that are referred to.

Then the following overview of analysis steps required for planning inspection for fatigue cracks based onprobabilistic methods is given:

1) Assess the need for new fatigue analysis for calculation of revised fatigue damages in order to direct theinspection to hot spots where fatigue cracks are most likely to occur. Reference is made to [5.1].

2) Perform new fatigue analysis as described in App.A for jacket structures, in App.B for semisubmersiblesand App.C for floating production ships (FPSOs).

3) Assess if more than one analysis model is required depending on operation area, subsidence andmodifications performed. If inspection has already been performed, it is recommended to transform thelifetime history into a timeline with constant damage rates as that will simplify the probabilistic analysis.Reference is made to [7.9].

4) The mean stress or effect of compressive part of the stress range is recommended to be considered forcalculation of fatigue damage in FPSOs when the calculated damage is used for planning in-serviceinspection for fatigue cracks. Reference is made to [10.5].

5) The calculated fatigue damage can be considered to be derived from an equivalent long term stressrange distribution described by a two parameter Weibull distribution. Reference is made to DNVGL-RP-0005 for description of Weibull distribution. This distribution is described by a shape parameter h and a

scale parameter q. In the following it is assumed that the shape parameter h is a constant and that thescale parameter q is calculated to correspond to the calculated fatigue damage at the considered hotspot. For this calculation it can be assumed that h = 0.8 for jacket structures and that h = 1.0 forsemisubmersibles and FPSOs.It is assumed that the scale parameter q is back calculated from the detailed calculated fatigue damagesfor each hot spot from analyses described in App.A to App.C.

6) Assess the consequence of a fatigue failure at the considered hot spot. This is required for assessmentof target reliability level and for selection of inspection method; i.e. is it acceptable to rely on leakagedetection or another NDT method. Some guidance on consequence of failure is given in [7.11] and [8.4].

7) Target reliability level to be decided based on consequence of failure and guidance in Sec.8.

8) M k functions from App.D can directly be used for details shown in Figure 4-1 a, b, c, e and f. M k functionsfor a fillet weld as shown in Figure 4-1 d are not provided. In-service inspection of fillet welds is normally

not meaningful before a potential fatigue crack has grown to the surface.More complex structural details may have been analysed using the hot spot method described inDNVGL-RP-0005. Examples of such details are shown in Figure 15-1 and Figure 15-2. M k functions tobe used for details analysed by the hot spot method are also presented in [6.6]. To account for bendingthrough the plate also the stress at the back side of the plate is required in addition to the hot spotstress.The M k functions are depending on as-welded condition versus ground. The M k functions are alsodependent on attachment length as explained in [6.5] if not the stress is derived from FE analysis usingthe hot spot stress methodology (Then it is implicitly accounted for in the calculated values).

9) Select crack growth parameters that are relevant for the considered environment and potential crackgrowth area (most often from weld toes in base material while crack growth from imperfections in theweld can occur in highly loaded butt welds). Reference is made to [10.11].

10)Perform a deterministic crack growth analysis for control purpose similar to that described in [6.1] to




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[6.3]. Assume a median crack size equal 0.03 mm for as-welded details. Guidance on ground welds isincluded in [10.14].

11)Perform probabilistic crack growth analysis based on parameter distributions presented in Sec.10 usinga relevant and properly documented computer program.

12)Determine time to first inspection based on target safety level.

13)Assess and select most suitable inspection method keeping in mind required documentation of residualcapacity with a fatigue crack present in the structure.

14) If earlier inspections have been performed, the effect of these on estimated probability of presence of a fatigue crack should be made. Reference is made to [7.5]. Reference is made to Sec.11 for PoD.

15)Time to next inspection can be based on the updated probability values.

16)Verify analysis results according to deterministic crack growth curves.

17)For structures less than 15 years of age assess if the inspection interval may need to be reconsideredin terms of variability in annual weather statistics. This consideration may be more important for anFPSO than for a jacket structure and a semisubmersible. Worse weather conditions during a year or twothan accounted for in the long term statistics may have some effect on accumulated damage until timefor inspection planning and also for the next planned inspection interval. Reference is also made to [5.6]

18)When inspection of more than one connection is planned where the geometry and loading are similar,one should consider the effect of correlation in expected behaviour. Reference is made to [7.10]. Theamount of inspection may be reduced if defects have not been detected. However, the amount of inspection should be increased if defects have been detected at similar connections earlier.

19)For ground welds see M k functions in [D.2] and calibration in [D.6.4].




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Figure 4-1 Examples of details to be assessed with respect to fatigue and inspection

a) Butt weld welded from both sides b) Cruciform joint

c) Fillet welded cruciform d) Fillet welded cruciform with potential crack growth fromthe weld root

e) Fillet welded doubling plate f) Fatigue cracking at mouse hole




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SECTION 5 FATIGUE ANALYSIS BASED ON S-N DATA

5.1 GeneralExperience from operation of offshore structures in the North Sea shows that reliable fatigue analyses are

important for control of the integrity of the structures. Experience from operation of offshore structures andfrom structures brought ashore also shows that fatigue cracking is less likely when fatigue analysis of highquality has been performed. Many fatigue cracks have been initiated in secondary structural componentsthat have not been properly analysed. In some cases these cracks have also grown into primary members.

If reliable fatigue analysis has been performed for design, this analysis may also be used for planning in-service inspection. As explained in [1.1] the focus during design is often different from that of inspectionplanning where “consistent” calculated fatigue lives are preferred in order to achieve a sound relativeranking of where fatigue cracks are most likely to occur.

This may be exemplified by Figure 5-1 where joint A could be selected for inspection as this joint show theshortest calculated fatigue life. However, if a more refined fatigue analysis were performed, the calculatedfatigue life may be moved to B. This means that this joint in reality has a long fatigue life; the probability

of a fatigue crack is small, and one would more likely expect to find a crack at other joints shown in Figure5-1. Thus, in order to learn as much as possible from an in-service inspection of a hot spot in a platform,the selection of inspection points should be based on fatigue analyses that are made for this purpose andwhich are consistent as far as possible (such that a correct ranking of the joint in terms of actual fatiguelives is achieved).

Also realistic absolute values of calculated fatigue lives for different details are wanted as basis forprobabilistic inspection planning. This is of largest importance for new platforms where the time to firstinspection is being planned.

Figure 5-1 Example of calculated life versus actual life

Some typical differences between a fatigue analysis intended to be basis for inspection planning and afatigue analysis used for design are:

1) Not all areas are analysed in detail at the design stage. A screening analysis of fatigue utilisation issometimes performed such that further assessment is concentrated on details that require furtheranalysis before they can be concluded to fulfil the fatigue design criteria. This does not mean that otherdetails will not necessarily need in-service inspection.

2) Conservative assumption regarding SCF of complex details are often made to avoid time consuming FEanalysis which could provide a lower hot spot stress and document longer calculated fatigue life. The

reason for this is also that inspection and maintenance of a structure is handled by another part of theowner organisation during operational life than that involved in design.




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3) There may be collected information during fabrication and installation that can provide useful data forfatigue analysis to be used as basis for inspection planning. This can be information related to repairwelds that were difficult to perform or due to fabrication tolerances that were in the outer region of whatcould be found acceptable according to fabrication specifications. Such information may provide usefulinput for selection of hot spots to be further investigated for in-service inspection. This is information

that was not available when the design analysis was performed.4) The as built structure can often be somewhat different from that on design drawings used for design

analyses. This can typically involve non-structural elements that have been welded to primary parts of the structures and which may have significant consequences with respect to fatigue (Ref. e.g.hydrophone holder in brace in Alexander L. Kielland which was the main cause of accident). For thisreason it is also important that a review of the structure is performed to establish an “as-is structure” before a new fatigue analysis is performed for the purpose of inspection planning as described in App.A,App.B and App.C.

5) The operation of the platform may be different from that assumed during design especially for floatingstructures. This may be due to different ballasting or due to other operation than originally planned.This can also be due to another deck weight and associated draught than designed for. Otherparameters such as marine growth or information on environmental data may be changed and different

from that assumed at an early design stage.

6) Some structures are relatively old and it is realized that fatigue analysis methods have been improvedthe last 10 to 20 years as reflected in App.A, App.B and App.C. This regards also computer programsand computer efficiency which makes it easier to aim for more reliable fatigue analysis today than atthe time when some of the existing structures were designed.

In order to achieve “consistent” fatigue analyses it is necessary to establish a sound reference basis forassessing uncertainty from fatigue analysis to be used as input to the probabilistic fatigue analysis. If theanalysis is in line with what is recommended in this document, the uncertainty in hot spot stress can bederived from [10.16].

If significant data are lacking, an engineering assessment is required to assess the performed analysisrelative to that recommended herein and finally uncertainties to be used in the probabilistic analysis haveto be decided.

During the service life the geometry of the structure or the loading may change due to e.g. modificationsand seabed subsidence. Operational requirements may be changed for floating structures or they may bemoved to new areas with different environmental loading. This may lead to a need for different analysismodels for different time periods. The total accumulated damage can then be added. However, to takeinspection history properly into account it is considered convenient to transfer the history into a time linethat corresponds to damage rate accumulation at time of planning inspection. This can be done byconsidering damage rate accumulations for the different time periods that are analysed. Reference is madeto [5.2] for a more detailed description.

Each designer and design office has their special preferences when performing design in terms of analysisprocedures and computer programs. This leads to special challenges when the results from these analyses

are being used for planning in-service inspection for fatigue cracks. Therefore it is recommended to performa careful review and assessment of basic fatigue analysis methods used by the industry for the differenttypes of structures before a more detailed inspection planning is started. Reference is made to App.A, App.B and App.C for jacket structures, semisubmersibles and floating production vessels, respectively.

5.2 Fatigue damage accumulation from more than one analysismodel

5.2.1 GeneralThe presented analysis methodology for probabilistic analysis and updating of probability of failure due toinspection results is based on an assumption of one long-term stress distribution with a constant damage

rate during the whole service life. However for some structures several analyses may be required due toe.g. subsidence, modifications, repair or the structure is operating in different environments.




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Assume for example that a member above the splash zone was inspected before it settled through this zone.

The annual fatigue damage that has been accumulated after the inspection is thus likely to be significantly

larger than the annual fatigue damage before the inspection. This means that significant fatigue damage

might have accumulated since the performed inspection. This means that the relative effective time span

since the inspection is longer than time spans corresponding to the situation before and after the membersettled through the splash zone. Thus the value of the inspection is not as large as for a case where the

accumulated damage has been more constant over the years in service.

Another example could be that a platform was strengthened after some years and that an inspection was

performed without crack detection just before this strengthening. It is assumed that this strengthening

reduced the stress range at the considered hot spot significantly. Thus the accumulated fatigue damage

each year is now reduced and this should also lead to less inspection or the inspection interval can be

increased.

In such cases it is convenient to transform the actual installation year and time of inspection to a time line

showing the same fatigue damage rate for all the analysis models. After this the probabilistic analysis and

inspection updating can be performed as otherwise described for a situation with constantly accumulated

fatigue damage during the operational life.

5.2.2 Mathematical model for probabilistic analysis with models withdifferent fatigue damage ratesIn the following it is assumed that fatigue analyses have been performed for N different analysis models.

Each model is used for calculation of fatigue damage within the time interval for which this model is

physically correct. Thus there are also N time intervals.

Assume now for simplicity that the present time corresponds to time interval number N and that time

intervals 1 to N-1 corresponds to analysis models that corresponds to former in-service history of the

structure.

Each of the time intervals can be denoted i.

Each real time interval is denoted ∆T i for i = 1 to i = N .

Assume that the calculated fatigue damage rate (annual fatigue damage) in time interval N is d N.

Then it is convenient to scale all the other time intervals such that the same damage rate is achieved for

the whole period the structure has been in service as that in period N. The equivalent lengths of the other

time intervals are then derived by scaling as

where d i = calculated fatigue damage rate in time interval ∆T i such that the accumulated fatigue damage

during time interval ∆T i is

It is assumed that the time corresponding to start of time interval N is denoted T N. Then the start of each

of the other equivalent time intervals can be calculated as

(5.1)

(5.2)

(5.3)

11 −==∆=∆ N toi for

d

D

d

d T T

N

i

N

ii

eq

i

iii d T D ∆=

−

∆−=

1 N

i

eqi N

eqi T T T




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The equivalent installation year is calculated as

or

The equivalent fatigue life can be calculated based on current fatigue damage rate in time interval N as

Equivalent “end of life” year based on time interval N as reference is

Also the time for performed inspections has to be transferred into the equivalent time line. For an inspectionperformed in time period i at time T insp the following equivalent inspection time is derived:

Variables:

i time period number

Di accumulated fatigue damage ratio in period i

d i damage rate per year for period i

T N year start of period N

T i year start of period i

d N current damage rate

T i+1 end year period i

N number of time periods where the last period N also is used as a reference period

∆T i time interval period i

T insp time of inspection (year)

5.2.3 Example of analysisAn example of a transformation of the damage accumulation in three different analysis models to the sameannual damage (or damage rate) of today is shown as follows for a structure installed in year 1972.

Calculated fatigue damage rate from installation until 1986: 0.0106.

Calculated fatigue damage rate from 1986 until 2000: 0.0068.

Calculated fatigue damage rate from 2000: 0.0031.

The time line for actual performed inspections and the resulting time line for equivalent inspections are

shown in Figure 5-2. The equations in Sec.5.2.2 are used for this transformation to an equivalent time linewith damage rates from year 2000 as reference level.

(5.4)

(5.5)

(5.6)

(5.7)

(5.8)

−

∆−=1

1

1

N eq

i N

eq T T T

N

N

i

N

eq

d

D

T T −

−=

1

11

N d L

1

=

LT T eqeq

L += 1

( )i

eq

i

iinsp

ieq

i

eqeq

insp T

T T T T T T

∆

∆−+∆+=

−1 11




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If the damage rates in the first and third analysis models were interchanged, the time line would lookdifferent as shown in Figure 5-3.

In both examples the installation year is 1972 and the current damage rate is based on the analysis modelfrom year TN = 2000. In the first case an equivalent installation time is 1921 due to stretching of the time

period to correspond with the damage rate of today that is used for planning future inspections. This iscalculated from equation (5.5) as

From equation (5.1)

Example of transformation of inspection in 1996 into present timeline is derived from equation (5.8) as

The installation year for the second case is similarly derived as for the first case as

Figure 5-2 Example of calculated equivalent installation and inspection years.The damage rates in this example are decreasing for each T i

(5.9)

(5.10)

(5.11)

(5.12)

19210031.0

0068.0)19862000(

0031.0

0106.0)19721986(20001 =

−−

−−=eqT

310031.00068.0)19862000(

480031.0

0106.0)19721986(

2

1

=−=∆

=−=∆

eq

eq

T

T

( ) 199119862000

3119861996481921 =

−−++=eq

inspT

19870106.0

0068.0)19862000(

0106.0

0031.0)19721986(2000

1 =

−−

−−=eqT

1920 1940 1960 1980 2000 2020

Time for actual inspecions

Transformed time for inspection




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Figure 5-3 Example of calculated equivalent installation and inspection years; the damage rates in thisexample are increasing for each Ti

5.3 Jacket structuresInspection planning of jackets may be performed based on fatigue analysis methods as described in App.A.

5.4 SemisubmersiblesInspection planning of semisubmersibles may be performed based on fatigue analysis as described in App.B.

5.5 Floating production vesselsInspection planning of floating production vessels may be performed based on fatigue analysis as describedin App.C.

For design of floating production vessels it is normal practice to design details for full stress rangeindependent of mean stress. However, the probability of having fatigue cracks at hot spots subjected toglobal or local compressive stresses is significantly lower than for details subjected to tensile stress ranges.A factor for calculating an effective reduced stress range depending on mean compressive stress ispresented in Sec.10.5.

5.6 Long term dynamic loadingFor offshore structures it is often efficient to assume the long term stress ranges to be represented by atwo-parameter Weibull distribution. This distribution is described by a scale parameter q and a shapeparameter h. This is a practical description of the long term stress range response that can be used bothfor fatigue analysis based on S-N data and fracture mechanics.

As shown in App.A, App.B and App.C different analysis methods can be used for calculation of fatiguedamage for different types of structures from that of a deterministic discrete wave fatigue analysis to thatof a full stochastic analysis (in frequency or time domain).

For the purpose of probabilistic fatigue analysis it may be convenient to calculate a Weibull long term stressrange distribution that provides the same fatigue damage as that derived from the more direct calculationspresented in App.A, App.B and App.C. This can be performed by assuming a Weibull shape parameteraround 0.8 for a jacket structure and a shape parameter equal 1.0 for the floating structures if not moreaccurate information on shape parameters are available for the considered structure and hot spot.

The final probabilistic analysis results are not very sensitive to the selection of shape parameter as it is usedone way to determine the Weibull scale parameter and next it is used in the opposite way to calculate aprobability of a fatigue crack. Therefore it is important that the calculated fatigue damage is as correct aspossible. Here it is assumed that the calculated fatigue damage is determined by analysis described in

App.A, App.B and App.C. The situation would be very different if such fatigue analyses were not performedand the analyst was merely estimating a shape parameter for calculation of fatigue damage. In such a case

1970 1980 1990 2000 2010

Time for actual inspecions

Transformed time for inspection




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it is obvious that the results will be very sensitive to the value of the Weibull shape parameter. Referenceis made to of DNVGL-RP-0005 Sec.5 showing relations between stress range, Weibull shape parameter andS-N curves. Reference is also made to DNVGL-RP-0005 App.D showing the important part of the stressrange history relative to the S-N curves.

In order to simplify the analysis it is normally recommended to assign uncertainty to long term loaddistribution only to one parameter. Then it is easier to relate uncertainty to the scale parameter than to theshape parameter as the scale parameter represents a stress range in the long term stress distribution andengineers are used to the concept of maximum allowable stress range already from a design stage.Reference is for example made to DNVGL-RP-0005 Sec.5 showing maximum allowable stress ranges fordifferent Weibull shape parameters, DFFs and environments.

For structures less than 15 years old one should assess if the inspection interval may need to bereconsidered in terms of variability in annual weather statistics. Significant fatigue damage is expected toaccumulate each year if the calculated fatigue life is short. This may also imply short inspection intervalsand if the weather is less good during one year, this may result in significant increased accumulated fatiguedamage that year which may influence the need for inspection. If the calculated fatigue lives are longer,also the inspection intervals are longer and the accumulated fatigue damage within one inspection interval,

spanning over several years, are expected to be closer to a more typical mean value. This considerationmay be more important for an FPSO than for a jacket structure and a semisubmersible. Worse weatherconditions during a year or two than accounted for in the long term statistics may have some effect onaccumulated damage until time for inspection planning and also for the next planned inspection interval.For northern North Sea environment it was found that the calculated fatigue damage varies by a factor of4.3 from year to year for an FPSO and 1.9 for a semisubmersible based upon data for 29 years. Thevariations in wave height from one year to another year are larger for the larger wave heights. This explainsthe difference between the FPSO where global bending is main contribution to fatigue damage, and the splitforces which give the largest contribution to fatigue damage for the semisubmersible.




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SECTION 6 FATIGUE ANALYSIS BASED ON FRACTURE MECHANICS

6.1 Introduction

Fatigue of welded connections consists of a fatigue initiation phase, a crack growth phase and a final fracture

(phase). The fatigue test results from laboratory testing of welded connections include the cycles due tofatigue crack initiation and the following crack growth until failure. Most of the fatigue life in weldedstructures is associated with fatigue crack growth. In this document crack growth is assumed to occur fromsmall (somewhat fictitiously small) initial cracks sizes such that a similar fatigue life is calculated by fracturemechanics as that of S-N test data.

The stress condition at a cracked region can be described by the concept of stress intensity factors. Thegeneral expression for the stress intensity factor describing the stress condition at crack tip region in a bodywith far field stress normal to the crack 2a is

where

σ = remote stress as indicated in Figure 6-1.

a = half crack length for the considered internal crack; a = crack depth for edge cracks.

Y = geometry function. This function is equal 1.0 for a small crack in an infinite body. Otherwise it is afunction of geometry that normally is larger than 1.0 (under tension load; may be less for bending).

The elastic stress field at the crack tip region can be expressed by the following two-dimensional solutionusing polar coordinates

where K I is the stress intensity factor in the opening mode and the other symbols are shown in Figure 6-1.

From this equation it is seen that the stress field at a position (r,θ ) at the crack tip is known if also the stressintensity factor K I is known.

Normally the function Y is a function of the crack size and is written as Y(a). In addition to being a functionof crack size it is also a function of boundary conditions and type of loading (different in moment loading ascompared with tensile loading). A number of geometry functions can be found in handbooks on stressintensity factors. Then the more general equation for the stress intensity factor can be written as

It can be seen that it is the remote stress that becomes a significant parameter governing the value of thestress intensity factor in addition to the geometry function and the crack size.

During cyclic loading from σ min to σ max the considered connection is subjected to a stress range ∆σ = σ max-

σ min. From equation (6.3) it is seen that this stress range also corresponds to a range in the stress intensityfactor ∆K = K max – K min where the index I for the opening mode now is removed for simplicity.

(6.1)

(6.2)

(6.3)

aY K g π σ =

+

−

=

2

3cos

2sin

2cos

2

3sin

2sin1

2cos

2

3sin

2sin1

2cos

2

ϕ ϕ ϕ

ϕ ϕ ϕ

ϕ ϕ ϕ

π τ

σ

σ

r

K I

xy

y

x

aaY K I π σ )(=




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Then the following equation for range of stress intensity factor is derived

As an alternative to expressing the fatigue load in terms of stress range one can also express the same bythe range of the stress intensity factor when considering crack growth based on fracture mechanics. Anexpression for this was first formulated by Paris around 1963. This reads

where

da = increment in crack growth for dN stress cycles.

C and m are material parameters.

∆K th = threshold value for the stress intensity range. Below this threshold range there is no crack growthas indicated in Figure 6-2.

K mat = material fracture toughness. Unstable fracture of the connection may occur as the maximum stressintensity factor approaches the fracture toughness as indicated in Figure 6-2.

Figure 6-1 Illustration of stress field in front of a crack tip in a large plate

(6.4)

(6.5)

aaY K π σ )(∆=∆

( ) mat th

m K K K for K C dN

da≤∆≤∆∆=




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Figure 6-2 Illustration of crack growth equation

Equation (6.5) can be written as

By integrating left and right hand sides from an initial crack size a0 to a final crack size ac, the followingequation is derived

Here the following integral is defined

Then the equation for number of cycles during fatigue crack growth is derived as

Taking the logarithm on left and right hand sides the following equation is derived

Now the similarity between S-N formulation and fracture mechanics is observed from this equation whenlog(I/C) is put equal to loga in an S-N formulation. This means that in principle it is possible to construct S-

(6.6)

(6.7)

(6.8)

(6.9)

(6.10)

( ) dN

aY aC

da

mm

m=

∆ )(π σ

( )∆=

ca

a mmmaY a

da

C N

0 2/)(

1

π σ

( )=

ca

a mm aY a

da I

0 )(2/π

mC

I N

σ ∆=

σ ∆−= log)/(loglog mC I N




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N curves for different details based on fracture mechanics if proper geometry functions were available forthe considered detail. This would also require selection of a sound initial crack size as discussed in othersections of this document. The selection of a final crack size is of less importance for calculated number ofcycles to failure.

6.2 Example of crack growth analysisThe purpose of the following example is to present a soft transition to the more complex analysis based onfracture mechanics.

An example of a fatigue crack growth from internal defects in a cruciform is presented. Cruciform joints aremost often welded from both sides. In some cases partial penetration welds are used. This leaves some lackof penetration in the root area as shown in Figure 6-3. Also defects in the root may be detected in fullpenetration welds made from both sides if a good back gouging/grinding of the root has not been performedsuch that impurities are left in the root.

For short defects in the root of the connection in Figure 6-3 the geometry function Y = 1.0 can be assumed.

Then by integration of equation (6.7) the following expression is derived (as m ≠ 2.0)

and

The following values for the material parameters m = 3.0 and C = 5.21·10-13 (N, mm) in air environmentare inserted in this equation to derive number of cycles to failure calculated by crack growth analysis

The C parameter used here represents mean plus 2 standard deviations in crack growth test data for weldsin air (BS 7910). Thus using this equation for calculation of number of cycles implies a similar safety level

as using mean minus 2 standard deviation S-N curves as presented in design standards for fatigue.

There is some uncertainty associated with sizing of embedded defects using ultrasonic testing. Thisuncertainty should be kept in mind when acceptance criteria are being assessed. Also when it comes toprobability of detecting fatigue cracks during service life it is not an easy task to detect cracks growing frominternal defects before they are becoming large. Therefore, one may want to assess such defect with alarger safety factor than defects initiating from the outside weld toes.

(6.11)

(6.12)

(6.13)

f a

a

m

mm m

a

C N

02

1

1 21

2/

−∆

=

−

σ π

−∆

−

=

−−

12

2/

21

21

0

mC

aa

N mm

m

f

m

σ π

0.3

5.05.0

01210894.6σ ∆

−⋅=

−− f aa

N




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Figure 6-3 Cruciform joint with internal defect in the weld root

A plate thickness t = 25 mm is considered.

Normally the yield strength of the weld material is higher than that of the base material. Also with some

fillets as shown in Figure 6-3, the effective area at the defect region is larger than in a section through thebase plate. Thus, a fatigue crack can likely grow rather large before an unstable fracture is expected.However, this depends also on the fracture toughness of the material, service temperature etc.

In the following it is assumed that maximum allowable crack size 2af is equal half the plate thickness (12.5mm). This may be acceptable if the initial defect is not very long, but this may be a too long large final cracksize if a long defect is being considered like that of a continuous lack of penetration. (If the crack is

becoming large as compared with the total area used for force transfer, the stress intensity at the crack tipsis increased due to this reduction in net area at the crack and one should put the Y as a function of crackarea relative to the total area such that Y becomes larger than 1.0 and an increasing function as the crackgrows. However, the crack size is considered so long that this simplified two-dimension model can be used;but the crack is not so long that the assumption of assuming Y = 1.0 becomes significantly non-

conservative).It is assumed that the cruciform joint is fully utilized with respect to fatigue and that it for fatigue crackingfrom the weld toe is classified as F. From Table 2-1 in DNVGL-RP-0005 a stress range equal to 41.52 isderived for 107 cycles. Now the question is how large initial defect size can be accepted without getting alarger possibility for crack growth from the root than from the weld toe. This can now be solved from

equation (6.13) and the results are shown in Figure 6-4. The same design fatigue factor (=1.0) is here usedfor the weld as for the weld toe. It is observed that calculated crack growth from internal defects is longerthan for the outer weld toe until the initial crack size is approximately 8 mm. (For simplicity it is assumedthat the nominal stress level in the weld is not reduced due to the size of the fillet. Furthermore, a possibleeffect of crack curvature has not been accounted for as a simplified analysis has been performed forillustration). This illustrates that one can perform fracture mechanics analysis of internal defects rather

easily. For external defects the geometry function increases and for defects at weld toes also the geometryfunction for the weld toe has to be accounted for. This is described more in detail in the following sections.




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Figure 6-4 Calculated number of cycles as function of initial defect size in the root

6.3 Fracture mechanics models for surface cracks at weld toesGeometry functions for details with cracks can be found in handbooks on stress intensity functions and insome standards such as BS 7910 and API 579-1/ASME FFS-1. The total stress intensity consists of ageometry part and a part describing the local stress at the weld. The first part corresponds to that of thegeometry for calculation of hot spot stress and the stress magnification at the weld corresponds to the notch

stress increase at the weld that is normally included in a hot spot S-N curve. Thus the total stress intensityfactor at a weld can be presented as

where

M k = function describing the stress field due to the weld notch and type of loading. M k is a stressmagnification factor which includes the effect of local stress concentration from the notch at the weldtoe as proposed by Bowness and Lee (2000). M k functions are presented in BS 7910 (2013) for filletweld angles equal 45o. More general equations are presented in HSE document OTO 2000/077(2002). M k functions are presented in App.D.

K g = function describing the stress intensity at the considered crack due to geometry of the detail andtype of loading

A semi-elliptic surface crack at a weld toe is considered as shown in Figure 6-5.

The fatigue crack growth of this surface crack per stress cycle is assumed to follow the Paris and Erdoganequation at any point along the crack front. From this equation an increment dr( θ ) in increased crack sizeduring dN load cycles can be calculated as

where θ is the location angle along the crack front, C r( θ ) and m are material parameters for that specific

(6.14)

(6.15)

g k K M K =

m

r r K C

dN

dr ))()((

)(θ θ

θ ∆=




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point, ∆K r ( θ ) is the range of the stress intensity factor for the considered load cycle.

It is assumed that the fatigue crack shape remains semi-elliptical as the crack propagates, i.e. the crackdepth, a, and the crack length, 2c, are sufficient to describe the crack front. Then the general differentialequation (6.15) can be replaced by two coupled differential equations

where t ini is the crack initiation time and ∆K th is the threshold level for the stress intensity below which thecrack is not propagating. a0 is initial crack depth and 2c0 is initial crack length. The subscripts a and c referto the deepest point A and the end point of the crack at the surface of the semi-elliptic crack at B,

respectively.

The general expression for the stress-intensity factor is

where σ tot is the total applied stress and Y(a,c) is the geometry function accounting for the global geometryand the loading condition. The stress intensity factors for a surface crack in a finite plate subjected tomembrane and bending loads proposed by Newman and Raju (1981) are applied to represent the ellipticcrack:

Here Y m and Y b are the geometry functions for pure membrane and pure bending loading, respectively.Suffix m refers to membrane loading and b refers to bending loading. The factor α is the membrane to totalstress ratio.

Then the stress intensity factors that also include the effect of the weld notch at positions A and B can becalculated as:

where M kma, M kba are the geometry functions at position A for membrane and bending stress, respectively,and M kmc, M kbc are the geometry functions at position B for membrane and bending stress, respectively.See also App.D for geometry functions for the weld notch.

Equations (6.21) and (6.22) can be inserted into equations (6.16) and (6.17) and a numerical solutionprocedure is applied to solve these coupled ordinary first order differential equations.

(6.16)

(6.17)

(6.18)

(6.19)

(6.20)

(6.21)

(6.22)

0)(;)( ; at a K K K C

dN

dainithaaa

m =∆>∆∆=

0)(;)( ; ct c K K K C

dN

dcinithccc

m =∆>∆∆=

( ) acaY K tot g π σ ,=

( ) ( ) ( ) )1(,,, α α −+= caY caY caY bamaa

( ) ( ) ( ) )1(,,, α α −+= caY caY caY bcmcc

( ) ( ) ( ) ( )( ) aca M caY ca M caY K kbabakmamatot a π α α σ )1(,,,, −+=

( ) ( ) ( ) ( )( ) aca M caY ca M caY K kbcbckmcmctot c π α α σ )1(,,,, −+=




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Figure 6-5 Semi-elliptic crack at a weld toe

In the following, the equivalent one dimensional crack growth model is applied for illustration purposes only.Then the crack growth formula reads

The geometry function Y m for membrane loading in a plate is determined with the procedure of Newmanand Raju (1981) and BS 7910:2013. The following geometry function is proposed for calculation of stressintensity factor in general:

where

M = bulging factor used for cracks in curved structures like shell structures; ref. BS7910. For plated

structures M =1.0.The equations provided below apply to flat plates with semi-elliptical cracks.

The finite-width correction function ƒ w is given by:

for (2c/W) ≤ 0.8

where

W = width of plate.

Normally the cracks are small as compared with the global geometry in structures where the forces aretransferred such that f w =1.0.

M m for membrane loading

The stress intensity magnification factor for semi-elliptical cracks loaded by membrane stress is equal to:

where:

for 0 ≤ a/2c ≤ 0.5

(6.23)

(6.24)

(6.25)

m

ca K C dN

da

)),((∆=

m M w f M mY =

2/1

sec

=

T

a

W

c f w

π

Φ

+

+= /

4

3

2

21 θ f g T

a M

T

a M M M m

( )ca M /09.013.11 −=




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for 0.5 < a/2c ≤ 1.0

for 0 ≤ a/2c ≤ 0.5

M 2 = 0.2 (c/a)4 for 0.5 < a/2c ≤ 1.0

for a /2c ≤ 0.5

M 3 = -0.11 (c/a)4 for 0.5 < a/2c ≤ 1.0

g = 1 + [ 0.1 + 0.35 (a/T) 2 ]( 1 - sinθ )2 for a / 2c ≤ 0.5

g = 1 + [ 0.1 + 0.35 (c/a) (a/T)2 ]( 1 - sinθ )2for 0.5 < a/ 2c ≤ 1.0

ƒ θ = [(a/c)2 cos2θ + sin2θ ]1/4 for 0 ≤ a/ 2c ≤ 0.5

ƒ θ = [(c/a)2 sin2θ + cos2θ ]1/4 for 0.5 < a/ 2c ≤ 1.0

The complete elliptic integral of the second kind Φ is given by:

for 0 ≤ a /2c ≤ 0.5

for 0.5 < a /2c ≤ 1.0

The definitions of a, c and θ are shown in Figure 6-5.

The following simplifications can be made:

At the deepest point on the crack front:

g = 1.0

ƒ θ = 1.0 for 0 ≤ a/ 2c ≤ 0.5

ƒ θ = (c/a)0.5 for 0.5 < a/ 2c ≤ 1.0

At the ends of the crack, θ = 0

g = 1.1 + 0.35 (a/T)2 for 0 ≤ a/ 2c ≤ 0.5 g = 1.1 + 0.35 (c/a) (a/T)2 for 0.5 < a/ 2c ≤ 1.0

ƒ θ = (a/c)0.5 for 0 ≤ a/ 2c ≤ 0.5

ƒ θ = 1.0 for 0.5 < a/ 2c ≤ 1.0

If a/ 2c > 1.0 use solution for a/ 2c = 1.0.

M m for bending loading

whereM m is calculated from equation (6.22).

(6.26)

[ ])/(04.01)/(1 acac M +=

54.0

)/(2.0

89.02 −

+

=

ca

M

[ ]24

3 )/(0.114)/(65.0

0.15.0 ca

ca M −+

+−=

65.1

464.11

+=Φ

c

a

65.1

464.11

+=Φ a

c

mb M H M =




DNV GL AS

where

for 0 ≤ a/2c ≤ 0.5

for 0.5 < a/2c ≤ 1.0

for 0 ≤ a/ 2c ≤ 0.5

for 0.5 < a/2c ≤ 1.0

where

for 0 ≤ a/ 2c ≤ 0.5

for 0.5 < a/ 2c ≤ 1.0

for 0 ≤ a/2c ≤ 0.5

for 0.5 < a/2c ≤ 1.0

The following simplifications can be made:

At the deepest point on the crack front, θ = p/ 2 so that H =H 2 and:

g = 1.0

ƒ θ = 1.0 for 0 ≤ a/ 2c ≤ 0.5

ƒ θ = (c/a)0.5 for 0.5 < a/ 2c ≤ 1.0

At the ends of the crack, θ = 0

g = 1.1 + 0.35 (a/T)2 for 0 ≤ a/ 2c ≤ 0.5

g = 1.1 + 0.35 (c/a) (a/T)2 for 0.5 < a/ 2c ≤ 1.0

ƒ θ = (a/c)0.5 for 0 ≤ a/ 2c ≤ 0.5

ƒ θ = 1.0 for 0.5 < a/ 2c ≤ 1.0

and

H = H 1

If a/ 2c > 1.0 use solution for a/ 2c = 1.0.

A schematic crack growth analysis procedure is shown in Figure 6-6. The threshold stress intensity factorhas been set equal to zero.

It is a challenge to perform fracture mechanics analysis that corresponds with observed fatigue cracking ofdifferent details. One reason for this is lack of reliable stress intensity factors for typical details used inoffshore structures.

The stress intensity factor as function of crack size depends significantly on the local stress field i. e. whetherthe stress is due to membrane loading or bending loading. This can be derived from a FE analysis of a hotspot region without a crack present. The complexity increases when a change in stress distribution duringcrack growth is to be accounted for. This can only be properly quantified by a FE analysis including a cracksuch that proper boundary conditions can be accounted for in the analysis. This is of significant importancefor different types of tubular joints.

It may be noted that the Newman Raju equations for stress intensity factors presented above have beenderived from FE analyses with cracks present but subjected to a static determinate loading. This means that

( ) θ q H H H H sin121 −+=

( ) ( ))/6.0/2.0 T acaq ++=

( ) ( ))/6.0/2.0 T aacq ++=

( ) ( )( )T acaT a H //11.0/34.011 −−=

( ){ }( ) ( ) ( ){ }( )25.175.0

1 //38.1/93.155.0//41.004.01 T aacacT aac H +−++−=

( ) ( )2

212 //1 T aGT aG H ++=

( )caG /12.022.11 −−=

( )acG /77.011.21 +−=

( ) ( ) 5.175.0

2 /47.0/05.155.0 cacaG +−=

( ) ( ) 5.175.0

2 /14.0/72.055.0 acacG +−=




DNV GL AS

redistribution of stresses due to restraint at boundaries during crack growth is not accounted for. Thus theuse of these equations will normally lead to inspection intervals to the safe side.

It is recognised that the S-N data are more correct (or closer to the laboratory test data) in general thanthat of calculations based on fracture mechanics. Analysis results from fracture mechanics are dependent

on more parameters than that of S-N data: crack growth parameters, initial crack size and stress intensityfactors during crack growth. Therefore a calibration of the fracture mechanics model is made such that itprovides fatigue lives in agreement with the test data and that it provides a similar calculated probability offailure as that derived from S-N data (test data that includes initiation and crack growth). This is furtherexplained in D.6, Sec.9 and Sec.6.

It is important that the calculated crack growth period is realistic because it is the crack growth curve thatprovides an estimate of time to detect a growing crack before it is defined to reach a critical size. Due tothe significance of the crack growth shape it is also recommended to perform a deterministic crack growthanalysis for critical details; reference is made to Sec.3.2 and to validation of probabilistic analysis in Sec.12.

The fatigue initiation time for details that have been weld improved may become a significant part of thefatigue life. A reason for weld improvement is often large hot spot stress ranges. This can also imply thatthe crack may grow rather fast at such regions as soon as it has been initiated. Therefore proper crack

growth curves are of significant importance for planning inspection at such areas.




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Figure 6-6 Schematic crack growth analysis procedure




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6.4 Alternative methods for derivation of geometry functions

Accurate analyses to determine geometry functions or stress intensity factors for different details mayrequire significant work. Therefore simplifications are most often made to arrive at practical solutions. Thefollowing levels of accuracy may be described:

For less experienced analysts it is often easier to perform detailed analyses than making engineeringassessment. Thus level 3 would be expected to provide the most accurate results. However, this is also themost time consuming method.

For level 3 it is also recommended to include the geometry of the welds, accurate boundary conditions andrelevant loading such that a further assessment of the geometry function, equation Y in (6.19), is notrequired.

Level 2 is considered to be acceptable for smaller cracks that have not grown through the plate thicknessand where redistribution of stresses during crack growth is considered to be less important for the analysisresults. Here the hot spot stress can be separated into a membrane part and a bending part and asuperposition of stress intensities from these parts (from Newman and Raju) can be assumed to govern thecrack growth. This solution will represent a two-dimensional stress field through the plate thickness. Thus,this may be a conservative approach if the hot spot stress is of local nature and the stress decreases awayfrom the hot spot such as at bracket toes ended on plates (such that the half axis c in Figure 6-5 has grownaway from the main hot spot area).

Level 1 is the simplest way to derive a geometry function. It is assumed that an S-N classification can bemade based on the actual geometry. When the S-N curve is known, also the hot spot stress can be derived

from DNVGL-RP-0005 Table 2-1 (Ref. column in this table for structural stress concentration embedded indetail). Now it may be an engineering challenge to decide on how to split the stress into a membrane partand a bending part before the procedure under level 2 is followed further. Here it should be rememberedthat the membrane part implies a larger crack growth than that of bending. Therefore, it is recommendedto put more weight into membrane than to that of bending if uncertainty exists.

Example of a level 1 method

Assume as an example of a level 1 method that a hot spot at the end of a long attachment is considered.Then the following steps are followed for assessment:

— Reference is made to Table A-7 and end of detail 1 in DNVGL-RP-0005. This gives S-N class F3.

— From DNVGL-RP-0005 Table 2-1 a SCF equal 1.61 is derived for the F3 class.

— The fracture mechanics is calibrated against an F-curve which includes a SCF equal 1.27 according tothe same DNVGL-RP-0005 Table 2-1. Reference is made to App.D for documentation of calibration. Nowit is assumed that the fracture mechanics part is performed with the same L/T = 40/25 = 1.6 as usedfor calibration (L is attachment length and T is plate thickness). Reference is made to Sec.6.5. Then thegeometry function in equation (6.19) can be increased with the resulting stress increase for detail 1 by1.61/1.27 =1.27.

— Then the fracture mechanics analysis can be continued as outlined in [6.1] to [6.3].

6.5 Geometry functions for plated structures with longer

attachments

Reference is made to S-N curves in DNVGL-RP-0005.The SCF for attachment is presented in Figure 6-7 when the D-curve is used as a reference together with a nominal stress approach.

Level Description

1 geometry known without any further clear information about geometry function for the stress intensity factor

2 finite element analysis of the hot spot region performed without including any crack in the analysis model

3 finite element analysis of the hot spot region performed with different crack sizes included




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Figure 6-7 SCF as function of attachment length in fatigue a DNVGL-RP-0005

The calibration of fracture mechanics and S-N data was performed for an attachment length equal L = 40mm. This corresponds to F-class S-N curve in DNVGL-RP-0005. Reference is also made to detail 8 in DNVGL-RP-0005 Table A-7. This curve has an implicit SCF = 1.27 (Ref. DNVGL-RP-0005 Table 2-1). Thus, it isproposed to use the M k factor for L = 40 mm and derive a SCF for longer attachment than L = 40 mm. Thusone needs to define a stress concentration factor that is defined relative to an F-detail. This is achieved bydividing the SCF for the D-curve in Figure 6-7 by the SCF inherent the F-curve (= 1.27). The result fromthis calculation is also shown in Figure 6-7. Now a slight modification is performed at L = 40 mm tocorrespond with SCF = 1.0 at L = 40 mm to get a final resulting curve for attachment length SCF as shownin Figure 6-8. This curve is represented by the following expression:

The following recommendation is given:

— For longer attachments than the validity range for the M k factors (2.75L/T) it is recommended to

perform the analysis with a M k factor corresponding to L = 40 mm and multiply this factor by the SCFfrom equation (6.24). Reference is made to App.D for background.

(6.27)

mm300> L for SCF

mm L for L LSCF

L

L

27.1

3009179.0002188.010400.3 26

=

≤++⋅−= −




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Figure 6-8 Additional SCF on M k factor

6.6 Hot spot stress in plated structures derived from finiteelement analysis

The following recommendations are given when hot spot stresses in plated structures have been derivedfrom FE analysis:

— For hot spot stress derived from FE analysis with method A in DNVGL-RP-0005 one can use the M k factor

for L= 0.5T and relevant weld toe angle θ .

— For hot spot stress derived from FE analysis with method B in DNVGL-RP-0005 one can use the M k factorfor L= 0.5T and relevant weld toe angle θ multiplied with factor 1.12.

— For hot spot stress at simple butt welds welded from both sides (that corresponds to S-N curve D inDNVGL-RP-0005) one can use M k for L = 0.5T and weld toe angle θ =15o.

— For hot spot stress at single sided butt welds welded from one side one can use M k for L = 0.5T andweld toe angle θ =15o multiplied with SCF from DNVGL-RP-0005 Table 2-1 that corresponds to therepresentative S-N curve (Example SCF = 1.43 for the F1-curve which is typically recommended for asingle sided weld).

— The nominal stress S-N curves should be used for fatigue life assessment for hot spots at cruciform jointconnections without any web stiffening in the direction of main force flow according to DNVGL-RP-0005[4.3.7]. For these connections one can perform crack growth analysis with direct use of the equationsand parameters presented in Sec.6.1.

Both the membrane and the bending stress through the plate thickness are required for fatigue analysisbased on fracture mechanics. Thus also the stress at the back side of the plate at the considered hot spotshould be derived from the FE analysis. The membrane stress is:

The bending stress is:

(6.28)

(6.29)

2/ sideback spot hot m σ σ σ +=

2/ sideback spot hot b σ σ σ −=




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6.7 Simple tubular joints

Reference is made to App.B in DNVGL-RP-0005 for definition of simple tubular joints and parametric SCFfor these.

The equations for stress intensity factors presented in Sec.6.1 can also be used for assessment of tubular joints. (By a simple tubular joint are understood welded connections between tubulars without internal orexternal stiffeners. A tubular joint does not include girth welds). A large fraction of the stress concentrationin simple tubular joints is due to local bending over the thickness. Therefore it is recommended to split thehot spot stress into a membrane stress and a bending stress before the fracture mechanics analyses areperformed.

As fatigue cracks are growing deep there is also considered to be more load shedding in tubular joints thanin the joints where stress geometry functions have been presented in Sec.6.1. From HSE report 2000/077a load shedding function for T-type tubular joints has been presented. This factor reduces the geometryfunction by a factor significantly lower than 1.0 when the crack grows deep as shown in Figure 6-9.However, an adequate set of equations on a general basis cannot be found in the literature in order thatthis effect can be included in an RP for planning in-service inspection for fatigue cracks.

Thus, a load shedding in tubular joints can in general only be properly accounted for when FE analysis ofthe joints has been performed with rather large cracks included in the FE model.

The stress intensity solutions by Newman and Raju are derived from cases of cracks in bodies subjected toloading at their free ends. They are basically statically determinate structures. However, if some degree ofredundancy is introduced, the local stiffness changes as the crack grows. In general the decrease of localstiffness of the cracked section reduces the membrane force and the moments acting on the cracked sectionwhich results in a reduction in stress intensity at the crack tip.

If the stress intensity factors for real joints are calculated with a crack present in the FE model, loadshedding will automatically be included in the derived stress intensity factor. In this case it is alsorecommended to use two slope crack growth parameters in order to avoid a non-conservative analysis

procedure.

Figure 6-9 Load shedding in tubular joints from HSE report 2000/077




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The stress intensity factor for the deepest position of a semi-elliptical crack in a tubular joint can be derived

where

index “a” indicates geometry functions at the deepest point of the crack

DOB = degree of bending at the hot spot

σ hot spot = hot spot stress derived from FE analysis or from nominal stress times stress concentrations intubular joints derived from parametric equations, see DNVGL-RP-0005.

The stress intensity factor for the ends of a semi-elliptical crack in a tubular joint can be derived

index “c” indicates geometry functions at the crack ends.

It is observed from the equations for stress intensity factors that the DOB is a significant parameter. Itsvalue depends on type of joint, geometry and thus also on size of SCF. A large SCF can normally beconsidered to be associated with a rather large DOB for a simple tubular joint.

The degree of bending can simply be defined as

where

σ b = bending stress

σ t = total stress = membrane stress + bending stress

SCF inside = stress concentration on inside

SCF outside = stress concentration on the outside as derived from parametric equations for tubular joints

This equation may not be useful for engineering as SCFinside is normally not known without making a FEanalysis of the considered joint. However, there is now a section included in DNVGL-RP-0005 on the SCFsfor the inside of tubular joints. These are expressed by a reduction factor R related to the SCF for theoutside. Thus the equation for degree of bending can also be written as:

It should be noted that the DOB has been assessed for the data base that was used to derive the S-N curvefor tubular joints (the T-curve). A mean value for DOB in the HSE data base is reported as 0.81. Other meanvalues of interest in the data base are L/T = 1.17 and θ = 43o. This may be useful information for calibrationof crack growth with S-N data.

For large β values there is not much bending over the brace thickness. From Dijkstra and De Back (1981)it is assessed that DOB = 0.35 for β = 1.0 for an X-joint. A similar value of DOB is obtained for a tubularwelded to a fixed plate which will result in a SCFoutside= 1.54 and a SCFinside= 0.46 based on analyticalconsiderations due to Poisson’s effect. This also gives DOB = 0.35. This may be considered to be a lowerbound value for β = 1.0 for axial force and out of plane bending moment.

The hot spot stress in K-joints subjected to axial forces is due to membrane stress and local bending overthe chord thickness. DOB equal 0.5 is derived assuming that half of the hot spot stress is membrane stress

(6.30)

(6.31)

(6.32)

(6.33)

( ) ( ) ( ) ( ) ( )( ) a DOBca M caY DOBca M caY kbabakmamatot aTubular π σ ,,1,,, +−=

( ) ( ) ( ) ( ) ( )( ) a DOBca M caY DOBca M caY K kbcbckmcmctot cTubular π σ ,,1,,, +−=

−==

outside

inside

t

b

SCF

SCF DOB 1

2

1

σ

σ

( ) R DOB −= 12

1




DNV GL AS

and the other part is bending stress. The DOB is significantly larger for a K-joint with β = 0.39. Here it wouldbe acceptable to use equation (6.31) for the chord side. For the brace side it is assessed to be safer to usea DOB equal 0.5.

Then the following guidance with respect to value for DOB may be given:

— It is conservative for crack growth analysis to assume a small DOB value (or the amount of crack growthwill be overestimated if a too low DOB value is assumed as membrane stress results in faster crackgrowth than bending stress over the thickness).

— The DOB is lowest for tubular geometries with β = d/D close to 1.0 subjected to axial force and out ofplane bending moment with DOB = 0.35. (Here d = diameter of brace and D = diameter of chord). Thismay be considered to be a lower bound value for β = 1.0 for axial force and out of plane bendingmoment.

— For all types of joints DOB may be derived from equation (6.31) for in-plane bending.

— For T-, Y- and X- joints with β lower than 0.8 DOB may be derived from equation (6.31) for axial loadand bending moments. DOB = 0.35 can be assumed for joints with β ≥ 0.90 for axial load and out-of-plane bending. A linear interpolation between β = 0.80 and β = 0.90 may be used to derive DOB in thisrange of β values.

— For K- joints with β lower than 0.8 a DOB may be derived from equation (6.31) for bending moments.For β ≥ 0.90 a DOB = 0.35 can be used for out-of-plane bending. A linear interpolation between β = 0.80and β = 0.90 may be used to derive DOB in this range of β values for out-of-plane moment.

— The hot spot in K-joints without overlap subjected to axial load is normally in a region between thesaddle and the crown point between the brace members. Here DOB may also be derived from equation(6.31) for the chord side and a DOB = 0.5 can be assumed for all β values for the brace side.

— DOB = 0 for the chord crown where the SCF in T- and Y-joints is due to global bending of the chord.

6.8 Stiffened tubular jointsFor highly stiffened tubular joints it is assessed to be conservative to assume DOB = 0.35 for all types of joints and loading conditions.

Reference is also made to Stacey et al. (1996) and Slater et al. (1996). Cracks in heavily stiffened jointscan initiate at several locations at approximately the same time which can result in shorter crack growthperiods and therefore shorter inspection intervals may be recommended than for simple tubular joints.

If the SCF for stiffened tubular joints are larger than 3.0, there is likely to be significant bending over thethickness at the hot spots and the recommendations in Sec.6.7 can be considered used.




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SECTION 7 ASSESSMENT OF PROBABILITY OF FATIGUE FAILURE

7.1 GeneralOne of the most important parts of a reliability evaluation of a structure is to identify potential failure modes

and to define the failure mechanisms in terms of mathematical models, i.e. defining the limit-state functionor safety margin. The failure criteria are modelled through limit state functions, defined such that theoccurrence of failure is represented through a negative limit state function value.

There are large uncertainties associated with fatigue of offshore structures. These uncertainties may,however, be reduced over the service life through monitoring and in-service inspections. The additionalinformation achieved through these actions will give more confident estimates both on the present state ofthe structure and on the expected future behaviour.

With additional information is here meant data such as the outcome from NDT determining the status withrespect to fatigue damage accumulation and potential fatigue cracks in the structure. Procedures to accountfor this additional information in the determination of the reliability of the structure are presented in thefollowing.

An example of development of a crack from an initial defect distribution to a critical crack size is indicatedschematically in 7-1. The crack growth is shown on the positive vertical axis and time for crack growth isshown on the horizontal axis. The development of calculated probability of a fatigue failure is shown in thedownward direction of the vertical axis. At time t1 the initial defect distribution have likely grown wider dueto uncertainties in the crack growth parameters and crack driving stress range.

It is assumed that an inspection is performed at time t1. In this example it is assumed that defects are notfound. The inspection is assumed to be associated with a significant probability of detecting large cracks.Thus, provided that cracks are not detected during an inspection, it is likely that large cracks are not presentat the considered hot spot. Due to the actual probability of detection curve a narrower defect distributionafter inspection is indicated like that shown in the figure (as it is likely that the largest defects would havebeen detected if present). This also means that the probability of a fatigue failure in the nearest future canbe considered to be lower than that assumed before the inspection. This is also indicated by an updated

probability of failure curve in the figure. If no inspection at t1 was performed, the reliability of the detailwould be unacceptable at time t2. Now, after inspection at time t1, the reliability of the detail with respectto fatigue is considered to be acceptable until time t3 when a new inspection is required to fulfil theacceptance criterion (maximum acceptable failure probability).




DNV GL AS

Figure 7-1 Schematic illustration of crack growth and probability of fatigue failure before and after aninspection

7.2 Failure probability at design stage7.2.1 GeneralThe failure criteria are typically time dependent due to the time dependent fatigue damage accumulationover the service life and possibly also due to the time dependent loading (Ref. [7.9]).

A limit state function can be defined as:

where R is a function modelling the fatigue capacity and S is a function modelling the load effect. Both R and S are defined from underlying stochastic variables. If the loading S is larger than the capacity R, the

limit state function is negative which means fatigue failure. The capacity can also be considered as aconstant distribution in an S-N diagram as indicated in Figure 7-2. The accumulation of load cycles S(t) canbe illustrated by another distribution in the same diagram that moves to the right as more cycles areaccumulated. The distribution denoted S(t1) is not resulting in any calculated probability of failure.However, the distribution denoted S(t2) has so many accumulated load cycles that there is a probabilitythat the accumulated load history is larger than the fatigue capacity. The probability of this to occur definesthe probability of fatigue failure over the service time and can be expressed as

In the derivation of the failure probabilities, special attention should be paid to the type of probability that

is derived; an accumulated or time limited failure probability or an annual failure probability as explainedin the following sections.

(7.1)

(7.2)

)()()( t S t Rt M −=

( )0)()( ≤= t M P t P F




DNV GL AS

Figure 7-2 Illustration of accumulated fatigue damage with time

There are some cases where reliabilities can be calculated by analytic approaches and one example isincluded in the following section for illustration purpose. For simplicity it is assumed that the fatigue damageis calculated based on a single slope S-N curve and that the fatigue damage can be calculated according toequation

A single sided butt weld in plates between equal thickness t = 25 mm is selected as an example. This detailis assumed to be classified as F1 according to DNVGL-RP-0005 (2015). This gives log a ̅ = 11.699 for thecharacteristic or design S-N curve. Then the mean S-N curve is derived log a = log a ̅ +2 · slogN. With slogN =0.20 log a = 11.699 + 0.20 · 2 = 12.099. Fatigue failure is assumed to occur when the Palmgren-Miner’sfatigue damage becomes equal or larger than 1.0. The limit state function for this can be written as inequation (7.1) with R and S as indicated in Figure 7-2. The limit state function can also be written as g =1-D where D is accumulated fatigue damage and failure is defined for g ≤ 0. For g = 0 one may take thenatural logarithm of this function for definition of a new limit state function such that it reads g = -ln D.From equation (7.3) and by using mean S-N data (log a) the following limit state function is derived

Here the parameters n, a and q can be considered as random variables. For simplicity the negative inverseslope m of the S-N curve and the shape parameter in the Weibull long term stress range distribution arekept constant; m = 3.0 and h = 1.0. These parameters are normally kept constant in reliability calculationsin order to be able to estimate sound values of the associated parameter distributions for log a and the scaleparameter q. The random variables in equation (7.4) are termed zn, za and zq and all are supposed to benormally distributed. z n = ln n represents uncertainty in number of actual stress cycles. This uncertainty isnormally considered to have a rather small impact on the end result as compared with uncertainties in theload and response and the S-N data. There is also uncertainty in the Palmgren-Miner’s damageaccumulation rule and this uncertainty may be represented by the same parameter. The expected value µlnn

= ln n0 and the standard deviation is σ lnn. In the following σ lnn = 0.30 is used. z a represents uncertainty inS-N data. This uncertainty is normally presented in a logarithmic format with base equal 10. Thus, the

(7.3)

(7.4)

+Γ =

h

mq

a

n D m 10

+Γ −−+−=

h

mqman g 1lnlnlnln




DNV GL AS

expected value reads µ lna= E(log10a) · ln10 and the standard deviation reads slna = sloga · ln10. zq represents uncertainty in load and load response data. This uncertainty can be represented by a mean value µ lnq= lnq and a normalized standard deviation in a normal distribution as CoV = σ / µ . Then the followingapproximation is made for further analysis slnq ≈ CoV . Then the limit state function can be written as

As all variables are normally distributed, also g is normally distributed, and the mean value is derived as

The variance is derived as the sum of the individual variances as

Then the reliability index can be calculated as

and the probability of a fatigue failure is calculated from a statistical table for a normal distribution as

Now the following numerical examples can be provided: Assume 20 years’ service life with n0 =108 cycles. µ lnn= ln n0= 18.4207.A Weibull long term stress range distribution with shape parameter h = 1.0 is assumed. The scale parameterq is determined from equation (7.3) as q = 4.368 MPa for DFF =10, q = 6.525 for DFF = 3.0 and q = 9.411for DFF = 1.0.Γ (1+3.0/1.0) = 6.0. ln (6)=1.7918. σ lna = 0.46. σ lnq = 0.25 is assumed.For DFF = 10 this gives µ lng = 1.473 µ g =3.2236, σ g = 0.928, β = 3.4669 and P f = 0.000263. For DFF = 3 β = 2.1720 and P f = 0.0149.For DFF = 1.0 β = 0.9905 and P f = 0.1610.

When these results are compared with the numerical derived results in Figure 9-3 in DNVGL-RP-0005(2015) it is observed that this analytical calculated values are somewhat to the safe side.

7.2.2 Accumulated and annual failure probabilityFatigue damage is accumulated over the service life for structures subjected to dynamic loading and it ispractical to relate this damage to an accumulated failure probability. This means that the calculated failureprobability is the probability that the structure fails during the time period prior to the time considered.

The annual failure probability is obtained by subtracting the accumulated failure for failure prior to the yearconsidered from the accumulated failure probability at the end of the year considered. Then the annualfailure probability from year t i to t i+1 is derived as

(7.5)

(7.6)

(7.7)

(7.8)

(7.9)

(7.10)

+Γ −−+−=

h

mmz z z g

qan 1ln

+Γ −−+−=

h

mm qan g 1lnlnlnln µ µ µ µ

2

ln

22

ln

2

ln

2

qan g m σ σ σ σ ++=

2/12

ln

22

ln

2

ln

lnlnln

)(

1ln

qan

qan

g

g

m

h

mm

σ σ σ

µ µ µ

σ

µ β

++

+Γ −−+−

==

( ) ( ) β −Φ=≤= 0 g f P f P

)()()to( 11 iiii t P t P t t P −=∆ ++




DNV GL AS

Examples of accumulated probability of failure and annual probability of failure with respect to fatigue arepresented in DNVGL-RP-0005 Sec.9 as function of DFFs (or the inverse of DFFs). Similar curves withaccumulated probability of failure and annual probability of failure depending on uncertainty in long termloading are also presented in [8.2].

7.2.3 Time-limited failure probabilityThe type of failure probability derived for structures not degrading over time is depending on theformulation of the time varying loading. For example if the loading is expressed as the annual largest load,it is the annual failure probability that is derived when a probability that the load exceeds the capacity iscalculated. Expressing the same calculation using the 100 years largest load results in the determination ofthe 100 years failure probability (given that the structure is not degrading over time). This corresponds toa probability of being exceeded equal to 10-2 on an annual basis. This type of probabilistic analysis isrelevant for calculation of a collapse of the structure given that there is a fatigue crack present.

7.2.4 Probability of being exceededThe concept of probability level is being used in design of ship structures. It is also used in the fatigue

analysis described in App.C. This is a notation with a different meaning from that described in [7.2.2] and[7.2.3].

The notation is used with reference to a Weibull description of a long term distribution of stress ranges, orwave heights. The probability level is here defined as the probability that a value is being exceeded. Forexample if there are n0 = 108 load cycles during 20 years, the probability that a wave height or a loadingis being exceeded during these load cycles in these 20 years is 1 /n0 =10-8. Thus it can be seen that this israther different from that of an annual probability.

The equation for the relation between wave height and probability of being exceeded reads

This can be deduced from the definition of the Weibull distribution. Reference is also made to Chapter 2 ofthe Fatigue Handbook (1985).

A probability level referred to in App.C equal 10-4 means that the wave height corresponding to thisprobability level for a Weibull shape parameter equal 1.0 is

where H max is maximum wave height during 20 years. Thus from this equation it is seen that a probabilitylevel 10-4 corresponds to half a maximum wave height during 20 years with a Weibull shape parameter hequal 1.0.

A similar expression can be derived for stress ranges

where

∆σ 0 = q · (ln(n0))1/h where q is scale parameter and h is shape parameter in a Weibull distribution (that canshow a different shape parameter from that in equation (7.11).

(7.11)

(7.12)

(7.13)

h

n

n

H H

/1

0max log

log

1

−=

max

/1

8

4

max2

1

10log

10log1 H H H

h

=

−=

h

n

n/1

0

0log

log1

−∆=∆ σ σ




DNV GL AS

If one simply defines ∆σ 0 as the largest stress cycle during n0 cycles and similarly defines ∆σ as the largeststress cycle during n cycles, the following expression is derived

This equation is practical for transformation of stress ranges between different probability levels. Thus,considering e.g. an offshore structure subjected to wave loading during 20 years, the number of cycles istypically 108. The largest stress range during 20 years can be denoted as ∆σ 20. The corresponding numberof cycles during 100 years is 5 · 108. The largest stress range during 100 years can be denoted as ∆σ 100.Equation (7.14) can be used to establish the relation between these two stress ranges.

7.3 Implementation of monitoring resultsMeasurements of platform response, which might become available over the service life, will increase theknowledge of the structural behaviour and thereby reduce the prediction uncertainties related to theloading. This will increase the confidence in the evaluation of the structural integrity.

Monitoring results can be applied directly in the assessment of the actual fatigue damage accumulation andin the prediction of the degradation rate by improved estimate of the long term loading as well as by reduced

uncertainty related to the long term loading. This additional information can be applied together withinformation becoming available from inspections of the structure for assessment of the structural integrity.

7.4 Inspection planning and inspection programmeIn inspection planning, the inspection has still not been made, such that the outcome of the plannedinspection is not known, and may accordingly not be accounted for in the calculation of probability of failure.

The inspection planning does not have any influence on the estimated future failure probabilities unless itis associated with a certain action. This action might for example be that all detected cracks are planned tobe repaired, or that all detected cracks above a critical pre-defined acceptance level are to be repaired. Thismeans that in practise one can initially plan the first inspection only. Then one has to assess the inspectionresults before the next inspection interval is planned.

7.5 Inspection updatingThe difference between inspection updating and inspection planning is in this context emphasised.Inspection updating is use of information that has become available through inspections, and inspectionplanning is planning of the future inspection programme and how different possible future outcomes fromthese inspections should be assessed such as repair philosophy.

Inspection updating is based on the utilisation of information that becomes available at discrete timeintervals over the service life when the structure is being inspected for fatigue cracks. This information isapplied both in the assessment of the present condition and in the prediction of the future behaviour.Inspection updating then determines the calculated updated future failure probability of the structureaccounting for this additional information.

When an inspection for fatigue cracks has been carried out, there are three different levels of informationthat may become available from the inspection:

(7.14)

(7.15)

h

n

n/1

0

0log

log

∆=∆ σ σ

( ) h

h

h

n

n

/1

100

/1

8

8

100

/1

100

2010020

92.0105log

10log

log

log

σ σ

σ σ

∆=

⋅∆

=

∆=∆




DNV GL AS

— No detection: This implies that potential fatigue cracks are smaller than the detection ability of theinspection equipment being applied.

— Detection: This implies that fatigue cracks have been observed.

— Detection with sizing measurement : This implies that fatigue cracks have been observed and that thesize of the cracks has also been quantified through measurements.

In addition there is a possibility for false identifications, which is not being covered further in this context.

In order to exemplify this information, the following events are defined:

The limit state event as presented by equation (7.1) where M less than zero implies failure.

The detection event:

where ad is the detectable size of a crack and d(t i ) defines the level of damage accumulation at the time ofinspection t i. The detectable size of a crack is given directly from the PoD curve for the inspection equipmentbeing applied.

H larger than zero implies that the crack is smaller than the detection ability of the inspection tool, resultingin no detection of a crack. H less than zero implies that the crack is larger than the smallest detectable crack.

The sizing event:

where am is the measured crack size, which may be associated with uncertainty. The sizing event is zero asthe crack size at time t i is measured to be am.

The probability of having failure at time t prior to an inspection is then

The calculated probability of having failure at time t after an inspection at time t 1 not resulting in anydetection can be expressed as

For N multiple inspections not resulting in any detection, the following formulation applies

The calculated probability of having failure at time t after an inspection at time t 1 resulting in crack detectionwithout any sizing measurement is then

The additional information from the inspection is included in the probability formulation throughconditioning, implying that the failure probability is estimated conditioned on the observed outcome fromthe inspections that have been carried out. The more available information that is included in the modellingof the failure probability, the more accurately the integrity of the structure can be assessed.

7.6 Description of probabilistic fatigue analysis models

Probabilistic fatigue analysis can be based on standard S-N data and use of Palmgren-Miner rule togetherwith a long term stress range distribution.

(7.16)

(7.17)

(7.18)

(7.19)

(7.20)

(7.21)

)()( id i t d at H −=

)()( imi t d at D −=

( )0)()( ≤= t M P t P F

( )0)(|0)()( 1 >≤= t H t M P t P F

( )0)(0)(0)(|0)()( 21 >∩∩>∩>≤= N F t H t H t H t M P t P

( )0)(|0)()( 1 ≤≤= t H t M P t P F




DNV GL AS

The limit state function applied in the probabilistic analysis is expressed as

where the random variable ∆ describes general uncertainty associated with the fatigue damageaccumulation and D is the accumulated fatigue damage.

Defining ν 0 as the mean number of stress cycles per time unit over the service life, the total accumulatedfatigue damage in a service period T can be expressed as

where Dcycle is the expected fatigue damage per stress cycle, depending on the local stress range responseprocess and the associated S-N curve.

Applying a bi-linear S-N curve and assuming the stress range distribution to be Weibull distributed, the

expected damage per stress cycle is calculated as:

where q and h are distribution parameters in the Weibull distribution, and γ (;) and Γ (;) are the Incompleteand Complementary Incomplete Gamma functions. Reference is made to DNVGL-RP-0005 App.D. Referenceis also made to DNVGL-RP-0005 for constants in the two-sloped S-N curve. s1 is transition from one part ofthe S-N curve to the other part.

The fatigue damage for floating offshore structures is derived from the weighted sum of the accumulated

fatigue damage within each short-term stationary condition (sea state), for which the stress process isassumed stationary Gaussian and narrow banded. This assumption implies that the stress range distributionbecome Rayleigh distributed. The expected damage per stress cycle within each short term condition j isthen defined from the above expression with shape parameter h = 2 and scale parameter ,where σ j is the standard deviation of the stress response process in short-term condition j .

7.7 Description of probabilistic crack growth analysisProbabilistic crack growth analysis can be based on the same equations as used for deterministic crackgrowth analysis presented in Sec.11.

The variables in the differential equation for non-threshold crack growth models can be separated andintegrated to give

where a(t) is the crack depth at the time t and N(t-t ini ) is the total number of stress cycles in the time period[t ini ,t]. C and m are crack growth parameters defined in [10.11].

(7.22)

(7.23)

(7.24)

(7.25)

D D g −∆=∆),(

cycle DT D ⋅ ν⋅= 0

+Γ +

+=

h

q

s

h

mmq

a

h

q

s

h

mmq

acycle D 111

1

122

2

;11

;11

γ

jq σ 22=

( )−

=

∆=

)(

1

)(

0

init t N

i

miC

t a

a

mamY

daσ

π




DNV GL AS

The sum in equation (7.25) can be estimated by , giving

where the term D(aN ) is an indicator of the damage accumulated by the growth of a crack from its initialvalue a0 to a crack size aN after N stress cycles.

For fatigue crack growth models including thresholds, the fatigue damage indicator can be expressed as

where G(a) is a reduction factor in the range 0-1, depending on the threshold level ∆K th and the stress rangeprocess ∆σ , ref. Madsen et al. (1987).

7.8 Formulation of inspection updatingThe effect of an inspection on the fatigue reliability of structures depends on the detection ability of theparticular NDT method used. The detection ability as a function of a defect size (crack depth, a, or cracklength, 2c) is defined by a PoD curve, see Sec.11.

Regardless of whether or not cracks are detected, each inspection provides additional information to thatavailable at the design stage, which can be used to update the reliability. Inspection updating is based onthe definition of conditional probability

P(F|I) is the probability that event F occurs given that event I occur e.g. inspection result.

An inspection results in either no detection or the detection of a crack, ref. Madsen et al. (1986)

In the first case, no cracks were found in the inspection after the time ti, implying that any cracks weresmaller than the smallest detectable crack size

Adi. Adi is obviously a random variable, since a detectable

crack is only detected with a certain probability. The distribution function for Adi is equal to the PoD function.When more inspections are performed the random variables Adi are mutually independent.

In the second case, a crack size Aj is observed after the time t j. Aj is also random due to possiblemeasurement errors and/or due to uncertainties in the interpretation of the measured crack size.

For each inspection which does not result in crack detection, an event margin, M i, can be defined similar tothe safety margin used to describe fatigue failure. The event margins for a one dimensional crack growthmodel may be formulated as

(7.26)

(7.27)

(7.28)

(7.29)

(7.30)

∆− m E init t N σ )(

∆−= m E init t N C N a D σ )()(

( )= N a

a

mm

N

aY aG

daa D

0 )()(

π

P F I

P F I

P I ( | )

( )

( )=

∩

dii At a ≤)(

j j At a =)(

−−

=

mS E

init

it N C dx

A

am

xm

xY i

M

di

)(

)(

1

0

π




DNV GL AS

These event margins are positive.

An event margin for each measurement resulting in detection of a crack can similarly be defined as

These safety margins are zero.

The calculated failure probability in the time period after the inspection is derived by applying probabilistic

conditioning on the inspection outcome. This is illustrated schematically in Figure 7-3. It is indicated that

more knowledge about the structural behaviour and calculated accumulated fatigue damage is achievedafter an inspection. If cracks are not detected, it is indicated that the structure is acceptable for another

time period. The length of this period depends on calculated fatigue life, shape of the crack growth curve

(amount of local bending at the hot spot and possibility for redistribution of stresses during crack growth),

and reliability of the inspection method as indicated in the figure. This may be explained by information thatthe actual situation is better than that one predicts before the inspection. The improved situation may be

due to less long term loading, lower hot spot stress, better fabrication than expected when compared with

S-N data used, less damage accumulation than predicted by Palmgren-Miner rule or due to a combinationof these effects.

The calculated failure probability with a detected crack that is not repaired is also indicated in Figure 7-3.The development depends on calculated fatigue life and further crack growth development. Therefore an

engineering assessment is recommended when fatigue cracks are detected.

Also if cracks are found and repaired, the curve for calculated accumulated probability of failure may be

different from that indicated in Figure 7-3. If a repair is carried out, one will normally try to make the repair

more reliable than that of the original detail. This can be modification of local geometry or weldimprovement by for example weld toe grinding.

A number of examples of inspection planning are shown in Sec.15.

Figure 7-3 Schematic illustration of calculated accumulated probability of fatigue failure depending oninspection findings and repair

(7.31)

∆−−

= m E init jt N C dx

A

a

m xm xY

j M

j

σ

π

)(

)(

1

0




DNV GL AS

7.9 Change in damage rate over service lifeWhen fatigue damages are added together from more than one analysis, it is recommended to transfer thedifferent damage rates into one time line that represent the same damage rate as of today over the fullservice life. This is recommended in order to take the effect of inspection properly into account. A procedure

for this is described in detail in [5.2].

7.10 Effect of correlationThe effect of correlation with respect to long term fatigue loading and fatigue capacity at different hot spotsis discussed in the commentary section in [D.4.2]. The effect of correlation is considered to be mostsignificant for details showing a long crack growth period.

In order to consider correlation with respect to possibility for fatigue cracking at two different hot spotsthere need to be similar or equal geometry of the considered details, fabricated in the same way and thelong term loading have to be approximately the same at the two hot spots. Otherwise, if the load effectsdiffer by some 10-20% the correlation effect is substantially reduced even if the geometry is the same.When inspection has been performed, the effect of correlation also depends on the probability of detectionof the inspection method used. See also [D.4.2].

The amount of inspection may be reduced in the inspection planning if there are many similar details thatare subjected to a similar long term stress range loading. Then it may be sufficient to select a limitednumber of details for inspection.

The effect of correlation can lead to reduced amount of inspection as long as fatigue cracks are not detected;but the opposite occurs if cracks are detected, then the amount of inspection needs to be increased.

7.11 Residual strength of the structure or system effects with afatigue crack presentFatigue crack growth through the thickness of a joint or connection does not necessarily mean that theconsidered structure is close to collapse. The reason for this is that jacket structures, semisubmersibles andfloating production vessels are rather redundant structures. One reason for this is requirements imposed indesign related to the ALS in NORSOK N-001.

Residual capacity with a crack present in the structures is considered in [8.4]. [D.4.1.3] provides somesimplified guidance with respect to system failures. This is considered important for assessment of targetsafety level. It is assessed that simplified procedures will normally be sufficient for documentation of safetylevel. It is likely that a limit on number of fatigue cracks in the structures will govern more the assessmentof safety level than an advanced assessment of system reliability. In this respect it also becomes importantto select connections for inspection such that a possible progressive failure path is avoided (by progressivefailure of several joints such that a failure mechanism is established).




DNV GL AS

SECTION 8 TARGET RELIABILITY

8.1 GeneralThe recommended target values depend on the failure consequence. This is normally assessed also at the

design stage through selected design fatigue factor (DFF) for the considered hot spot. This information mayalso be used as basis for back calculation of required reliability during the in-service life of the structure,how the fatigue analysis is performed, in service experience from similar types of structures in relation toaccuracy of performed fatigue analysis, and the crack growth curve for a potential fatigue crack. The targetreliability level depends on how likely is it that a fatigue crack can be detected before it becomes critical(this should also be an outcome from the inspection planning based on the proposed methodology), numberof potential fatigue cracks in the structure that may become critical during the same time period, age ofstructure and experience from earlier inspection in terms of detected fatigue cracks in relation to expectedfatigue cracks based on fatigue analysis. This also depends on general information about the amount ofdetected cracks in the structure as predicted by analysis; or if there are strong indications that the fatigueanalysis is conservative.

— Many of these considerations would be included in an assessment by an experienced structural engineer

when developing an inspection plan for a structure without using probabilistic analysis.— It is difficult to transfer all engineering judgement into numerical requirements to target safety values

in a standard to be used for general inspection planning. However, it is hoped that with the guidancegiven in the following sections also engineers working with probabilistic analysis will be in a position todecide on sound target values that will lead to a more uniform safety level during the life-time of thestructure.

8.2 Calculated probabilities of fatigue failureCalculated probabilities of fatigue failure are shown in Figure 8-1 and Figure 8-2 for different uncertaintiesin calculated load effect (as input to S-N data). Results for CoVs on load effect on hot spot stress from 0.10to 0.30 are presented. The analyses are based on 20 years’ service life for a floating structure with a mean

zero-up-crossing frequency equal 0.13, a Weibull long term stress range distribution with shape parameterh = 1.0. In addition uncertainty in the Palmgren-Miner rule is included as log normal with median 1.0 andCoV = 0.30.

Thus the uncertainties that are considered to contribute most significantly to a calculated probability offatigue failure are included in the derivation of the two figures. These figures may be used to assess thesafety level implicit in a design with a specified Design Fatigue Factor.




DNV GL AS

Figure 8-1 Accumulated probability of fatigue crack failure as function of design fatigue factor

Figure 8-2 Annual probability of fatigue crack failure as function of design fatigue factor




DNV GL AS

8.3 Target probability of failure for different design fatiguefactorsThe accumulated and annual probability of failure as a function of DFF are given in Figure 8-1 and Figure8-2, respectively. Assuming a CoV = 0.20 to be representative for a mean uncertainty in load effect for

typical offshore structures, the target probabilities of failure are given in Table 8-1.These values are also proposed as acceptance criteria for establishing the inspection intervals for NDTinspection.

Thus in order to derive target values for inspection planning it is necessary to assess consequences of afatigue failure at the different hot spots. Normally this is assessed during design and DFF are determinedand specified in the design premises for the structures according to NORSOK N-001 or standards referredto by the Classification Societies.

These target values are considered to apply to rather sound structures. If the condition of the consideredstructure is such that several fatigue cracks might be expected to be detected during a planned inspectionand that these cracks can be a threat to the integrity, a higher target level should be aimed for.

The annual probabilities of failure listed in Table 8-1 are presented for the last year in a service life of 20years. For another service life (derived by × years) an annual probability of failure can be derived as

8.4 Target probability of failure as function of consequence of afatigue failure

8.4.1 GeneralA risk matrix with consequence of failure along the horizontal axis and probability of failure along the verticalaxis is shown in Figure 8-3.

The probability of a fatigue failure increases over time because of time-dependent accumulation of fatigue

damage during cyclic loading. Inspection increases knowledge of potential fatigue cracks in the structure,and may reduce the estimation of the risk by reducing calculated probability of failure.

The consequence of a fatigue failure is considered to be less dependent on time. However, if there are manyhot spots with potential fatigue cracks in the structure, also the consequence of a fatigue failure mayincrease as more fatigue damage is accumulated in the structure.To reduce the consequence of a fatigue failure one may introduce mitigating measures in terms ofstrengthening; but it can also be inspection of surrounding structure for assessment that it has a soundcapacity without any deficiency.

In general, the target level on the structural failure probability is defined dependent on the consequenceand nature of failure as described in [7.11]. The evaluation of the consequence of failure comprises anassessment with regard to human life, environmental impact and economics as described in NORSOK N-

001.It must be kept in mind that the structural reliability analysis described herein does not include gross errors

Table 8-1 Relation between Design Fatigue Factor and probability of failure for CoV = 0.20 on the load

effect

Design fatigue factor Accumulated probability of a fatigue failure Annual probability of a fatigue failure the last yearin 20 years’ service life

1 1.1 × 10-1 1.0 × 10-2

2 2.2 × 10-2 3.0 × 10-3

3 7.1 × 10-3 1.1 × 10-3

5 1.3 × 10-3 2.4 × 10-4

10 9.1 × 10-5 2.0 × 10-5

(8.1)

x p p annual f xannual f

2020=




DNV GL AS

that have to be analysed by other techniques, i.e. by traditional risk analysis. Possible sources for grosserrors and evaluation of their probabilities must be evaluated separately for each structure. Thus, it shouldbe noted that calculated probabilities of failure cannot be taken as an absolute measure of the frequency offailure. Rather it is a nominal measure reflecting the engineers’ belief, or confidence, in the reliability giventhe current knowledge about the structure. Thus, if the available information changes, the estimated

reliability normally changes as well.

From Table 8-1 and equation (8.1) an annual probability of a fatigue failure can be derived for a connectionfor a non-redundant structure with a Design Fatigue Factor equal 10. This failure probability is acceptedaccording to NORSOK N-001 for members where the consequence of a failure is large and which cannot beinspected or repaired during service life. Thus, this failure probability can also be considered as a targetfailure probability for members with large consequence of failure. This target failure probability can bedenoted as P f annual x -Target with DFF = 10. A failure probability that the remaining structure fails given that thereis fatigue crack failure present at the considered connection is described by failure probability P SYS. Thenthe following equation can be used for derivation of target failure probabilities for such connections wherethe consequence of a fatigue failure has been accounted for

where

pf annua x l– Target with DFF = 10 is derived from equation (8.1) for DFF = 10.

P SYS is failure probability of the remaining structure given that there already is a fatigue failure per definitionat the considered hot spot.

Figure 8-3 Risk matrix with consequence of failure and probability of failure

8.4.2 Consequence of fatigue crack in a jacket structureJacket structures with more than 3 to 4 legs are redundant structures where the residual strength is

significant even with one member removed. Normally also a fatigue crack can be of a significant size andstill load can be transferred through the joint. This depends on type of joint and loading as described in

(8.2)

SYS P

p P 10DFFwithTargetxannualf

Targetannualf

=−=




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[D.3]. Thus an assessment of residual capacity of the joint should be performed for a detectable crack sizebefore it is concluded that the capacity should be assessed with a member removed.

X-type brace framing is considered more redundant than that of K-type brace framing.

The safety documentation for a jacket structure is often based on the ratio between a calculated load

carrying capacity r (resistance) and a corresponding load effect s (stress). This ratio

is called the safety factor or the reserve strength ratio (RSR). The actual numerical value of the safety factordepends on the definition of R and S . In a probabilistic formulation the safety factor as introduced above isa random variable

where R and S are random variables. The probability that the structure fails is then

Non-linear analysis is often used to calculate the reserve strength ratio. To assess the consequence of afatigue failure, the failed member may be removed and a similar ratio can be calculated. Then uncertaintieson load and resistance can be introduced in a probabilistic analysis for calculation of probability of astructural failure. The safety factor for this condition can be defined as residual strength factor (RSF). Whenthe RSF has been calculated, an estimate of the probability of a failure, given that the considered elementhas failed, can then be derived as

This assessment is considered to be safe for typical jacket structures with CoV on wave height not largerthan 10% and CoV on capacity not larger than 10 to 15%.

8.4.3 Consequence of fatigue crack in a floating production vesselThe development of a through thickness crack in the hull will often not imply impairment of the structuralintegrity but may rather serve as an initiating event for e.g. gas leakage, an explosion or a fracture.

Scenarios that typically are regarded to have a high consequence with respect to loss of human lives and/or pollution may be listed as:

— Through thickness crack in the plating surrounding the cargo tanks:- leakage of hydrocarbons through bulkhead(s) from cargo tank into ballast tank- leakage of hydrocarbons through deck head from cargo tanks.

— Loss of one member of the flare tower.

— Through thickness crack in crane pedestal.

— Through thickness crack in moonpool wall at main deck or bottom shell level.

Typical scenarios with medium consequence with respect to loss of human lives and/or pollution may belisted as:

— Through thickness cracks in main deck, side shell and bottom plating.

Typical scenarios with low consequence with respect to loss of human lives and/or pollution may be listedas:

(8.3)

(8.4)

(8.5)

(8.6)

s

r rsr =

S

R RSR=

( ) ( ) ( )01 ≤−=≤=≤ S R P S R P RSR P

4.26.010 24 ≤≤= +− RSF for P RSF

SYS




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— Crack in secondary elements such as cracks starting at the bracket toes of longitudinal connection toweb-frames in the ship side.

P SYS = 1-10-1 may be indicated for a high consequence crack.

P SYS = 10-2 may be indicated for a medium consequence crack.

P SYS = 10-3-10-4 may be indicated for a low consequence crack.

When considering the consequence of a fatigue crack, also potential number of fatigue cracks need to beconsidered as indicated in [8.4.1].

The annual target probability of a fatigue failure can be presented as

where

x = service life or planned design life.P SYS is failure probability of the remaining structure given that there already is a fatigue failure per definitionat the considered hot spot.

For inspection planning it is often more convenient to consider accumulated probability of failure thanannual probability of a fatigue failure. This target failure probability can be presented as

where P SYS is defined above.

The equations for target failure probabilities can be deduced from [8.3].

(8.7)

(8.8)

SYS

Target annual f P x

P 4108.2 −⋅

=

SYS

ccumulated P

P 4

Targetaf

10−

=




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SECTION 9 CALIBRATION OF FRACTURE MECHANICS MODELS TOTEST DATA

9.1 General

Calculated fatigue lives based on S-N data are considered to be more reliable than those based on fracturemechanics. S-N data are derived directly from fatigue tests while fracture mechanics is based on calculationwhere additional parameters are required as input to the analysis. Thus, it is reasonable to make acalibration such that the probability of a fatigue failure based on fracture mechanics follows that of S-N datauntil first in-service inspection. After the first inspection the results will depend on the fracture mechanicsmodel, the reliability of the inspection method and whether cracks are found or not.

The fatigue initiation time in the model has a significant effect on calculated inspection interval. Thus it isimportant to thoroughly assess the crack growth in order to safely update the probability of fatigue crackingbased on the applied PoD curves.

Furthermore it is important to include the initiation time for welded connections where the weld notch isremoved by grinding or machining and for components where the fatigue cracks may initiate in the base

material.The total number of cycles to failure can be presented as a sum of initiation of a crack and crack growth.For the purpose of inspection planning a calibration of fracture mechanics to fatigue test data is performedsuch that a full fatigue life can be calculated by fracture mechanics from relatively small fictitious cracks.

9.2 Performed calibration for as-welded detailsThe crack growth from fracture mechanics should be consistent with S-N data for relevant joints. However,it should be kept in mind that crack growth in actual structures can be different from that of the test data(size, residual stresses, mean stress effect, boundary conditions and type of loading: axial versus bending).It is thus important that the time needed for fatigue crack initiation or distribution of initial crack sizes isdetermined from calibration with test data derived under controlled conditions in a test laboratory with well-known loading.

Reference is made to [D.6] where a detailed calibration of fracture mechanics to that of S-N data ispresented. Here two different analysis models have been developed. It is assessed that the second modelwith an initial crack size distribution is the preferred one as this model provides results that are in line withthat observed in laboratory tests both for cruciform type specimens and with simple butt welds.

Given a good correspondence between the analysis models based on fracture mechanics and S-N data it isnot necessary to perform a further calibration of these methods as long as the guidance on all associatedparameters are input to the analysis to be performed. Reference is also made to [10.10] to [10.15] regarding significant input parameters to probabilistic fatigue analysis.

This also implies use of geometry functions presented in [D.2.1]. These geometry functions should also beused for butt welds welded from both sides with weld length L = 0.5 times the thickness and weld shapeangle θ = 15o.

9.3 Performed calibration for ground detailsCalibration of crack growth for ground details to S-N data is presented in [D.6.4]. This section also givesrecommendations on input parameters to be used for planning inspection of ground details.




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SECTION 10 ASSESSMENT OF INPUT PARAMETERS TOPROBABILISTIC ANALYSIS

10.1 Uncertainty modelling

The uncertainties to be considered in the structural reliability analysis are represented by modelling thebasic variables as stochastic variables that reflect the current knowledge of the variables and analysismodels. The uncertainties may in general be grouped as:

— Physical uncertainty , also known as inherent or intrinsic uncertainty which is a natural randomness of aquantity such as variability in current, uncertainty in yield stress etc.

— Statistical uncertainty is uncertainty due to limited amount of information such as a limited number ofobservations. Unlike physical variability the statistical uncertainty arises solely as a result of lack ofsample data. Hence, it will decrease and finally vanish as the amount of data increases.

— Measurement uncertainty is uncertainty caused by imperfect instruments and sample disturbance whenobserving a quantity such as a fatigue crack size.

— Model uncertainty is uncertainty due to imperfections and idealisations made in the applied physical and

probabilistic models and reflects a general confidence in the model to describe "real life". It may furtheraccount for unknown effects of other variables and their interaction which are not included in theanalysis model.

— Bias is in general defined as difference or a ratio between expectation of an estimator ê and the quantitye being estimated. When assessing load effect and fatigue capacity it may be practical to use the ratiobetween these two parameters. In order to avoid misunderstanding it is recommended to define thenominator and the denominator in each case where bias is used. Ref. e. g. SCFs for tubular joints in[D.5.3].

Note that uncertainties related to human errors also denoted as “gross errors” are normally not coveredwithin the framework of structural reliability.

For all variables a probability distribution must be assigned based on engineering judgement and experience

from similar types of problems, physical knowledge, analytical results or distribution fit to availableobservations of the uncertain quantity.

An overview of distribution parameters for inspection planning for fatigue cracks is shown in Table 10-1.

Table 10-1 Overview of input parameters to probabilistic analysis

Variable Reference Comment

Weibull scale parameter, q 10.16

Weibull shape parameter, h Assumed constant

S-N data DNVGL-RP-0005 Is implicit in calibrated fracture mechanics analysis and need notbe considered if all inspection planning is based on the fracturemechanics model presented in this document.

Palmgren-Miner damageaccumulation

10.2

Cycle rate 10.3 Assumed constant

Fabrication tolerances 10.4

Residual stress and meanstress

9.5 Assumed to be included in the S-N analysis before the Palmgren-Miner sum is calculated such that it needs not be furtherconsidered in the probabilistic analyses.

SCF for tubular joints 10.6 This uncertainty is accounted for when selecting load uncertaintyfrom [10.16.2].

Hot spot stress derived from FEanalysis

10.7 This uncertainty is accounted for when selecting load uncertaintyfrom [10.16.3] for semisubmersibles and [10.16.4] for FPSOs.




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10.2 Fatigue damage accumulation modelFatigue is a gradual process where the accumulated damage increases with time. For different reasons therates of damage accumulation may be different from one time interval to another as explained in [5.1].Reference is made to [D.3] for a more detailed description of methodology that can be used for assessment.

S-N data and uncertainties in S-N curves are derived from DNVGL-RP-0005.

The variability in the Palmgren–Miner rule depends among different factors on mean stress. As the S-Ncurves are established based on a rather high mean stress value a log normal distribution with median valueequal 1.0 and CoV = 0.30 can be used if not documented otherwise.

10.3 Cycle rateThe uncertainty in number of stress ranges due to wave loading is normally considered to be less importantfor the calculated fatigue reliability for offshore structures subjected to wave loading. Also the effect of cyclerate on damage is similar for fracture mechanics as in fatigue analysis based on S-N data.

The uncertainty in cycle rate due to wave loading is normally small as compared with other uncertaintiesand can thus be neglected. A mean zero-up-crossing frequency can be determined based on best estimatesfrom calculated responses. A frequency around 0.16 sec-1 is typically used for fixed offshore structures inthe North Sea while a somewhat lower frequency is typically determined from analysis of floating structures.

10.4 Fabrication tolerancesFabrication tolerances leading to SCF for welded connections are important for fatigue design of butt weldsand cruciform joints. However, it is normally of less importance for other types of joints. SCF for butt weldsin plates and cruciform joints are presented in DNVGL-RP-0005.

The significance of tolerances is similar for fatigue analysis based on S-N data and fracture mechanics.However, in fracture mechanics it is normal practice to separate the stress into membrane stress andbending stress while in S-N analysis the effect of SCF is an increase in membrane stress (as that stresscondition is used together with S-N data).

For probabilistic analysis the term 0.1t should be removed from the equations for SCF in DNVGL-RP-0005.The reason for this is that the SCF in DNVGL-RP-0005 is normally used together with a characteristic valueof a fabrication tolerance in a deterministic analysis. The design approach will provide too conservative

values in design if full scatter is accounted for in the S-N data at the same time as a fabrication tolerancevalue far from the mean value is used. Therefore a correction by a term “-0.1t” is used in a deterministicdesign for derivation of SCF. The actual distribution of tolerances is used in a probabilistic analysis andtherefore a best estimate of the SCF should be used to arrive at relevant values.

For probabilistic analysis it can be assumed that the tolerances are normal distributed with zero mean andthat the tolerance requirement in the fabrication specification corresponds to the 5% percentile value. Thusthe standard deviation in the distribution can be determined as maximum fabrication tolerance divided by1.64 (which corresponds to the 5% fractile value in a normal distribution).

10.5 Residual stress and mean stress

10.5.1 GeneralResidual stresses and mean stresses are important factors that may govern the fatigue capacity. In design

Stress magnification at weldsand geometry function

10.10

Crack growth parameters 10.11

Threshold value in crack growth 10.12

Crack size at initiation of crackgrowth

10.13

Table 10-1 Overview of input parameters to probabilistic analysis (Continued)

Variable Reference Comment




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standards for land structures and fixed offshore structures it is normally assumed that there are residualstresses at the hot spot corresponding to yield stress in tension and that the whole stress cycle is providinga stress cycling at the hot spot in tension independent of mean stress. In ship structures it is realised thatnominal stress ranges into compression are less detrimental than that of tension. Also in fracture mechanicsanalysis it is possible to account for residual stress and mean stress through calculation of effective stress

intensity ranges.

The hot spot stress range in braced structures shows mean stress not far from zero. It is seen from Figure10-3 that the reduction factor on stress range is close to 1.0 in this region. Keeping in mind the increasedcomplexity of including mean stress effect in the assessment it is not considered cost optimal to include thiseffect for jackets and semisubmersibles as the effect is considered to be small for these structures.

There may be a significant effect of mean stress in butt welds in jacket legs with some topside weights.However, these welds normally show long fatigue lives without accounting for the mean stress effect. Itmight also be of interest for jacket piles, but these cannot be inspected and should be designed withsufficient design fatigue factor such that the reliability is acceptable without in-service inspection.

For floating production vessels it is proposed to use a reduction factor depending on nominal mean stresslevel for calculation of an effective stress range for the purpose of inspection planning.

10.5.2 Shake-down of residual stresses and proposed assessmentprocedureMeasurements of residual stresses at welded connections show that significant tensile stresses may bepresent after fabrication. The residual stresses at a weld toe may be as large as yield stress of the basematerial. When the structure is subjected to an external loading, some different developments of the stresscondition at the hot spot may occur as illustrated in Figure 10-1. Here a residual stress normal to a weldtoe is assumed equal 215 MPa. In Figure 10-1 a an example is shown where the increased stress at the hotspot due to external load is not so large that local yielding at the hot spot will occur. The stress at the hotspot is increased from position a to b in the figure. This means that the residual stresses will not be changedafter unloading. Here it is assumed that the stress increase at the considered hot spot is equal to the hot

spot stress times a notch stress concentration factor Kw which is due to the local weld geometry. The valueof Kw is in the order of 1.5.

In Figure 10-1 b an example is shown where the increased stress at the hot spot due to external load implieslocal yielding at position c. It is assumed that the load is increased to level b when calculated elastically.This implies a permanent plastic straining at the hot spot from c to d before the structure is unloaded withthe same load amplitude from d to e which follows an elastic curve. Due to the permanent strain elongationintroduced at the hot spot, the residual stress has now been reduced to position e.

This procedure for shake-down can be used further as indicated in Figure 10-1 c to establish a criterion forshake-down of residual stresses to zero. The requirements for this is that the tensile notch stress range isequal the material yield stress. Without shake-down of residual stresses to zero, the reduced effects ofcompressive residual stress amplitudes have to be considered differently.

The effect of loading condition with respect to shake-down of residual stresses may be larger for floatingstructures due to differences in load conditions than the load from wave environment only as illustrated inFigure 10-2.

Then the following conditions for a maximum load that is likely to occur during the first year in service areconsidered:

1) Shake-down of residual stress cannot be documented.

2) Shake-down of residual stress can be documented.

3) The requirement for documentation of shake-down reads

where

(10.1) yw year spot hot K σ σ ≥1max




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σ y = actual yield stress of base material at the considered hot spot as derived frommaterial certificates

K w = 1.5

σ hot spot max 1 year = maximum hot spot stress that can likely occur during first year in service.

Figure 10-1 Examples of load cycles with different effect on remaining residual stresses at hot spot

Figure 10-2 Change in spot stress due variation in load condition

a) No shake-down b) Partial shake-down c) Shake-down to zero residual stress

0

100

200

300

400

500

600

0.000 0.002 0.004 0.0

S t r e s s ( M P a )

Strain

Yield strength

a

b

Residual stress

after fabrication

0

100

200

300

400

500

600

0.000 0.002 0.004 0.0


Strain

a

b

c d

e

Residual

stress after

shake-down

0

100

200

300

400

500

600

0.000 0.002 0.004 0.0


Strain

a

b

c d

e




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10.5.3 Mean stress reduction factorThe following mean stress reduction factor may be used:

where

σ mean eff = σ mean where shake-down to zero residual stress has been documented

σ mean eff = σ mean+ σ Res otherwise

σ Res = Residual stress at the hot spot. If the amount of residual stress is not known, it may be assumedequal the material yield strength as derived from material certificates.

Tensile stresses are positive and compressive stresses are negative.

This means that if shake-down of residual stress cannot be documented for a relevant load the first year inservice, significant compressive stresses at the hot spot is required before the positive effect of compressivestresses on calculation of fatigue life can be included.

The reduction factor on stress range as function of mean stress is illustrated in Figure 10-3.

Alternatively crack growth analysis may be performed assuming crack closure for the compressive part ofthe stress cycle when the crack has grown through 1/3 plate thickness such that the crack tip is grown outof the main tensile residual stress field.

(10.2)

≤∆

∆+

≥∆

=

5.0;2.09.0,6.0max

5.0;0.1

σ

σ

σ

σ

σ

σ

eff meaneff mean

eff mean

m f




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Figure 10-3 Reduction factor on stress range as function of mean stress

10.6 Stress concentration factors for tubular jointsThe method for derivation of hot spot stress for tubular joints was calibrated against S-N data and SCF fortubular joints were developed based on calibration of FE analysis with measurement data from testedtubular joints. These SCF have later been accepted as providing a reliable design basis for structures withtubular joints with respect to fatigue. Reference is made to ISO 19902 and DNVGL-RP-0005. However, thereare significant uncertainties in use of SCF for real structures when hot spot stresses are derived fromparametric equations for SCF for tubular joints. It is proposed to describe this uncertainty by a normaldistribution with CoV = 0.20. There is likely a bias present as the calculated SCF are expected to be to thesafe side. This effect may be quantified in special cases if needed; otherwise it is proposed to assume amean value equal 1.0 for simplicity.

10.7 Calculation of hot spot stressThe uncertainty in calculation of hot spot stress derived from detailed FE analysis depends somewhat onthe detail considered but is in general in the order of CoV = 5-10%. The uncertainty in calculation of hotspot stress is considered to be less significant when calculating probability of fatigue reliability in platedstructures as compared with uncertainty in loading and S-N data. A normal distribution may be assumedfor the hot spot stress distribution.

10.8 S-N dataReference is made to DNVGL-RP-0005 for S-N classification of details in plated structure and S-N data. Thisreference also includes an S-N curve for tubular joints.

The failure criterion for the S-N curve for tubular joints is crack growth through the thickness. The S-N data

for plated structures are mostly derived from small scale test specimens. This means that the failurecriterion depends to some extent on mean stress and stress range used for the testing. However, the




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residual stresses in test specimens are normally significantly lower than in actual structures. Also thepossibility of redistribution of stresses is different in actual structures as compared with test specimens.Therefore, it is difficult to compare failure criterion in small scale test specimens with that of real structures.

10.9 Critical crack size in real structure as compared with failurecriterion in S-N curve used for designMost fatigue cracks are growing in the base material after they have been initiated at a weld toe. Anassessment of this can be performed from information that fatigue cracks tend to grow normal to theprincipal stress direction.

Materials used in offshore structures are ductile and brittle fracture is not considered to be a critical failuremode for material that shows Charpy values larger than 40 Joules at the lowest service temperature. Specialconsiderations may be needed for structures in colder climate. Thus assessment of fracture can normallybe based on gross yielding at local details when including the cracked areas. When assessing probability ofunstable fracture, it should be remembered that a large tensile membrane loading on a through thicknesscrack in a plate is more critical than local bending loads such as e.g. observed in typical tubular joints where

local through thickness cracks of some length have been found acceptable based on laboratory testingwithout reduction in the ultimate capacity.

For out of plane bending of tubular joints in conductor frames one can assume that 40 % of the fatigue lifeis likely left after a crack has grown through the thickness. This information is needed for planninginspection with FMD.

10.10 Stress magnification at welds and geometry functionsThe uncertainty in the function describing the local stress condition at the weld depends very much on howit is derived. In BS 7910 two different approaches are presented for derivation of weld stress magnification.One is based on a two-dimensional FE approach and another on a three-dimensional approach. The firstone is rather conservative as compared with the more refined three-dimensional one which also is included

in [D.2].M k functions for cruciform joints are listed in App.D for welded and ground conditions. The uncertainty inthese is not considered to be large as compared with other uncertainties. Larger uncertainties may beintroduced if the functions are used outside the prescribed validity range. The validity range with respect toattachment length should be noted. A procedure is presented on how to derive M k functions for longerattachment lengths than 2.75L/T (where L = attachment length as defined in [D.2.1] and T = platethickness).

The M k functions in App.D can also be used for tubular joints.

The uncertainty related to these functions should be seen in relation to the distributions used for initiationand crack growth parameters. The resulting fatigue life as calculated by fracture mechanics should not showa more narrow distribution than that of S-N data (as directly derived from laboratory testing).

Based on the calibration work presented in [D.6] the following guidance is given:

— the M k function is normal distributed with mean value of 1.0 and CoV equal to 0.1

— the geometry function is normal distributed with mean value of 1.0 and CoV equal to 0.05.

10.11 Crack growth parametersThe crack growth parameters in Table 10-2 can be used for crack growth analysis. Log C is assumed to benormal distributed. The material parameter m is assumed to be constant. This parameter is also beingdenoted as a crack growth exponent.

It should be noted that most fatigue cracks are initiated at weld toes and grows into the base material. Insome cases cracks may also grow from internal imperfections in highly dynamically loaded butt welds. This

should be assessed for the higher S-N curves above curve D when flush grinding of the butt welds havebeen needed for documentation of acceptable fatigue life.




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The ratio between crack growth in sea water with cathodic protection and air has been derived from S-Ndata can be calculated from

where

F = calculated fatigue life

h = Weibull shape parameter

This function is valid from 1 to 1000 years.For longer calculated fatigue lives than 1000 years this ratio should be put equal 1.0.

Figure 10-4 Calculated fatigue life ratio between detail in air and detail in seawater with cathodic protectionbased on S-N curves in DNVGL-RP-0005

Table 10-2 Crack growth parameters

Environment Position of potentialcrack

Mean value of C (Unit N andmm)

Standard deviation inlog C

m

air base material 1.83 × 10-13

0.11 3.0weld metal 1.83 × 10-13 0.22 3.0

seawater withcathodic protection

base material air value multiplied with factorfrom equation (10.3)

0.11 3.0

weld metal air value multiplied with factorfrom equation (10.3)

0.22 3.0

free corrosion base material and weld 8.35 × 10-13 0.22 3.0

(10.3)

( )

h

F F F h F f

1523.10429.2

38.2log245.0

2

)(log275.0

3

)(log07.0,

−

+−−=




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10.12 Threshold value in fracture mechanics versus S-N curveA threshold value ∆K th, in accordance with BS7910, is used as a fixed value: ∆K th = 63 Nmm-3/2. A highervalue can be used if the stress range is not purely tensile.

Use of a threshold value complicates analysis under variable long term loading. A possibility is to neglect

the threshold value when calculating crack growth. However, it is considered to be important to use thesame threshold value for calibration of parameters in fracture mechanics as used later for planninginspection. It is conservative to set the value equal to zero.

10.13 Crack initiationFrom the calibration work presented in [D.6] it was found that the initial crack size distribution a0 can bemodelled by exponential distribution with median value equal 0.03 mm.

10.14 Effect of weld improvements on crack initiationThe M k function is significantly reduced for shallow cracks when weld toe grinding is performed. Referenceis made to App.D for calibration of fracture mechanics with S-N data.

10.15 Effect of corrosionCorrosion pitting in tubular joints has been assessed to not significantly reduce the fatigue life more thanthat accounted for by use of S-N data in a corrosive environment.

However, corrosion reduces the possibility to detect fatigue cracks. In floating production vessels it isimportant to keep the coating intact. General corrosion should be accounted for by reducing effectivethickness in the fatigue analysis. S-N data for free corrosion (Ref. DNVGL-RP-0005) should be consideredused for calculation of fatigue life and for probabilistic analysis for planning inspection of corroded areas.

10.16 Fatigue loading

10.16.1 GeneralIn the following it is assumed that the long term stress range distribution is presented in terms of a two-parameter Weibull distribution as explained in [5.6]. See also DNVGL-RP-0005 for definition of Weibull twoparameter distribution. It is assumed that the shape parameter is constant and that the uncertainty inloading is expressed by the scale parameter. It is assumed that the uncertainty related to the scaleparameter is normal distributed.

Unless detailed information is available, all the analysis methods in the following sections should beassumed to be un-biased.

10.16.2 Jackets

Uncertainties in calculated fatigue loading proposed for probabilistic analysis of jackets are shown in Table8-1. These uncertainties are related to the nominal load effect in the members. Thus for calculation of hotspot stress in tubular joints also the uncertainty in the derivation of SCF or hot spot stress has to beconsidered. This depends on analysis method as shown in Table 10-4.

The presented uncertainties are related to a discrete wave fatigue analysis. If only a stochastic analysis isperformed, it is assessed that similar uncertainties can be assumed for the joints below the splash zone.The uncertainty in analysis results for joints in the splash zone depends very much on linearization andanalysis method used and needs to be assessed in each case.

App.A should also be used as basis for selecting the relevant CoVs from Table 10-4. Other values of CoVsmay be considered used if the analysis approach deviates from those specified. It is assumed that theuncertainty related to the calculation of hot spot stress is normal distributed.

A CoV = 5% can be used for stress concentration for butt welds. It is assumed that thickness transitions

are properly accounted for by relevant SCF. It is assumed that the uncertainty related to the stressconcentration is normal distributed.




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The resulting uncertainty for the calculated hot spot stress can be derived as

where

CoV Fatigue loading

is derived from Table 10-3.

CoV Analysis is derived from Table 10-4.

With combinations of CoV from Table 10-3 and Table 10-4 a resulting CoV for the hot spot stress in therange 0.15 to 0.30 is derived.

As an example a CoV = 0.30 is derived for a joint in the splash zone based on fatigue analysis with SCFsfrom parametric equation (= (0.222+0.202)0.5). This information can be used together with recommendeddesign factors from NORSOK N-001 and [8.3] for assessment of target reliability.

10.16.3 SemisubmersiblesUncertainties in calculated fatigue loading proposed for probabilistic analysis of semisubmersibles areshown in Table 10-6.

It is assumed that the lowest value of CoV can be selected for probabilistic analysis if a good analysispractice as presented in App.B is followed using a hot spot analysis model. It is assumed that thisuncertainty also includes the uncertainty due to hot spot stress analysis as described in [10.7].

Table 10-3 Uncertainty on calculated fatigue loading

Location CoV

20 metres below MWL and below 0.12

below splash zone down to 20 metres below MWL 0.17splash zone and above 0.22

Table 10-4 Uncertainty in calculated hot spot stress at tubular joints for different analysis methods

Analysis method; ref. App.A CoV Comment

conventional SCF approach 0.20 type of joint defined by geometry and force flow

load path method 0.16 joint defined based on loading at each step in wave

generalized influence functions 0.12

influence coefficients and refined fatigue 0.08

Table 10-5 Uncertainty in calculated hot spot stress at butt welds from analysis

Analysis method CoV Comment

conventional SCF approach 0.05

(10.4)22

Analysisloading Fatigue spot Hot CoV CoV CoV +=




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The different analysis methods are outlined in more detail in App.B.

10.16.4 Floating production vesselsUncertainties in calculated fatigue loading proposed for probabilistic analysis of floating production vesselsare shown in Table 10-7.

It is assumed that the lowest value of CoV can be selected for probabilistic analysis if a good analysispractice as presented in App.C is followed using a hot spot analysis model. It is assumed that thisuncertainty also includes the uncertainty due to hot spot stress analysis as described in [10.7].

The different analysis methods are described in more detail in App.C.

Table 10-6 Uncertainty in calculated fatigue loading for different analysis methods

Analysis method Stress concentration model CoV Comment

complete shell model

with sub-modelling

hot spot from sub-model 0.12 Sink-source and Morison.

Use of sub-models with refined mesh.complete shell model SCF from local models 0.16 Sink-source and Morison.

SCF from literature.

combined beam andshell model

SCF from literature 0.25 Sink-source and/or Morison.The extent of the beam and shell models mayvary depending on the design. For typical beamstructures a beam model alone may be used.

simplified method -beam model

SCF from literature 0.40 Morison model with contingency factor 1.1.Beam model representing all structure.Simplified fatigue analysis.

Table 10-7 Uncertainty in calculated fatigue loading for different analysis methods

Analysis method 1) Stress Concentration model CoV Comment

full ship model, direct stochastic hot spot sub-model 0.15 All hot spot models where therequirements to mesh size isfulfilled.

full ship model, screening analysis of

areas without lateral loading; directstochastic analysis

SCF from literature 0.20 Main deck details such as

penetrations and doublingplates.

component stochastic analysis SCF from literature 0.25 Stiffener end-connections,plate weld to stiffeners, web-frames and bulkheads.

simplified methods SCF from literature 0.30

1) Intermediate models are not planned to be used as basis for the probabilistic analyses.




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SECTION 11 PROBABILITY OF DETECTION

11.1 Inspection reliability for relevant inspection methodsNon-destructive testing (NDT) is commonly used to localise and size defects in structures. The detection

ability for the NDT method is defined as a function of a defect size, through probability of detection (PoD)curves. PoD curves are provided for the following inspection methods:

— flooded member detection (FMD)

— eddy current (EC)

— magnetic particle inspection (MPI)

— alternating current field measurement (ACFM).

General visual inspection (GVI) and close visual inspection (CVI) are considered efficient for generalassessment of the condition of the structures, but can hardly be used to detect fatigue cracks before thesize of the cracks has grown large in length or through the plate thickness.

Thorough cleaning for marine growth is crucial in order to be able to discover fatigue cracks. Also closephotos of cleaned hot spot areas may provide useful information about potential fatigue cracks.

11.1.1 Flooded member detection FMD is used for inspection of through thickness cracks in braces in jacket structures. This methodology canbe used for members that are not water filled from installation like braces (with potential fatigue crack onthe brace side and not on the leg side that normally is water filled) or joints that have not been reinforcedby grout. The reliability of this inspection method is assessed to be good and a probability of detection equal0.95 can be assumed.

When FMD is used, it should be established whether through thickness cracks at hot spots can be acceptedbased on required capacity for ultimate load. Experience shows that FMD is efficient for conductor framesin jacket structures where out-of-plane moments contribute significantly to the calculated fatigue damage.

Capacity for ultimate load is here of less concern than for the main load carrying braces.

11.1.2 Leakage detectionLeakage detection can be considered as a reliable barrier with respect to fatigue crack detection insemisubmersibles and FPSOs. It is assumed that this method can only be relied upon in redundantstructures where the plated structures show material with appropriate fracture toughness.

The fracture toughness can be derived from SENT type CTOD specimens for assessment of capacity ofthrough thickness cracks in plated structures. A SENT test normally provides significantly larger fracturetoughness than SENB specimens which are CTOD specimens tested in bending.

A critical crack length can then be determined from BS 7910 by neglecting presence of residual stress ascracks are often propagating into the base material. If it is likely that a potential crack will follow the weld

toe, a relevant residual stress should be included in the analysis.

When relying on leakage detection, it should be verified that there is sufficient time from a significantprobability of detecting a fatigue crack until failure such that a repair can be performed if needed.

11.1.3 Probability of detection curves for eddy current, magnetic particleinspection and alternating current field measurementThe distribution functions for PoD for EC, MPI and ACFM are assumed to be similar and can be presented as

(11.1)b

X

aa PoD

+

−=

01

11)(




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where

a = crack depth in mm

X 0 = distribution parameter (= 50% median value for the PoD)

b = distribution parameterThe PoD curves are dependent on qualification and execution of work. If no other documentation isprovided, the PoD curves in Figure 11-1 can be used.

EC has become a preferred inspection method during service life as it can be used to detect fatigue crackswithout removing coating. Earlier it was normal practice to perform inspection of surface cracks by MPI,

however, then the coating had to be removed. It was found difficult to reinstall a good quality of the coatingand local corrosion was observed at the inspected areas. Now MPI is being used to verify crack indicationsdetected by EC as this inspection method also can give spurious indications.

The physics in applying EC above water is only marginally different from underwater applications and,although working conditions can be more severe under water, these are compensated for by special qualityassurance measures, like using slave monitors. A similar performance as under water is thus also expectedabove water, and the generated PoD curve is regarded representative also for above water applications.

ACFM is used for detecting and sizing surface breaking flaws. ACFM has been developed as an extension ofthe successful alternating current potential drop (ACPD) technique. It was initially conceived for use underwater to detect flaws in offshore structures and to overcome the fact that ACPD was unsuitable for suchapplications because of the need for good electrical contact between probes and the structure's surface.Now, however, ACFM is also applied to structures both in and out of the water. (It has the advantage oversome other techniques that the structure requires minimal cleaning and that it can be applied over paintand other coatings up to several millimetres in thickness).

ACFM is an electromagnetic technique. A sensor probe is placed on the surface to be inspected and analternating current is induced into the surface. When no defects are present the alternating currentproduces a uniform magnetic field across the surface. Any defect present will perturb the current, forcing itto flow around and underneath the defect; this causes the magnetic field to become non-uniform andsensors in the ACFM probe measure these field variations.

Table 11-1 PoD curves for EC, MPI, ACFM

Description X 0 b

at ground welds or similar good conditions above water 0.40 1.43

normal working conditions above water 0.45 0.90

below water and less good working conditions above water 1.16 0.90




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Figure 11-1 PoD curves

Figure 11-2 PoD curves for EC, MPI and ACFM




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11.2 Ultrasonic testingWelds may be inspected by use of ultrasonic testing (UT) for e.g. cracks in outer shell under the mean waterlevel starting from the outside. UT can also be used for inspection of internal craxcks. The PoD curve for UTis defined by:

Here, “a” is the depth of the crack. The parameters X 0 and b are calculated by curve fitting to experimentsdocumented in Nordtest: X o = 0.410 and b = 0.642.

The PoD curve is dependent on qualification and execution of work. If no other documentation is provided,the PoD curves in Figure 11-3 can be used for inspection planning. It should also be noted that there existdifferent versions of UT and some of these are more reliable than represented with this PoD curve.

Figure 11-3 PoD curve for UT inspection

11.3 Visual inspectionThere is little information available related to PoD data for CVI based on test data. Assuming that the accessis moderate, the cracks will be rather deep before they can be detected. Where the plate thicknesses arenot large, this implies that the cracks are grown through half the plate thickness. Then the time before thecracks grow through the thickness may be short. It is also observed that the probability for detecting a crackthat can be repaired by grinding is very low.

The PoD curves for visual inspection as presented in Figure 11-4 are based on judgement and not on tests.The reliability of a visual inspection is strongly dependent on cleaning of the inspected area. Here it isassumed that a good cleaning is performed. The reliability of visual inspection is also dependent on type offatigue crack. If the fatigue crack is along a weld toe without going through the plate thickness, it is

considered to be more difficult to detect than a crack going through the thickness. Also the loading conditionat the time of inspection is considered to influence the reliability of inspection as a through thickness crack

(11.2)

( )b X aa P

0/1

11)(

+−=




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subjected to membrane loading or bending loading tending to open the crack is easier to detect than a crackwithout external tensile loading. Thus the presented PoD curves for visual inspection should be usedtogether with engineering judgement depending on actual inspection conditions such as cleaning, lightconditions etc.

With a good cleaning high resolution image (HRI) photos are considered to qualify to the highest PoD curvein Figure 11-4.

Figure 11-4 are presented on the form:

where x = crack length and the parameters X 0 and b are presented in Table 11-1.

Figure 11-4 PoD curve for visual inspection

11.4 Methodology to provide reliable probability of detectioncurves for other inspection methodsThe reliability of an inspection process depends on:

— capability of the actual technique— degree of reliance on operator skill

(11.2)

Table 11-2 TPoD curves for visual inspection

Description X 0 b

easy access 15.78 1.079

moderate access 37.15 0.954

difficult access 83.03 1.079

( ) b X x x P

0/1

11)(

+−=

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 50 100 150 200 250 300 350 400

P r o b a b i l i t y

o f d e t e c t i o n

Crack length in mm

Easy

Moderate

Difficult




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— inspection procedure used

— auditability.

In its simplest form PoD is a percentage of cracks detected. However, in practice this must refer to cracksof a particular size; i.e. cracks must be grouped together in a certain size range. The PoD can be referred

to crack length or depth, and how relevant this is depends on the inspection technique.

It provides a basis on which to compare inspection methods. The techniques must be evaluated in the sametrial using the same samples in order to be compared in a realistic manner. The PoD performance onlyrelates to the trial in which it was derived. The defects must be real. If one wants to know how good atechnique is at detecting cracks, one must evaluate it on real cracks - not artificial defects or slots. Thesamples must be representative for the components to be inspected in the field (shape, size and materialproperties).

There must be sufficient numbers of defects to make the trial representative. In practice this means thatone cannot do trials on slots and relate that to real inspection in the field. One cannot rely on repeatinspections of the same crack.

The way in which the PoD is reported must refer to the way in which the trial was conducted. The PoD isoften presented as a PoD curve.

It is also assessed that the PoD is a function of surface of the hot spot areas and depends on amount ofcorrosion and cleaning. By visual inspection it is easier to detect fatigue cracks in a white coated area thanin an area that is corroded.

The existing PoD curves have been developed from test data except for the PoD curve for visual inspectionthat is based on judgement.

An engineering assessment of the test data is recommended. The data should be assessed in terms ofrequirements to cleaning and preparation of areas to be inspected. The working conditions at relevant hotspot areas should be considered. This also means that actual PoD curves can hardly approach 100%detection probability even for deep cracks if conditions at the actual inspection areas are somewhat

uncertain.

11.5 Inspection methods for jackets

The following choice of inspection methods may be proposed for jacket structures:

— GVI by ROV

— FMD of members where the use of this technique is considered efficient

— Cleaning and CVI

— EC may be used for connections that are considered significant for the integrity of the structure.However, effort should be made to plan inspection such that use of divers is not needed.

11.6 Inspection methods for floating structures

The following choice of NDT inspection methods may be proposed for a floating production vessel:

— Internal details that are accessible: EC or equivalent

— External details above mean water line (MWL): EC or equivalent

— External details below MWL:

— UT from inside (this may also include time of flight or phased array).

— MPI by diver from outside if possible.

— Inaccessible details: look for through thickness cracks on accessible side (leakage detection). It should

be rendered probable that a through thickness crack can be repaired before it becomes critical withrespect to global structural integrity.




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11.7 Effect of measurements on action effectsMeasurements of action effects can significantly reduce the uncertainty from the action response. It ispreferred that the measurements of environment are performed at the same time as the action effects aremeasured. Otherwise a longer measurement interval will be required (several years) to achieve reliable data

that can be used to update the long term action effects.




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SECTION 12 VALIDATION OF RESULTS

Probabilistic analysis for planning inspection for fatigue cracks is a valuable tool to provide a consistent basisfor preparing an inspection programme. It is important that the results are assessed by engineering judgement before the numerical values are transferred into an inspection plan.

It should be kept in mind that it is very important to assess the consequence of a fatigue failure before atarget safety level is selected. It should also be kept in mind that it is the length of the crack growth periodtogether with the reliability of the inspection method that is decisive for the calculated inspection interval.

This implies that longer inspection intervals can be expected for joints subjected to significant bending loadover thickness and joints with possibility for redistribution of stress during crack growth than for joints withmore pure membrane loading where redistribution of stress during crack growth cannot be documented(assuming the same calculated fatigue life in both cases).

This also implies that joints which are weld improved to achieve a long target fatigue life do not achieve thesame long inspection interval because the crack growth life of such connections can be rather short. Thereason for this is that a significant part of the fatigue life is spent in the crack initiation phase and the timeinterval for possible detection of the crack does not become long due to a rather high stress range whichmost often was the reason for the improvement during construction.

Depending on the above mentioned crack growth characteristics the inspection intervals for joints with thesame calculated fatigue life may increase or decrease with time depending on the geometry of the detailand loading and methodology used for inspection.

It can be useful for the engineering understanding of structural behaviour to perform a deterministic crackgrowth analysis for details of significant importance for the structural integrity.

Examples of connections with different crack growth characteristics are shown in Figure 3-2. It is seen thatthe time interval for a reliable inspection is dependent on the crack growth characteristics which again isdependent on type of connection. Crack growth characteristics for a simple tubular joint in “as-welded”condition is indicated in Figure 3-2 a. It is observed that there is a significant time interval (td to tT) fordetection of the crack before it grows through the chord thickness (T).

In some situations it is difficult to achieve a sufficient calculated fatigue life without weld improvement suchas grinding of the weld toe. This means that the hot spot stress range is larger than if an acceptable fatiguelife could be documented without grinding. After grinding the crack initiation period becomes longer, butthe crack growth period is shortened due to increased stress range, ref. Figure 3-2 b. This reducessomewhat the time interval for detection of cracks.

Other details show less possibility of redistribution of stresses during crack growth. A butt weld subjectedto pure axial loading is an example of this as shown in Figure 3-2 c in “as-welded” condition. It is observedthat due to higher membrane stress the crack growth is faster and the time interval for detecting the fatiguecracks is reduced as compared with a simple tubular joint. If the nominal stress normal to a butt weld is solarge that machining/grinding the weld is made flush with the base material as shown in Figure 3-2 d, theinitiation time will likely be longer, but the crack growth will be even faster. This should be kept in mind

when planning in-service inspection of such connections.




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SECTION 13 INSPECTION PLANNING

When the probabilistic analyses have been performed, it is necessary to go through the inspection plan andmake it practicable for the following inspection.

SECTION 14 REPORTING OF INSPECTION RESULTS

A systematic reporting of performed inspections and possible findings is crucial in order that a reliableinspection planning for fatigue cracks can be performed based on probabilistic methods. The following itemsshould be considered:

— description of deficiencies so that the reader can understand position of the damage and extent of thedamage or crack size

— photos to be used for documentation of condition

— photos of deficiencies to be taken both close to and at a distance for orientation of position in structure

— remove sediments before taking pictures

— specify if follow-up inspection is necessary.

SECTION 15 EXAMPLES OF INSPECTION PLANNING FOR FATIGUECRACKS

15.1 GeneralThis section includes examples of inspection planning based on use of probabilistic methods. It is realisedthat fatigue analysis and probabilistic analysis requires significant engineering skill and experience.Therefore some examples on this are included for guidance.

Some examples of details to be considered for inspection are shown in Figure 15-1 and Figure 15-2.

Figure 15-1 Examples of details to be assessed with respect to fatigue and inspection




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Figure 15-2 Examples of details where the hot spot method might have been used in design or inreassessment of fatigue life prediction

a) Detail 1 from Figure 15-1 b) Detail 2 from Figure 15-1

c) Detail 2 from Figure 15-1 d) Detail 2 and 4 from Figure 15-1

e) Detail 2 and 3 from Figure 15-1




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15.2 Example of analysis of a welded doubling plate

15.2.1 Example detailAn example of analysis is presented in the following where the analysis steps in Sec.4 are followed.

A doubling plate on a pontoon of a semisubmersible as shown in Figure 15-3 is considered. The plate size l is 200 mm. The plate thickness is 25 mm and it is placed below the splash zone area. The area is protectedagainst corrosion by anodes.

The semisubmersible is 15 years old. The hot spot area has been inspected by means of EC every fifth year.The connection has been calculated by a global shell model analysis to be 20 years.

The owner would like to use the platform for another 15 years. The owner would like to plan an optimalinspection for the remaining life in service. The owner would also like to know if the calculated probabilityof a fatigue crack at this plate is so large that a grinding of the area is recommended.

Figure 15-3 Doubling plate on semisubmersible

15.2.2 Analysis steps and assessmentThe following assessment steps of Sec.4 are made:

1) Based on an assessment of the analysis performed at the design stage it is found that there isinsignificant improvement only to be achieved in accuracy of the calculated fatigue life by a new fatigueanalysis. The following considerations have been made during this assessment:

— A similar operation of the platform is planned for the next 15 years as that already has passed.

— There is no new knowledge regarding environmental criteria.

— The detail is rather well defined with respect to nominal S-N curves and the nominal stress rangedistribution is normally associated with less uncertainty than calculated hot spot stress from FEanalysis.

— The performed design analysis has been compared with the analysis methodology in App.B and it isfound that the design methodology do not deviate significantly from that described in App.B.

If one of these parameters listed above were assessed differently, it might be recommended to calculatea new fatigue life.

2) Based on an assessment of step 1 it is assessed that step 2 can be skipped without further work.

3) Based on an assessment of step 1 it is assessed that step 3 can be skipped without further work.

4) The mean stress is normally not included for fatigue assessment of semisubmersibles.

5) From section [10.3] a mean up-crossing frequency 0.16 secs-1 is derived (Another value might havebeen derived from the performed fatigue analysis). Number of cycles in 20 years:




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n0 = 60·60·24·365·20·0.16 = 1.01·108 cycles.From DNVGL-RP-0005 Table A-7 the considered detail is classified F1. From DNVGL-RP-0005 Table 2-1this detail warrants an SCF = 1.43 relative to that of nominal stress at the detail.Then the equations for calculation of fatigue damage in DNVGL-RP-0005 [D.13] is used for calculationof the Weibull scale parameter q that corresponds to the nominal S-N curve F1 with and shape

parameter h = 1.0. q = 9.186 MPa. ∆σ 0 = 169.31 MPa. This stress range can also be compared with themaximum allowable stress range from DNVGL-RP-0005 Table 5-3 for F1 curve for seawater withcathodic protection and 108 cycles. For this number of cycles ∆σ 0 = 169.6 MPa (as a control). For hotspot stresses obtained from a global shell model a COV of 0.16 is applied as specified in Table 10-6 in[10.16.3].

6) The consequence of a fatigue failure at the considered hot spot is assessed. A fatigue crack through theplate is considered to imply leakage into tanks. However, a fatigue crack is not considered to jeopardizethe integrity of the structure.

7) The target probability of failure is derived from Sec.8. The fracture toughness of the plate material isassumed to be so large that a local through thickness crack in the plate is considered to be acceptablewith respect to the integrity of the structure according to NORSOK N-001. This means that the

probability of failure given that a through thickness crack is present is less than 10-2

. Thus,P SYS = 10-2. Then the target probability is derived from equation (8.8) as P f accumulate Target = 10-2.

8) The considered detail is assessed against the validity of the geometry functions from [D.2.1]. It is foundthat the doubling plate is so long that a modification of the M k factors is needed. From [6.5] an SCF =1.22 to be multiplied by M k factors for L = 40 mm from [D.2.1] is derived.

9) The crack growth is assumed to be in the base material from the weld toes of the doubling plates. Thereare anodes on the structure. This gives from [10.11] with h = 1.0 for a semisubmersible:

f(F, h) =1.646 from equation (10.3).C = 3.01·10-13 (N, mm) and standard deviation in log C = 0.11.

10)A deterministic crack growth analysis is performed. Mean values are used except for Log C where thepercentile corresponding to mean plus two standard deviations is used with log C = -12.301. Referenceis made to Figure 15-4.

Figure 15-4 Deterministic crack growth curve for the doubling plate

11)A probabilistic fatigue analysis is performed using a relevant computer program where the inputparameters to the analysis are derived as:




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— Long term loading and uncertainty in loading as described in item 5.

— Geometry functions as described in [10.10].

— Initial crack distribution as described in [10.13].

— Crack growth parameters from item 9 with associated uncertainty presented in [10.11].

12)Time to first inspection after year 15 is analysed without taking into account results from formerinspections. The result is shown in Figure 15-5 based on target safety level from item 7 and PoD curvefor EC from [11.1.3] is used for calculation of effect of inspection according to the methodologydescribed in [7.5] and [7.8]. The first interval after inspection is 2 years and the next two intervals are5 and 6 years, respectively (provided that cracks are not found).

Figure 15-5 Effect of inspection after year 15

13)Here leakage detection may be an alternative inspection method. However, if one would like to havethe option of a grind repair before a through thickness crack has been detected, one will likely considerusing an inspection method that is efficient for detection of surface cracks such as EC. The applied PoDcurve is obtained from Figure 11-2 for under water inspections.

14)Time to first inspection after year 15 is analysed taking into account results from former inspections.The result is shown in Figure 15-6.




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Figure 15-6 Effect of full inspection history taking into account previous inspections

15)Based on the performed analysis it is assessed that the next inspection should be performed within 4years. Thereafter typical required inspection intervals are 4 to 6 years. As the considered detail is belowwater level it may be difficult to perform grinding to reduce the need for inspections.

16)The derived result is compared also against deterministic crack growth analysis in Figure 15-4. It ischecked that there are planned a number of inspections within the period until a failure due to fatiguecracking is expected. This may be seen as a robustness check of the performed analysis.

17) It is assumed that the structure is so old that difference in environmental data from that of mean longterm data will not significantly influence the inspection interval. However, the time to next inspectionmay be considered reduced if significant storms are experienced during the coming years.

18)An assessment of the effect of correlation on amount of inspection to be made if there are similarconnections subjected to a similar loading. This also depends on inspection history and in-serviceexperience.

15.2.3 Analysis that accounts for grinding after 15 years in serviceIn order to reduce the required inspections for the next 15 year period from that in Figure 15-5 it isconsidered to grind the weld. The calculation of time to first inspection is performed by using thespecifications for as-welded joints before 15 years of service. Before grinding the weld is inspected in order

to determine if fatigue cracks have developed during the first 15 years of operation. As can be seen in Figure15-7 further inspection is not needed taking into account the inspection and grinding operation after 15years. This indicates that fatigue life improvement of the connections showing the shortest calculatedfatigue lives may be found efficient during service life if a significant extension of the operational life is beingplanned.




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Figure 15-7 Time to first inspection after 15 years taking into account inspection and grinding

15.2.4 Analysis when grinding is performed before installationFor comparison an analysis where grinding is assumed to be carried out before the structure is installed (i.e.at t = 0) is also carried out. The results are presented in Figure 15-8.

Figure 15-8 Inspection plan for doubling plate when grinding is performed prior to operation




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15.3 Example of analysis of a butt weld between stub and bracein jacket structure

15.3.1 Example detail

A butt weld between a stub and brace in a jacket structure is considered. A sketch of the welded detail isshown in Figure 15-9. The connection is located 18 metres below the mean water level (MWL). The wallthickness of the stub is 30 mm and the brace has a thickness of 20 mm and an OD of 1200 mm. Theconnection has been calculated by a conventional fatigue analysis to a fatigue life of 30 years.

Figure 15-9 Sketch of butt weld between stub and brace in jacket structure

15.3.2 Analysis steps and assessmentThe operation is planned for 30 years and the operator would like to plan an optimized inspection. Theanalysis steps in Sec.4 are followed.

The following assessment steps are made:

1) The calculated design fatigue life of the butt weld is based on a recent fatigue analysis and it is concludedthat there is no need to perform a new fatigue analysis.

2) Based on the conclusion from step 1 this step can be skipped.

3) The jacket is not yet in operation and the dynamic loads are based on the current metocean data. Thisstep may however be relevant in future update of the inspection plan.

4) Including the mean stress effect is not considered to be relevant for jacket structures.

5) The design life of 30 years is calculated based on the D curve for seawater with cathodic protection, ref.DNVGL-RP-0005. Assuming a mean up-crossing frequency of 0.16 s-1 and Weibull shape parameter of h = 0.8 the Weibull scale parameter in the long term stress distribution is q = 7.92 MPa.

According to [10.16.2] the uncertainty on loading is COVFatigue loading = 0.17 and stress concentrationfactor COVAnalysis = 0.05. Using equation (10.4) the combined uncertainty on calculated hot spot stress

is COVHot spot = 0.18.

An SCF of 1.66 is calculated according to DNVGL-RP-0005 by using δ t = 5mm, δm = 3mm and δ0 = 0mm.Based on the calculated SCF the degree of bending is derived as DOB = 0.4 (where DOB is defined asbending stress divided by total stress in the connection (without notch stress).

6) The consequence of a fatigue failure is assessed and the loss of the brace is not considered to be criticalwith regard to the overall integrity of the structure.

7) The target probability of failure is derived from Sec.8. A through thickness crack is considered not to besignificant for the integrity of the structure according to NORSOK N-001. This means that the probabilityof a failure given that a through thickness crack is present is less than 10-2. Thus, PSYS = 10-2. Thenthe target probability is derived from equation (8.8) as Pf accumulate Target = 10-2.

8) The M k factor is derived according to [D.2.1]. For butt welds the M k factor is calculated by setting L/t =

0.5 and weld angle θ = 15º.9) The fatigue crack is assumed to initiate at the weld toe and grow into the base material. The structure




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is protected against corrosion with anodes. For a calculated design fatigue life of 30 years and Weibullshape parameter of h = 0.8 the following crack growth properties are applied:

f (F ,h) = 1.746 from Equation (10.3). Hence, C = 1.746·1.83·10-13 = 3.19·10-13 (N, mm) and standarddeviation in Log C = 0.11. Normally the fatigue lives are calculated based on either a deterministic or astochastic analysis of the structure and a Weibull distribution is established that corresponds to the

same calculated fatigue life. Thus, the selection of Weibull shape parameter is not affecting the endresults as long as a change in the shape parameter leads to a corresponding change in the scaleparameter.

10)A deterministic crack growth analysis is carried out. Mean values are used except for Log C where thepercentile corresponding to mean plus two standard deviations, i.e. Log C = -12.276. The results arepresented in Figure 15-10.

Figure 15-10 Deterministic crack growth curve for the girth weld

11)A probabilistic fatigue analysis is performed using relevant computer program.

12)Time to first inspection is assessed to be 16.1 years. The full inspection plan can be obtained based onresults presented in Figure 15-11.




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Figure 15-11 Inspection plan for butt weld between stub and brace in jacket structure

13)EC is the preferred inspection method for under water inspections of the jacket. The PoD curve isobtained from Figure 11-2.

14)The jacket is not set in operation, and hence, there is no previous inspection history.

15)Based on the performed analysis the next inspection should be performed within 9 years of the firstinspection provided that fatigue cracks are not found during the first inspection at year 16. Further

inspection within the defined operational period of 30 year is not needed provided that fatigue cracksare not found during the former inspections.

16)Not included here.

17)There are several years between each inspection and it is assumed that difference in environmental datafrom that of mean long term data will not significantly influence the inspection interval.

18)The effect of correlation with other inspected connections is not considered here.

19)The considered weld is not toe ground.

15.3.3 Probability of the fatigue crack being larger than a given sizeThe expected crack size will change both as a function of time and inspections carried out during operation.In order to illustrate this relation the probability of the crack depth being larger than 5mm and 15mm is

presented in Figure 15-12 and Figure 15-13, respectively. It is seen that the calculated probabilities are notvery different for the different crack sizes.




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Figure 15-12 Probability of the fatigue crack depth is larger than 5 mm

Figure 15-13 Probability of the fatigue crack depth is larger than 15 mm

15.3.4 Design point values of stochastic variablesThe design point values of the stochastic variables, i.e. the most probable combination of variable values,of the stochastic variables are presented as a function of time in Figure Figure 15-14 to Figure 15-18.




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Figure 15-14 Design point values for the Weibull scale parameter as a function of time

Figure 15-15 Design point values for the uncertainty in M k as a function of time




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Figure 15-16 Design point values for Log C as a function of time

Figure 15-17 Design point values for initial crack depth as a function of time




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Figure 15-18 Design point values for the geometry function uncertainty as a function of time

15.3.5 Influence of inspections on stochastic variablesAs a consequence of inspection the distribution of the stochastic variables will be updated. The updateddistributions based on inspections after t = 16.1 years and t = 25.4 years assuming no findings (see Figure15-11) are presented in Figure 15-19 to Figure 15-23. The entire distribution is presented on the left handside with a close-up of the interval of the design point values presented in Figure 15-14 to Figure 15-18 onthe right hand side.

Figure 15-19 Probability density function for the Weibull scale parameter before and after inspections




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Figure 15-20 Probability density function for the uncertainty in M k before and after inspections




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Figure 15-21 Probability density function for Log C before and after inspections




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Figure 15-22 Probability density function for the initial crack depth before and after inspections




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Figure 15-23 Probability density function for the geometry function uncertainty before and after inspections

15.3.6 Analysis when cracks are found during inspectionUntil now it is assumed that cracks have not been found during inspection. In the following it is assumedthat a 1 mm deep indication is detected during the first inspection performed after 16.1 years in service.Repair is not carried out at once and the operator would like to find out how long further operation can be justified. An analysis is carried out as stepwise described in [15.3.2] where it is assumed that an indicationof 1mm in depth was found when inspecting after 16.1 years. In order to account for possible sizing errora standard deviation of 0.5 mm of the measured size is assumed.

Based on a probabilistic analysis where the inspection finding is accounted for, the next inspection isrequired after 21.5 years as shown in Figure 15-24. Note that this is approximately 4 years earlier thanwhat would have been required if no indication had been found in the first inspection.

A second inspection is carried out after 21.5 years and now the indication is 1.5 mm deep (assumed for the

present example). Again, a standard deviation of 0.5 mm is assumed to account for sizing error. Theupdated inspection plan is presented in Figure 15-25 showing that next inspection is required at time equal27.2 years. The design point values of the stochastic variables as a function of time are presented in Figure15-26 to Figure 15-30.




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Figure 15-24 Time to next inspection given finding for a crack of 1 mm at t = 16.1 years that is not repaired

Figure 15-25 Time to next inspection given finding of a crack of 1 mm at t = 16.1 years and 1.5 mm at t =21.5 years that is not repaired




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Figure 15-26 Design point values for the Weibull scale parameter as a function of time for the probabilisticanalysis presented in Figure 15-25

Figure 15-27 Design point values for the uncertainty in M k as a function of time for the probabilistic analysispresented in Figure 15-25




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Figure 15-28 Design point values for Log C as a function of time for the probabilistic analysis presented inFigure 15-25

Figure 15-29 Design point values for the initial crack depth as a function of time for the probabilistic analysispresented in Figure 15-25




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Figure 15-30 Design point values for the geometry function uncertainty as a function of time for theprobabilistic analysis presented in Figure 15-25

15.4 Topside support of floating production storage andoffloading

15.4.1 Example detailA topside support of an FPSO is considered. A sketch of the support is shown in Figure 15-31 where thedetail labelled A is considered. A FE analysis with a local sub-model of the support was used for deriving thehot spot stresses. Based on a D curve in air the calculated fatigue life of the considered hot spot is 30 years.The fatigue life of the back side was assessed to 250 years.

The FPSO was just put into operation and there is hence no inspection history for the considered detail.




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Figure 15-31 Sketch of topside support of FPSO

15.4.2 Analysis steps and assessmentOperation is planned for 30 years and an inspection plan for this period is needed. The analysis steps inSec.4 are followed.

1) The following assessment steps are made:

2) The calculated fatigue lives are from recent analysis and additional analysis is not considered necessary.

3) Based on the conclusion from step 1 this step can be skipped.

4) The FPSO is scheduled to operate at the same field during its entire design life.

5) Mean stress effect is not considered here.

6) The design life of 30 years is calculated based on a D curve in air according to DNVGL-RP-0005.Assuming a mean up-crossing frequency of 0.16 secs-1 and Weibull shape parameter of h = 1.0 theWeibull scale parameter in the long term stress distribution at the hot spot is q = 12.7 MPa. The scaleparameter at the back side is 7.6 MPa. This results in a membrane component of qm = 10.15 MPa andbending component of qb = 2.55 MPa, i.e. DOB = 0.2.

7) The uncertainty on loading is COVFatigue loading = 0.15 according to Table 10-7.

8) The consequence of a through thickness crack is not considered to be critical with regard to the overallintegrity of the structure.

9) The target probability of failure is derived from Sec.8. A through thickness crack is considered not to besignificant for the integrity of the structure according to NORSOK N-001. This means that the probabilityof failure given that a through thickness crack is present is less than 10-2. Thus, PSYS = 10-2. Then thetarget probability is derived from equation (8.8) as Pf accumulate Target = 10-2.

10)The M k factor is according to [D.2.1] when the fatigue life is calculated by the hot spot stress method.The M k factor is calculated by using L/t = 0.5 and weld angle θ = 45º. The attachment length is above300 mm, and hence, SCFL = 1.27 according to Equation (6.24).

11)The fatigue crack is assumed to initiate at the weld toe and grow into base material. Crack growth curvefor air is applied:

12)C = 1.83·10-13 (N, mm) and standard deviation in Log C = 0.11.13) Included below.




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Figure 15-32 Deterministic crack growth curve for topside support

1) A probabilistic fatigue analysis is performed using a relevant computer program.

2) Time to first inspection is assessed to 11.6 years. The full inspection plan can be obtained based onresults presented in Figure 15-33.

Figure 15-33 Inspection plan for detail A of top side support

1) EC is considered to be the most suitable inspection method. The detail is located on topside and the PoDcurve for normal working conditions is assumed, see Figure 11-2.

2) The detail has no inspection history.

3) Not relevant, see step 14.

4) Not performed here.

5) Not relevant as the structure is scheduled for 30 years of operation.

6) The effect of correlation with other inspected connections is not considered here.

7) Toe grinding has not been performed on the considered weld.




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15.4.3 Inspection plan after relocating floating production storage andoffloadingIt is now assumed that the FPSO has been in service under the given conditions for 15 years. The FPSO isthen moved to a location with twice the fatigue damage rate. The topside support is inspected during the

relocation of the FPSO without findings. There is no available documentation indicating that the detail hasbeen inspected before this. Due to the new operating conditions a new inspection plan needs to beestablished. Equivalent time scale is introduced as described in [5.2.2] in order to account for differentdamage rates during service. The probabilistic analysis is performed by using an equivalent installation yearwhich is dependent on the damage rates and the time the FPSO has been operated under the differentconditions. Before relocation the FPSO was operating for 15 years with a damage rate of d 1 = 1/30 = 0.033.The current rate is d 2 = 0.067. According to equation (5.1) the equivalent installation year is obtained bythe following equation:

Based on the equivalent installation year the updated inspection plan can be obtained from Figure 15-34.The corresponding results when plotted against calendar time are presented in Figure 15-35.

Figure 15-34 Inspection plan for the topside support when relocated after 15 years of operation

(15.1)

5.7067.0

15033.015

1

11 =

⋅−=−=

−

N

N

i

N

eq

d

D

T T




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Figure 15-35 Inspection plan for the topside support when relocated after 15 years of operation




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SECTION 16 REFERENCES

/1/ NORSOK N-001. Structural Design. rev.8, September 2012 /2/ NORSOK N-003. Action and action effects. 2 edition, September 2007 /3/ NORSOK N-004. Design of Steel Structures. rev.3, 2012

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through Inspection Results [IOS’87], Glasgow, U.K. 1987 /64/ Vårdal OT and Moan T Predicted versus Observed Fatigue Crack Growth. Validation of Fracture Mechanics

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/73/ Wirsching PH and Chen YN. Considerations on Probability-Based Fatigue Design for Marine Structures. Journal ofMarine Structures 1, 1988, pp. 23-45 /74/ Dalsgaard Sørensen J and Ersdal G. Risk Based Inspection Planning of Ageing Structures. OMAE08-57404, 27th

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/85/ Scherf I and Thuestad T. Fatigue Design of the Oseberg Jacket Structure. Proceedings OMAE, Houston, Texas.1987

/86/ Watanabe I, Branner K, Cariou A, Fukasawa T, Kang Gue X, Kapsenberg G and Rizzuto E. Special Task CommitteeVI.1 Fatigue Loading. 15th International Ship and Offshore Structural Congress 2003, San Diego USA

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/96/ Lotsberg I, Olufsen O, Solland G, Dalane J I and Haver S: Risk Assessment of Loss of Structural Integrity of aFloating Production Platform due to Gross Errors, Marine Structures, 2005, Vol. 17, pp. 551-573

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/112/ Ridley JA. A Study of Some Aspects of Slamming. NMI Report R 158 OT-82113, 1982. Department of Energy,NMI Project 302025 /113/ Lotsberg I. Stress Concentration due to Misalignment at Butt Welds in Plated Structures and at Girth Welds in

Tubulars. Journal of Fatigue 2009 /114/ Smedley S and Fischer P. Stress Concentration Factors for Ring-Stiffened Tubular Joints. Fourth int. symp. On

tubular structures, Delft, 1991 /115/ Buitrago J, Healy BE and Chang TY. Local Joint Flexibility of Tubular Joints [Offshore Mechanics and Arctic

Engineering Conference]. OMAE, Glasgow, 1993 /116/ Goble, Rausche, Likins and Associates Inc.: GRLWEAP Program for Wave Equation Analysis of Pile Driving.

Version 2003 /117/ SPLICE, Structure/Pile /Soil Interaction Analysis, User’s Manual. May 1st 2002. /118/ WAJAC, Wave and Current Loads on Fixed Rigid Frame Structures, User Manual. Dec. 3rd 2010 /119/ DNV SESAM Report No.: 92-7052, Rev. 1, 1 September 2000 /120/ FRAMEWORK, Steel Frame Design, User Manual, December 20th 2007

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, 2007 /122/ Scherf I and Thuestad T. Fatigue Design of the Oseberg Jacket Structure. OMAE, Houston, 1987 /123/ Zhao X-L, Herion S, Packer JA, Puthli RS, Sedlacek G, Wardenier J, Weynand K, van Wingerde AM and Yeomans

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APPENDIX A FATIGUE ANALYSIS OF JACKETS

A.1 Introduction

The purpose of this appendix is to provide guidelines for fatigue analyses of existing jacket structures, such

that the analysis results can be used as a sound basis for planning in-service inspection for fatigue cracks.

In order to satisfy reliability requirements, the ageing jacket structures require an increased focus onmapping of potential hot spot areas where fatigue crack development may occur. This is achieved mainlyby the use of flooded member detection programs (FMD), but supplemented in the case of filled members,important members or very short FMD intervals, by Diver EC and/or ROV CVI (HRI) inspections. The totalquantity of inspections is dependent on the lifespan predicted by fatigue analyses.

The knowledge gained through all changes (from the design assumptions) from fabrication and through in-service experiences, e.g. records from transportation, pile driving, subsidence development, inspection andrepair history, damages and other anomalies as well as reinforcements and modifications, shall beaccounted for in the fatigue analysis.

More accurate fatigue lifespan predictions than those predicted at the design stage can be achieved byimplementing advances in calculation techniques. Such advances may include: generalized influencefunctions (Efthymiou), local joint flexibility (Buitrago), calibrated fatigue loads derived frominstrumentations, directional wave slam (Ridley), update of SCFs, new S-N curves according to DNVGL-RP-0005 or refined analysis where detailed FE models of the tubular joints are included as superelements inthe global frame model in order to better identify the hot spot locations and to achieve more accuratecalculation of the hot spot stress ranges.

The results from the fatigue analyses will together with the redundancy analysis and the Risk BasedInspection (RBI) analyses, accounting for the inspection and repair history, provide the basis for selectionand scheduling of hot spot areas to be inspected for fatigue cracks during in-service life.

The document also addresses calculation of fatigue damage accumulation in the:

— pile welds, accounting for fatigue damage accumulation during pile driving as well as during service life

— welded connections in the upper horizontal jacket frame

— stub/brace connections

— riser and outfall connections.

A.2 Robustness

A robust inspection strategy provides the capability to detect both predicted and unpredicted fatiguedamages before the consequences become unacceptable for the integrity of the structure.

Unpredicted fatigue damages may occur as a result of for example:

— undocumented/unanalysed fabrication defects,

— undocumented/unanalysed temporary phase fatigue (transportation, wind),

— analysis deficiencies (data, modelling, assumptions etc.).

The scheduled in-service inspection programmes developed using fatigue life prediction (this document)and subsequent RBI assessments, should therefore be supplemented by the following inspectionprogrammes:

1) regular GVI inspections of all structural members

2) regular FMD inspection of all air filled structural members

3) regular inspection of scour, seabed debris, marine growth, anode condition, cathodic protectionpotential.




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A.3 Environmental data

A.3.1 Long term distribution of individual wave heightsThe long term distributions of individual wave heights developed for the actual platform location or area

shall be used.

A.3.2 Scatter diagramsThe directional scatter diagrams developed for the actual platform location or area shall be used.

A.3.3 CurrentCurrent can be ignored in the global fatigue analysis as the effect of current on calculated stress range isrelatively small.

A.3.4 Marine growthThe marine growth can be based on measurements from previous platform inspection data.

If the measurements do not show significant different profiles from the profile recommended in NORSOKN-003, /2/, it is recommended to use the NORSOK profile. Measured profiles consistently and significantlyhigher than assumed in the analyses must be remedied by removal of marine growth or by reanalysis withrevised profiles.

Painted jackets may have less marine growth than unpainted and this can be accounted for in the analysisif such an effect is properly documented.

A.3.5 Water depth and subsidenceThe analysis shall be carried out with basis in the expected still water depth, which is equal to the lowestastronomical tide (LAT) plus one half the astronomical tide range.

In some areas the subsidence can be significant. Future predicted seabed subsidence may affect/enhance

the fatigue damage accumulation rate in some weld connections. In order to properly account for this effectfor members governed by global as well as by local wave loads, it is recommended to consider fatigueanalyses for different time intervals where the actual water depth is used for each analysis. This may implyuse of several different analysis models. Then the final accumulated fatigue damage is obtained bysummation of damages calculated for each time interval during in-service life.

A.3.6 Soil dataThe soil data from the actual platform location shall be used when selecting soil parameters for developmentof relevant soil stiffness representation for the fatigue analysis of the jacket structure and when selectinginput soil parameters for assessment of accumulated fatigue damage in the piles during pile driving.

A.4 Basis for selection of fatigue analysis methodA fatigue analysis of a jacket structure involves numerous uncertainties, and small changes in an inputparameter may affect the theoretical fatigue life significantly. Experiences from in-service inspection andinspection of decommissioned jacket structures as well as experiences from platform measurements aretherefore important to increase our confidence in the fatigue analysis methodology. A probabilistic fatigueanalysis can be a tool to assess the relative importance of the parameters involved in a fatigue analysis.

The main groups of methods for response analyses are shown in Figure A-1.

For the following reasons, a deterministic discrete wave fatigue analysis approach (Group F) isrecommended for jacket structures:

— The hot spot stress at any location varies with the geometry and instantaneous force flow in all membersentering the tubular joint. The generalized influence function concept, which relies on the superposition

of linear elastic stress fields, can be used in a deterministic discrete wave fatigue analysis approach.Care should be taken using this approach to calculate hot spot stress in a frequency domain spectral




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response analysis.

It is important that all connections are handled consistently, and the best tool available for this purposeat present is the use of the generalized influence function concept developed by Efthymiou.

— A deterministic discrete wave fatigue analysis approach is more accurate for the upper region of the

jacket as a linearization of the drag term has to be performed in a frequency domain response analysis.— Variable buoyancy may induce fatigue damage in the upper part of the jacket.

The global dynamics is considered to be small if the first natural period is less than 2.5 sec, for foundationsprings corresponding to a sea state governing the fatigue damage accumulation.

If the fundamental natural period (T) is larger than 2.5 sec, it is still recommended to perform adeterministic discrete wave fatigue analysis.

The dynamic effects can then be accounted for by weighted dynamic amplification factors (DAFs) that canbe derived from frequency domain response analyses.

The DAFs can be calculated for each considered member as the ratio of the response with dynamics and theresponse without dynamics included in the analysis. The response is calculated for each wave direction by

integration of the response over the sea scatter diagram.Thus a weighted DAF for a considered wave direction can be derived as

where

DDynamics included = Fatigue damage calculated (Palmgren-Miner summation) using an S-N curve with aconstant slope m = 4.0 where the fatigue damage is calculated by integration of

damage over all sea states where the dynamic response has been included in thetransfer function for the response.

DQuasistatic analysis = Fatigue damage calculated using an S-N curve with a constant slope m = 4.0 wherethe fatigue damage is calculated by integration of damage over all sea states withoutincluding the dynamic response in the transfer function.

For jacket structures in deeper waters, the dynamic effects may be significant. A frequency domain analysisappears as the preferred method as the dynamic effects as well as the geometric effects are properlyaccounted for through identification of the ‘peaks and valleys’ in the transfer functions. However, as statedabove care should be taken when a frequency domain approach is used together with the influence functionconcept.

The following fatigue analysis approach is therefore proposed for jacket structures:

1) Calculate the fundamental natural period of the jacket structure.2) If the fundamental natural period is less than 2.5 sec, perform a quasi-static deterministic discrete wave

fatigue analysis based on hot spot stresses calculated according to Model A in /31/. (Influence functionformulation, accounting for multi-planar effects).

3) Repeat item 2 based on hot spot stresses calculated according to Model C in /31/. (Conventional SCFapproach).

4) For the following reasons, compare the results from item 3 with the results from item 2:

a) As part of the quality control. Experience from practical use of the ‘generalized influence functionconcept’ is limited. Efforts should be made to explain the reason(s) for any major differences inresults in order to identify any possible errors in the input or any error in the computer program.

b) Form basis for selection of uncertainties to be applied in the probabilistic inspection analyses, e.g.

for some joints the force flow are emphasized, for other joints the results from the spectral analysisis considered acceptable etc.

(A.1)0.4/1

=

analysis staticQuasi

included Dynamics

w D

D DAF




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5) If the fundamental natural period is equal to or greater than 2.5 sec, calculate DAFs according to themethodology described here. Perform a deterministic discrete wave fatigue analysis based on hot spotstresses calculated according to Model A in /31/and include the effect from the dynamic amplification.

6) Repeat item 5 based on hot spot stresses calculated according to Model C in /31/.

7) For the reasons explained in item 4, compare the results from item 6 with the results from item 5.8) If the fundamental natural period exceeds 3.0 sec, perform in addition a frequency domain spectral

fatigue analysis of all weld connections. An analysis brief outlining in detail the analysis procedure andcriteria shall be prepared prior to the analysis and approved by the operator.

9) As part of the quality control, compare the results from item 8 with results from item 5 and item 6.

10)Complex tubular joints outside the validity range of the Efthymiou’s formulae shall be handledseparately.

Further refinements may be considered, such as:

— Detailed FE models of joints included as separate superelements in the global space frame model tobetter identify hot spot locations and for a more accurate prediction of hot spot stresses.

— Non-linear time domain spectral analysis if needed to account for all effects in one analysis.

Figure A-1 Methods for response analyses

Analysis type F is normally used for fatigue analysis of jackets when the first natural period is less than 2.5secs.

Analysis types C and E are used for calculation of dynamic amplification when the first natural period islarger than 2.5 secs.

Analysis type D is used for non-linear pushover analysis for calculation of RSF.

Analysis types A and B involve time domain analysis that is normally not used for fatigue analysis of jacketstructures.




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A.5 Platform modelling

A.5.1 Geometry of platform and frame analysis modelA.5.1.1 General

The computer model for existing installations should be taken from the operator’s structure integritymanagement system. For guidance on such systems, see /9/ and /124/.

Changes to the model should be considered, dependent on changes in geometry and loads over the yearsand which are registered in the change log in the structure integrity management system.

The global co-ordinate system used for the analysis should be described.

A description of the computer model should be made. This model description should include:

— jacket legs

— piles/foundation

— bracing system

— conductors

— deck structure— risers, caissons and outfalls.

A.5.1.2 Superelements

The computer model of the main jacket consists normally of only one superelement.

Another superelement can be used to represent the piles with soil springs.

Guidelines on the modelling of piles for fatigue analysis are presented in [A.5.2]. Figure A-2 shows a modelwhere the piles have been included as a superelement.

A third superelement may be used to represent the conductors below the mud line. Alternatively, theresistance from conductors below the mud line may be represented by linearized stiffness matrices at mudline level.

However, other arrangements may be considered depending on the computer program used for the analysisand depending on the existing geometry model in the integrity management system.

A.5.1.3 Coordinate system

Global coordinate system

An example of a global coordinate system is presented in Figure A-3.

The model for the structural analysis has its axis system oriented with the origin at the lowest elevationoriented vertically and in the platform geometric centre laterally.

The global X-axis points towards platform North. Z-axis points upward and the Y-axis points towardsplatform West.

Member local coordinate system

Reference is made to [A.5.10].

The coordinate system used should be described in the analysis report.




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Figure A-2 Super element no. 3 – Assembly

Figure A-3 Coordinate system for the structural model and wave load model

A.5.2 Jacket to pile/soil connectionA.5.2.1 Integrated complete pile model

In cases where it is found appropriate to be able to perform specific fatigue damage evaluations not only inthe pile top, but also along the pile embedded in soil, an integrated complete pile model should be provided.




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This may be required when piles with many cross section changes are used, as often encountered in “oldtime” jacket designs.

The piles of the platforms should then be modelled as separate superelements and included as integratedparts of the computer model in the analysis, enabling an evaluation of the wave induced fatigue damage

along the entire pile. The structure-to-ground connections should be simulated by linear springs locatedalong the piles under the mud line at the level of each pile node. Springs should be included for each of thethree translational motions in the local coordinate system of the pile elements. See Figure A-4.

The distance between the pile nodes should not exceed one pile diameter at a depth down to 15 pilediameters below mud line.

The springs should be linearized based on the wave loads associated with wave heights which are withinthe range of waves with the major contribution to the calculated fatigue damage.

The springs are to be established based on an examination of the results from a separate pile-soil interactionanalysis, e.g. with the SPLICE program, with typical fatigue loads applied at mud line. The non-linear soilbehaviour should be linearized to match a typical load for the major fatigue contribution, e.g. loads

corresponding to 7 m wave height for a jacket in the North Sea.The pile model should extend to a depth where lateral displacements and rotations become insignificant.For the axial response from the soil below this level a single spring should be applied at the bottom of thepile model. This spring should be linearized for a typical axial load from a separate pile-soil interactionanalysis where the full pile length is modelled. The axial spring stiffness should be taken from this analysisas the ratio of axial load and displacement at the depth in question.

The pile model should be generated based on available soil data and pile drawings. If the piles have differentcharacteristics (e.g. ‘main piles’ and ‘leg pile group/cluster’), these should be treated separately.

When piles are closely spaced, e.g. in a group around the corner legs, they will interact through the soil witha slightly reduced stiffness (group effects). This group effect should be accounted for, especially for thelateral behaviour. The group effect should be considered by analysing the entire group of piles with the

SPLICE program in SESAM or in a similar program. For this purpose an elastic soil with linearly increasingE-modulus on the form E=a+bz should be defined. For the moderate load level relevant for fatigue analysisthe E-modulus may be chosen close to that for infinitesimal strains (e.g. 50-70% of that).

The piles should be loaded laterally with a load (horizontal force and pile top moment) considered to berepresentative for fatigue. The average lateral displacement of the pile heads should be noted. Then a singlepile analysis should be performed with the same acting load, but defining a ‘y-factor’ by which alldisplacement values of the p-y curves is to be multiplied. The y-factor should be adjusted until the samelateral displacement is obtained as the average displacement from the group analysis. The linearization oflateral springs to be applied to the structural model should be based on the single pile analysis with y-factor.

A.5.2.2 Interaction through the use of pile stiffness matrix

New designs commonly make use of piles with no or possibly one cross section change with depth. This ismost often chosen in order to aid pile driveability. In such cases it can normally be easily proven that thehighest stresses and fatigue damage occur at the pile top. In these circumstances the jacket-pile interactioncan be represented by the use of a properly linearized stiffness matrix as boundary at each pile connection.The matrix should be linearized to match resulting displacements and rotations for a typical shear force andcorresponding pile top moment and for a typical vertical force. This can e.g. be obtained from two pileanalyses where the typical shear force is applied with and without the corresponding pile top moment.

The piles in a pile group can be analysed together in the SPLICE program (or a similar program) defining alinearly increasing E-modulus with depth to solve the pile group interaction (see [A.5.2.1] above). Applyingthe typical forces and pile top moment to each of the pile heads, the matrix can be derived based on theaverage resulting displacements and rotations from all the piles.

In order to demonstrate that fatigue damage is most severe at the pile top one should present the stressesfrom the selected typical pile loads as a function of depth.




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Figure A-4 Location of springs

A.5.3 Combined cross-section for tubular members with insertsIf tubular members with inserts are used in design with cement grout in the annulus between the tubularsections, the following methodology can be used to simulate the stiffness of the composite members in thecomputer model.

In order to achieve correct nominal forces and moments, the members shall be given the following

dimensions in the stiffness model:

(A.2)

(A.3)

π

A

A

I Douter 28 +=

π

A

A

I Dinner 28 −=




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and

where

I = I Outer tubular +I Inner tubular (combined moment of inertia)

A = AOuter tubular + AInner tubular (combined section area)

Note that the real outer diameter (+marine growth) must be used in the hydrodynamic model.

The equivalent leg member dimensions must not be confused with the equivalent chord thickness in[A.12.9] for computation of SCFs in grouted joints.

A.5.4 ConductorsAll the conductors shall be simulated with correct diameter and position. Since the conductor is free to move

in the axial direction relative to the conductor frames, only lateral hydrodynamic loads and no bendingmoments will be transferred to the conductor frames.

Connections to the ground may for the conductors be represented by a stiffness matrix connected to eachof the conductors. The matrix should be developed for a wave height assumed to initiate a relative largecontribution to the fatigue damage, simulating the average response of the conductors within the soil whentheir group effect interaction is accounted for. The matrix should be developed based on pile analysesperformed with the SPLICE program (or a similar program).

Group effects due to the close spacing of conductors should be accounted for. The group interaction is inSPLICE accounted for by calculating displacements of the soil surrounding any pile (conductor) at any levelcaused by loads transferred to the soil from all the other piles. For this purpose an elastic soil with linearlyincreasing E-modulus on the form E=a+bz is defined. For the moderate load level relevant for fatigue theE-modulus may be chosen close to that for infinitesimal strains (e.g. 50 to 70% of that).

All conductors must be included in the analysis, each loaded with the same load at mud line. The resultingaverage of displacements and rotations for all conductors should be used in calculating a representative ‘average stiffness matrix’ applied to each of the conductors. Axial and torsional stiffness are not importanthere, but should be included for completeness.

A.5.5 Conductor framesThe conductor frames shall be simulated as accurately as required for proper transfer of forces from theconductors to the surrounding structure.

A proper simulation of the local vertical and horizontal hydrodynamic loads should be aimed for.

A.5.6 Topside support structureFor newer structures it has become normal practice to include a more refined stiffness model of the topsidesupport structure (TSS). However, a deck structure can be simulated in a simple manner for the purposeof fatigue analysis. The main requirement to the deck model is to maintain the global stiffness of the deckstructure, including the shear stiffness of the deck plates. This may be achieved by use of shell elements.A plate structure as shown in Figure A-5 may also be transferred into an equivalent beam system with thefollowing cross sectional areas:

whereν = Poisson’s ratio = 0.3 for steel

(A.4)

(A.5)

2

inner outer D DT

−=

t k

Bk A s

)1(2

)(2

2

ν

ν

−

−=




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k = length ratio = L/B (L > B)

Figure A-5 Equivalent cross-sectional areas

A.5.7 Grout reinforced tubular membersThe following procedure can be used to derive equivalent properties, area and moment of inertia, forgrouted tubular members (tubular filled with concrete).

Young’s modulus steel Es = 210 000 MPa

Young’s modulus concrete Ec = 30 000 MPa

Other values for Young’s modulus for concrete can be used when documented.

Ratio Young’s modulus steel to concrete h = Es /Ec = 7Equivalent area can be calculated as:

where

R = Outer radius

T = Tubular thickness

(A.6)

(A.7)

(A.8)

t Bk

Ac

)1(2

)1(2

2

ν

ν

−

−=

t k

Bk Ad

)1(2

)1(2

2

3

2

ν

ν

−

+=

η π π π /)())(( 2222 T RT R R R A ee −+−−==




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Equivalent moment of inertia can be calculated as:

From the equation for moment of inertia an expression for equivalent thickness is obtained as:

with

The equation for equivalent thickness is derived by approximation. Its accuracy can be assessed bycomparing moment of inertia derived from the left and right parts of equation (A.9). If the accuracy is notacceptable, the results can be improved by iteration using an improved alpha value from equation (A.11)by setting T = Te.

This leads to an equivalent area that is in the order of 20% too small. However, this only affects axialstiffness which is already large and thus global forces will be calculated with sufficient accuracy.

Thus the hot spot stress for axial load will be slightly conservative using this approach.

The hot spot stress due to bending is correct as the equivalent section modulus is correct.

A.5.8 Eccentricity at joints and rigid ends (work point offsets)An eccentricity (offset) is in effect an infinitely stiff coupling between a node and a beam end.

Eccentricities may be defined for beams in the pre-processor by applying an eccentricity to a member or agap to a joint. Applying an eccentricity is preferable. The eccentricity is given as a vector in the global, localor transformed coordinate system and pointing from the node towards the element end, see Figure A-6.

Figure A-6 Eccentricity (or offset) is given as a vector from node to element end

Tubular joints with eccentricity less than one quarter of the chord diameter can be considered centric in theanalysis model for calculation of internal forces in the structure; i. e. the simulation of the eccentricity canbe ignored. However, it is important that correct eccentricities are included for calculation of SCFs (throughthe gap value in the parametric equations).

In programs like SESAM it may be easiest to include eccentricities already in the global analysis model asit then automatically can be accounted for when calculating SCFs without requirement to additional

(A.9)

(A.10)

(A.11)

( )[ ] ( )[ ] η π π π

/)(444

44444 T RT R RT R R I ee −+−−=−−=

−−=

2

2

2

3

3

1

R R RT e

α

( ) ( ) 434444

1T RT T RT R R +−−+−−=

η

α




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specification. The minimum gap to be accounted for can be given (e.g. in SESAM) as a constant value. Ifthe calculated gap value is greater than a set minimum, the calculated value will be used. If the calculatedgap is smaller than a set minimum, but still positive (gap), the gap will be set to the minimum gap. If thereis a joint overlap, the overlap data will be used.

A.5.9 Local chord flexibilityIn frame analysis of jacket structures it has been standard practice to model the joints as stiff joints, ref.Figure A-7. However, simple tubular joints without ring stiffeners or inside grout are normally more flexiblethan that of axial stiff members. Therefore, the actual bending moments due to local loading on the tubularmembers or due to frame action are less than that calculated at the tubular joint. The calculation of thesemoments is improved by using springs in the joints that account for the local flexibility of the joints, ref.e.g. Buitrago /115/.

Local joint flexibility may be assigned based on a pure geometry configuration or a load path.

Figure A-7 Simulation of local chord flexibility

A.5.10 Local coordinate systemThe local x-axis is by definition the neutral axis of the cross section and pointing from beam end 1 towardsbeam end 2. Beam ends 1 and 2 are implicitly defined when creating the beam element; end 1 is the firstnode given when creating the element (eccentricities will, however, imply that the beam ends do notcoincide with the nodes). The local y-z-plane is normal to the local x-axis, and defining a local coordinatesystem involves determining the orientation of the local y- and z-axes.

Beam elements for which local coordinate systems are not explicitly defined will be given default localcoordinate systems as follows: The local z-x-plane is parallel with the global Z-axis and with the positivedirection of the local z-axis in the direction of the positive global Z-axis. If the local x-axis is parallel withthe global Z-axis, then the local z-axis is defined to be parallel with the global Y-axis.

An example with hot spot numbering for pipe elements related to the local coordinate system from SESAMis shown in Figure A-8.




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Figure A-8 Relation between local axes and hot spot numbers for tubular cross sections

An example of default hot spot numbering for tubular cross sections in SESAM related to the local coordinatesystem is shown in Figure A-9. Hot spots 7 and 19 are always crown points while 1 and 13 are always saddlepoints.

Figure A-9 Hot spot numbering system for tubular joint

A.5.11 Leg pile group/clusterThe leg pile group/cluster should be part of the global analysis model as shown in Figure A-10.

The pile sleeves can be connected to the main legs using tubular sections or using shear plates.

A standard analysis procedure can be followed when tubular sections are used (Efthymiou’s stressconcentration factors as referred in DNVGL-RP-0005).

The analysis procedure for a plated structure may be dependent on the analysis program that is being used.It is recommended to prepare a FE model of the pile cluster and the connection to the leg. An example of

such an analysis model is shown in Figure A-11.Stress concentration factors for selected hot spots in Figure A-11 may be calculated using a unit axial forcein the leg and then use sound boundary conditions at all other connections.

Then the final fatigue analysis can be performed using sectional forces in the leg together with calculatedSCFs and hot spot curve D, ref. DNVGL-RP-0005.

Note that a more onerous S-N curve should be applied to simple cruciform connections using the hot spotstress methodology (ref. DNVGL-RP-0005 [4.3.7]).




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Figure A-10 Analysis model of jacket structure with leg pile group/cluster




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Figure A-11 Analysis model of pile cluster

A.5.12 Corrosion allowanceHalf the additional thickness, i. e. corrosion allowance of the elements in the splash zone should be includedboth for stiffness analysis and stress analysis.

If long time in-service experience reveals no corrosion, the original dimension can be used in the analysis.

A.6 Basic criteria and analysis assumptions

A.6.1 Selection of wave heights and associated wave periodsThe fatigue analysis shall be based on the long term distribution of individual wave heights and thedirectional scatter diagrams developed for the actual field.

It is suggested to include as many wave heights as reasonable per direction (at least 10 wave heights and

associated wave periods that contributes significantly to the calculated fatigue damage), and assign thewave period as defined in the environmental specification.

For the spectral approach it is proposed to include as many frequencies as possible to describe the mostimportant ‘peaks and valleys’.

A.6.2 Wave directionsA total of at least eight wave approach directions, equally separated around the platform, shall be used inthe fatigue analysis. See Figure A-13.

A.6.3 Selection of wave positionsTo ensure as accurate estimation of the maximum local stress ranges as possible for all connections, the

nominal forces and moments shall be computed for at least 24 equally spaced positions of the fatiguewaves.




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A.6.4 Water depthReference is made to [A.3.5].

A.6.5 Wave theory

The deterministic discrete wave fatigue analysis shall be based on Stokes 5th order wave theory for typical jacket structures. However, the wave theory to be recommended is a function of water depth. For furtherguidance see DNV-RP-C205.

A.6.6 Hydrodynamic loads for fatigue analysisA.6.6.1 Morison’s equation

The force exerted by waves on cylindrical objects depends on the ratio of wavelength to diameter. Forslender offshore structures, defined as ratio wavelength over diameter larger than five (l/d>5), the memberdoes not significantly modify the incident wave. The wave force is expressed as a sum of the drag and inertiaforce by use of Morison’s equation:

where

A p : projected area

V : displaced volume

U : component of the velocity vector of ambient flow normal to the member axis

r : water density

dU/dt : component of particle acceleration vector normal to the axis of the member

C D : drag coefficient

C M : inertia coefficient

For extreme storm waves the effect of the inertia term is insignificant, while for fatigue waves the inertiaterm and the drag term shall be considered as equally important. The significance of each of thehydrodynamic coefficients is further dependent on member diameter and position in the structure.

It is emphasized that the fatigue damage accumulated may be significant even for rather high sea states.

The hydrodynamic loads may be calculated with e.g. WAJAC in SESAM or by a similar program.

A.6.6.2 Hydrodynamic coefficients

Forces on members in the ocean environment predicted by Morison’s equation are engineeringapproximations, see API RP 2A-WSD /125/ and Sarpkaya. Morison’s equation can match measured dragand inertia forces reasonably well in any particular half wave cycle with constant CD and CM, but best fitvalues for the hydrodynamic coefficients vary from one half cycle to another. Variation of CD and CM can be

related to the parameters in Table 6-1.

(A.12)

Table A-1 Parameters affecting the hydrodynamic coefficients

Parameter Equation Comment

Kinematic viscosity: υ = 10-6 m/s2

Water density: ρ = 1025 kg/m3

dt dU V C U U AC F F F M p Dinertiadrag ρ ρ +=+= 5.0




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According to the literature, e.g. Sarpkaya, /126/, the drag- and inertia coefficients are dependent on thewave position, the Keulegan-Carpenter number, the Reynolds number and the roughness; i.e. they can be

expressed as:

As there is no simple way to deal with the two relations above, the following should be noted:

1) Time is eliminated as an independent variable and time-invariant averages are considered.

2) The Keulegan-Carpenter number is applicable to strictly harmonic flow.3) The Reynolds number is based on maximum particle velocity during one wave cycle.

4) Proper characterization of the roughness would require many parameters, i.e. the shape of roughness,density, uniformity etc. API, states that natural marine growth on platforms will generally havee > 10-3, which conforms well when calculating ‘e’ based on advised k ∈ <0.005m, 0.05m> from APIRP 2A-WSD /125/.

5) Morison’s equation is strictly valid for sinusoidal motion and even for this simple case CD and CM arefound to be dependent on four dimensionless parameters. For more complex motions such as a realwave environment, many more dimensionless parameters will appear. It can be hoped that essentialparameters for determination of CD and CM will not be so extensive that useful correlation can beachieved for practical cases.

It is thus concluded that simultaneous measurements of stresses and waves is the only means to verify/calibrate the procedure to predict the long term nominal stress ranges for fatigue life estimation.

Surface roughness

The steady flow coefficient, CDS, depends on the relative surface roughness. This dependency is expressedin API RP 2A-WSD /125/ for cylinders that are densely covered with marine growth.

The effect of soft, flexible growth on CDS is poorly understood, however tests indicate that the soft, fuzzygrowth has little effect as CDS is being determined predominantly by the underlying hard growth. Furthertests have indicated that anemones and kelp produce drag coefficients similar to those of hard growth.

Surface roughness also affects the inertia coefficient in oscillatory flow. Generally as CDS increases with theroughness, CM decreases.

Reynolds numberHydrodynamic coefficients for circular cylinders are dependent on the Reynolds number.

Dynamic viscosity: µ = r ⋅ u = 1.025-3 kg/ms

Relative surface roughness: k: absolute roughness heightD: effective diameter including marinegrowth

Reynolds number Um: maximum wave-induced orbitalvelocity

Keulegan-Carpenter number: T: wave periodThe magnitude of K indicates therelative importance of drag and inertiaterms

(A.13)

Table A-1 Parameters affecting the hydrodynamic coefficients (Continued)

Parameter Equation Comment

Dk e =

υ

DU R m

m =

D

T U K m=

=

=

T

t

D

k R K f C

T

t

D

k R K f C

m M

m D

,,,

,,,

2

1




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For offshore structures in the extreme design environment, Reynolds numbers are well into the post-criticalflow regime, where CDS for circular cylinders is independent of Reynolds number. However, in less severeenvironments, such as considered in fatigue calculations, some platform members could enter into thecritical flow regime. Use of the post-critical CDS in these cases will be conservative for static wave forcecalculations but non-conservative when calculating damping of dynamically excited structures.

Further guidance on the dependence of circular cylinder CDS on Reynolds number can be found in e.g.Sarpkaya.

Keulegan-Carpenter number

The Keulegan-Carpenter number is a measure of the unsteadiness of the flow; it is proportional to thedistance normal to the member axis travelled by an undisturbed fluid particle in a half wave cycle,normalized by the member diameter. For a typical jacket in design storm conditions, Keulegan-Carpenternumber, K, is generally greater than 40 for members in the ‘wave zone’, and as can be seen from figuresbelow, both CD and CM are for such conditions well within the zone where they are constant.

However for typical fatigue waves the Keulegan-Carpenter number is varying from zero and upwards, andthe CD and CM are varying accordingly.

For dependency of the drag coefficient on Keulegan-Carpenter number and surface roughness see from APIRP 2A-WSD /125/.

For dependency of the inertia coefficient on Keulegan-Carpenter number and surface roughness see fromAPI RP 2A-WSD.

Note that for members that are not nearly vertical, the effect of wake encounter, as characterized by Kdependence in the referred figures, is small. Nearly vertical can be considered as within 15° of vertical.

For horizontal and diagonal members, it is sufficient for engineering purposes to use the theoretical valueof CM at K → 0 and the steady flow value of CD at K → ∞.

Hydrodynamic coefficients

It is proposed to use waves with wave height equal to 7 m and associated period as basis for computation

of hydrodynamic coefficients as waves of this magnitude are expected to contribute significantly to thecalculated fatigue damage for typical North Sea structures.

Alternatively, the coefficients may be based on the wave causing most calculated fatigue damage. This mayrequire an iteration process in that a fatigue analysis has to be performed in order to gain knowledge aboutcontribution to the calculated fatigue damage.

Alternatively, the hydrodynamic coefficients are calculated for each member for all waves for which theplatform is analysed.

Wave kinematics is calculated using Stoke’s 5th order wave theory. In computations of Keulegan-Carpenternumber a marine growth thickness of 100 mm is applied for all members, thus increasing the outer diameterby 200 mm in calculations of Keulegan-Carpenter number.

The hydrodynamic coefficients are calculated based on recommendations in API RP 2A-WSD.

Illustration of calculation of CD and CM is indicated in Figure A-12.




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Figure A-12 Illustration of calculation of CD and CM

A.6.6.3 Simulation of member groups

In some cases it is convenient to simulate a group of members by one element. To reproduce representativehydrodynamic forces, the ratio between some parameters must be kept. These are:

Buoyancy:

Drag force:

Inertia force:

where

ρ = density of water

D = tube diameter (including marine growth)

C D = drag coefficient

C m = added mass coefficient

C M = mass coefficientV = volume per unit length

4

2 Dπ ρ

2

2

1v DC D ρ

a D

C VaC Va M m4

2π ρ ρ ρ =+




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v = water particle velocity

a = acceleration of water particle

From this the following relations for equivalent properties can be derived.

For maintenance of buoyancy:

For maintenance of drag force:

For maintenance of inertia force:

A.6.6.4 Marine growth accumulation

Reference is made to [A.3.4]. The thickness of the marine growth is added to the radius of the consideredmember for calculation of effective area and volume.

A.6.6.5 Hydrodynamic loads on the anodes

The anodes will increase the global wave and current loads. As explained in e.g. /130/, the flow around apipe where anodes are attached is extremely complex.

It is recommended that the drag coefficient for all structural jacket members is increased with 10% toaccount for wave loads on the anodes.

Alternatively, the load contribution from the anodes can be estimated based on the number, size andlocation of the anodes.

It can be assumed that the anodes will not affect the mass coefficient.

A.6.6.6 Shielding effects in the conductor group

The shielding effects in the conductor group are uncertain for fatigue waves, and shall not be accounted forin the fatigue analysis.

A.6.7 Effect of current and windNo current or wind is included in the analysis because these have minor effect on the calculated fatigue life.

A.6.8 Effect of buoyancyThe stress variation caused by variable buoyancy in the upper part of the jacket may significantly contributeto the fatigue damage in the joint connections of these members.

It is emphasized that when using SESAM for the fatigue analysis it is not possible to achieve correct hotspot stresses based on force flow through the joints when variable buoyancy loads are present in additionto wave loads. Thus, when analysing fatigue lives in the splash zone it is recommended to use SCFs basedon Efthymiou’s Model C, i.e. the conventional SCF approach. This may be different in other analysisprograms.

Alternatively the fatigue damage due to variable buoyancy can be calculated separately and added to thecalculated fatigue damage from the Morison loading.

(A.14)

(A.15)

(A.16)

=

=n

i

i D D1

2

D

DC

C

n

i

i Di

D

== 1

2

1

2

D

DC

C

n

i

i Mi

M

==




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A.7 Deterministic discrete wave fatigue analysis

A.7.1 Fatigue analysis procedureFor reasons explained in [A.3], a deterministic discrete wave analysis approach is recommended for

calculation of fatigue damage at welded connections in the jacket structure, including pile welds. Referenceis also made to Appendix K of NORSOK N-004, /3/.

In order to properly describe the long term stress range distributions, the jacket structure should beanalysed for at least ten (10) waves per direction. Each wave is stepped through the structure as describedin [A.6.3].

Stokes 5th order theory shall be used.

The jacket structure shall be analysed for at least eight wave directions. These are distributed equally at45º intervals as shown in Figure A-13.

Fatigue damage is calculated according to Palmgren-Miner’s rule. Reference is made to DNVGL-RP-0005[2.2].

It should be noted that for tubular joints the critical section may be on the chord side of the weld or thebrace side of the weld. Both these regions have to be analysed for fatigue as it is not possible beforehandto predict what region will provide the largest hot spot stress (as this depends on the actual geometry).

Equations for SCFs for simple tubular joints are presented in DNVGL-RP-0005 App.B both for the chord andthe brace side.

The fatigue damages from different analysis models should be added together.

Calculated fatigue damages in the piles during service life are added to the fatigue damages calculated forthe pile driving.

For jacket platforms with a fundamental natural period exceeding 2.5 sec (with fatigue foundation springs),

the dynamic effects may be accounted for according to the procedure in [A.4].

The analysis approach outlined in [A.4] is recommended for jacket structures in deeper waters with a highfundamental natural period.

Figure A-13 Wave directions (platform directions)

A.7.2 Prediction of fatigue damage accumulation in the upper horizontalpanelsThe horizontal members in the upper horizontal panels of the jackets may be subjected to slamming and

variable buoyancy loads. The slamming loads can be calculated based on the method referred to as the “Ridley comprehensive method”. Reference is made to /112/ and [A.8.1].




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A.8 Fatigue caused by local hydrodynamic loads

A.8.1 Slamming loadsSlamming loads occur whenever a member is suddenly immersed by wave action. A procedure for analysis

of load effect from slamming has been presented by Ridley, /112/.It is recommended to use the procedure denoted as “Ridley comprehensive” for the fatigue analysis of theslamming loads.

An example of calculated annual fatigue damage of horizontal members 2.0 m above the water line is shownas function of length to diameter and diameter to thickness in Figure A-14 and Figure A-15, respectively.

An example of slamming analysis on a horizontal member is shown in Figure A-16 and Figure A-17 forillustration. The relationship between calculated fatigue damage due to slamming and buoyancy can bedifferent from that shown here.

The largest calculated fatigue damage due to slamming is observed when the horizontal members are within± 3.0 m from the water line. Outside these limits the calculated fatigue damage due to slamming issignificantly lower as also indicated from Figure A-17.

Figure A-14 Calculated annual fatigue damage with respect to L/D for h = 2.0 m

0.00001

0.0001

0.001

0.01

0.1

1

10

20 25 30 35 40 45 50 55 60

Length to diameter (L/D)

C a l c u l a t e d

a n n u a l f a t i g u e d a m a g e

D/t = 14.7

D/t = 19.6

D/t = 23.5

D/t = 29.3

D/t = 39.1

D/t = 58.7




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Figure A-15 Calculated annual fatigue damage with respect to D/t for h = 2.0 m

Figure A-16 Member position relative to mean water level as function of time (and subsidence)

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

10 20 30 40 50 60

Diameter to thickness (D/T)

C a l c u l a t e d

a n n u a l f a t i g u e d a m

a g e

L/D = 20.4

L/D = 27.3

L/D = 34.1

L/D = 40.9

L/D = 54.6

Approximation of height above (MWL=LAT+tide)

-4

-2

0

2

4

6

8

1970 1980 1990 2000 2010 2020

Year

h [ m ]




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Figure A-17 Calculated annual fatigue damage for a horizontal member in the splash zone

A.8.2 Vortex induced oscillationsVortex induced oscillations may occur due to wave and current loading depending on member geometryand boundary conditions. It is recommended to perform the design such that vortex induced vibrations arenot likely to occur.

Guidance on analysis of vortex induced vibrations can be found in DNV-RP-C205 Sec.9.

A.9 Fatigue analysis due to transportThe fatigue analysis used at the design stage (if available) shall be reviewed to identify and includesignificant fatigue damage contributors to the in-service fatigue damage. If data regarding transportationroute, sea-states, and other pertinent information regarding transportation and installation is available,these should be used as deemed necessary to achieve a correct ranking of expected fatigue life and henceprioritization of in-service inspections.

It is emphasized that for some of the existing installations, the fatigue damage accumulated duringtransportation from the fabrication yard is not known. This may explain observed cracks which cannot bepredicted through in-place fatigue analyses alone, and underlines the importance of regular generalinspections also for fatigue (ref. [A.2]).

A.10 Fatigue analysis methodology for pile driving

A.10.1 Evaluation of pile driving fatigue for designCalculation of pile driving fatigue needs in design to be based on prediction of the pile driving performanceapplying the following stepwise approach:

1) Determine from drawings the characteristics of the piles. When piles with different dimensions are used,each type of pile should be analysed. Pile followers should be modelled as detailed as possible, basedon ‘typical’ followers or specifically designed followers as relevant at time of the design.

2) Based on agreed soil design parameters calculate the soil resistance during driving (SRD) as a functionof driving depth. This includes skin friction profile and tip resistance as well as the integrated SRD. Since

skin friction at a certain depth gradually reduces as the pile is driven beyond that depth, skin frictionprofiles varying with depth of driving should be accounted for.




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3) GRLWEAP analyses (or analyses with a similar pile driving analysis program) should be performed atminimum 3 different depths of penetration, selected to represent driving situations in the layered soil.Changes in driving performance due to change in driving resistance (due to layering) or due to changeof follower make-up should be taken into account in the choice for representative depths of analysis.

4) GRLWEAP analysis should be performed at each of the chosen depths to establish the relation between

accumulated SRD and blow counts. The input skin friction profile and tip resistance (given as % of totalresistance) is scaled in incrementally increasing steps to establish this relation.

5) Combine results from steps 2. and 5. to derive expected blow counts versus penetration.

6) Derive from the relevant GRLWEAP analyses the stress ranges at the selected locations at the pile (crosssection changes, final mud line position, position of max ‘free field’ moment from wave loading).

7) Apply SCF at wall thickness transitions.

8) Calculate the pile fatigue damage from pile driving phase from results of steps 5, 6 and 7 using relevantS-N curve in air, see [A.15.2].

A.10.2 Evaluation of the pile driving fatigue based on pile installationrecordsThe following stepwise approach should be followed for the case where the fatigue damage from pile drivingcan be calculated based on records from installed piles:

1) Determine from drawings the characteristics of the piles. When piles with different dimensions are used,each type of pile should be analysed. Pile followers should be modelled as detailed as possible, basedon ‘typical’ followers or specifically designed followers depending on available information.

2) Determine from pile driving records which pile has experienced the most intense pile driving.

3) Divide the pile-driving into minimum 3 different phases with a representative pile penetration for eachphase and derive number of blows per phase from pile driving records.

4) With GRLWEAP (or a similar pile driving analysis program) determine for each of the phases the ultimatepile resistance which gives a blow count that matches the representative blow count from the piledriving record.

5) Derive from the relevant GRLWEAP analyses the stress ranges at the selected locations at the pile (crosssection changes, final mud line position, position of max ‘free field’ moment from wave loading).

6) Apply SCF at wall thickness transitions.

7) Calculate the pile fatigue damage from pile driving phase based on relevant S-N curve in air, see[A.15.2].

A.10.3 Pile driving analysisGRLWEAP (GRL Wave Equation Analysis of Pile driving) is a program that simulates a foundation pile underthe action of an impact pile driving hammer, using wave equation theory, where the hammer, drivingsystem and pile are modelled as a number of discrete masses separated by springs. The soil resistance ismodelled as non-linear springs in combination with dashpot damping. A hammer data file is included in the

program package, containing the required hammer modelling data for a wide range of commonly usedhammers, including the steam powered, single acting hammers used for a number of the early jacketstructures. If another program than GRLWEAP is used for simulation of pile driving, this should include thefollowing features:

— Possibility to model the hammer ram with several elements in order to account for the mass andstiffness distribution along the height of the ram.

— Possibility to set hammer efficiency.

— Modelling of the hammer anvil (helmet) and cushion with proper masses, stiffness and damping.

— Modelling of hammer assembly (surrounding housing).

— Modelling of the pile with proper mass and stiffness distribution and damping.

— Inclusion of a ‘splice model’ being able to handle slacks and no transfer of tension, e.g. between hammer

and pile top, or when followers are used, between follower and pile or between separate followers.— Possibility to model relative distribution of soil resistance with depth and Smith type viscous damping,




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and to prescribe quake values (required displacements to mobilise full resistance) for skin friction andend bearing.

The program should have possibility to compute the following:

— The blow count (number of hammer blows per unit length of permanent set) of a pile as function ofultimate static soil resistance values for given dynamic soil resistance parameters and given a hammerand driving system (helmet, hammer cushion, pile cushion).

— The axial stresses in the pile corresponding to the computed blow count (both maximum compressionof the downward propagating wave and the maximum tension of the reflecting wave).

— The energy transferred to the pile.

Stress ranges during the driving shall be established by adding the compressive and tensile stresses fromthe respective analyses.

The results from the analysis program should be reviewed, and pile stress ranges at various depthscorresponding to the selected driving phases, and at selected locations along the pile should be extracted.Selected locations should be e.g. locations of cross section changes or at weld bead locations. Subsequently,the resulting pile driving fatigue damage should be calculated at these locations, using an appropriate S-N-curve and SCF.

Reference is made to /116/ for further information on GRLWEAP.

The fatigue mechanism under pile driving may be considered complex. However, the stress range in thepile as derived from GRLWEAP analyses have been calibrated with measured values. During hammering ofthe pile a wave of compression is followed by tension. There may be some time lag between the two stresspeaks depending on location on the pile considered. However, tension occurs before a new compressionwave is introduced such that a cycle of stress range contributing to the fatigue damage is well defined.

When calculating pile driving fatigue based on existing pile installation records, GRLWEAP (or a similarprogram) should be applied to determine the ultimate pile resistance which gives a blow count that matchesthe blow count from the pile driving record. This should be performed for at least 3 phases of the pile drivingwith correspondingly different representative pile penetration levels, as is illustrated in Figure A-18. Thesplit in phases/levels should be selected related to changes in resistance and/or change in pile length (e.g.in accordance with add-ons installed or change or adding of followers). Similar phases of pile driving andcorresponding representative depths for analyses should be evaluated when performing traditional piledriving fatigue analyses with estimation of pile driving resistance from soil data.

Hammer impact causes a shock wave to propagate through the pile causing compressive and tensilestresses in the pile as illustrated in Figure A-19, which shows the variation of axial force with time at aselected location. The stress range selected for pile driving fatigue is the absolute difference betweenmaximum compressive and tensile stress.




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Figure A-18 Overview 3 pile driving phases




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Figure A-19 Shock wave in pile due to hammer impact, showing force at a specified pile node with time

A.10.4 Geometry of pilesThe wall thickness of the piles and the different pile configurations regarding consecutive installation of add-ons to the pile during pile driving, or use of followers should be accounted for.

The different pile configurations and pile driving records should be assessed to find the piles that haveexperienced the most intensive pile driving when calculating pile driving fatigue based on existing pileinstallation records. These piles should then be modelled and analysed with GRLWEAP.

A.10.5 Soil data

A.10.5.1 Calculation of soil resistance during driving (SRD)

The method chosen for calculating soil resistance during driving should be well documented and derived forsoil conditions that are similar to those in question. For typically North Sea conditions of overconsolidated

clay and dense sand, the method by Alm and Hamre /124/ should be used. Other methods may beconsidered if properly documented to be calibrated for or shown to fit similar soil conditions and piledimensions. The method should, however, use correlations with CPT qc resistance for calculation of drivingresistance in sand. Conservative high estimate qc profiles should be defined based on the available records.Particular care should be made if the records show refusal, i.e. not being able to define the qc resistance.

A.10.5.2 Soil input to GRLWEAP analyses

When GRLWEAP is applied to determine the stress ranges for the installed piles, the ultimate pile resistancewhich gives a blow count that matches the blow count from the pile driving record, a triangular distributionof soil resistance along the embedded length of the pile may be assumed. 50% of total resistance as tipresistance can generally be used. The resulting stress range at the selected locations of the pile is normallynot very sensitive to this choice.

When GRLWEAP is applied for pile driveability analyses and corresponding pile fatigue analyses for a newdesign, it is recommended to apply the expected (calculated) friction and tip resistance distribution as a




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direct input.

The dynamic part of the resistance can be represented using a Smith type damping coefficient of 0.65 s/mfor skin friction in cohesive soil, 0.15 s/m for skin friction in non-cohesive soil, and 0.5 s/m for tip resistancein all soils. The quake values (the displacement to mobilise full resistance) can be assumed to be 2.5 mm

for both skin friction and tip resistance. However, if the method used for calculation of SRD is calibrated byuse of other values for damping and quake, these values should be applied for the GRLWEAP analyses.

A.10.6 Hammer dataThe actual hammer used for pile installation should be used for calculation of stress ranges in the piles. Thehammer model may be found in the hammer library of the analysis program to be used. Wheneverrecognised hammer models implemented in a program hammer library is not used, the modelling of thehammer should be documented and justified.

For driveability back calculation analysis used to determine stress ranges it is conservative to assume a highenergy transfer. Thus realistically high estimate of energy transfer or hammer efficiency should be appliedfor back calculation analysis.

A.10.7 Calculated fatigue damage at selected hot spot areasThe fatigue damage due to driving should be determined at selected locations of the piles to capture thelocations where high contribution to damage isolated from pile driving can be expected as well as locationswhere the highest contribution from wave loading occur.

The highest contribution from pile driving always occurs at the location of cross sectional changes, partlydue to the stress concentrations resulting from the propagating waves being reflected at locations ofdiscontinuities and partly due to the geometrical stress concentration effects.

The highest contribution from wave loading is either at the top of the pile or somewhat further down intothe soil where the maximum bending moments in the pile occur. The position of the lower momentmaximum should be determined from laterally loaded pile analyses.

A.11 Fatigue of grouted pile/sleeve connections subjected toalternating loading

Grouted pile/sleeve connections shall be designed to satisfactorily transfer the design loads from the pilesleeve to the pile. The following failure modes of grouted pile to sleeve connections need to be considered:

— Transfer of the design shear load between the pile and the surrounding grout annulus due to axial forceand bending moment in the pile in ULS and ALS.

— Transfer of design shear force from sleeve to pile (shear force acting normal to the longitudinal pile axis)at the lower part of grout during a storm loading in ULS and ALS.

— Fatigue of the grouted connection for alternating axial load and bending moments in the pile.

— Fatigue of the grout for cyclic contact pressure between sleeve and pile.

Reference is made to section K.5 on grouted connections in NORSOK N-004, /3/.

A.12 Stress concentration factors

A.12.1 Definition of stress concentration factorA stress concentration factor can be defined as a stress magnification at a detail due to the detail itself ordue to a fabrication tolerance with the nominal stress as a reference value. The maximum stress is oftenreferred to as the hot spot stress that is used in relation with S-N data for fatigue life calculation. This hotspot stress is thus derived as the SCF times the nominal stress.

Reference is also made to DNVGL-RP-0005.




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A.12.2 Effect of fabrication tolerancesFabrication tolerances are considered to be most important for simple butt welds in plates and tubularmembers. Reference is made to DNVGL-RP-0005 [3.3.7]. Reference is also made to NORSOK M101, /6/.

A typical fabrication tolerance used in fabrication specifications for butt welds is the smaller of 0.15t and 4

mm.

A.12.3 Stress concentration factors at butt welds at stubs to braces andin pilesSCFs for girth welds in tubulars and piles are presented in DNVGL-RP-0005 [3.3.7].

A.12.4 Stress concentration factors for weld beadsWhen using the S-N curve recommended for weld beads in [A.15.2], it is assumed that the notch effect dueto the weld bead is accounted for in the S-N curve. This means that SCF = 1.0.

A.12.5 Stress concentration factors for conesSCFs for simple tubular to cones are presented in DNVGL-RP-0005 [3.3.9].

A.12.6 Stress concentration factors for simple tubular jointsA.12.6.1 General

It should be noted that for tubular joints the critical section may be on the chord side of the weld or thebrace side of the weld. Both these regions have to be analysed for fatigue as it is not possible on beforehandto predict what region will provide the largest hot spot stress.

It is recommended that the calculation of hot spot stresses are based on Model A (or B) in /31/, i.e. withuse of the generalized influence function concept. See [A.6].

Tubular joints with geometry outside the validity range of the SCF formulae shall be identified, and the effecton the hot spot stress must be documented.

A procedure for superposition of stresses from bending about two axes and axial force is presented inDNVGL-RP-0005 [3.3.2]. 8 hot spots around the circumference of the tubular sections are to be analysed.

It should be noted that there exists a reprint from 1991 of Efthymiou’s paper /31/ presented in 1988. Somecorrections have been made in the 1991 version of the paper.

A.12.6.2 Analysis of T- and Y- joints

This section addresses the assessment of hot spot stress at T- and Y-joints:

— For long chord sections exceeding the validity of parametric equations for SCFs (Alfa larger than 40).

— When a chord is loaded by more than one support, e. g. more than one support along a chord by riseror conductor support. (The reason for this is that the SCF from the parametric equation Efthymiou takesinto account only the bending moment in the chord from the force in one brace).

It is important to perform analysis using a relevant fixation moment at the ends of the beam as thissignificantly influences the bending moment in the chord below the brace in the T-joint. It is the bendingmoment in the chord that is governing the SCF at the crown position of the chord, see example in FigureA-20.

The following guidance for the C-value in DNVGL-RP-0005 is given:

C = 0.5: Fixed ends of the chord.

C = 1.0: Free ends of the chord.

C = 0.7: This is the value usually used according to the guidance in DNVGL-RP-0005.

The value of C is made such that it should be the same as the buckling length coefficient for the chord. For

example for fixed ends the buckling length is only 0.5 times the chord length.In SESAM the C-value is also defined under buckling.




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(In SESAM this is also defined by use of the same command as used for member buckling length).

The validity of the SCF equations is presented as an alpha value between 4 and 40. The alpha factor isdefined as

A more efficient analysis procedure for T- and Y- joints has been included in the SESAM program. Referenceis made to /113/. This procedure is included in DNVGL-RP-0005 as an alternative solution. Use of thisprocedure will remove the need for this section in this guideline on fatigue analysis as correct hot spot stresswill be directly derived as output from the analysis. Also the upper limitation of the factor will no longer berequired. Thus, the alternative solution (equations 6b and 7b in Table B1 of DNVGL-RP-0005) isrecommended used.

It is recommended to use a SCF for the attachment equal 1.3. Thus, it is possible to perform a fatigueassessment of the chord crown position based on calculated stress range in the chord together with an

appropriate SCF for the attachment.

A.12.6.3 Several attachments on long elements

It should be noted that the following section needs not be applied if the recommended SCFs from equations6b and 7b in Table B1 are used for fatigue analysis.

Otherwise the equations for SCFs in DNVGL-RP-0005 from Efthymiou for T- and Y-joints are established fora chord with a single load that is subjected to a loading similar to that shown in Figure A-20 (Ref. equations6a and 7a in Table B1 of DNVGL-RP-0005). The axial loading in the brace results in a bending moment inthe chord. It is the bending moment below the brace that is the reason for the stress concentration at thecrown position. It is observed that the length of the chord is an important parameter in this respect.

It should also be noted that a = 2L/D is limited to 40 in order to use the equations for the SCFs.

If the brace is not in the middle of the chord, it is recommended to calculate an equivalent length that givesthe same bending moment as one have at the considered brace. Equations required for this are shown inFigure A-21.

When more attachments are added to the same chord, the moment in the chord may most likely increase.This has to be considered in a fatigue analysis.

Example

An example of this is shown in Figure A-22 with attachments from several caissons. This results in a loadingas shown in Figure A-23. The bending moment in the chord in Figure A-23 is 3.3 times the bending momentif only a force P was acting in the middle of the chord. Thus, the SCF at the crown of the chord is in thiscase 3.3 times higher than that derived from the analytical equations for SCFs from DNVGL-RP-0005.

Figure A-20 Loading on chord with fixed ends from brace

(A.17)

D

L2=α




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Figure A-21 Moment distribution due to point load on beam fixed at ends

Figure A-22 Detail of frame at el. -41.50 with considered beam

Figure A-23 Loading on beam




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A.12.6.4 Caissons welded as T-joints to supports

Caissons welded to supports are shown in Figure A-24.

For the condition shown in Figure A-24 one should use C = 0.5 and the effective length for calculation ofmoment should be

Figure A-24 Caissons welded as T-joints to supports (at horizontal levels)

A.12.7 Classification of tubular jointsThe hot spot stress ranges shall be calculated by use of the generalized influence function concept, whichrelies on the superposition of linear elastic stress fields.

A.12.8 Stress concentration factors for ring stiffened tubular jointsSCFs for ring stiffened tubular joints are presented in Smedley and Fischer, /114/.

A linear superposition of stresses resulting from axial force, in-plane bending moment and out-of-planebending moment should be performed for tubular joints with more than one ring stiffener within thefootprint of the brace.

Tubular joints with geometry outside the validity range of the SCF formulae shall be identified, and the effect

on the hot spot stress must be documented.Due attention should be made to the important issues listed in DNVGL-RP-0005 [3.3.4].

(A.18)l Le

3

2=




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A.12.9 Stress concentration factors for grouted tubular joints

A.12.9.1 Fully grouted joints

Reference is made to DNVGL-RP-0005 for derivation of SCFs for fully grouted joints.

A.12.9.2 Grouted joints with insert pileReference is made to DNVGL-RP-0005 for derivation of SCFs for grouted joints with insert pile as shown inFigure A-25.

Figure A-25 Chord section with insert pile and grout

A.12.10 Stress concentration factors for caissons

The type of connection should be assessed. If there are welded connections similar to that of a tubular joint,one should use the Efthymiou’s equations, /31/, as presented in DNVGL-RP-0005 App.B. If the geometry isdifferent from this, the connections should be assessed case by case.

A.12.11 Stress concentration factors for square to circular membersEquations for SCFs for square to circular members can be found in /123/.

A.13 Tubular joints welded from one sideThe root area of single-sided welded tubular joints may be more critical with respect to fatigue cracks thanthe outside region connecting the brace to the chord. In such cases, it is recommended that stubs areprovided for tubular joints where high fatigue strength is required, such that welding from the backside canbe performed.

As an example, failure from the root has been observed at the saddle position of tubular joints where thebrace diameter is equal to the chord diameter.

It is likely that fatigue cracking from the root might occur for rather low stress concentrations. Thus specialattention should be given to joints other than simple joints, such as ring-stiffened joints and joints whereweld profiling or grinding on the surface is required to achieve sufficient fatigue life. It should be noted thatsurface improvement does not increase the fatigue life at the root.

Based on experience it is not likely that fatigue cracking from the inside will occur earlier than from theoutside for simple T, Y and K tubular joints. The same consideration may be made for X-joints with diameterratio β ≤ 0.90. For other joints and for simple tubular X-joints with β > 0.90 it is recommended that a fatigueassessment of the root area is performed.

Due to limited accessibility for in-service inspection a higher design fatigue factor should be used for theweld root than for the outside weld toe hot spot.




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Lack of penetration is hard to control by non-destructive examination, and it is considered more difficult todetect possible defects at a root area of a tubular joint welded from one side, than for a butt weld weldedfrom one side.

It is therefore emphasized that the documentation of fatigue strength of complex joints, such as for ring-

stiffened joints, may imply the need for rather comprehensive analyses if single sided welding is planned.Ultimately, it may be needed to include a detailed FE model of the tubular joint in the global space framemodel for the purpose of identifying the hot spots and calculate the fatigue life (refined fatigue analysis).Reference is made to [A.14.2].

General guidance on stiffened tubular joints is given in DNVGL-RP-0005 [3.3.4].

For tubular joints where an assessment of the root area is needed the guidelines provided in DNVGL-RP-0005 shall be followed.

A.14 Finite element analysis

A.14.1 Finite element analysis of tubular joints

A.14.1.1 Finite element model

Reference is made to DNVGL-RP-0005.

A.14.2 Detailed finite element models as superelements in the framestructureIf FE models are made of tubular joints, it is efficient and most reliable to include these as part of the framemodel, i.e. also referred to as a ‘refined fatigue’ approach.

The hot spot stress can be directly read out from the analysis results and the fatigue damage can becalculated directly using the T-curve.

This methodology may be used depending on assessment of several parameters, such as

— complexity of joints, e.g. multiplanar, overlap, ring stiffeners,

— joints where the geometry is outside validity range of parametric equations,

— joints where consequences of a fatigue crack is large,

— joints where calculated fatigue life is short,

— joints where access for in-service inspection is difficult or simply that inspection is considered expensive.

Normally a decision to carry out detailed FE analysis should be based on a total assessment of theparameters listed above.

Care should be taken to ensure that the correct global stiffness distribution is maintained in case of a

‘refined fatigue’ approach.

A.14.3 Finite element analysis of composite joints (grout reinforced joints)

A.14.3.1 Modelling

The analysis model of composite tubular joints should include the non-linear interface (contact/slip)between grout and steel parts.

The interface may be modelled with contact elements or similar allowing inclusion of friction for surfaces incontact.

Bond (adhesion) between steel surfaces and grout may not be included in the analysis.

Contacts for double skin grouted joints need only to be included between the grout and the outer tube (thechord).




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A.14.3.2 Grout material model

The material model of the grout may be taken as linear-elastic. The Young’s modulus may be taken as:

— Standard Portland grout, (e. g. Dutch Encilite), w/c ratio 0.35 - 0.4: E = 15 000 MPa

— Ducorit Grouts (S1, D4 and D5): According to /Ducorit/.

A.14.3.3 Analysis

The non-linear interface (contact/slip) gives rise to non-linear SCF values; e. g. the axial tension SCF isdifferent from the axial compression SCF. Furthermore, the SCFs depend upon the load level as the area incontact changes with the loading. The non-linear SCF may be converted into a set of standard linear(constant) SCF values for easy implementation in the space frame fatigue analysis. This conversion shouldbe performed in a conservative manner and take the fabrication/installation history of the actual detail intoaccount. The average or mean load on the actual joint should be considered when estimating SCFs to beused for fatigue analysis.

A.14.4 Finite element analysis of load carrying doubler plate jointsGuidance on FE analysis of load carrying doubler plates can be found in DNVGL-RP-0005. This document

also gives recommendation on derivation of structural stress and S-N curve to be used.

A.15 S-N data and selection of S-N curve

A.15.1 GeneralS-N curves to be used for fatigue analysis are presented in DNVGL-RP-0005.

S-N curves are presented for air environment, seawater with cathodic protection and seawater with freecorrosion.

A.15.2 S-N data for pilesThe transition of the weld to base material on the outside of tubular girth welds can normally be classified

to S-N curve E. If welding is performed in a horizontal position it can be classified as D. If welding isperformed from outside only, it should be classified as F3 for the weld root.

S-N curve E applies to weld beads.

S-N data corresponding to air environment condition is used for the pile driving phase.

S-N data corresponding to environment of seawater with cathodic protection is used for the operational life.

A.15.3 S-N curves for tubular jointsReference is made to DNVGL-RP-0005 Sec.2.

A.15.4 S-N curves for attachments to primary structureReference is made to DNVGL-RP-0005 Sec.2 and App.A.

A.15.5 S-N data for ground weldsReference to S-N data for ground welds is made to DNVGL-RP-0005 Sec.7 and App.D.

A.16 Fatigue damage and design fatigue factors

A.16.1 Accumulation of fatigue damageFatigue damage is calculated according to Palmgren-Miner's rule. Reference is made of DNVGL-RP-0005 [2.2].

The fatigue damages from different analysis models should be added together in addition to that fromtemporary phases.

Calculated fatigue damages in the piles during service life are added to the fatigue damages calculated forthe pile driving.




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A.16.2 Design fatigue factorsDocumentation of an extended service life should follow NORSOK N-006 /5/. Based on NORSOK N-006, anextended life can be considered as documented if the remaining calculated fatigue life based on normaldesign analysis is longer than the extended service life including relevant DFF. If the calculated fatigue life

is not sufficient, a reassessment of the structure is triggered according to NORSOK N-006. This involves anassessment of the structural safety which can be based on available data such as information fromperformed in-service inspections. This document can be used for planning of additional inspection for thepurpose of reassessment and/or for planning of future inspections.

DFF for pile driving are presented in NORSOK N-006 /5/ and /82/.

A.17 Verification and quality assurance

A.17.1 GeneralVerification of analysis is important in order to get confidence in the calculated fatigue lives. It is importantthat each part of the analysis is verified by the person who performs the analysis (self-check that should be

documented). Also an independent verification review by another person should be documented.

A.17.2 Use of check listsThe quality assurance of the computer analyses should be documented by check lists that are developedspecially for each type of program used in order to help removing pitfalls during execution of the analysiswork.

The check lists should finally be signed by the analyst and the verifier.

For fatigue analysis using the SESAM program the following types of check lists have been developed:

— geometry input files (Preframe)

— load input files (Wajac)— post processing files (Framework).

A.17.3 Experience from fatigue analysesSome important items that should be paid special attention to during verification are listed as (based onexperience from performed analyses):

— Information on welding of butt welds in piles (welding from one side or both sides and transition inthickness on inside or outside, as this information is important with respect to S-N data and associatedSCFs).

— Input data on load calculation.

— Wave data (Wave heights and periods).— Environmental data relative to platform orientation.

— Correct geometry of the platform (“as is” geometry within each considered time period).

— Correct calculation of springs used for piles and conductors.

— Local geometry of the tubular joints (such as gap between members as these may have influence oncalculated SCFs).

— Correct analysis of the chord crown positions for long caisson elements and chord element with severalattachments.

— Length of chord members at T- and Y-joints that gives representative bending moments in the chord.Ref. also [A.12.6.2].

However, the last two items can be removed if the recommended alternative SCF equations in 6b and 7bin Table B-1 in DNVGL-RP-0005 are applied.




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APPENDIX B FATIGUE ANALYSIS OF SEMISUBMERSIBLES

B.1 Introduction

B.1.1 PurposeThis appendix gives recommended procedure for state of the art fatigue analyses methods to be used fortypical two – pontoon semi-submersibles with bracings or ring-pontoon semi-submersibles withoutbracings.

The purpose of this document is to describe a standard analysis procedure that can be used as basis forprobabilistic in-service inspection planning. This basis should include advice on:

— basic global fatigue analysis models for semi-submersibles

— effect of methodology and refinement used in design analyses performed for derivation of a calculatedfatigue life

— load effects and capacity.

The approach including an updated, state-of–the-art, fatigue analysis is recommended and considered togive the most benefits to the owner for a safe and continuous operation of the vessel.

The scope of work covered in this guideline is review and assessment of basic fatigue analyses methodsused by the industry for semi-submersible vessels, braced or un-braced (ring pontoon).

The procedure is prepared as an industry practice for the state-of-the-art fatigue calculation of semi-submersibles in order to reduce the uncertainties in the input to the inspection planning.

The procedure makes it possible to define what is considered to be a reliable analysis with lowest possibleuncertainty in calculated fatigue lives and corresponding low uncertainty in input parameters to theinspection planning for fatigue cracks. It also makes it possible to define what is understood by less gooddocumented fatigue analysis where the input parameters to the probabilistic inspection planning should be

associated with a larger uncertainty.

The approach including an updated, state-of–the-art, fatigue analysis is recommended and considered togive the most benefits to the owner for a safe and continuous operation of the semi-submersible.

B.1.2 GeneralThe structural analysis is normally performed based on a shell model representing the main structural load-carrying elements.

The FE model is normally created based on construction or as-built drawings applicable for the unitrepresenting actual dimensions/sizes.

In case of any degradation of the structure, this should be accounted for in the analysis to be performed.

B.1.3 Reference documents and governing standardsThis document has been prepared based on existing NORSOK standards and DNV Offshore Standards (OS)and Recommended Practices (RP) as given in reference list.

B.1.4 Units and constantsConsistent units should be applied. As an example the following units are suggested used for the analysis:

Length m (meter)

Force N (Newton)

Time s (second)

Mass kg (kilo)Stress Pa (N/m2) converted to MPa (MN/m2) by factor 10-6.




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Other units can be used, but it is essential that the units of each term in the equation

are consistent. M is the mass of the model, C is the damping, K is the stiffness, x is the displacements,are the velocities, are the accelerations, and F is the force.

Further, the S-N curves are to be adapted to the unit of the stress range in MPa.

The fatigue analyses should be based on linear elastic behaviour where the following constants areproposed:

B.1.5 Drawings used as basis for the analysisFor new-build semi-submersible structures the as-built drawings will normally be applied and representedin the analysis model in addition to visual confirmation of significant details on board.

The as-is condition of older units should be represented with respect to actual thickness for reassessmentor life extension studies. Measured scantlings may be used for parts where degradations due to corrosionetc. are documented. Modifications or re-construction performed during the life time of the unit should beaccounted for in the reassessment analysis.

B.1.6 Overview of structural conditionB.1.6.1 Coating and corrosion status

The semi-submersible needs to have an adequate corrosion protection (CP) system installed as the unitsmost commonly are designed without any corrosion allowance for the structural parts.

The coating and corrosion status of the semi-submersible should therefore be documented. The corrosionstatus is typically found in inspection reports or in the hull integrity management (HIM) system for the unit.If the original coating has been impaired during the unit’s service life and the extent of corrosion is foundto be significant, this needs to be taken into account both with respect to plate/element thickness used inthe analysis model and when selecting S-N curves to be used whether they should represent cathodicprotection or free corrosion.

The coating and corrosion protection need to be in satisfactory condition in order to protect the structurefor further degradation and assure that the analysis model represents the future condition of the structurefor the operation period to be planed.

B.1.6.2 Structural modifications, repair and weight updates

Modifications, repair of the semi hull and/or replacement of equipment are often performed during the unit’sservice life. For conversions or life extension projects these modifications can be quite substantial. Theseare important aspects with respect to fatigue capacity; hence, these modifications and weight updates haveto be incorporated in the finite FE model geometry and mass description. Since these modifications oftenare done in separate working packages, it is important that these updates are well documented whenrevising the original structural design and lightweight for the unit. It can therefore be necessary withmultiple analysis models in order to capture these modifications and updates with respect to overalloperational lifetime.

B.1.7 Operational historyThe operational history of the semi-submersible, i.e. time spent at different locations should be documentedas the unit’s total history should be accounted for in the fatigue assessment.

The operational history is typically described through site specific wave scatter. Wave scatter typically givenfor characteristic nautical zones may be used in lieu of other more specific data.

(B.1)

Young’s modulus E = 2.1·1011 N/m2

Poisson’s ratio ν = 0.3

Gravity g = 9.81 m/s2

Steel density ρ s = 7850 kg/m3

Water density ρ w = 1025 kg/m3

F Kx xC x M =++

x

x




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B.1.8 Heading profileThe operational heading profile can be considered if properly documented. Uniform distribution in variousdirections might be applied for units operating for shorter periods on different sites.

Site specific directional long term wave scatter should be applied for units operating on one location for

longer periods. For further description reference is made to DNV-RP-C205 [3.4].

B.1.9 Weight report and stability manualThe analysis model should reflect current as-is weight description for the considered analysis period. Hence,a recent weight report of the unit’s lightship weight is required. Note that for units which have had extensiveupgrades and modification of weights, ref. [B.1.6.2], also needs to be accounted for. As a minimum theweight report should include the following:

— hull lightweight

— topside weight description; description of topside equipment on and above main deck

— variable loads

— mooring and riser loads.A description of how the different weights are represented in the analysis model is given in [B.5].

The stability manual gives the tank filling program for the actual loading conditions. As a minimum the tankprogram should include the following information:

— identification of each tank – tank program

— volume and centre of gravity for each tank

— filling fraction for each tank

— permeability for each tank

— fluid density for each tank.

B.1.10 Weight distributionThe basis for the unit’s mass and mass distribution should be information given in weight reports, lightweight documentation etc., which are provided by the rig owner.

Weight balance between weight report (corrected based on inclination tests if available) and analysis modelshould be obtained. Weight check of the different parts; pontoon columns, braces and deck should beperformed. Ballast distribution is important in order to represent the actual motion response for the semi-submersible.

A ballast condition representing a “normal” condition should be applied. If significant differences inoperation condition (weight/ballast), several load conditions (draft variation) representing the differentphases should be accounted for.

In case of major updates and modifications, data for each configuration should be provided. Changes instiffness and force distribution need to be accounted for. Operating history with respect to location shouldalso be considered.

B.1.11 SoftwareAn applicable software package with the necessary feasibilities for performing the analyses as described inthis document should be applied.

B.2 Environmental conditions

B.2.1 GeneralThe following sub-sections give a description of the environmental properties relevant for fatigue assessmentof semis with general recommendations covering calculation and application of wave and wind loads.




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B.2.2 Environmental dataThe most significant environmental loads for the hulls of column-stabilised units are normally those inducedby waves. In order to establish the characteristic response, the characteristics of waves have to bedescribed in detail.

Stochastic methods for fatigue analysis (FLS) are recognised as the best methods for simulating theirregular nature of wave loads. Motion characteristics are determined by stochastic methods by usingrelevant site specific data or North Atlantic environmental data for worldwide operation.

The Pierson-Moskowitz wave spectrum should be applied for evaluation of dynamic response in short termsea states for units in worldwide operation. Other spectra might be used if site specific characteristic datais known. If the semisubmersible is used for worldwide operation, data representing these conditions shouldbe used (equivalent to North Atlantic Ocean scatter diagram). The representation of wave loads on thestructure is further outlined in [B.5].

Marine growth, wind, ice, snow and current loading are normally omitted for fatigue assessment.

If a design wave approach is being used, a wave spectrum applicable for the site specific data (e.g.Jonswap) should be applied for determination of the ultimate limit state conditions.

B.2.3 Wave loads

B.2.3.1 Scatter diagrams

The basic description of the wave conditions usually takes the form of a 2-dimensional scatter diagram (Hs,Tp /Tz diagram), showing the relative frequency of various combinations of significant wave height and peakwave period (or zero-up-crossing period). Each of these combinations corresponds to a wave spectrum,usually expressed by some standard form, e.g. Pierson-Moskowitz spectrum with a cosine type directionalityfunction.

B.2.3.2 Scatter diagrams for previous and current locations

As mentioned in [B.1.7], long term representation of environment should reflect the unit entire operationalhistory. For units operated for a longer period on one field with designated orientation, site specific scatterdiagrams should be obtained for the actual areas and included in the fatigue calculations.

For units which have been operated as drilling units in various locations the representation of waveenvironment for the operational time is proposed used based on an equivalent wave scatter. The generalwave scatter area typically described by world-wide or North Atlantic wave scatter, ref. DNV-RP-C205App.C, should be used (Table B-1).

B.2.3.3 Wave spectra

Typical standardized wave spectra are recommended used for fatigue analyses of semis. For wind generatedseas the wave spectrum is typically given as:

Table B-1 Wave scatter (HS, TZ) as presented for the North Atlantic




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— Pierson-Moskowitz (PM) – single parameter wave spectrum

— JONSWAP – three parameter wave spectrum.

The choice of spectrum should reflect the geographical area with local bathymetry and the severity of thesea state. In most cases the actual wave spectrum are given in relevant Metrological Ocean Criteria suppliedby vessel operator/owner.

For moderate and low sea states in open sea areas, the wave environment is often composed of both wind-sea and swell. A two peak spectrum may be used to account for both wind-sea and swell. The two peakwave spectrum is expressed as either by the general Ochi-Hubble spectrum or the Thorsethaugen spectrum,with the latter typically describing wave and swells in the North Sea. Reference is made to DNV-RP-C205[3.5] for further description of wave spectra.

B.2.3.4 Wave spreading

The effect of wave spreading (short crested sea) should be taken into account in the fatigue calculation witha spreading function of the form cosn( ∆θ ), see Figure B-1.

n = 4 can be used as exponent in the power for all sea states for wind generated sea.

Note that for swell n ≥ 6. Alternatively swell can be modelled by a Poisson distribution as described in DNV-RP-C205 [3.5.8.8].

Figure B-1 Wave spreading functions for different values of the cosine power n

B.2.4 WindWind induced fatigue damage for a semi is in generally related to slender topside structures, e.g. flare towerand helideck support structures. The wind fatigue damage is normally calculated separately from waveinduced damage, where damage from each of the two processes is later combined according to proceduresgiven in DNVGL-RP-0005.

The effect of wind in combination with wave action is normally not accounted for in the fatigue calculationof the hull structure. Ref. DNV-RP-C103 [3.5.3].

B.2.5 Current

Current is considered as a stationary and constant load with respect to dynamic loading; hence, for fatigueassessment of semi-submersible the effect of current is not taken into account. Ref DNV-RP-C103 [3.5.2].




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B.2.6 Marine growth, ice and snowActions due to marine growth, ice and snow are normally omitted from fatigue assessment of the hull. SeeDNV-OS-C101 Ch.2 Sec.5. However, the effect of marine growth shall be considered, where relevant, e.g.where drag loading is significant for the response.

B.3 Fatigue analyses methods for semi-submersibles

B.3.1 Spectral fatigue analysis methodology

B.3.1.1 General

The fatigue strength of the platform should be assessed using a spectral fatigue analysis (frequently alsodenoted stochastic analysis or frequency domain analysis).

A full spectral fatigue analysis can be performed using either a structural global model or a local hot spotmodel. The method requires that the dynamic wave loads are transferred directly from the hydrodynamicpanel model to the relevant structural model. External wave loads, internal tank loads and inertia loads shallbe considered in a consistent manner to maintain equilibrium.

The analysis method is based on a spectral procedure, which includes the following assumption forcalculation of fatigue damage:

— Wave climate is represented by long term scatter diagrams (summation of short term conditions).Assumed to be represented as a Gaussian process.

— Rayleigh distribution applies for stresses within each short term condition.

— Cycle count is according to zero-up-crossing period, Tz, of short term stress response.

— Fatigue damage summation is according to Miner’s rule for linear cumulative damage.

The spectral method assumes linear load effects and responses. The hydrodynamic loads and structuralresponses should be calculated using 3D potential theory and FE analysis, respectively.

Principal stresses used for calculation of fatigue are based on hot spot stress methods using spectralmethods (also denoted as stochastic methods). The hot spot stress is either calculated using a local hot spotmodel (SCF model) or derived from nominal stresses combined with associated SCFs, see [B.5.4].

Other load effects, such as slamming, sloshing, vortex shedding, dynamic pressures, mooring and risersystems should be included if they are considered to influence the fatigue utilization of the area or detail.For more detailed description of these load effects reference is made to DNV-RP-C103.

The correlation between different loads and actions should be considered in the fatigue assessment. Forfurther details see DNVGL-RP-0005.

The global FE analysis shall be performed for all relevant wave load cases, i.e. wave headings and waveperiods, for each applicable loading condition. Resulting deformations are then transferred from the globalmodel to the actual sub model by means of displacements where they form the boundary displacements for

each corresponding load case.

The long-term distribution of waves are described by a set of wave spectra, with varying significant waveheight (Hs), zero up-crossing spectral peak period (Tz) and probability of occurrence (scatter diagrams).

The response distribution of stress amplitudes for each sea state is obtained by combining wave spectrumwith transfer functions for local stresses.

The total fatigue damage (Miner sum) is then computed by summing up the contributions from each seastate taking into account their probability of occurrence, wave spreading, the S-N curve and an appropriatestress concentration (hot-spot stress) for the actual detail/area.

A typical global FE model including topside structures is shown in Figure B-2.

For large sub models or sub models exposed to lateral pressure loads, these models have also to be

analysed by the hydrodynamic load program for calculation of local dynamic pressure loads and inertialoads.




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Figure B-2 Example of global FE model

B.3.1.2 Basic input parameters to spectral fatigue analysis

The frequency spacing is to be carefully selected with due reference to the peak in the wave spectrum forthe fatigue sea states such that all “peaks” and “valleys” in the transfer function are properly described foreach direction.

Wave periods within the range 3 to 25 seconds should normally be represented in the analysis, when it isassumed that the design waves are in the range T = 8 to 12 sec., and that the natural period of the semi-submersible is in the range 18 to 24 sec.

The following criteria are suggested used for the spectral fatigue analysis (minimum criteria):

B.3.2 General principlesB.3.2.1 Wave theory for spectral fatigue analysis

Linear wave theory is to be used for the spectral analysis.

B.3.2.2 Linearization of drag forces

Linearization of the drag term is applied in the spectral analysis. However, as the drag term is assumed togive a very small (insignificant) contribution to the dynamic response, a simplification is introduced.Therefore, a linearization velocity of 1.0 m/s is proposed used in the fatigue analysis.

Alternatively a stochastic (for each sea state) linearization may be applied representing a sea state assumedto contribute most significantly to the fatigue damage. See also DNV-OS-C103 Ch.2 Sec.4[2.5].

B.3.2.3 Damping

The hydrodynamic damping might be adjusted with the results obtained from a model test. However, if nototherwise documented the damping for a semi-submersible can be taken as 3% of critical damping and berelated to the heave resonance period of the unit.

Normally, the wave periods contributing to the fatigue damage are lower than the natural period in heaveand hence small variations of the damping have a small influence on the results. More care is needed with

respect to the determination of the damping when the wave periods that contribute significantly to thefatigue life are close to the heave natural period.

number of wave directions 24 (separated by 15° intervals)

number of wave frequencies 26

minimum angular frequency (rad/sec)a heave period around 20 secs is considered

0.125 ➨ period T = 25.0 sec.

maximum angular frequency (rad/sec) 2.1➨

period T = 3.0 sec.wave spectrum Pierson-Moskowitz

scatter diagram site specific (or worldwide)

directional probabilities equal probabilities from alldirections or site specific

wave energy spreading of the form: cosn(∆θ)




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B.3.3 Fatigue damage calculationThe fatigue damage calculation is performed based on the long-term stress distribution established for thehot spots where the fatigue life is calculated. See DNVGL-RP-0005.

A schematic flow diagram of the fatigue analysis is shown in Figure B-3.

The global fatigue analysis is performed based on the global model. In this analysis the shell element(membrane) stresses are applied in combination with for example the S-N curve F3, see DNVGL-RP-0005,for cathodic protected material. A SCF equal to unity is considered for the mapping. This analysis istherefore a fatigue (damage) life scan based on nominal stress level. It covers typical details such asstiffener terminations, attachments etc. This analysis is used for mapping of the most severe fatigue areas,but is not applicable for cut outs, complex connections between brace and columns etc., where a moreaccurate analysis, i.e. sub-models, is to be used.

Figure B-3 Schematic flow diagram of fatigue damage calculations

For the sub-models, a more exact modeling of the geometry is normally performed. Therefore, the stressesat the element surfaces as derived from the element stress points (total 8-points) are in general applied inthe fatigue damage calculation.

In areas with high calculated damages, the details should be re-calculated using the procedure as outlinedin [B.6.3.2] and [B.6.3.3].

B.3.4 Design fatigue factorDesign fatigue factors (DFF) will typically be dependent on the level of criticality with respect to safety andavailability for inspection and repair. DFF due to hull safety as given in DNV-OS-C101 shall always beconsidered for design of permanently installed units. However, for the purpose of planning inspection theDFF is not recommended to be incorporated in the calculated fatigue damage. It will be considered whenthe target reliability level in the probabilistic analyses is assessed.

B.3.5 Workmanship and fabrication tolerancesThe fabrication procedure for the actual semi-submersible should be supplied by the construction yard(fabricator). Fabrication tolerances should follow the guidelines given in DNV-OS-C401 or NORSOK M101.




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If larger tolerances are used than accounted for in the S-N curves, the SCF may be calculated based onactual tolerances, ref. DNVGL-RP-0005.

B.3.6 Stress concentration factorsSCFs may be determined based on fine mesh FE analyses. Alternatively, a suitable tabulated SCF may beselected. Reference is made to DNVGL-RP-0005 and DNV-RP-C206.

B.3.7 S-N curvesThe S-N curves to be used throughout the fatigue assessment are mainly the design S-N curves obtainedfrom DNVGL-RP-0005.

B.3.8 Thickness correctionThe thickness of the material can increase the stress at notches such as at the weld toes and therefore thecrack growth can be increased in thicker plates. This is accounted for by a thickness correction factoradopted for the various S-N curves. Reference is made to DNVGL-RP-0005 for parameters to be used in thefatigue calculation.

B.3.9 Mean stress effectResidual stresses due to welding and construction may be reduced over time as the vessel is subjected toexternal loading and due to change in loading condition during operation. If it is likely that a hot spot regionis subjected to a tension force implying local yielding at the considered region, the effective stress rangefor fatigue analysis can be reduced due to the mean stress effect also for regions affected by residualstresses from welding.

Mean stress effects are normally neglected for fatigue assessment of welded connections in semi-submersibles as the effect is not easy to quantify at the welded region.

The mean stress can be accounted for in base material. Reference is made to DNVGL-RP-0005 [2.5].

B.4 Hydrodynamic analysis modelB.4.1 GeneralThe sea keeping and hydrodynamic load and vessel motion analysis shall be carried out using 3D potentialtheory with a recognized computer program. The program shall calculate response amplitude operators(RAOs, or transfer functions) for motions and loads in long crested regular waves, ref. DNV-RP-C103.

The hydrodynamic load model shall give a good representation of the wet surface of the unit, with respectto both geometry description in terms of load transfer and hydrodynamic requirements.

The following sections give a general description of minimum model requirements needed in ahydrodynamic load and motion analysis.

The basis for the hydrodynamic analysis model is the structural model established for the unit, see [B.5].

B.4.2 Coordinate systemThe same coordinate system should be used in all superelements being part of the global model, i.e.:

— x-axis: parallel with longitudinal pontoons - positive in forward direction

— y-axis: perpendicular to longitudinal pontoons and positive towards platform port side

— z-axis: vertical upward direction at pontoon lower horizontal plane

e.g. with origin at keel level in the center of structure.

B.4.3 Hydrodynamic modelsB.4.3.1 General

In order to establish the hydrostatic and hydrodynamic wave loads acting on the structure, a panel model,a Morison model and a mass model need to be established.




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The panel model represents the external (wet) surfaces of the model, i.e. the hull structure from undersidepontoon (baseline) to the operating draft level above baseline. Symmetry may be used for the panel modelsuch that only one side of the structural part is modeled. The panel model is used for the calculation of theforces from the waves using a sink-source technique.

The Morison model should be established for the platform. The purpose of this model is to represent Morisonforces (drag action) on the unit.

In addition a mass model is established in order to properly represent the unit’s operational massdistribution in the motion response analysis.

B.4.3.2 Panel model

The panel model is basically generated for the description of the outer shell of the semi-submersible. Themodel is typically developed using either 4- or 8-noded shell elements. As the structure usually is symmetricabout xz-plane, it is recommended to use mirroring through the xz-plane as this will significantly reducethe computer time.

The hydrostatic and dynamic loads are calculated by use of a panel model that is used in combination witha wave load program. The purpose of establishing a panel model of the vessel is to calculate the

hydrodynamic loads from potential theory. The hydrodynamic properties such as added mass, potentialdamping and wave excitation forces can then be calculated.

The panel model extends from baseline, el. 0.0 m, and up to still water level for the operating draft, FigureB-4. If hydrodynamic pressure at still water line is considered important, the method described in [C.5.5.4] is to be applied. The model consists of the same number of elements as in the outer surface of the structuralmodel for the pontoon. In the area of the column, the panel model has a refined mesh for curved areas, i.e.in areas with major changes in geometrical shape. Both 6-noded and 8-noded elements are used in thepanel-model. It is recommended to have a continuous mesh, but this is not always necessary.

Symmetry in geometry can be utilized when creating the model allowing for modeling of ¼ or ½ of the wetpart of the platform. If ½ of the structure is modeled, the symmetry (xz plane) option can be applied in thewave load program; if relevant. The panel model represents the wet part of the pontoons, columns andbraces.

The calculated wave loading is transferred from the panel model to the corresponding surfaces of thestructural model within the wave load analysis program by use of geometrical correspondence.

Figure B-4 Example of panel model (half model) with use of symmetry

B.4.3.3 Morison model

A Morison analysis model is established in addition to the panel model. The Morison model consists of beamelements representing the transverse bracing system spanning between the columns, see Figure B-5. TheMorison model accounts for the effect of viscous damping and drag forces.

In the structural fatigue analysis the model is normally included with an insignificant stiffness, i.e. the wall

thickness of the braces elements (tubes) is put equal 0.001m. This is to avoid that the volume of the bracesis included twice in the hydrodynamic model.




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This analysis model is also used in combination with the wave load program to include Morison forces actingon the bracings. A drag coefficient, Cd, equal 0.7 and a mass coefficient, Cm, equal 1.0 (the total masscoefficient, CM, then becomes 2.0) should be applied in the analysis.

The diameter of the Morison beam elements is made to avoid buoyancy in the hydrodynamic analysis and

to achieve this it can be modelled as 1/1000 of the true diameter. Then, in order to calculate correctly thedrag forces, the applied Cd coefficient is given 1000 times the basic value, i.e. 1000 × 0.7, with a resultingvalue equal to 700.

The beam elements attract the drag loading, which is transferred to the global structural FE-model (i.e. thestructural model where the stiffness of the transverse braces is included). The coupling between the Morisonmodel and the structural model can be represented by “bicycle wheel” elements; see Figure B-6, which areincluded in the structural model.

When a ring-pontoon semi-submersible platform is analysed, the Morison model is not included due toconsistency as insignificant drag load can be assumed for large diameter structures.

Figure B-5 Example of Morison analysis model

Figure B-6 Typical bicycle wheel connection to structural model

B.4.3.4 Mass model

All loading, excluding hydrostatic and dynamic loads and self-generated structural load, should bedistributed to a beam model of the platform. This beam model, referred to as the mass model, includespontoons, trusses, columns and a beam grid system at the intersection of the deck bulkheads to the upperand the lower deck. The model is divided into three parts; pontoons, columns and deck. The model shouldconsist of a sufficient number of nodes to assure a proper mass distribution.

The beam model for the lower hull should be given a low stiffness (1/1000 of normal) in order not tocontribute to the global stiffness. However, the deck structure above the main deck (above upper hull) is

represented by normal beam stiffness in order to properly transfer the topside masses to the deck structure.The applied masses are transferred to the structural model of the pontoons (6 lines), to the columns (5-




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lines) and to the deck structure (at deck bulkhead intersection to upper deck and lower deck) for thestructural analysis as indicated in Figure B-7.

Tank filling can be included if more accurate distribution of the masses are required for the analysis.Alternatively to the mass elements, a tank filling approach might be applied in the hydrodynamic analysis.

Results from analyses with respect to applied masses should be controlled towards the target data given inthe relevant documentation as referred above. I.e. one should ensure that the applied loads are accordingto the weight data recorded (weight report) for the unit and adjusted towards the buoyancy test reports/measured displacement (inclination test etc.).

A data check for the masses is necessary for documentation of equilibrium in the analysis model.

Figure B-7 Example of mass model for analysis

B.5 Structural analysis model

B.5.1 General stiffness modelFinite element analysis is required to obtain accurate stress distribution in the hull structure of a semi-submersible. With computer performance and data storage continuously increasing, the level of detail inthe FE models is consequently improved.

The structural model is mainly generated by using a shell element model while beam elements are used forsimulating stiffeners and girder flanges. The global model is normally a relatively coarse model of the unit,which represents actual global stiffness of the platform load-bearing structure. Thus the global modelincludes normally:

— the longitudinal stiffness of the pontoons

— the stiffness of the braces

— the stiffness of the vertical column— the stiffness of the main bulkheads as well as the shear and bending stiffness of the upper hull.

A typical FE model of a semi-submersible is shown in Figure B-8. Each color represents a superelement inthe analysis model.

The FE model of the unit is to be established based on the drawings approved for construction and/or as-built drawings. The actual as-is condition should be reflected in the model by thickness reduction due tocorrosion if relevant and adequate selection of S-N curve due to environment. See [B.2].




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Figure B-8 Example of global analysis or stiffness model

The analysis model consists of an upper and a lower hull. The lower hull comprises columns, pontoons, andthe transverse bracing system. The upper hull comprises the main deck including the deckhouses and living

quarters. Both the lower and the upper hull are welded plate structures with primary and secondarystiffening. The analysis may be based on the use of the superelement technique implying utilization of thesymmetry in the structure.

Smaller openings such as doors, man holes, pipe penetrations are normally not modelled. Larger openingsare normally modelled/accounted for, as the stiffness of these areas is reduced due to the opening.

The analysis model can be built up of several parts (superelements), where each part represents a portionof the main structural elements. These structural parts are assembled through the model hierarchy to formthe complete structure.

In addition several detailed FE models (local models – with same stiffness as for the global model) mightbe established to calculate the fatigue life of fatigue prone areas/details for the unit, [B.5.4].

The same coordinate system as described and applied for the hydrodynamic analysis model should also be

used for the structural model, ref. [B.4.2].

B.5.1.1 Pontoons

The longitudinal bulkheads, girders and pontoon shell should be represented in the model by a correctstiffness. Local reinforcements such as thruster foundations and minor reinforcement might be omitted inthe global analysis model.

The transverse bulkheads and frames in the pontoon are normally modeled in order to achieve arepresentative geometric stiffness between the pontoon’s vertical shell sides and the longitudinal bulkhead.If this stiffness is omitted, the pontoon may deflect incorrectly depending on the distribution of the ballastin the pontoon and the length of the free span between the columns.

Depending on the geometry of the foundation of the access trunk, see e.g. Figure B-9, it may have to beincluded in the global analysis model. Some trunks are made as a separate pipe in the pontoon ending in a

bulkhead on each side. Such a trunk will normally not contribute to the global stiffness (Stresses at the endsof the trunk due to elongation of the lower part of the pontoon from bending of the pontoon can beconsidered in hand calculations or by local analysis models).




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Figure B-9 Example of different access trunks in a typical section through a pontoon

B.5.1.2 Columns

The vertical elements of the structure are important for the global stiffness. Hence, transverse andlongitudinal bulkheads and column shell should be properly included in the analysis model.

The decks and the stringers in the columns are normally included in the structural model. By such amodeling there is a better correspondence between the mass model and the structural analysis model andspurious stress peaks are avoided. Another advantage by this modeling is that the steel weight is morecorrectly distributed.

The decks where the braces are connected to the column have to be modeled more detailed in order toproperly transfer the brace forces into the column.

The trunk is normally included in the model similar to the one in the pontoon. The trunk will attract stressfrom the global response. Often the trunk continues down through the pontoon and up through the upperhull. The trunk, or vertical access shaft, will influence on the global stiffness and should therefore beincluded in the structural model.

Geometry such as chain trunks is normally not modeled as long as they do not contribute to the global

stiffness.

B.5.1.3 Braces

The braces are modeled with bulkheads/ring-stiffeners together with the outer shell. Longitudinal stiffenersare included in the model since they contribute to the global stiffness. The outer shell of the braces and thelongitudinal internal stiffeners inside the braces are all normally modeled with shell elements.

Cycle wheels (beam elements) are modeled within the braces/diagonals in order to make it possible toconnect the Morrison model to the structural brace elements. The sectional property of these beamelements can typically be:

— outer diameter 0.2 [m]

— thickness 0.001 [m].

The Young’s modulus is 2.1·1011 Pa (2.1·105 MPa). The beams in the wheel are modeled in such way thatthey do not contribute to the global stiffness, but transfer the drag loads properly from the Morison modelto the structural model.

B.5.1.4 Upper hull and deck

The bulkheads and main girders connecting the columns are normally included in the structural model. Thebulkheads act as girder-webs, while the upper hull decks act as flanges. In addition, the deck representsthe shear stiffness of the upper hull even though the thickness of the deck may be small. Local details suchas brackets, buckling stiffeners, smaller cut-outs such as doors etc. are normally neglected in the globalmodel.

For the upper hull, the girders may be omitted as long as they do not contribute to the global stiffness.

Structural elements representing a relevant stiffness should be included in the analysis model when theycontribute to the global stiffness.

Integrated trunkSeparate trunk




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B.5.1.5 Mooring and risers

Loads from moorings and risers are not considered to influence first order motions significantly. However,in order to preserve static equilibrium, their static contribution should be included in the analysis. The staticcontribution may be included either by vertical pre-tension forces according to static weight of these items,or as point masses. The point masses will also be included in the dynamic behaviour of the unit, but is

negligible for catenary and semi-taut mooring. For taut mooring the stiffness of the mooring system shouldbe included in the analysis in order to represent accurate behaviour of the unit. Care should be taken whendistributing the point masses to avoid any unintended mass asymmetry.

B.5.1.6 Model assembly

It is important that the connections between the upper hull to columns, column to braces and column topontoons etc. are modeled accurately. In these areas it is necessary to include bulkheads, deck frames andstringers as they contribute to the global stiffness.

B.5.2 Finite element modelingB.5.2.1 Element types

8-noded shell elements or improved 4-noded shell elements with additional internal degrees of freedomshould be used for the FE modeling of the structure. 6-node triangular elements can be used in areas wherea mesh of 8-noded shell elements otherwise is difficult to fit. The triangular elements are stiffer than thequadratic elements and should therefore normally be avoided.

3-noded beam elements should be used for the modeling of stiffeners etc. 2-noded beam elements aresufficient for the mass model.

A sufficient number of elements are needed over the web height in order to represent the necessary bendingflexibility. If too few elements are used over the height, the bending stiffness may be too high.

8-noded shell elements are recommended used particularly in areas of steep stress gradients. Attentionshould be paid to possible underestimation of stress; especially at weld toes of type b) in Figure B-6 (ref.DNVGL-RP-0005). Use of 4-noded shell elements with improved in-plane bending properties is a goodalternative to that of 8-noded shell elements.

B.5.2.2 Element mesh

A recommended element mesh depends on the geometry of the unit. A typical maximum size of theelements used for a global model of a semi-submersible is approximately 2×2 meter. However, the size isoften smaller due to shift in plate thickness and due to internal structure such as bulkheads, frames,geometric details etc. Another aspect to be considered is to model the elements as rectangular as possible,and with a length to breadth ratio less than 4:1.

Where stiffeners are lumped, the element edges should be as straight as possible in order not to producespurious hot spots.

It is recommended to get an overview of the internal structure and the transitions in plate thickness beforethe modeling of the global structure is started. In this way later adjustments of the analysis model can be

avoided. It is recommended to start modeling of the columns and the connections to the braces. Typically16 elements around the brace are used. For a circular brace with a transition cone and a quadraticconnection to the columns, 4 to 5 8-noded elements in each quarter around the circumference will normallybe sufficient for the modeling of the transition.

The element distribution in the column cross-section is then determined based on the modeling of the brace-column and the column. Furthermore, the element distribution is given by the internal structure in thepontoon such as longitudinal and transverse bulkheads, trunk, plate thickness etc. Typical 4 to 5 8-nodedelements are used for the rounded column corners. Compromises with respect to element meshing mayhave to be done with respect to thickness transition in order to limit the size of the analysis model.

The bilge radius of the pontoon has usually a smaller extension than that of the columns. Hence, 2 or 3 8-noded elements will normally be sufficient for the modeling of the curvature in the pontoons.

The interface with the mass model should also be considered when planning the element mesh.When using the structural model as the panel model in the hydro-dynamic analysis, the height of the




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elements below the water plane should typically be:

— first element 0.5 to 0.6 m

— second element 1.0 to 1.3 m.

Figure B-10 shows a column where the two drafts (operation) and (survival) are considered, i.e. smallerelements are used below the water plane than above.

If the structural model is used also for the panel model, the element diagonal shall not exceed thewavelength/4. The elements should if possible be in the range 2×2m. This implies that the minimumwavelength investigated should be longer than 2m· ·4 = 11.3m. This is considered acceptable for fatigueanalysis of a typical semi-submersible.

The number of elements below the water plane area that will be “wet” should be less than the maximumnumber of panels allowed in the program. The element size may be increased to meet this requirement.Normally this is performed by merging elements in areas with high density of elements. This can be areaswith complex geometry and/or thickness transitions.

Figure B-10 Typical element mesh for a column

B.5.2.3 Stiffener representation

The stiffeners in the longitudinal direction should be included in the global analysis. Normally, the stiffenersare lumped to the element edges. It is important that the stiffeners are modeled without any offset. If thestiffeners are modeled with offset, bending stress will be introduced in the plate due to water pressure. Thecalculated bending stress will not be correct, due to the coarse mesh and the larger stiffeners, which areused in the global model. The bending of the stiffeners is considered in the local model.

An increase of the plate thickness to account for the area of the stiffeners is not recommended as the shearstiffness will then be overestimated (the stiffeners do not contribute to the shear stiffness of the plate). Thestiffness in the transverse direction would also be overestimated by an increased plate thickness. Thus, bysuch modeling the stress in the transverse direction and the shear stress will be underestimated due to theincreased stiffness.

The stiffeners should be lumped in the analysis model as shown in Figure B-11 for HP/L (bulb and anglesections) or T stiffeners. A similar lumping should be performed for flat-bars. The stiffeners on bulkheads

are usually not modeled as they do not contribute to the global stiffness. One exception is e.g. below thecolumn in the pontoon where they contribute to the vertical stiffness.

2




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Figure B-11 Example of lumping of stiffeners

B.5.3 Boundary conditionsAll 6 degrees of freedom in the analysis model need to be defined in order to avoid singularity in the globalstiffness matrix. The global analysis model should be supported at the underside of the pontoons e.g. in thecrossing between longitudinal and transverse bulkheads as indicated in Figure B-12.

Three (3) vertical supports should be defined by springs representing the water plane stiffness of thestructure:

where Aw (m2) is the water plan area.

k = 1025 kg/m3 × 9.81 m/sec2 × Aw (m2) = 10055 × Aw (m2) N/m

Figure B-12 Boundary condition applied for analysis

The spring stiffness below each column is then kspring = k/3 = kz 1,2,3. In addition, horizontal supporting,

(B.2)

1.5Stiffener 3 Stiffeners 1.5Stiffener

ww A g k ⋅⋅= ρ




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in transverse and longitudinal direction, is represented by springs equal 0.1 (10% of vertical stiffness isapplied in the horizontal direction) of the total vertical spring stiffness.

The transverse horizontal stiffness is applied in one (1) support point, y-direction, and two (2) supports areapplied in the longitudinal, x direction.

B.5.4 Local models or sub-models

B.5.4.1 Sub-modelling technique

The sub-modelling technique allows a part of the global model to be re-analysed to produce more accurateresults locally without changing or re-running the original global model. By creating a separate model,typically with a more detailed structural description of a specific area, the responses from the globalstructural model can be transferred to the boundaries of the local model by means of complex prescribeddisplacements. In this way the local detail or model does not need to be an integrated part of the globalmodel.

For the complex connections and where the dynamic stresses are found to be most severe, a sub-modelingtechnique should be used for calculation of the hot spot stresses for fatigue damage calculation. This

approach gives the same results as if the detailed local models were included directly in the global model,but due to the need for reducing the size of the analysis model (degrees of freedom), a sub-modelingtechnique is proposed.

The sub-modeling technique includes the following steps:

— Calculation of the global response from the different wave frequencies and directions by using the globalmodel.

— Transfer of the displacements from the global model nodes corresponding to the boundaries of the localmodel, to the local model.

— Separate calculation of the wave loads acting on the local model (if exposed to sea pressure). For smalllocal models the wave loads may be omitted.

— Calculation of the stresses in the local model from the wave loads and the prescribed displacements.

The highest stresses in the refined areas are the hot spot stresses, which are further used in the fatiguecalculations.

B.5.4.2 Sub-modelling requirements

Although the sub-model technique offers good flexibility, there are some precautions which need to betaken into account in order to ensure reasonable transfer from global model to the local model. Theseprecautions can vary for different program systems.

— The sub-model shall be compatible with the global model. This means that the boundaries of the sub-model should coincide with those elements in the parent model from which the sub-model boundaryconditions are extracted. The boundaries should preferably coincide with mesh lines as this ensures thebest transfer of displacements to the sub-model.

— If differences in stiffness between local and global model exists, stresses will not be consistent.Therefore, the main difference from a global to a local model should be the mesh size (refined mesh)at the hot spot region(s).

— The boundaries of the sub-model shall coincide with areas of the parent model where the displacementsare well defined. For example, the boundaries of the sub-model should not be midway between twoframes if the mesh size of the parent model is such that the displacements in this area cannot beaccurately determined.

— Linear or quadratic interpolation (depending on the deformation shape) between the nodes in the globalmodel should be considered. Linear interpolation is usually suitable if coinciding meshes are used.

— The sub-model shall be sufficiently large so that boundary effects, due to inaccurately specifiedboundary deformations, do not influence the stress response in areas of interest.

— If a large part of the model is substituted by a sub-model, then mass properties must be consistent

between this sub-model and the global model. Inconsistent mass properties will influence the inertiaforces leading to imbalance and erroneous stresses in the model.




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— External loads acting on a local model, e.g. topside equipment or external/internal pressures should beincluded in the sub-model.

— Transfer of beam element displacements and rotations from the parent model to the sub-model shouldbe especially considered.

— Transitions between shell elements and solid elements should be carefully considered.

B.5.4.3 Local hot spot model - SCF model

The aim of the FE analysis is to calculate the stress at the weld toe due to the presence of the attachment,denoted hot spot stress, shot spot (i.e. local stress - hot spot stress). The SCF due to local geometry effectis then defined as

For details with complex geometry and load description, it may be difficult to determine a nominal stresslevel and corresponding SCF using a model with relatively coarse and simplified geometry. Local FE analysesmay thus be used to calculate the stress distribution in the region of the hot spot, such that these stresses

can be used either directly in the fatigue assessment, local hot spot model, of given details or as a basis forderivation of stress concentration factors, SCF model.

If a SCF-model is used, there might be stiffness differences between the global model itself and SCF model,which again will lead to incorrect stress distribution in the SCF model. This is typically seen in the SCFmodels of the column brace connection where boundary conditions are applied just above and below thebrace. The stresses in top and bottom of the brace connection are almost equal in the SCF-model, but ifusing a sub-model/global model the stress levels are higher at the bottom, as the stiffer pontoon attractsmore stresses than the relatively softer column. Hence, it is recommended to use the sub-model techniqueinstead of the SCF-model as more accurate results will be achieved.

Thus the main objective of the FE analysis is to provide reasonably accurate stresses at a region outsidethe weld affected zone. Therefore, the model should have a fine mesh for sufficiently accurate calculationof the SCF, e.g. t × t mesh size around a hot spot region. For more detailed description of the hot spot

modelling principles and methodology reference is made to DNVGL-RP-0005.

For fatigue assessment, fine element (refined) mesh models should be made for critical stress concentrationdetails and for details not sufficiency covered by SCF given in recognized standards, see for exampleDNVGL-RP-0005 and/or DNV CN 30.7.

B.5.4.4 Potential sub-models of a semi-submersible

Element size for stress concentration analyses is normally to be in the order of the plate thickness.Normally, 8-noded shell elements or 20-noded solid elements should be used for the analysis.

The following typical areas should be given particular attention:

— hot spot stress at the cruciform plate connections in way of brace-brace-, pontoon-column- and column-deck intersections

— hot spot stress in welded supports of for example fairleads, chain stopper, winches, riser, porches, cranepedestal, drilling derrick, flare tower, etc.

— hot spot stress at local column/brace connection (to pontoon)

— hot spot stress at attachments

— details in way of the moonpool

— large and small penetrations

— corners at door openings

— stiffener and girder terminations

— weld profiling of cruciform joints

— cast insert pieces.

Local structural models of these regions are required in order to determine the hot-spot stresses, ref.[B.5.4.1].

(B.3)nominal

σ σ ⋅= SCF spot hot




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For more detailed description of modelling of mooring/riser foundation reference is made to DNV-RP-C103[5.2].

The size of the analysis model should be of such an extent that the calculated stresses at the hot spots arenot significantly affected by the assumptions made for the boundary conditions.

B.5.4.5 Examples of sub-models for semis-submersiblesEight (8) detailed FE models (local models) of parts of the structure are for calculation of hot spot stressesfor critical details for semi-submersibles as listed in Table B-2 are exhibited as examples of the hot spotareas addressed in [B.5.4.4].

The models listed in Table B-2 are considered to represent typical fatigue prone details/areas. The modelsconsist of 8-noded shell elements including details like:

— internal brackets/gusset plates etc.

— distance between gusset plate termination and ring stiffener

— offset of ring stiffeners/bulkheads to knuckle points

— brackets

— cut-outs.

The shell element size in the most fatigue sensitive areas is approximately equal the plate thickness. Thisis in accordance with DNVGL-RP-0005 [4.3]. The mesh is coarser in the rest of the model in order to reducecomputing time, but it is still detailed enough to represent the stiffness correctly. The welds are notmodeled, but accounted for in the fatigue damage evaluation through proper selection of S-N curves.

Examples of sub-models applicable for FE analysis using the hot-spot method are shown in Figure B-13 toFigure B-17.

The sub models are intended for derivation of “hot spot stresses” and prepared according to guidelines givenin DNVGL-RP-0005.

Table B-2 Example of local models applied for analysis

Model/Connection

Corner column connection to pontoon and braces

K-joint on transverse horizontal with horizontal braces

Centre column connection with transverse brace

Diagonal connection to pontoon at center column

Corner column connection to center longitudinal bulkhead of pontoon

Diagonal connection to deck/corner columnColumn deck connection in transverse direction

Diagonals and connection to deck




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Figure B-15 Lower hull diagonal to pontoon deck/column. Column connection towards pontoon longitudinalcenter bulkhead

Figure B-16 Hull sub-elements – Longitudinal diagonal deck connection




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Figure B-17 Diagonals connected to upper hull (deck)

B.6 Actions and response calculation

B.6.1 Wave loadsThe hydrodynamic model is described in [B.4.3]. A spectral fatigue analysis (frequently also denotedstochastic analysis or frequency domain analysis) is applied.

B.6.1.1 Hydrostatic condition

There should be equilibrium of the forces from the hydrodynamic panel model and from the mass model.This means that there should be a balance between:

— mass and displacement

— centre of gravity and centre of buoyancy with respect to heel and trim.

Any slight imbalance between the mass model and hydrodynamic model should preferably be corrected bymodification of the mass model. A rule of thumb is that sum of mass and buoyancy should be less than 1%of total weight.

A slight modification of the mass model is usually needed in order to balance the hydrodynamic panel modeland mass model. If the unbalanced load is less than 5% of the wave excitation force, then the load balancemay be achieved by adjusting the point masses.

Another issue one should assess is the natural frequency of the semi-submersible which is given as afunction of system mass and stiffness. For semi-submersibles it is the natural period in heave that is of




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largest interest as this period is close to occurring wave periods. For heave motion, the system stiffness isreflected in water plane area and the weight of the unit including added mass. For roll and pitch motion, thenatural frequency is given as a function of radii of gyration, rnn, and transverse and longitudinal metacentricheight, GMT and GML. It is important that the ratio between these two parameters is reasonable. The radiiof gyrations are products of the local distribution of masses relative to axis through centre of gravity, i.e.

the better representation of mass in the global mass model the more correct are the radii of gyration. Themetacentric height is a function of the loading condition. If the metacentric height in the hydrodynamicmodel is different from that given in reference document or model tests, it can be adjusted by introducinga restoring matrix.

B.6.1.2 Hydrodynamic loads on structural finite element models

The hydrodynamic loads, presented as inertia loads and lateral pressure loads, should be transferred to thestructural model in a proper way. In the spectral analysis as described in [B.3.1.1], the loads can be directlyapplied to the global FE model. If loads are applied correctly, the global FE model will be close to equilibrium,and thus the reaction forces at global structural model boundaries should be close to zero. The effect ofsimultaneously acting dynamic loads should be accounted for in the analysis. Loads due to viscous dampingshall be included and transferred to the structural model.

It is of great importance that loads from the hydrodynamic model are transferred to the structural modelin a correct manner. Analysis routines which ensure sufficient verification and qualification of analysismodels, methodology and results should be established. [B.7] presents a procedure involvingdocumentation, verification and qualification of analyses work in addition to the hydrostatic balancing of theglobal model described in [B.4].

B.6.2 Fatigue analysis

B.6.2.1 Calculation of wave frequent response

The short term distribution of load responses for fatigue analyses may be estimated using the wave climate,represented by the long term distribution of H s and T z in a wave scatter diagram for the actual area, ref.[B.2.3]. Each short term sea state is then combined with an appropriate wave spectrum, S η (w|H s , T z ) asdescribed in [B.2.3]. The transfer function is derived based on a linear relationship between unit waveheight and stresses, H(w|H s , T z ). Then the response spectrum is given by the wave spectrum and thetransfer function as:

The spectral moments of order n of the response process for a given heading are calculated as:

where the wave spreading function f s( Ɵ ) = cosn( Ɵ ) as described in [B.2.3.4]. The stress range response forfloating structures can be assumed to follow the Rayleigh distribution within each short-term condition. Thestress range distribution for a given sea state i and heading direction j is then derived as:

where m0 is the spectral moment of order zero. Then a summation of the fatigue damage within each seastate and heading direction can be applied, ref DNVGL-RP-0005.

The total calculated fatigue damage is then computed by summing up the contributions from each sea state

taking into account their probability of occurrence, wave spreading, the S-N curve and an appropriate stressconcentration or hot spot stress for the considered detail.

(B.4)

(B.5)

(B.6)

),|(|)|(|),,|( 2

z s z s T H wS H T H S η σ θ ω θ ω =

ω θ ω ω θ σ

ω

θ

θ d T H S f m z s

n

sn

O

O ),,|()(90

90 +

−=

−−=∆

ij

ijm

F 0

2

8exp1 σ

σ




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B.6.2.2 Load cases applied in the fatigue analysis

A total of 624 complex load cases are proposed applied for the spectral fatigue analysis. This includes 24wave directions, evenly spaced at 15°, applied in combination with 26 frequencies per direction accountingfor peaks and valleys in the transfer functions. Normally the range 3 to 25 sec is included in a transferfunction.

Other selection of load cases should be considered in each case depending on the platform characteristic.

B.6.3 Fatigue calculationB.6.3.1 General

The fatigue damage calculation is performed based on the long-term stress distribution established for thefatigue calculation points.

Fatigue calculations based on the global model are normally performed using the membrane principalstresses as the local stiffeners are not modeled and the bending stresses tend to be overestimated.

For the sub-models, a more exact modeling of the geometry is normally performed. Therefore, the stressesat the element surfaces as derived from the element stress points (total 8-points) are in general applied in

the fatigue damage calculation.In areas with high calculated damages, the details should to be re-calculated using the procedure asoutlined in [B.6.3.2] and [B.6.3.3].

The fatigue capacity depends on:

— corrosion protection effectiveness for the lifetime of the structure (incl. maintenance)

— coating condition i.e. painted or black iron

— fabrication tolerances

— workmanship.

B.6.3.2 Calculation of hot spot stresses

Reference is made to DNVGL-RP-0005 for hot spot stress calculation.B.6.3.3 Recalculation of the fatigue life for highly utilized areas

Normally the local bending is small for connections in a semi-submersible structure, however, if theseeffects are to be considered reference is made to DNV-RP-C103.

The procedure can be used for locations where the bending stress is significant, i.e. large difference betweenthe damage calculated by applying membrane stresses and surface stresses where redistribution of stressesoccurs under crack growth. Thus, this methodology cannot be used where a local bending moment isrequired for moment equilibrium.

B.7 Documentation and verification of analyses

B.7.1 Documentation of analysesThe analysis shall be verified in order to ensure accuracy of the results. Verification shall be documentedand enclosed with the analysis report.

The documentation shall be adequate to enable third parties to follow each step of the calculations. For thispurpose, the following should, as a minimum, be documented or referenced:

— basic input (drawings, loading manual, metocean specification, etc.)

— assumptions and simplifications made in modelling and analysis

— analyses models

— loads and load transfer

— analysis methodology

— analyses results (including quality control)— discussion and conclusion; recommendation for further work if relevant.




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Check lists for quality assurance shall also be developed before the analysis work commences. It issuggested that project-specific checklists are defined before the start of the project and included in theproject quality plan. These checklists will depend on the engineering practices and software to be used.

B.7.2 Documentation of hydrodynamic propertiesIt is important that the hydrodynamic properties used in the analysis are properly documented. Typicalproperties to be documented are listed below:

— viscous damping level, including method for calculating additional damping

— hydrostatic properties, including:


— centre of gravity and centre of buoyancy

— operational draft conditions including, trim and heel angles

— water plane area

— longitudinal and transverse metacentre height

— radii of gyration— restoring matrices

— Motion reference point.

— scatter diagram and sea states, wave spectrum and wave spreading applied

— check of RAOs for roll, pitch, heave, surge, sway, and yaw; compare towards similar semi-submersiblesif relevant

— sectional loads, bending moment and shear force

— accelerations with respect to topside assessment

— sea pressure and internal tank loads (if included).

B.7.3 Verification of structural modelsAssumptions and simplifications are required for most structural models and should be listed such that theirinfluence on the results can be evaluated. Deviations in the model compared with the actual geometryaccording to drawings shall be documented.

The set of drawings on which the model is based should be referenced (drawing numbers and revisions).The modelled geometry shall be documented preferably as an extract directly from the generated model.The following input shall be reflected:

— plate thickness

— beam section properties

— material parameters

— boundary conditions— element type

— element mesh and geometry representation

— Mass distribution and balance. Masses in model versus actual structure.

B.7.4 Verification of calculated loads and structural load transferInaccuracy in the load transfer from the hydrodynamic analysis to the structural model is among the mainerror sources in this type of analysis. The load transfer can be checked on the basis of the structuralresponse or on the basis of the load transfer itself.

It is possible to verify a correct transfer in loads by integrating the stress in the structural model. The

resulting sectional forces should be compared with the results from the hydrodynamic analysis.Weight and center of gravity should be compared with wave load analysis.




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B.7.5 Verification of responseThe response should be verified at several levels to ensure that the analysis is correct. The following aspects

should be verified as applicable for each load considered:

— global displacement patterns/magnitude— local displacement patterns/magnitude

— global sectional forces

— stress levels and distribution

— sub model boundary displacements/forces

— Reaction forces and moments.

B.7.5.1 Global displacement patterns and magnitude

In order to identify any serious errors in the modelling or load transfer, the global action of the semi-

submersible should be verified against expected behaviour and magnitude.

B.7.5.2 Local displacement patternsDiscontinuities in the model, such as missing connections of nodes, incorrect boundary conditions, errors in

Young’s modulus etc., should be investigated on basis of the local displacement patterns and magnitude.

B.7.5.3 Global sectional forces

Different values of section forces between hydrodynamic load analysis and structural analysis indicate

erroneous load transfer or mass distribution.

B.7.5.4 Stress levels and distribution

The stress pattern should be according to global sectional forces and sectional properties of the semi-

submersible. Peak stress areas in particular should be checked for discontinuities, distorted element shapes

or unintended fixations (e.g. 4-noded shell elements where one node is out of plane with the other three

nodes).

Where possible, the stress results should be checked against results from design load analysis, e.g. brace

stress due to design waves.

B.7.5.5 Sub-model boundary displacements/forces

The displacement pattern and stress distribution in a sub model should be carefully evaluated in order to

verify that the forced displacements and forces are correctly transferred to the boundaries of the sub-model.

Ideally the nominal stress level in the global and the local model should be of a similar magnitude. Peak

stresses at the boundaries of the model may indicate problems with the transferred forces and

displacements.

B.7.5.6 Reacting forces and moments

Reacting forces and moments should be close to zero for a direct structural analysis. Large forces and

moments in the boundary conditions (springs) are normally caused by errors in the load transfer. The

magnitude of the forces and moments should be compared to the global excitation forces on the semi-

submersible for each load case.

B.7.5.7 Evaluate fatigue damage calculation

The calculated fatigue damage may also be compared with results from closed form calculation applying the

design wave approach (see DNV RP-C103 for further information) and assumption of Weibull long term

stress range distribution with shape parameter h = 1.0. It should be noted that DNVGL-RP-0005 [5.2] may

be useful for verification of analysis results. Here allowable stress ranges are presented as function of

Weibull shape parameter and structural detail. The presented results are derived based on the two-slopeS-N curves presented in DNVGL-RP-0005.




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APPENDIX C FATIGUE ANALYSIS OF FLOATING PRODUCTION

STORAGE AND OFFLOADING

C.1 Introduction

C.1.1 PurposeThis appendix describes preferred methodology on how to perform a global and local fatigue analysis of a

typical FPSO with both turret moored and fixed spreader moored arrangement.

The purpose of this appendix is to develop a recommended analysis procedure that can be used as basis

for probabilistic in service inspection planning. The document should include sufficient guidance on how to

establish a sound analysis basis for probabilistic in service inspection planning for fatigue cracks. This basis

should as a minimum include advice on:

— modelling of environmental loading and response

— modelling principles for analysis models of FPSO— hydrodynamic analysis methodology

— fatigue analysis methodology

— documentation and verification of analysis methodology.

This appendix gives recommended fatigue analysis methods to be used for offshore ships and FPSOs. The

fatigue analysis procedure is prepared as an industry best practice methodology for fatigue calculation of

FPSOs, with the purpose to reduce the uncertainties in the input to the probabilistic inspection planning.

The purpose of this appendix is to derive a reliable analysis procedure which gives reduced uncertainty in

calculated fatigue lives and corresponding low uncertainty in input parameters to the probabilistic

assessment. The purpose is also to define what is understood by less well documented fatigue analysismethodologies where the input parameters to the probabilistic inspection planning should be associated

with a larger uncertainty.

C.2 Basis for the analysis

C.2.1 GeneralThe following sections give a description of the most important documents and standards used as basis for

this guideline. In addition an overview of necessary information required with respect to fatigue assessment

of FPSOs is given.

C.2.2 Units and constantsConsistent units should be applied. As an example the following units are suggested used for the analysis:

Other units can be used, but it is essential that all units are consistent with respect to equation of motion.

Further, the S-N curves are to be adapted to the unit of the stresses. This document applies the units as

given above.

The fatigue analysis should be based on linear elastic behaviour where the following constants are

Length m (meter)

Force N (Newton)

Time s (second)

Mass kg (kilo)

Stress Pa (N/m2) converted to MPa (MN/m2) by factor 10-6.




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proposed:

C.2.3 As built drawingsFor new-build FPSO hull structures it is required to install and maintain adequate corrosion protection (CP)systems. Therefore, the fatigue analysis is often based on gross scantlings, or as-built.

For reassessment or life extension studies, an assessment of the thickness due to corrosion until the endof the service life may also be necessary depending on the coating condition, where measured scantlingscan be used for parts of the vessel’s operational lifetime. An average thickness may be used in analyses.

C.2.4 Overview of structural condition

C.2.4.1 Coating and corrosion status

The coating and corrosion status of the vessel should be documented. The corrosion status is typically foundin inspection reports. If the original coating has been impaired during the vessels service life andconsequently the extent of corrosion is found to be significant, this needs to be taken into account whenselecting S-N curve to be used whether it should be cathodic protection or free corrosion.

C.2.4.2 Structural modifications, repair and weight updates

Modifications, repair of the ship hull and/or replacement of equipment are often performed during thevessels service life. For conversions or life extension projects these modifications can be quite substantial.This can be important aspects with respect to fatigue capacity; hence, these modifications and weightupdates shall be incorporated in the FE model geometry and mass description. Since these modifications

often are done in separate working packages, it is important that these updates are well documented whenrevising the original structural design and lightship weight. It can therefore be necessary with multiplemodels in order to capture these modifications and updates with respect to overall operational lifetime forcalculation of accumulated fatigue damage.

C.2.5 Operational historyThe vessels operational history, i.e. time spent at different locations should be determined. For conversionswhere the vessel has been used for other purposes than an FPSO, the operational history should also bedetermined for this phase as the vessels total history should be accounted for in the fatigue assessment.

The operational history is typically described through site specific wave scatter diagrams. For conversions,an equivalent wave scatter can be created based on the vessels trading history. Wave scatter typically given

for characteristic nautical zones together with trading history may be used as basis for the equivalenttrading scatter.

C.2.6 Heading profileThe operational heading profile will depend on type of mooring, e.g. turret mooring or spread moored. Forturret mooring, where active positioning systems are used to obtain a pre-defined orientation of the vesseltypically bow up towards incoming waves, relevant wave directions should be determined together with aprobability of occurrence which reflects actual operational heading profile. Alternatively heading profile asgiven in DNV-RP-C206 may be used. Wave directions should have an interval of maximum 15°.

Site specific directional long term wave scatter should be applied for fixed spread mooring. If the vessel isorientated with a phase shift relative to geographical wave direction, the wave direction typically giving the

largest response should be included in the wave direction set, e.g. beam seas for maximum roll motions.For further description reference is made to DNV-RP-C206 [6.1.2.1] /32/.

Young’s modulus E = 2.1·1011 N/m2

Poisson’s ratio ν = 0.3

Gravity g = 9.81 m/s2

Steel density ρ s = 7850 kg/m3

Water density ρ w = 1025 kg/m3




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C.2.7 Vessel operational profile and number of loading conditionsFrom an analytical point of view it is difficult to include all phases of on-off loading program as the ballastand cargo tank filling is a gradual process. However, in order to capture the extremities in the on-off loadingprogram it is recommended to use the operational ballast and fully loaded condition reflected in the

operational on-off loading program as a minimum. An overall fatigue damage can typically be determinedby assuming the vessel is operating 50% of the time in ballast condition and 50% in fully loaded condition.An additional intermediate loading condition does not necessary increase the accuracy of the fatigueanalyses. However, additional analysis may be required for assessment of ship sides where the differencein draught is large.

C.2.7.1 Cyclic load due to on- and off-loading

The cyclic load due to on-off loading needs to be determined. The on-off loading response is typically thestatic still water stress taken from the ballast and fully loaded condition. The difference in stress level forthe two loading conditions will give a still water stress range, which together with the wave induced stressrange from the actual loading conditions may serve as input to the low cycle fatigue assessment, ref.[C.4.9].

C.2.8 Weight report and stability manualThe analysis model should reflect current as-is weight description, hence, a recent weight report of thevessels lightship weight is required. Note that for vessels which have had extensive upgrades andmodification of weights, ref. [C.2.4.2], these issues also need to be accounted for. As a minimum the weightreport should include the following:

— longitudinal breakdown of hull lightship weight

— topside weight description; description of topside equipment on and above main deck

— variable loads

— mooring and riser loads.

A description of how the different weights are modelled is given in [C.5.3.2].

The stability manual gives the tank filling program for the actual loading conditions. As a minimum the tankprogram should include the following information:

— identification of each tank – tank program

— volume and centre of gravity for each tank

— filling fraction, permeability and fluid density for each tank.

C.3 Environmental conditionsReference is made to [B.3] for environmental conditions for modelling of load effects on FPSOs.

C.4 Fatigue analyses methods for floating production storage and

offloading

C.4.1 OverviewThe choice of methodology for fatigue assessment of an FPSO will strongly depend on both the structurallayout and acting load on the actual detail. For the hull structure the most relevant analysis methods are:

— full stochastic analysis

— full ship hull model

— intermediate model

— local hot spot model.

— component stochastic analysis

— side longitudinal and plating.




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In addition, more detailed specific analyses may be recommended. This includes:

— low cycle fatigue (LCF) due to on- and offloading of vessel

— mooring analyses with respect to wave frequent (WF) and low frequent (LF), including combination ofsuch effects

— turret/hull interface including combination of hull girder response and mooring / riser response— wind induced fatigue response of flare tower, including vortex induced vibration analyses.

The following sections give a description of the full stochastic and load component stochastic analysis dueto wind generated seas along with low cycle fatigue assessment due to on- and off-loading of vessel. Fordescription of mooring analyses and wind induced fatigue response reference is made to DNV-RP-C206,DNV-RP-F204 and [C.4.10] respectively.

C.4.2 Spectral fatigue analysis methodologyC.4.2.1 General principles

In connection with fatigue assessment of an FPSO two principal spectral fatigue analysis methodologies arerecommended:

— full stochastic method using either a global model, an intermediate screening model or a local hot spotmodel

— DNV load component method or equivalent using a cargo-hold FE model.

These methods are based on a spectral procedure which includes the following assumptions for calculationof fatigue damage:

— wave climate is represented by site specific wave scatter diagram.

— Rayleigh distribution applies for stress response within each short term condition.

— cycle count is according to zero-up-crossing period, t z, of short term stress response.

— Miner summation is according to linear cumulative damage.

The spectral method assumes linear load effects and responses. The hydrodynamic loads and structuralresponses should be calculated using 3D potential theory and FE analysis, respectively.

The hot spot stress methods using spectral methods (also denoted as stochastic methods) is recommendedfor fatigue damage accumulation. The hot spot stress is either calculated using a local hot spot model (SCFmodel) or derived from nominal stresses combined with associated SCFs.

The analyses should consider relevant non-linear effects that affect the stress and have a probability ofexceedance level larger than 10-4. (See [7.2.4] for definition of exceedance level). An example of such aneffect is the intermittent wetting of the side shell and the resulting effect on the linearized pressure loads,ref. [C.5.5.4]. Other load effects, such as slowly varying response, impact loads and ship springing, shouldbe included if they are significant for the calculated fatigue life. Reference is made to DNV-RP-C206 for moredetailed description of these load effects.

C.4.2.2 Full spectral fatigue analysis methodology

A full spectral fatigue analysis can be performed using either a structural global model, intermediatescreening model or local hot spot model. The method requires that the dynamic wave loads are transferreddirectly from the hydrodynamic panel model to the relevant structural model. External wave loads, internaltank loads and inertia loads shall be considered in a consistent manner to maintain equilibrium. A typicalglobal FE model including selected topside process modules is shown in Figure C-1.




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Figure C-1 Typical global FE model (colour coding reflect different super elements)

Figure C-2 shows example flow chart for implementing the full stochastic fatigue analysis using a global

model together with a local sub-model. In this case the sub model may either be an intermediate screeningmodel or a more refined hot spot model (SCF model).

Figure C-2 Example of full stochastic analysis procedure flowchart for a global model

The advantage of a direct stochastic analysis is that all linear load effects are automatically included by anintegrated hydrodynamic and structural analysis program. The fineness of the panel model and finiteelement mesh should correspond with the type of the analysis to be performed, i.e. global or local fatigueanalysis. A global structural model may be constructed using a relatively coarse mesh, ref. [C.6.4], whichprovides a reliable calculation of nominal stresses in deck plating. For shell plating subjected to lateralpressure loads from sea water or tank fluids, the global model is considered to be too coarse to fullyrepresent the bending stress between stiffeners and web frames.

The global FE analysis should be performed for all relevant wave load cases, i.e. wave headings and waveperiods, for each loading condition. Resulting deformations are then transferred from the global model tothe actual sub-model by means of complex displacements where they form the boundary displacements foreach corresponding load case. Note that for large sub-models or sub-models exposed to lateral pressure

loads, these models should also be analysed by the hydrodynamic load program for calculation of localdynamic pressure loads and inertia loads. The fatigue damage contribution from each cell in the wave




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Figure C-3 Example of load component stochastic fatigue analysis flowchart

The load component analysis can be utilized at different detail levels reflected in the FE models applied in

the analysis. In principle, the load component analysis can be divided into the two following approaches:— load component based analysis with use of a SCF model.

— load component based analysis using available SCFs together with nominal stresses.

The two approaches are described below:

Load component based analysis with use of SCF models

Use of SCF models is the most detailed component based fatigue analysis method. Stress concentrationsmodels are used for calculation of hot spot stresses, and these models do not necessitate separation of localaxial stress from bending stress. The principles for establishing and using stress concentration models aregiven in [C.6.7].

Load component fatigue analysis using available SCFs

This approach will normally be used in the classification of new built structures.

If SCFs for the given detail are available, e.g. DNVGL-RP-0005 App.A and DNV-CN-30.7, then calculation offatigue life may be based on the SCFs combined with nominal stresses. The main difference between thisapproach and that given in the section above (with use of SCF models) is that different SCFs may berequired, depending on whether the stress is caused by axial load or bending load at the actual location.

The flowchart shown in Figure C-4 presents an overview of the combination of stress transfer functions inorder to give a combined stress for use in subsequent fatigue calculations. It should be noted that thisapproach using SCFs is applicable only for geometries with similar dimensions to those for which the SCFsare derived. Stress concentration models should be used for other geometries.




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Figure C-4 Example of load component stochastic fatigue analysis flowchart using nominal stress level

combined with relevant SCF

C.4.3 Fatigue damage calculationThe fatigue damage calculations should be performed according to DNVGL-RP-0005. Damage contributions

from each of the analysed loading conditions should be summed up based on the fraction of time that eachload condition is considered to be present.

C.4.4 Design fatigue factorDesign fatigue factors (DFF) used in design depend on the consequence of a fatigue failure and the

possibility for inspection and repair. DFF due to hull safety given in NORSOK N-001 shall always be

considered for permanently installed units. In this RP it is not recommended to directly incorporate DFF in

the calculated fatigue damage. The consequence of failure will be assessed when the target reliability level

in the probabilistic analyses is determined.

C.4.5 Workmanship and fabrication tolerancesFabrication procedure for the actual vessel should be supplied by designer and fabricator. Alternatively DNVCN 30.7 App.F gives an example of default values for workmanship tolerances based on what is considered

to be normal shipyard practice. If greater tolerances are used, the SCF may be calculated based on actual

tolerances, see DNVGL-RP-0005.

C.4.6 S-N curvesReference is made to DNVGL-RP-0005 for S-N curves.

C.4.7 Stress concentration factorsSCFs may be determined based on fine mesh FE analyses. Alternatively, a suitable tabulated SCF may be

selected. The fatigue life of a weld toe detail is governed by the hot spot stress range. For weldedcomponents other than butt welded connections, the hot spot stress is obtained by combining the nominal




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stress with the geometric SCF, defined as follows:

The nominal hot spot S-N curve in DNVGL-RP-0005 is given for butt welded specimens where the hot spotstress is equal to the nominal stress, i.e. SCF = 1.0.

The relation between the hot spot stress range to be used together with the S-N curve D and the nominalstress range is:

Any effect contributing to an increase in stress level at hot spot (excluding the localized stress concentrationdue to the weld profile) shall be considered when evaluating the hot spot stress.

C.4.8 Mean stress effectResidual stresses due to welding and construction may be reduced over time as the vessel is subjected toexternal loading and due to change in loading condition during operation. If it is likely that a hot spot regionis subjected to a tension force implying local yielding at the considered region, the effective stress rangefor fatigue analysis can be reduced due to the mean stress effect also for regions affected by residualstresses from welding.

It should be noted that the mean stress effect as presented herein is considered only in connection with theprobabilistic methods for planning of inspection of FPSOs. The reduction factor on the derived stress rangefor welded connections can be derived from [10.5.3].

For reduction factors for base material reference is made to DNVGL-RP-0005.

C.4.9 Low cycle fatigueAccording to DNV-RP-C206 it is not normally necessary to calculate fatigue damage from low cycle fatigue(LCF) in transverse or longitudinal bulkheads due to on and off loading operations provided that all thefollowing conditions are met:

— cyclic lateral pressure acting on one side of the plating only

— number of on and off loading cycles is less than 1000 during the operational lifetime

— SCF for considered detail is less than 2.0 for normal steel and 1.44 for high strength steel (by normalstrength steel is here understood material with yield strength f y = 230 MPa and by high strength steelis understood material with yield strength f y = 315 MPa.

If these conditions are not satisfied, then the fatigue damage from cyclic stress ranges due to on and off

loading should be calculated as for high cycle fatigue typically by using one stress block in the equation forfatigue damage as given in DNVGL-RP-0005.

Low cycle fatigue analysis should be performed for structural elements which experience a full load reversalduring on and off loading operation for loading sequence given in Table C-1. (The difference between loadscenarios in step 2 and step 4 gives a significant stress range).

For an FPSO the following locations may be vulnerable in view of low cycle fatigue, ref. [C.8]:

(C.1)

(C.2)

Table C-1 Loading sequence that may contribute to low cycle fatigue damage

Loading scenario Primary tank Adjacent tank

1 Empty Empty

2 Full Empty

3 Full Full

4 Empty Full

nominal σ

σ spot hot SCF =

nominal σ σ ∆⋅=∆ SCF spot hot




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— web stiffener on top of inner bottom longitudinal and hopper slope longitudinals when wide frame spaceis employed

— lug connection to web plate and web plate connection to longitudinals in areas of high girder shear stressor where web stiffener is not fitted on top of longitudinal flange

— heel and toe of horizontal stringer of transverse bulkhead where frequent alternate loading is anticipated— inner bottom connection to transverse bulkhead where frequent alternate loading is anticipated

— lower stool connection to inner bottom for a loading condition with one side tank empty and the othertank full

— any other locations under repeated high static stress ranges.

The damage contribution from low cycle fatigue needs to be combined with the damage from wavegenerated response. The total combined stress can be expressed as:

where

where ∆σ LCF is the static hot spot stress range, ∆s0 is the hot spot high cycle fatigue stress rangecorresponding to a probability of exeedance level of 10-4, nLCF is number of cycles from low cycle fatigueand n0 is number of cycles from high cycle response (108). (See [7.2.4] for definition of probability ofexceedance level).

The calculated hot spot stress should be combined with the hot spot stress S-N curve D. However, wherelarge stress cycles imply local yielding at the hot spot, the calculated hot spot stress from a linear elasticanalysis should be increased by a plasticity correction factor, k e, before the S-N curve is entered forcalculation of fatigue damage; hence:

where the plastic correction factor is given as:

C.4.10 Wind induced fatigue responseWind induced fatigue damage for an FPSO is in general related to slender topside structures, e.g. flare towerand helideck support structures. The wind induced fatigue damage is normally calculated separately fromwave induced damage, where damage from each of the two processes is later combined according toprocedures given in DNV-OS-E301 or alternatively DNVGL-RP-0005.

The most appropriate technique for determining buffeting wind-induced cyclic stresses is referred to as thepower-spectral density approach. A power spectrum describes a time-dependent variable relating theenergy distribution over a range of frequencies. All phase information is averaged out. Analysis methodswhereby output spectra are obtained from input spectra via transfer functions are required for randomprocesses such as wind or wave loading, where only a statistical description of the environmental forces canbe given. In the spectral analysis method of fatigue due to wind, the stress spectrum is obtained from the

input wind spectrum combined with the structure stress transfer function at the hot spot. Because of thenature of the fluctuating wind force, there is a direct linear relationship between the wind speed and force

(C.3)

and(C.4)

(C.5)

for

for

(C.6)

)(5.0 loaded

w

ballast

w

k

LCF

k

comb σ σ σ σ ∆+∆⋅+∆=∆

ballast

static

full

static

k

LCF σ σ σ −=∆

h

LCF i

wn

n/1

0

0log

log1

−⋅∆=∆ σ σ

e

loaded

w

ballast

w

k

LCF e

k

comb

k

e k k ⋅∆+∆⋅+∆=⋅∆=∆ ))(5.0( σ σ σ σ σ

−

∆⋅+= )1

24.00.1

y

ek σ

σ

yσ σ 2>∆

0.1=ek yσ σ 2≤∆




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spectra. This allows the structure stress spectra to be related to wind speed spectra through a transferfunction that reflects structural dynamic behaviour.

In addition to buffeting wind response, fatigue damage of slender topside structures needs to be assessedwith respect to vortex-induced-vibration response (VIV). This type of response is related to steady state

wind action, where the wind, depending on member length, diameter, fixation, surface roughness andReynolds number, may cause the member to oscillate.

For VIV response each member is assessed separately, considering the members eigen mode relative toshedding frequency, Vcrit, which then may cause the resonant shedding behaviour. It is normally sufficientto only consider the first mode relative to bending response for flare tower and helideck support structurewith moderate member span length. Also only transverse oscillation, i.e. normal to incoming wind directionis considered. For more detailed description reference is made to NORSOK N-003.

C.5 Hydrodynamic load and motion analysis

C.5.1 General

The sea keeping and hydrodynamic load and vessel motion analysis shall be carried out using 3D potentialtheory with a recognized computer program. The program shall calculate response amplitude operators(RAOs, transfer functions) for motions and loads in long crested regular waves, ref. DNV-RP-C206 /32/.

C.5.2 Co-ordinate systemIt is inherent in the analysis procedure that the modelling coordinate system is clearly defined and ensuresconsistency in the analyses. As an example the modelling coordinate system can be defined with the origolocated in ships AP in the centre line at baseline (BL) with global x-axis pointing in forward direction, globaly-axis pointing in port direction and global z-axis pointing in upwards direction as shown in Figure C-5.

Figure C-5 Coordinate system for a global analysis model

C.5.3 Hydrodynamic analysis modelling

The hydrodynamic load model shall give a good representation of the wetted surface of the ship with respectto the geometry description in terms of load transfer and hydrodynamic behaviour.

The following section gives a general description of the minimum model requirements needed to ahydrodynamic load and motion analysis. The requirements are dependent on type of analysis whether it isa full stochastic analysis or a component stochastic analysis.

C.5.3.1 Hydrodynamic panel model

The sink-source model is often referred to as the panel model and is basically a description of the vesselouter shell. The model is typically developed using either 4- or 8-noded shell elements. As the vessel usuallyis symmetric through the xz-plane, it is recommended to use mirroring about the xz-plane as this will reducethe computer time significantly as compared with a full model.

The element size of the panels for the 3D hydrodynamic analysis shall be sufficiently small to reduce

numerical inaccuracies. In general, suitable accuracy is normally achieved using a mesh of at least 40 to 60stations along the length of the ship, each of at least 15 to 20 nodes, giving a total of 600 to 1 200 elements




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per half ship side. As a rule of thumb, the mesh should have at least 5 elements per shortest wave lengthin ship longitudinal direction, assuming that the shortest wave length is less than or equal to approximately10% of the ship’s length.

The element mesh should provide a good representation of areas with large transitions in shape; hence, the

bow and the aft areas along with the area around the bilge and close to the still water level (SWL) are oftenmodelled with a higher element density than the parallel mid ship area. For these areas an element sizetypically around 1/10 of the shortest wave length in the ship’s longitudinal direction are recommended. Incase of load transfer, the panel model should have approximately the same geometrical shape as the globalstructural model. A typical panel model for an FPSO is shown in Figure C-6.

Figure C-6 Panel (sink-source) Model

The model displayed in Figure C-6 does not include the turret as the moonpool is an open area in the panelmodel. As stated in [6.2.3] in DNV-RP-205 /7/, internal turrets are generally not necessary for the globalhydrodynamic analysis since the vertical dynamic buoyancy forces are often a small fraction of the totalbuoyancy force. However, experience shows that having an open moonpool in the panel model may resultin non-physical effects in the transfer function around 5 to 10 seconds. If more than one peak is seen in theheave transfer function in this period range, it is recommended to perform an additional analysis with closedmoonpool. If it is considered necessary to use a panel model with a closed moonpool, the moonpool in thestructural model should be closed with non-structural elements in order to obtain correct load transfer.

C.5.3.2 Hydrodynamic mass model

The mass model should include a description of the total mass including lightship weight, variable loads,riser and mooring loads and tank filling content. However, depending on type of analyses there are different

requirements with respect to level of detail for the mass model. Typical information required for the massmodelling is given in [C.2.8].

The mass model shall ensure a proper description of local and global moments of inertia around thelongitudinal, transverse and vertical global ship axes. This is particularly important for a full stochasticanalysis where a direct load transfer to the structural model is applied.

The global mass model is often equal to the global structural model for full stochastic analysis, thus utilizingthe weight of the primary steel included in the structural model. However, given the structural model beingrelatively coarse, additional weights may be included to fully represent the light ship weight.

A commonly used approach has been to divide the hull into 10-20 different sections and define each sectionwith its unique material property, i.e. material density for mass description of the hull structure. Thedensities are then tuned towards a target weight. Additional mass points are often evenly distributed around

the hull structure in order to avoid the tuned steel density being too different from nominal steel density(7850 kg/m3).




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For modelling of topside weight on and above main deck a common approach has been to use a combinationof evenly distributed mass points and mass tents. Mass tents are used for large equipment weights (> 25tonnes) whereas distributed point masses are used for smaller weights (< 25 tonnes). The mass tentsshould represent a rigid motion, hence, the tent legs and tent platform are given a stiffness typically 100times higher than the normal stiffness or Young’s modulus (ref. Mat1 in Figure C-7) with dummy dimensions

typically being tubular elements with diameter =1.0 m and thickness = 0.06 m. Further, in order to avoidsplit forces from the mass tents, vertical support legs are included ensuring connection between main deckand mass tents. These legs are modelled with a nominal Young’s modulus (2.1x105 N/mm2) thus avoidingintroduction of unphysical stiffness relations in deck / topside intersection. Pinned connections are appliedin support legs towards deck. A schematic figure illustrating typical mass tent is shown in Figure C-7. Atypical mass model used for full stochastic analysis is shown in Figure C-8.

Figure C-7 Typical mass tent model

The mass of tank content are for most software automatically calculated in the hydrodynamic load program.However, for direct load transfer analyses the tanks need to be defined either by means of point masses orlateral hydro pressure. If mass points are used, the mass should be connected to the structural hull throughmultiple elements, often referred to as element spokes. If hydro pressure definitions are used, the wetsurface shall be defined for each tank. Based on the wet surface definitions, the hydrodynamic load programis able to identify actual tank volume. Additional tank properties such as filling fraction, fluid density andtank permeability should reflect actual tank filling program for actual loading conditions and are most oftendefined in the hydrodynamic load program. A typical tank definition with use of wet surface elements isshown in Figure C-9.

Moorings and risers are not expected to influence first order motions significantly. However, in order to

preserve static equilibrium, their static contribution shall be included in the analysis. The static contributionmay be included either by vertical pre-tension according to static weight of these items, or as point masses.Care should be taken when distributing the point masses to avoid any unintended mass asymmetry whichwill have influence on the roll motions.




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Figure C-8 Global mass model used for full stochastic analyses

Figure C-9 Modelled tanks including names used for wet surface definitions

For a component stochastic analysis the level of detailing with respect to mass description is lower than for

a full stochastic analysis. As the component stochastic analysis relies on sectional forces in terms of global

hull girder response as load input, a reasonable longitudinal mass description is required. For the

hydrodynamic analysis, the mass distribution between two successive load sections should include, at least,

three mass points in the longitudinal direction and two mass points in the transverse direction. In order to

give a proper description of both local and global moments of inertia, these mass points should have the

correct longitudinal position relative to the station coordinates, correct transverse position relative to the

ship centreline, and correct vertical position relative to the baseline, i.e. be correct with respect to the global

modelling coordinate system. A typical mass model used for component stochastic analysis is shown inFigure C-10. The diameter of the blue rings indicates the mass intensity at a given point.




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Figure C-10 Typical mass model for component stochastic analyses

C.5.4 Modelling of FPSO directionalityThe mooring arrangement needs to be taken into account when considering the vessels directionalityrelative to environmental geometrical direction. The majority of the FPSOs are equipped with either of thetwo mooring arrangements:

— internal / external turret moored arrangement

— fixed spread moored arrangement

For turret moored arrangement the vessel is free to rotate about the turret by free weather vaning orthruster assistance. In order to minimize the roll response and the loads on the mooring systems the vesselis typically orientated with the bow up towards incoming waves. However, it is rather difficult to maintaina steady fixed direction for the vessel. This effect is accounted for by including wave directional wavespreading together with a corresponding distribution. Operational data can be applied if available;alternatively the distribution as given in Table C-2 may be used. A further discussion is given in DNV-RP-C206 [6.1.2] /32/.

For fixed spread moored arrangement due consideration should be made with respect to vessel orientationrelative to environmental geometrical direction. Often the vessel is orientated with shift relative to thegeometrical direction. For these cases one should ensure that the wave headings which presumably givelargest responses, e.g. head, diagonal, beam and following seas, are applied. With directional wave scatteroften given with 45° interval relative to geometrical direction, the geometrical wave direction closest tovessel orientation should be applied. Alternatively, equivalent directional wave scatter can be establishedbased on scaling of adjacent directional scatter. As an example Figure C-11 shows a vessel with 20° shiftrelative to geometrical wave direction.

Table C-2 Directional distribution of waves for turret moored arrangement

Wave heading Distribution [%]

Head seas 60.0

+/- 15° off 15.0

+/- 30° off 5.0




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Figure C-11 Directional shift between geometrical and vessel orientation

C.5.5 Calculation of wave loads and vessel motions

C.5.5.1 Hydrostatic condition

There should be balance in masses/forces between hydrodynamic panel model and mass model. This meansthat there should be balance between:


— centre of gravity and centre of buoyancy with respect to heel and trim.

Any slight imbalance between the mass model and hydrodynamic model should preferably be corrected by

modification of the mass model. A rule of thumb is that sum of mass and buoyancy should be less than 1%of total weight.

A slight modification of the mass model is usually needed in order to balance the hydrodynamic panel modeland mass model. If the unbalanced load is less than 5% of the wave excitation force, then the load balancemay be achieved by adjusting the point masses close to FP and AP.

Another issue one should assess is the vessel’s natural frequency which is given as a function of systemmass and stiffness. For FPSOs it is the natural periods in heave, pitch and roll that are of interest. For heavemotion, the system stiffness is reflected in water plane stiffness and is thus a product of outer hull geometryand draught level. For roll and pitch motions, the natural frequency are given as a function of radii ofgyration, rnn, and transverse and longitudinal metacentric height, GMT and GML. It is important that theratio between these two parameters is reasonable in order to obtain correct natural frequency. The radii ofgyrations are products of the local distribution of masses relative to axis through centre of gravity, i.e. the

better representation of mass in the global mass model, the more correct is the radii of gyration. Themetacentric height is a function of the loading condition. If the metacentric height in the hydrodynamicmodel is different from that given in the reference document or the model tests, it can be adjusted byintroducing a restoring matrix which basically is a spring. This is further addressed in [C.5.5.3].

C.5.5.2 Calculation of roll damping

The roll damping computed by 3D linear potential theory includes moments acting on the vessel hull as aresult of the creation of waves when the vessel rolls. At roll resonance, however, the 3D potential theorywill not fully account for the total roll damping, which consequently leads to over-prediction of the rollmotion, ref. DNV-RP-206 /32/.

Often information about roll damping of FPSOs is quite limited and is typically given in the form of decaytest from model tests or a fraction of critical damping without corresponding return period. As the fatigue

damage can be quite sensitive to the roll motion, particularly for spread moored FPSO a reasonablerepresentation of the roll motion is required.




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In order to adequately predict the total roll damping at roll resonance, the effect from damping mechanismsnot related to wave-making, such as vortex-induced damping (eddy-making) near sharp bilges, drag on thehull (skin friction), and bilge keels should be included. Vortex-induced damping and damping from skinfriction is typically incorporated into the hydrodynamic program based on empirical formulations fitted tomodel test data.

Results from experiments indicate that non-linear roll damping on a ship hull is a function of roll angle, wavefrequency and forward speed. As the roll angle for fatigue analysis is generally not known in advance anddepends on the scatter diagram considered for the fatigue analysis, an iteration process is required to derivethe non-linear roll damping.

An iteration procedure for calculating maximum roll angle is presented. The procedure requires a stripmodel in addition to a relevant sea state corresponding to probability level of 10-4 based on actual wavescatter diagram used in the stochastic iteration:

1) Define iteration criteria; maximum number of iterations and convergence criteria.

2) Define an initial roll angle, θ0, for all wave headings.

3) Run hydrodynamic analysis using θ0 from 2.

4) Calculate long term roll motion, θn, with respect to a pre-defined sea state.5) If calculated roll angle, θn, is equal to θ0, correct roll damping is achieved; if not, insert the calculated

roll angle, θn, and repeat activity 2 through 5 until convergence is achieved.

C.5.5.3 Free surface effect in tanks

Free surface effects in tanks shall be included in the hydrodynamic motion analyses as it has significanteffect on the response. In many software programs this effect is automatically included by considering theactual tank filling for each tank. However, if this effect is not automatically calculated, it must be manuallyincluded. This can be done by introducing springs in form of a restoring matrix. The spring stiffness can befound by means of manual iteration. Typically for roll motion, the spring stiffness in position [4,4] of therestoring matrix is adjusted until the correct transverse metacentric height, GMT, is achieved. Themetacentric height is usually given in the Trim and Stability report.

C.5.5.4 Intermittent wet surface

By default the external sea pressure is calculated up to still water line (SWL) for frequency-domain analyses.However, due to the effect of intermittent wet and dry surfaces it is recommended that the pressuredistribution in the splash zone is modified, ref. DNV-RP-C206 /32/ and DNV-CN-30.7 /33/.

The external sea pressure distribution is defined as normal pressure according to the long-term valuescalculated at 10-4 probability level, hence, the pressure field around actual water line (zwl) is based on asingle equivalent wave (10-4 probability level) and not the different sea states given in the wave scatterdiagram, ref. DNV-CN-30.7.

Due to intermittent wet and dry surfaces, the pressure range above Tact - zwl is reduced, see Figure C-12.The dynamic external pressure amplitude (half pressure range), pe, related to the draft of the load conditionconsidered, may be taken as:

where

(C.7)

pd = dynamic pressure amplitude below waterline taken from the hydrodynamic analysisr p = reduction of pressure amplitude in splash zone

= 1.0 for zw < Tact - zwl

= for T act - z wl < z w < T act + z wl

= 0.0 for T act + z wl < z w z

wl =distance in meter measured from actual waterline corresponding with wave amplitude withprobability level of 10-4. (In the area of side shell above z = T act + z wl it is assumed that the externalsea pressure will not contribute to fatigue damage.)

d pe pr p ⋅=

wl

wwl act

z

z z T

2

−+




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Figure C-12 Reduction of sea pressure in splash zone

C.5.6 Combination of transfer functions using load component stochasticmethodThe combined stress response can be determined by a linear complex summation of stress transferfunctions. The combined local stress transfer functions may be found by combining the complex response

transfer function for unit loading conditions as:

where

A1 = stress per unit vertical bending moment.

A2 = stress per unit horizontal bending moment.

A3 = stress per unit relative lateral external pressure load.

A4 = stress per unit relative lateral internal pressure load.

A5 = stress per unit axial load. A6 = stress per unit acceleration load, ax, ay, az.

H 1( ω |θ ) = transfer function for combined local stress.

H v( ω |θ ) = transfer function for vertical bending moment at a representative section.

H h( ω |θ ) = transfer function for horizontal bending moment.

H p( ω |θ ) = transfer function for external pressure in centre of the considered panel.

H e( ω |θ ) = transfer function for liquid cargo pressure in centre of the considered panel.

H a( ω |θ ) = transfer function for axial load.

H acc( ω |θ ) = transfer function for acceleration loads (includes also topside loads).

Ak is the local stress response due to a unit sectional load for load component k. The Ak factors may bedetermined either by FE analyses or by a simplified method for replacement of the described loads by unit

=

pdT = pd at z = T act

T act = the draft in m of the considered load condition ρ = density of sea water

(C.8)

g

pdT

ρ ⋅

4

3

)|()|()|()|()|()|()|( 654321 θ ω θ ω θ ω θ ω θ ω θ ω θ ω σ accae phv H A H A H A H A H A H A H +++++=




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loads. Note that it is important to ensure compatibility between the reference (coordinate) systems used inboth the load model and the stress analysis model.

The factors Ak may be determined by adding unit sectional loads at the considered sections, to determinethe effect of each individual load component when the hull pressure distribution is determined from a wave

loading program. Negative dynamic pressures do not occur at the waterline (intermittent wet and drysurfaces) and hence the stress range is proportional to the pressure amplitude. The effective stress rangefor longitudinal details in the waterline region may be estimated using the reduction factor, r p, as describedin [C.5.5.4]. Alternatively, the stress range distribution may be determined from the pressure ranges byintegration of pressures in each wave height (or sea state) in the long-term environmental distribution.

C.5.7 Calculation of wave frequent responseThe short term distribution of load responses for fatigue analyses may be estimated using the wave climate,represented by the long term distribution of H s and T z in a wave scatter diagram for the actual area. Eachshort term sea state is then combined with an appropriate wave spectrum, S η ( ω |H s , T z ) as described in [B.2].The ship response spectrum based on the linear model, S σ ( ω |H s , T z , θ ), is directly given by the wavespectrum, S η ( ω |H s , T z ), the transfer function H( ω |H s , T z ), defined as:

The spectral moments of order n of the response process for a given heading are calculated as:

where the wave spreading function f s( θ ) = cosn( θ ), as described in App.B with n = 4. The stress rangeresponse for ship structures can be assumed to follow the Rayleigh distribution within each short termcondition. The stress range distribution for a given sea state i and heading direction j is then derived as:

where m0 is the spectral moment of order zero. A summation of the fatigue damage within each sea stateand heading direction can be applied, ref DNV-RP-C206 /32/.

The response due to swell may be calculated similar to the response to wind generated wave response,using the JONSWAP spectrum with peak enhancement factor in the range 8 to 15 and cos8θ spreadingunless otherwise stated. The response due to wind induced waves is independent of response due to swell,and the combined effect can be obtained by adding the variances of these responses. The zero-up-crossing

period of the combined response through the mean level can be computed using the sum of the respectivespectral moments, ref DNV-RP-C206.

C.5.8 Application of hydrodynamic loads on the structural finite elementmodelsThe hydrodynamic loads, presented as inertia loads and lateral pressure loads, should be transferred to thestructural model in a proper way. For a full stochastic analysis as described in [C.4.2.2] the loads can bedirectly applied on the global FE model. If loads are applied correctly, the global FE model will be close toequilibrium, and thus the reaction forces at global structural model boundaries should be close to zero. Theeffect of simultaneously acting dynamic ship loads should be accounted for in the analysis. Loads due toviscous damping shall be included and transferred to the structural model.

For the load component analyses methodology, ref [C.4.2.3], the loads are manually applied according toprocedure given inn [C.5.6].

(C.9)

(C.10)

(C.11)

),|(|)|(|),,|( 2

z s z s T H S H T H S ω θ ω θ ω η σ =

ω θ ω ω θ σ

ω

θ

θ d T H S f m z s

n

sn

O

O ),,|()(90

90 +

−=

−−=∆

ij

ijm

F 0

2

8exp1 σ

σ




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It is of great importance that the loads from the hydrodynamic model to the structural model are transferredin a correct manner. Analyses routines which ensure sufficient verification and qualification of analysismodels, methodology and results should be established. [C.7] presents a procedure involvingdocumentation, verification and qualification of analyses work in addition to the hydrostatic balancing of theglobal model described in [C.5.5.1].

C.5.9 Additional load effectsC.5.9.1 Cyclic loads due to on and off loading

The effect of cyclic loads due to on and off loading is discussed in [C.4.9] and [C.2.7.1].

C.5.9.2 Bilge keel fatigue assessment

The bilge keel is seldom included in the global structural model. However, its effect with regards to rollmotion is included in the analysis as described in [C.5.5.2]. Therefore, if a structural fatigue assessment ofthe bilge keel and supporting hull structure is required, a local hot spot model must be developed.

The local bilge keel model may be introduced as a conventional sub-model, thus including global responsefrom the hull. However, the lateral pressure load acting on the bilge keel must also be included. This can

be accounted for by introducing Morison elements. The Morison elements are basically beam elements withspecified load diameter and thickness, drag coefficient and added mass coefficient used for calculating dragand inertia loads on the bilge keel.

In order to avoid additional stiffness introduced from the Morison model, the E-modulus can be set to 1/1000 of nominal steel stiffness. As a minimum the following parameters should be defined for the Morisonelement:

— the hydrodynamic load diameter and thickness of element

— drag coefficient

— inertia coefficient

— sea state described in terms of wave scatter, HS and TZ for drag linearization.

C.5.9.3 Miscellaneous load actionsOther load effects that may be included are loads due to slamming, sloshing, green seas and springingeffects. However, it should be emphasized that most of these load effects represent analysis areas stillunder development with respect to analytical theory, software and practical application. Slamming, sloshingand green seas include impact effects for which values and application to fatigue analysis are complex, ref.DNV-RP-C206 /32/.

C.6 Modelling principles for finite element models

C.6.1 GeneralFinite element analysis is required to obtain accurate stress distribution in the FPSO hull structure. Withcomputer performance and data storage continuously increasing, the level of detail in the FE models isconsequently improved. However, it is important to be aware of the actual application of different modelsand the advantages and disadvantages inherent in the different models.

There are several levels of FE models used in analysis of FPSOs. In this RP the following models arerecommended for analyses of hull structure:

— global structural model covering entire hull structure

— intermediate screening model

— local hot spot model / stress concentration model

— cargo hold model used in the DNV load component stochastic analysis.

C.6.2 Methodology for choosing critical areas and hot-spotsIn order to ensure a reasonable and manageable work load in terms of fatigue analyses of FPSOs, it isimportant to make an evaluation of which areas and details which potentially are most probably subjected




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to fatigue damage. The approach to identify structural details which may have fatigue capacity belowrequirements may be based on the following methodology:

— review of as-built structural drawings

— review of the hull inspection records and repair history

— review of historic reports and design reports for structural details with low fatigue life— review of known fatigue problems of ship structures in general and FPSO hulls with similar design

— use of global hull screening models, based on stochastic fatigue analyses, ref. [C.6.4]

— use of intermediate sub-models, where the global model is too coarse for screening purposes, ref.[C.6.5].

C.6.3 Sub-modelling techniqueThe sub-modelling technique allows a part of a global model to be re-analysed to produce more accurateresults locally without changing or re-running the original global model. By creating a separate model,typically with a more detailed structural description of a specific area, the responses from the globalstructural model can be transferred to the boundaries of the local model by means of complex prescribed

displacements. In this way the local detail / model does not need to be an integrated part of the globalmodel.

Although the sub-model technique offers good flexibility, there are some precautions which need to betaken into account in order to ensure reasonable transfer from the global model to the local model. Theseprecautions can vary for different program systems:

— The sub-model shall be compatible with the global model. This means that the boundaries of the sub-model should coincide with those elements in the parent model from which the sub-model boundaryconditions are extracted. The boundaries should preferably coincide with mesh lines as this ensures thebest transfer of displacements to the sub-model.

— Curved areas shall be given special attention. Identical geometry definitions do not necessarily lead tomatching meshes. Displacements to be used at the boundaries of the sub-model will have to beextrapolated from the parent model. However, only radial displacements can be correctly extrapolatedin this case, and hence the displacements on the sub-model boundaries can be erroneous.

— The boundaries of the sub-model shall coincide with areas of the parent model where the displacementsare well defined. For example, the boundaries of the sub-model should not be midway between twoframes if the mesh size of the parent model is such that the displacements in this area cannot beaccurately determined.

— Linear or quadratic interpolation (depending on the deformation shape) between the nodes in the globalmodel should be considered. Linear interpolation is usually suitable if coinciding meshes are used.

— The sub-model shall be sufficiently large such that boundary effects due to inaccurately specifiedboundary deformations do not influence the stress response in areas of interest. A relatively large meshin the global model is normally not capable of describing the deformations correctly.

— If a large part of the global model is substituted by a sub-model, then mass properties in the sub-model

must be consistent with the global model. Inconsistent mass properties will influence the inertia forcesleading to imbalance and erroneous stresses in the model.

— External load acting on a local model, e.g. topside equipment or external and internal pressures shouldbe included in the sub-model.

— Transfer of beam element displacements and rotations from the parent model to the sub-model shouldbe carefully considered.

— Transitions between shell elements and solid elements should be carefully considered, if used.

C.6.4 Global structural modelThe global hull analysis is intended to provide a reliable description of the overall stiffness and global stressdistribution in the primary members in the hull. The following effects shall be taken into account:

— vertical hull girder bending including shear lag effects— vertical shear distribution between ship side and bulkheads




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— horizontal hull girder bending including shear lag effects

— transverse bending and shear.

A complete FE model may also be necessary for the evaluation of the vertical hull girder bending of shipsthat have a complex arrangement of continuous structures above the main deck, such as long topside

modules. The mesh density of the model shall be sufficient to represent global deformations and nominalstresses due to the effects listed above. Local stiffness effects, e.g. topside and deck intersection andbending between stiffeners and frames due to lateral pressure loads from seawater and tank fluids, willoften not be sufficiently represented in the global model. Reference is made to DNV-RP-C206 [4.2] /32/ forstructural modelling principles for the global model. An example of a FE model of global hull structure isshown in Figure C-13.

Figure C-13 Global structural model; colour coding correspond to super element ID

C.6.5 Intermediate modelIntermediate models can be developed for areas where the global structural model is considered too coarsefor screening purposes. The screening model is applied as a semi-coarse model with a detail levelsomewhere between a global structural model and a refined hot spot model. This implies that the screeningmodel is not suited for obtaining absolute fatigue damage by means of hot spot methodology. However, byconsidering the relative fatigue damages based on a fixed set of S-N curves and SCF, the screening modelwill provide useful information on where potential hot spots will be located, hence, the intermediatescreening model’s primary objective is therefore to identify where refined hot spot models are required.

The intermediate screening model is in general made by use of 8-noded shell elements. A reasonablenumber of elements between longitudinal stiffeners are necessary in order to be able to assess stresses dueto out of plane bending of plate fields. It should be noted that the screening model is not refined enough torepresent the local stress effects due to the detailed geometry in terms of hot spot stress.

The mesh densities of the screening model should be developed with due consideration to the specific typeof details and area that should be further assessed. Model simplifications can be made for details and areaswhich are not considered relevant for the actual assessment. For example if the outer shell knuckle lineswere to be screened, the web of the stiffeners close to knuckle lines are typically modelled with shell

elements while the flanges are modelled using beam elements. Stiffeners located further away from theknuckle line are modelled using beam elements. Carlings (or larger manholes) are in general modelled using




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shell elements. The ship side, longitudinal bulkhead, double bottom, web frames, transverse bulkheads andstringers should all be included in the model.

In order to avoid boundary distortions, the intermediate screening models should be modelled with anoverlap of one frame spacing.

C.6.6 Structural modelling for DNV load component stochastic analysisThe cargo hold model is used to analyse the deformation response and nominal stresses of the primary hullstructural members in the midship area. The FE model shall normally include the tank or hold underconsideration, plus one half of the adjacent tank / hold at each end of the considered tank or hold, i.e. themodel extent comprises ½ + 1 + ½ holds or tanks. A model covering the half breadth of the ship may beused provided there is symmetry with respect to both the structure and the loading. A cargo hold modelwith xz-symmetry plane are shown in Figure C-14.

The fineness of the mesh used for the cargo hold/tank analysis shall be decided based on the method ofload application and type of elements used. The element mesh for the cargo hold or tank model shallrepresent the deformation response and shall be detailed enough to enable analysis of nominal stressvariations in the main framing / girder system. The following points may be used as guidance:

— A minimum of two 8-noded elements (shell or membrane elements) over the web height are necessaryin areas where stresses are to be derived. Alternatively three 4-noded elements over the web/girderheight can be used.

— In general element length is equal to ¼ of the web frame spacing but not larger than 800 mm. Thisshould ensure a reasonable representation of flexibility of the frames.

— Girder webs shall be modelled by means of shell elements in areas where stresses are to be derived.However, flanges may be modelled using beam and truss elements.

— Web and flange properties shall be modelled according to the actual geometry. The axial stiffness of thegirder is important for the global model and hence reduced efficiency of girder flanges should not betaken into account.

Figure C-14 Cargo hold model – symmetric about xz-plane

As opposed to the intermediate screening model and local hot spot models, which are run as integrated sub-

models, the loads for the cargo hold model are applied as normalized unit loads representing local loads atdifferent areas in the model. The different loads, e.g. sea loading, shall be separated into several load cases




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such that effects of local pressure at the different areas of the vessel can be combined with correct phaseinformation. Hull girder forces and moments shall be applied to the ends of the model and shall be analysedas separate load conditions. Complex summation of transfer functions shall be used to combine the globalhull girder response with the response from the local loads, ref. [C.5.6].

Different component load cases may require that different boundary conditions are applied to the model.For example, to compute the stress response due to lateral pressures the model shall be vertically andhorizontally supported by distributed springs located at the intersections of the transverse bulkheads withship sides and the longitudinal bulkheads, longitudinal girders and deck, inner bottom and outer bottom.The spring constants shall be calculated for the longitudinal bulkheads and the ship sides. Calculations shallbe based on actual bending and shear stiffness for a model length of three cargo holds. Symmetryconditions shall be applied at the model ends.

C.6.7 Local hot spot model (SCF model)For details with complex geometry and load description, it may be difficult to determine a nominal stresslevel and corresponding SCF using a model with relatively coarse and simplified geometry. Local FE analyses

may thus be used to calculate the geometric stress distribution in the region of the hot spot, such that thesestresses can be used either directly in the fatigue assessment of given details or as a basis for derivation ofSCF. The aim of the FE analysis is to calculate the stress at the weld toe (hot spot) due to the presence ofthe attachment, denoted hot spot stress, σ hot spot . The stress concentration factor due to local geometryeffect is then defined as

Thus the main objective of the FE analysis is to provide a reasonably accurate model of the geometry toprovide stresses at a region outside the weld affected zone. Therefore the model should have a fine meshfor sufficiently accurate calculation of the SCF, e.g. t × t mesh size around the hot spot region. Reference

is made to DNVGL-RP-0005 for a more detailed description of the hot spot modelling principles andmethodology. Figure C-15 shows a local hot spot model assessing longitudinal stiffener termination aroundmoonpool area.

Figure C-15 Hot spot model including several hot spot details

(C.12)nominal

σ σ ⋅= SCF spot hot




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C.6.8 Floating production storage and offloading specific structuresC.6.8.1 Topside support structures

The following effects should as a minimum be considered for modelling of topsides and supporting structurefor fatigue assessment:

— Influence of global hull bending moments and forces at the connection of the topsides to the deck.

— Impact of topsides inertia loads on stresses in longitudinal bulkheads, transverse bulkheads and webframes.

— Impact of deck deformation loads on deck and support interface structure, including:

— relative horizontal displacement between the topside modules and deck

— relative curvature of the hull on supports in a vertical plane.

— Relative displacement due to torsional deformation.

— Relative displacement due to the deformation of the cargo holds (transverse bulkheads) due to internaland external pressure.

— Friction forces from topside support arrangement; i.e. sliding and elastomeric bearing arrangement.Boundary conditions should be modelled such that they reflect the actual support arrangement.Typically these forces are included through linear elastic springs.

Refined stress analysis for the most fatigue critical supports and topside nodes should be performed basedon responses using the sub-modelling technique described in [C.6.3].

C.6.8.2 Mooring / riser foundation

The general arrangement of the mooring system determines where the mooring line loads and riser loadsare applied to the hull. Various structural elements may need to be considered, such as fairleads, chainstoppers, winches, riser porches, bend stiffeners, etc. Local structural models of these regions are requiredin order to determine the hot-spot stresses, ref. [C.6.7]. Reference is made to DNV-RP-C206 [4.6] for amore detailed description of modelling of mooring and riser foundation.

C.6.8.3 Hull / turret interface structureThe modelling principles for the hull / turret interface structure depend on turret type, turret location andthe load application. In DNV-RP-C206 [4.8] /32/ gives a description of the different modelling requirementsfor both external and internal turret designs. In DNV-RP-C206 Sec. 8 /32/ a description of the hull and turretfatigue assessment is given. This description is quite extensive including topics such as:

— turret functionality requirements including load effects and load application

— overview and structural principles of different turret designs

— management of hull / turret interface analyses

— recommended fatigue methodology for hull / turret interface structure.

C.7 Documentation and verification of analyses

C.7.1 Documentation of analysesThe analysis shall be verified in order to ensure accuracy of the results. Verification shall be documentedand enclosed with the analysis report.

The documentation shall be adequate to enable third parties (e.g. owner and the class society) to followeach step of the calculations. For this purpose, the following should, as a minimum, be documented orreferenced:

— basic input (drawings, loading manual, metocean specification, etc.)

— assumptions and simplifications made in modelling/analysis

— analysis models

— loads and load transfer— analysis methodology




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— analysis results (including quality control)

— discussion and conclusion; recommendation for further work, if relevant.

Checklists for quality assurance shall also be developed before the analysis work commences. It issuggested that project-specific checklists are defined before the start of the project and are included in the

project quality plan. These checklists will depend on the engineering practices and associated software tobe used.

C.7.2 Documentation of hydrodynamic propertiesIt is important that the hydrodynamic properties used in the analysis are properly documented. Typicalproperties to be documented are listed below and should be based on the selected probability level (10-4)for long-term analysis:

— Viscous damping level, including method for calculating additional damping

— hydrostatic properties, including:


— centre of gravity and centre of buoyancy— operational draft conditions including trim and heel angles

— water plane area

— longitudinal and transverse metacentre height

— radii of gyration

— restoring matrices

— motion reference point

— scatter diagram / sea states, wave spectrum and wave spreading applied

— sectional loads, bending moment and shear force

— accelerations with respect to topside assessment

— sea pressure and internal tank loads.

C.7.3 Verification of structural modelsAssumptions and simplifications are required for most structural models and should be listed such that theirinfluence on the results can be evaluated. Deviations in the model compared from the actual geometryaccording to drawings shall be documented.

The set of drawings on which the model is based should be referenced (drawing numbers and revisions).The modelled geometry shall be documented preferably as an extract directly from the generated model.The following input shall be reflected:

— plate thickness

— beam section properties

— material parameters— boundary conditions

— element type

— mass distribution / balance.

C.7.4 Verification of calculated loads and structural load transferInaccuracy in the load transfer from the hydrodynamic analysis to the structural model is among the mainerror sources for this type of analysis. The load transfer can be checked on the basis of the structuralresponse or on the basis of the load transfer itself.

A correct transfer of the dynamic loads can be checked by integrating the stress from the structural model,i.e. global FE-model, for a reasonable number of sections. The resulting moments and shear forces should

then be compared with the results from the hydrodynamic diffraction analysis. The load transfer for thehydrostatic response can be checked by comparing the hydrostatic hull girder response from stability




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analyses or trim and stability manual with the stresses from the global FE-model.

Figure C-16 Global bending moment along the hull; extracted from hydrodynamic and structural model

10 sections are usually sufficient in order to establish a proper description of the bending moment and shearforce distribution along the hull as indicated in Figure C-16. The first and last sections should correspondwith the ends of the FE model.

C.7.5 Quality assurance using the load component analysis methodThe following issues need to be clearly defined and understood by all involved parties as a part of the qualityassurance using the load component analysis approach:

— hydrodynamic model roll tuned for a pre-set probability level

— integration direction for all sections defined and communicated between the structural andhydrodynamic analysts

— position, number and neutral axis of sections agreed with structural analyst

— panels for external pressure defined at correct positions

— element normal on panel model.




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Figure C-17 Description of bending moments for different analyses

C.7.6 Verification of scaling factors for the DNV load component methodThere are several sources of error when using the load component based fatigue approach. It is thereforeimportant to ensure that thorough checks are completed and documented such as the scale factors and loaddesign conversion used in the analysis, see Figure C-17.

The following factors must be considered in order to establish the correct scaling factors to be used forconverting the unit load condition results into the correct magnitude for post-processing:

— units of the stress analysis results

— units of the hydrodynamic analysis results

— units necessary for entering the S-N curve calculations

— integration directions and resulting directions of moments from the hydrodynamic analysis.

When defining the sign for the scaling factors, it is imperative that the integration direction and resultingsign of the force and moment are discussed and agreed between the hydrodynamics specialist and thefatigue analyst. This is important in order to achieve correct phase relationship between the different loadcomponents and to establish correct scaling factors to convert the unit load cases into correct results duringpost-processing.

C.7.7 Verification of responseThe response should be verified at several levels to ensure that the analysis is correct. The following aspectsshould be verified as applicable for each load considered:

— global displacement patterns and magnitude

— local displacement patterns and /magnitude

— global sectional forces

— stress levels and distribution

— sub-model boundary displacements and forces— reaction forces and moments.




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C.7.7.1 Global displacement patterns/magnitude

The global action of the vessel should be verified against expected behaviour and magnitude in order toestablish the correct scaling factors to be used for converting the unit load condition results into the correctmagnitude for post-processing.

C.7.7.2 Local displacement patternsDiscontinuities in the model, such as missing connections of nodes, incorrect boundary conditions, errors inYoung’s modulus etc. may be detected on the basis of the local displacement patterns and magnitude.

C.7.7.3 Global sectional forces

Global bending moments and shear force distributions for still water loads and hydrodynamic loads shouldbe according to the loading manual and hydrodynamic load analysis respectively. Small differences willoccur and can be tolerated. Larger differences (>5% in wave bending moment) can be tolerated providedthat the source is known and compensated for in the results. Different shapes of section force diagramsbetween hydrodynamic load analysis and structural analysis indicate erroneous load transfer or massdistribution.

C.7.7.4 Stress levels and distribution

The stress pattern should be according to global sectional forces and sectional properties of the vessel,taking into account shear lag effects. Peak stress areas in particular should be checked for discontinuities,inferior element shapes or unintended fixations (4-node shell elements where one node is out of plane withthe other three nodes).

Where possible, the stress results should be checked against simple beam theory checks based on adominant load condition, e.g. deck stress due to wave bending moment (head sea) or longitudinal stiffenerstresses due to lateral pressure (beam sea).

C.7.7.5 Sub-model boundary displacements and forces

The displacement pattern and stress distribution of a sub-model should be carefully evaluated in order toverify that the forced displacements are correctly transferred to the boundaries of the sub-model. Ideallythe nominal stress level in the global and local model should be in the same order. Peak stresses at the

boundaries of the model indicate problems with the transferred displacements.C.7.7.6 Reacting forces and moments

Reacting forces and moments should be close to zero for a direct structural analysis. Large forces andmoments are normally caused by errors in the load transfer. The magnitude of the forces and momentsshould be compared to the global excitation forces on the vessel for each load case.

C.7.8 Verification of hull and turret interfaceWith two parties involved with the design of the hull and turret interface structure it is important to ensurethat the same information is used and that similar results are produced. Primarily there are two main issuesto be checked:

— hydrodynamic results

— deflections.

Since both the turret designer and the hull designer are normally performing a hydrodynamic analysis forthe hull this information should be used for verification. As a minimum the following items are to bechecked:

— accelerations at midships and turret location

— sectional forces and moments at midships and turret location

— wave drift forces

— roll damping

— mass / buoyancy and centre of buoyancy.

Deflections at the bearing level shall be compared upon completion of the FE analysis for the hull model.Any significant deviations should be corrected before the analysis is finalized.




DNV GL AS

C.7.9 Assumptions and uncertainties related to selected methodologyThe fatigue analyses procedure is prepared as an industry best practice standard for fatigue calculation ofFPSOs. Even though the presented fatigue methodology is considered to be best practise there are stillassumptions and uncertainties which are complex and rather comprehensive to assess which could

influence the calculated fatigue results:— On and offloading program – During design extreme loading conditions in terms of operational ballast

and fully loaded are established. These loading conditions are typically applied in fatigue calculationstogether with relevant intermediate condition(s) and applied relevant distribution. However, the loadingconditions and on and off loading sequence is often changed during the vessels operational life and thiswill affect the cumulative fatigue damage. This is often difficult to account for if the extent of analysesis to be kept at a reasonable level.

— Wave spreading – For wind generated seas it has been proposed to use a wave spreading of cosn(θ)where n = 4. However, sensitivity tests have shown that the fatigue life can be quite sensitive to thewave spreading. This is very dependent on detailed geometry, location and dominating load component.

— Principal stress direction – In DNVGL-RP-0005 /7/ an upgrade of the S-N curve can be done given theprincipal stress direction is oriented parallel to the weld intersection line. However, for dynamic wave

response the principal stress direction will very often depend on the phase of wave and direction, i.e.the orientation of the principal stress direction will shift when the wave are passed through. It is ratherdifficult to determine how this will affect the cumulative damage and if an upgrade of S-N curve asproposed in DNVGL-RP-0005 is applicable.

— Effect of plate bending – A reduction of hot spot stress may be considered for details with pronouncedplate bending. The effect is applicable only for details where the stress distribution under fatigue crackdevelopment is more similar to a displacement controlled situation than a load controlled condition.

— Fatigue degradation relative to workmanship - The calculated fatigue lives are based on the assumptionthat normal fabrication standard has been followed with respect to workmanship. Lower standardworkmanship will reduce the fatigue lives, while higher standards e.g. use of grinding etc. will increasethe fatigue lives, ref DNVGL-RP-0005 App.D.

— Shell versus solid model – For details with complex multi-axial stress description a solid element model

may give better representation of the local stresses at weld toe. However, development of such modelis quite time consuming and has therefore not been recommend in the current procedure.




DNV GL AS

C.8 Summary of analysis methods for floating production storageand offloading

Table C-3 Recommended analyses methods for FPSO Longitudinal Hull Structural Members

Critical structuraldetails

Example fatigue loads Analysis method Example

Butt welds

Hull girder bendingWave pressure loadsPressure loads frominternal fluidStresses due to on offloading

SCF from DNVGL-RP-0005 /7/,Full stochastic analysis

Doubler plates

Hull girder bending/shearloads and stresses due toon off loading

SCF from DNVGL-RP-0005 /7/Full stochastic analysis

Shell plating weld toframes andtransversebulkheads.

Hull girder bending /shear loadsWave pressure loadsPressure loads frominternal fluid

Full stochastic or DNV loadcomponent analyses

Longitudinals incl.bracket toes andheels

Hull girder bending /shear loadsWave pressure loadsPressure loads frominternal fluid.Relative deflection.Double side and doublebottom bending.

Full stochastic or DNV loadcomponent analyses




DNV GL AS

Rat holes anderection butt welds

Hull girder bending /shear loadsWave pressure loadsPressure loads frominternal fluid

SCF from DNVGL-RP-0005 /7/ or local SCF model.Full stochastic analysis

Table C-3 Recommended analyses methods for FPSO Longitudinal Hull Structural Members (Continued)






DNV GL AS

Deck penetrations Hull girder bending

SCF from DNVGL-RP-0005 /7/ or local SCF model.Full stochastic analysis.

Longitudinal girders / stringers

Hull girder bending /shear loads.

Wave pressure loads.Pressure loads frominternal fluid.Topside loads (girder /stringer towards maindeck).Stresses due to loading /offloading.

Full stochastic analysis.Low cycle fatigue

Structuralterminations

Hull girder bending /shear loads.Wave pressure loads.Pressure loads frominternal fluid. Full stochastic analysis

Bilge keel

Hull girder bending loads.

Wave pressure loads(drag and inertia).Pressure loads frominternal fluid. Full stochastic analysis

Table C-3 Recommended analyses methods for FPSO Longitudinal Hull Structural Members (Continued)






DNV GL AS

Table C-4 Recommended analyses methods for transverse hull structural members



Shear lugs andcut-outs

Wave pressure loads.Pressure loads frominternal fluid.Topside loads.Differential pressureloads. Full stochastic analysis

Hopper corners

Wave pressure loads.Pressure loads frominternal fluid.Differential pressureloads.

Low cycle fatigue.Full stochastic analysis.

Transverse frames

and gussets

Wave pressure loads.Pressure loads frominternal fluid.Topside loads.Differential pressure

loads.

Low cycle fatigue.

Full stochastic analysis.

Transversebulkheads

Wave pressure loads.Pressure loads frominternal fluid.Topside loads.Differential pressureloads.Sloshing loads.

Low cycle fatigue. DNVload componentanalyses.Full stochastic analysis.




DNV GL AS

Shell plating weldto longitudinals

Wave pressure loads.Pressure loads frominternal fluid.

DNV load componentanalyses.Full stochastic analysis.

Stringers

Hull girder bending /shear loads.Wave pressure loads.Pressure loads frominternal fluid.Topside loads.Stresses due toloading/offloading.

Full stochastic analysis.Low cycle fatigue

Pump sump

Hull girder bending /

shear loads.Pressure loads frominternal fluid. Full stochastic analysis.

Cross tie

Hull girder bending /shear loads.Wave pressure loads.Pressure loads frominternal fluid. Full stochastic analysis.

Butt weld

Hull girder bending /shear loads.Wave pressure loads.Pressure loads from

internal fluid.Topside loads. Full stochastic analysis.

Table C-4 Recommended analyses methods for transverse hull structural members (Continued)






DNV GL AS

Table C-5 Recommended analyses methods for FPSO specific members/details

Criticalstructuraldetails


Topsides modulesupports

Topside inertia loads.Variation of side shellpressure loadsDeck deformationloads Full stochastic analysis

Flare tower /flare tower

foundation

Inertia loads.Wind loads.Deck deformation

loads.

Full stochastic analysis,including wave and windactions.Combination of wave andwind according to DNV-OS-

E301 or DNVGL-RP-0005.

Riser porchesRiser loads.Hull deformation loads.

Full stochastic for wave loadsSimplified for riser loads




DNV GL AS

Fairlead /mooringfoundations

Mooring loads (Wave

frequent and Lowfrequent response).

Hull deformation loads.

Full stochastic analysis

Combination of Wavefrequent and Low frequentresponse according to DNV-OS-E301 or DNVGL-RP-0005.

Crane pedestalsCrane boom rest

Hull girder bending

loads.Variation of side shellpressure loads.Crane inertia loads.Crane loads.

Full stochastic analysis waveloads.Simplified analysis craneloads.Linear summation of damage.

Hull / turretinterface

Hull girder bendingloads.Variation of side shellpressure loads.Deck deformationloads.Riser loads.Mooring loads.Inertia loads.Temperature loads.

Full stochastic.See separate discussion

Turret

Hull girder bendingloads.Variation of side shellpressure loads.Riser loads.Mooring loads.Inertia loads.Temperature loads.

Full stochastic.See DNV-RP-C206 /32/

Table C-5 Recommended analyses methods for FPSO specific members/details (Continued)

Criticalstructuraldetails





DNV GL AS

APPENDIX D BACKGROUND AND COMMENTARY

D.1 Introduction

D.1.1 PurposeThe purpose of this appendix is to provide some additional background for the probabilistic methods forplanning inspection for fatigue cracks in offshore structures, given in the main part of the document.

D.1.2 ContentIt is assumed that a calculation of probability of a fatigue crack is based initially on S-N data. Such analysesare considered reliable if there are relevant test data and S-N curves for the considered detail and loadingcondition. If there are not relevant test data, one may consider performing additional fatigue testing. Analternative may be to use the notch stress approach presented in DNVGL-RP-0005 App.D for calculation ofS-N curves. Another alternative is to use fracture mechanics for crack growth analysis.

Fracture mechanics is also required for calculation of crack growth such that the PoD curves can be used toassess the effect of in-service inspections.

[D.2] presents geometry functions to be used for crack growth analysis of welded and grinded weld toes inplated structures.

There are many data required for performing a fracture mechanics analysis. For this reason it has beenrecommended to perform a calibration of the fracture mechanics to that of fatigue test data (or S-N data).This can represent a significant amount of work. Therefore, it has been suggested to perform this calibrationonce and then follow the procedure from this calibration. This requires that the fracture mechanics modelpresented in [D.6] is followed. It also implies that the initial crack size distribution derived from calibrationin [D.6] is used for the crack growth analysis in actual projects where probabilistic methods are being used.

The critical crack size at different details is considered in [D.3].

[D.4] provides some background for input parameters to the probabilistic fatigue analysis.

[D.5] gives some more background on input parameters to the probabilistic analysis with respect to loadingand SCFs.

A calibration of fracture mechanics to S-N data is presented in [D.6].

D.2 Geometry function for weld toes at cruciform joints

D.2.1 Health and safety executive (UK) report 2000/077Reference is made to HSE report 2000/077 which presents geometry function for cracks at weld toesgrowing through plates, ref. Figure D-1. Three-dimensional FE analyses were used to establish a databasefor different geometries and crack sizes (altogether 2038 analyses). Geometry functions were derived fromthis database. These geometry functions are included in the following section. These geometry functions

were also used as basis for the geometry functions for as-welded connections in BS 7910. The HSE reportincludes also geometry functions for ground welds which are included in this appendix as these are notincluded in BS 7910.




DNV GL AS

Figure D-1 Geometry analysed (HSE report 2000/077)

It should also be noted that the nature of the FE model used to calculate M k is such that the solutionsproduced are not applicable for z = 0, and near surface M k values should be used (z = 0.15 mm BS 7910)for the intersection of surface flaws with the weld toe and through-thickness flaws at weld toes.

M k for the deepest crack point in an as-welded joint subjected to membrane loading:

where

Table D-1 Validity range

as-welded joints use when the weld toe is “as-welded” or when it has been ground to a toe radius ofless than 10% of the main plate thickness T, i. e. 0.0 ≤ r/T<0.1

ground weld toe equations use when the weld toe has been ground to a toe radius of greater than 10% of themain plate thickness T, i. e. 0.1 ≤ r/T

crack depth ratio 0.125 ≤ a <T

crack aspect ratio 0.1≤ a/c ≤ 1.0

weld angle* 30o≤q≤60o

weld footprint 0.5≤L/T≤2.75

notes 1) the equations assume the weld angle in radians

2) The equations should not be used outside of their validity limits. If a validity limitis reached, the extreme value of the range should be used, e. g. if L/T = 3.0 thenL/T = 2.75 should be used.

*It has been verified that the Mk function can also be used for q = 15o. This weld angle is relevant for assessment ofbutt welds classified as D according to DNVGL-RP-0005.

(D.1)

+

+

=

T

L

T

a f

T

a f

c

a

T

a f M kma ,,,, 321 θ θ




DNV GL AS

4

050966.0

1 exp93163.043358.0,

3

21

AT

a

T

a

c

a

T

a f

A

T

a A A

+

+

=

−

+

6511.437571.067090.046190.0

2788.187238.0

3218.1

3409.115657.00343.1

23

4

3

61153.0

2

2

1

+

−

+

−=

+

−=

=

+

−

−=

−

ca

ca

ca A

c

a A

c

a A

c

a

c

a A

−

+

−=

T

a A

T

a A

T

a A

T

a f

10740.0

752

6

1,θ

8143.200027743.0

23.17624183.0

72368.064771.000038737.0

7

6

2

5

+−=

+=

−+−=

θ

θ

θ θ

A

A

A

( )

+

+

+

+

=

++

1615

2

141283

1311102

9

,, AT

a A

T

a A

T

a A

T

a A

T

L

T

a f

A A A A θ θ

θ




DNV GL AS

An example of M k function for membrane loading for L/T = 1.25 and θ = 45o is shown for crack depth inFigure D-2.

Figure D-2 M k as function of crack depth at deepest point for membrane loading

M k for the deepest crack point in an as-welded joint subjected to bending loading:

218.1112551.0027338.0

068225.097857.020188.0

41496.093311.020136.0

13798.021863.012914.0

8975.1025447.0051554.0

23124.0023369.00015061.0

00024554.035584.016489.0028378.0

023400.013667.0060159.0010766.0

38417.00084862.0082502.0

2

16

2

15

2

14

2

13

2

12

2

11

23

10

23

9

2

8

−

+

−=

+

−

=

−

+

−=

++−=

++=

−

+

−=

−

−

+

−=

−

+

−

=

++−=

T

L

T

L A

T

L

T

L A

T

L

T

L A

A

A

T

L

T

L A

T

L

T

L

T

L A

T

L

T

L

T

L A

A

θ θ

θ θ

θ θ




DNV GL AS

If 0.005 ≤ a/T ≤ 0.5, then:

where

(D.2)

+

+

=

T

L

T

a f

T

a f

c

a

T

a f M bak ,,,, 321 θ θ

4

10364.0

1 exp52086.0065916.0,

3

21

AT

a

T

a

c

a

T

a f

A

T

a A A

+

+

=

−

+

89887.037198.058706.028783.0

4744.100013242.0

61775.0

23851.0021401.0014992.0

23

4

3

0278.1

2

2

1

−

−

+

−=

−

=

=

−

−

−=

−

c

a

c

a

c

a A

c

a A

c

a A

c

a

c

a A

86

752 1,

A A

T

a A

T

a A

T

a f

+

−=

θ

51662.0468.12195.17

081012.016780.0047620.0

0036148.0459.15124.15

059156.019007.011052.0

2

8

2

7

2

6

2

5

−

+

−=

−+−=

−+−=

+−=

T

a

T

a A

A

A

A

θ θ

θ θ

θ θ

( )

+

+

+

+

=

++

1716

2

151393

1412112

10

,, AT

a A

T

a A

T

a A

T

a A

T

L

T

a f

A A A A θ θ

θ




DNV GL AS

Else if 0.5<a/T <1.0, then

An example of M k function for bending loading for L/T = 1.25 and θ = 45o is shown for various crack depthsin Figure D-3. In this figure the proposed procedure is not strictly followed for a/T larger than 0.5. A lower

limit of M kba may seem logic; however, it might also be less than 1.0 based on how the results for this factorare derived. However, the consequence of this is probable minor as most of the fatigue life most often isspent for small crack depths. A similar comment may also be given to Figure D-7 and [D.2.2].

Figure D-3 M k as function of crack depth at deepest point for bending loading

0089846.00025074.00014701.0

6611.13599.131288.0

7535.13975.135848.0

57647.03345.143912.0

90380.04489.161998.0

36546.028669.0034436.0

0022170.08188.154052.0065232.0

072404.055052.0014872.0013885.0

2008.18264.175722.0

2

17

2

16

2

15

2

14

2

13

2

12

23

11

23

10

2

9

−

−

−=

+

−

=

−

+

−=

+−=

−+−=

+

+

−=

−

−

+

−=

−

+

−

−=

+−=

T

L

T

L A

T

L

T

L A

T

L

T

L A

A

A

T

L

T

L A

T

L

T

L

T

L A

T

L

T

L

T

L A

A

θ θ

θ θ

θ θ

0.1=kba M




DNV GL AS

M k for crack ends in an as-welded joint subjected to membrane loading:

where

(D.3)

=

T

L

c

a

T

a f

c

a

T

a f

T

L

a

c

T

a f M kmc ,,,,,,, 321 θ θ

+

+

+

+

−+

=

87

2

643

2

2

1,, 511

Aa

c A

a

c A A

a

c A

a

c A

T

a A

T

a A

T

L

a

c

T

a f

25064.0033399.00071654.0

011400.00013595.000049192.0

00047844.000013651.0000054546.0

8508.1070664.00078157.0

2

4

2

3

2

2

2

1

−

−

=

+

−

=

−

+

−=

+

−

=

T

L

T

L A

T

L

T

L A

T

L

T

L A

a

c

a

c A

4954.168935.032380.0045206.0

13967.0010944.00031615.0

016479.00090620.00016713.0

7644.124311.0018640.0

23

8

2

7

2

6

2

5

+

−

+

−=

+

−

−=

−

+

−=

−

+

−=

T

L

T

L

T

L A

T

L

T

L A

T

L

T

L A

a

c

a

c A

1412

1,, 131110

2

92

A A

T

a A

T

a A

c

a A

c

a A

c

a

T

a f

−+

+

+

=

θ




DNV GL AS

An example of M k function for membrane loading for L/T = 1.25 and θ = 45o is shown for crack ends inFigure D-4.

903.64741.15423.37

22760.072927.011458.0

0021892.040928.025473.0

25959.02642.264023.0

50434.00013244.024523.0

38250.00029155.015209.0

2

14

2

13

2

12

2

11

2

10

2

9

+

−

=

−+−=

+

+

−=

++−=

++−=

−+=

c

a

c

a A

A

c

a

c

a A

A

A

A

θ θ

θ θ

θ θ

θ θ

[ ] [ ]

[ ]

+++

++=

++ 2423

22218

exp,,, 2120

2

191716

2

153

A A A A

T

a

A A AT

a

A A AT

L

c

a

T

a

f

θ θ

θ θ θ θ θ

14184.016138.0041574.0

1650.35008.48225.1

9885.138632.041373.010553.0

0641.13069.134950.0

18189.051648.014475.0

2

19

2

18

23

17

2

16

2

15

+

−

=

+−=

−

−

+

−=

+

−

=

−

+

−=

T

L

T

L A

A

T

L

T

L

T

L A

T

L

T

L A

T

L

T

L A

θ θ

6646.213902.0052530.0

0124.427816.0088591.0

6277.112171.0046138.0

97585.023516.019694.0043891.0

58821.039688.0098912.0

2

24

2

23

2

22

23

21

2

20

+

−

−=

−

+

=

+

−

−=

+

+

−

=

−

+

−=

c

a

c

a A

c

a

c

a A

c

a

c

a A

T

L

T

L

T

L A

T

L

T

L A




DNV GL AS

Figure D-4 M k as function of crack depth at crack ends for membrane loading

M k for crack ends in an as-welded joint subjected to bending loading:

where

(D.4)

= T

L

c

a

T

a

f c

a

T

a

f T

L

a

c

T

a

f M kbc ,,,,,,, 321 θ θ

9511

87

2

643

2

2

1,, AT

a A

T

a A

T

L

a

c

T

a f

Aa

c A

a

c A A

a

c A

a

c A

+

−+

=

+

+

+

+

014251.00013715.000039951.0

00086706.000014425.0000044010.0

5985.400037156.00023232.0

2

3

2

2

2

1

+

−

=

−

+

−=

+

−

=

T

L

T

L A

T

L

T

L A

a

c

a

c A




DNV GL AS

099981.04680.22144.127798.0

2302.116086.0082625.0011911.0

026862.00023212.00038508.0

00014693.00025078.000037981.0

4253.527810.0018524.0

16335.0017917.00046169.0

23

9

23

8

2

7

2

6

2

5

2

4

+ −

− =

+

−

+

−=

−

+

−=

+

+

−=

−

+

−=

−

−

=

T a

T a

T a A

T

L

T

L

T

L A

T

L

T

L A

T

L

T

L A

ac

ac A

T

L

T

L A

1513

1,, 141211

2

102

A A

T

a A

T

a A

c

a A

c

a A

c

a

T

a f

−+

+

+

=

θ

011759.039566.025922.0

047444.05895.260938.0

53196.00013671.020321.0

43562.00030652.013481.0

2

13

212

2

11

2

10

+

+

−=

++−=

++−=

−+=

c

a

c

a A

A

A

A

θ θ

θ θ

θ θ

053.37787.555974.6

38510.077317.0044960.0

2

15

2

14

+

+

=

−+=

c

a

c

a A

A θ θ

[ ] [ ][ ]

+++

++=

++ 2524

22319

exp,,, 2221

2

201817

2

163

A A A A

T

a A A A

T

a A A A

T

L

c

a

T

a f

θ θ

θ θ θ θ θ

1602.68563.90991.4

7198.122309.063093.014895.0

1470.14093.227882.0

12828.00308.1056177.0

2

19

23

18

2

17

2

16

+−=

−

−

+

−=

+

−

=

−

+

−=

θ θ A

T

L

T

L

T

L A

T

L

T

L A

T

L

T

L A




DNV GL AS

An example of M k function for bending loading for L/T = 1.25 and θ = 45o is shown for crack ends in FigureD-5.

Figure D-5 M k as function of crack depth at crack ends for bending loading

M k for ground weld toe

M k for crack deepest point of the crack subjected to membrane loading:

(D.5)

7495.514136.0050827.0

4136.927561.0085182.0

8961.311094.0047837.0

0546.116739.026741.0055459.0

77817.067499.0021387.0

14737.025288.0028513.0

2

25

2

24

2

23

23

22

2

21

2

20

+

−

−=

−

+

=

+

−

−=

+

+

−

=

−

+

−=

+

−

−=

ca

ca A

c

a

c

a A

c

a

c

a A

T

L

T

L

T

L A

T L

T L A

T

L

T

L A

( ) ( )θ 321 ,, f

T

L

T

a f

c

a

T

a f g M mak

=




DNV GL AS

where

An example of M k function for membrane loading for L/T = 1.25 and θ = 45o is shown for various crackdepths in Figure D-6.

+

+

−+

=

65311

42

1, A

T

a A

T

a A

T

a A

c

a

T

a f

A A

0351.176603.065009.0

86071.041009.022457.0

7356.79931.82172.3

2

3

2

2

2

1

+

−

=

+

−

−=

−

+

−=

c

a

c

a A

c

a

c

a A

c

a

c

a A

557.30039.1110745.02

4 +

−

=c

a

c

a A

3341.223884.033693.0

4916.91510.72494.1

2

6

2

5

+

+

=

+

−

=

c

a

c

a A

c

a

c

a A

108

1, 972

A A

T a A

T a A

T L

T a f

−+

=

0362.12995.129651.0

31065.0026458.0015584.0

19344.022280.0098096.0

23244.00066388.00021981.0

2

10

2

9

2

8

2

7

+

+

−=

+

+

=

+

−

=

+

+

−=

T

L

T

L A

T

L

T

L A

T

L

T

L A

T

L

T

L A

( ) 0.13 =θ f




DNV GL AS

Figure D-6 M k as function of crack depth at deepest point for membrane loading

M k for crack deepest point subjected to bending loading:

If 0.005 ≤ a/T ≤ 0.5, then

where

(D.6)( ) ( )θ 321 ,, f T

L

T

a f c

a

T

a f g M bak

=

+

+

−+

=

65311

42

1, AT

a A

T

a A

T

a A

c

a

T

a f

A A




DNV GL AS

Else if 0.5<a/T<1.0, then

An example of M k function for bending loading for L/T = 1.25 and θ = 45o is shown for various crack depthsin Figure D-7.

7718.59129.54851.3

0448.5877.54456.43

732.2221875.09459.2

9184.40652.69209.3

60176.047958.051457.0

4952.8626.60856.45

2

6

2

5

2

4

2

3

2

2

2

1

+

+

−=

−

+

−=

+

+

=

+

−

=

+

+

−=

+

−

=

c

a

c

a A

c

a

c

a A

c

a

c

a A

c

a

c

a A

ca

ca A

c

a

c

a A

108

1, 972

A A

T

a A

T

a A

T

L

T

a f

−+

=

1298.18378.387465.0

052756.0019043.00028790.0

026591.0044638.0037163.0

069432.0021490.00060502.0

2

10

2

9

2

8

2

7

−

+

−=

+

+

=

+

−

=

+

+

−=

T

L

T

L A

T

L

T

L A

T

L

T

L A

T

L

T

L A

( ) 0.13 =θ f

( ) 0.1=bak g M




DNV GL AS

Figure D-7 M k as function of crack depth at deepest point for bending loading

M k for crack end point subjected to membrane loading:

where

(D.7)( ) ( )θ 321 ,,, f

T

L

c

a

T

a f

a

c

T

a f g M mck

=

+

+

−+

=

65311

42

1, AT

a A

T

a A

T

a A

a

c

T

a f

A A

18232.0036501.00028700.0

632.240656.1028842.0

2

2

2

1

+

−

=

+

−

=

ac

ac A

a

c

a

c A




DNV GL AS

An example of M k function for membrane loading for L/T = 1.25 and θ = 45o is shown for crack ends inFigure D-8.

7623.757762.0016883.0

3387.254495.0035640.0

572.114014.78860.1

9199.79413.224850.0

2

6

2

5

2

4

2

3

−

+

=

−

−

=

+

−

=

+

−

=

a

c

a

c A

a

c

a

c A

ac

ac A

a

c

a

c A

1210

1,, 1198

2

72

A A

T

a A

T

a A

c

a A

c

a A

T

L

c

a

T

a f

−+

+

+

=

4032.5570.19693.25

043132.0067165.0021264.0

17469.0012290.00081421.0

093071.0014780.00038516.0

018504.0033387.00052426.0

0068564.0022235.00030300.0

2

12

2

11

2

10

2

9

2

8

2

7

+

−

=

−

+

−=

−

+

−=

+

+

−=

−

−

=

+

+

−=

T

L

T

L A

T

L

T

L A

T

L

T

L A

T

L

T

L A

T

L

T

L A

T

L

T

L A

( ) 0.13 =θ f




DNV GL AS

Figure D-8 M k as function of crack depth at crack ends for membrane loading

M k for crack end points subjected to bending loading:

where

(D.8)( ) ( )θ 321 ,,, f

T

L

c

a

T

a f

a

c

T

a f g M bck

=

+

+

−+

=

65311

42

1, AT

a A

T

a A

T

a A

a

c

T

a f

A A

8688.78643.222388.0

46051.012466.0013058.0

425.270236.443193.0

2

3

2

2

2

1

+

−

=

+

−

=

+

−

=

a

c

a

c A

a

c

a

c A

a

c

a

c A




DNV GL AS

An example of M k function for bending loading for L/T = 1.25 and θ = 45o is shown for crack ends in FigureD-9.

6913.540816.0038190.0

0179.96620.346115.0

2955.584291.019132.0

2

6

2

5

2

4

−

+

=

−

+

−=

+

−

=

a

c

a

c A

ac

ac A

a

c

a

c A

1210

1,, 1198

2

72

A A

T

a A

T

a A

c

a A

c

a A

T

L

c

a

T

a f

−+

+

+

=

169.42680.64952.52

0047289.010623.010998.0

31959.00036876.00056783.0

076791.0015240.00038941.0

022686.0031258.00045215.0

018110.0022350.00028759.0

2

12

2

11

2

10

2

9

2

8

2

7

−

+

=

+

−

=

−

+

−=

+

+

−=

+

−

=

−

+

−=

T

L

T

L A

T

L

T

L A

T

L

T

L A

T

L

T

L A

T

L

T

L A

T

L

T

L A

( ) 0.13 =θ f




DNV GL AS

Figure D-9 M k as function of crack depth at crack ends for bending loading

D.2.2 BS 7910 Guidance on Methods for Assessing the Acceptability ofFlaws in Fusion Welded StructuresThe M k factors in BS 7910 are based on HSE report 2000/077 by putting θ = 45o. However, there are anumber of printing errors in BS 7910 (2005). There is an addition to BS 7910 from 2007 where the errors

have been removed. The equations are also presented in the following. They are only presented in BS 7910for the as-welded condition. For ground welds the M k factors in [D.2.1] can be used.

Deepest crack points

M k for the deepest crack point in an as-welded joint subjected to membrane loading:

where

(D.9)

+

+

=

T

L

T

a f

T

a f

c

a

T

a f M kma ,, 321

4

050966.0

1 exp93163.043358.0,

3

21

g T

a

T

a

c

a

T

a f

g

T

a g g

+

+

=

−

+




DNV GL AS

In BS 7910 it is stated that if equation (D.9) gives a value of M k <1.0 assume M k = 1.0. This statement maybe questioned as explained in the text related to Figure D-3.

M k for the deepest crack point in an as-welded joint subjected to bending loading:

If 0.005≤a/T≤0.5, then

where

(D.10)

6511.437571.067090.046190.0

2788.187238.0

3218.1

3409.115657.00343.1

23

4

3

61153.0

2

2

1

+

−

+

−=

+

−=

=

+

−

−=

−

c

a

c

a

c

a g

c

a g

ca g

c

a

c

a g

−

+

−−=

T

a

T

a

T

a

T

a

f

10740.04199.176

2 8141.2121521.0

( )

+

+

+

+

=

87

2

6

23003.0

3 9493.133994.0,5

g T

a g

T

a g

T

a

T

a

T

L

T

a f

g

218.1112551.0027338.0

068225.097857.020188.0

41496.093311.020136.0

24587.017180.0090887.0015647.0

2

8

2

7

2

6

23

5

−

+

−=

+

−

=

−

+

−=

−

−

+

−=

T

L

T

L g

T

L

T

L g

T L

T L g

T

L

T

L

T

L g

+

+

=

T

L

T

a f

T

a f

c

a

T

a f M kba ,, 321

4

10364.0

1 exp52086.0065916.0,

3

21

g T

a

T

a

c

a

T

a

f

g

T

a g g

+

+

=

−

+




DNV GL AS

In BS 7910 it is stated that if equation (D.10) gives a value of M k <1.0 assume M k = 1.0. This statementmay be questioned as explained in the text related to Figure D-3.

M k for crack ends in an as-welded joint subjected to membrane loading:

Surface point

where

(D.11)

89887.037198.058706.028783.0

4744.100013242.0

61775.0

23851.0021401.0014992.0

23

4

3

0278.1

2

2

1

−

−

+

−=

−

=

=

−

−

−=

−

c

a

c

a

c

a g

c

a g

ca g

c

a

c

a g

5

021403.0102195.0

8113.2

2

g

T

a

T

a

T

a f

+

−−=

51662.0468.12195.17

2

5 −

+

−=

T

a

T

a g

( )

+

+

+

−

=

−

98

2

7

20077.0

3 14827.023344.0,6

g T

a g

T

a g

T

a

T

a

T

L

T

a f

g

0089846.00025074.0001470.0

6611.13599.131288.0

7535.13975.135848.0

31905.080220.038091.005980.0

2

9

2

8

2

7

23

6

−

−

−=

+

−

=

−

+

−=

+

−

+

−=

T

L

T

L g

T

L

T

L g

T

L

T

L g

T L

T L

T L g

=

T

L

c

a

T

a f

c

a

T

a f

T

L

a

c

T

a f M kmc ,,,,, 321




DNV GL AS

+

+

+

+

−+

=

87

2

643

2

2

1,, 511

g a

c g

a

c g g

a

c g

a

c g

T

a g

T

a g

T

L

a

c

T

a f

4954.168935.032380.0045206.0

13967.0010944.00031615.0

016479.00090620.00016713.0

7644.124311.0018640.0

25064.0033399.00071654.0

011400.00013595.000049192.0

00047844.000013651.0000054546.0

8508.1070664.00078157.0

23

8

2

7

2

6

2

5

2

4

2

3

2

2

2

1

+

−

+

−=

+

−

−=

−

+

−=

−

+

−=

−

−

=

+

−

=

−

+

−=

+

−

=

T

L

T

L

T

L g

T

L

T

L g

T

L

T

L g

a

c

a

c g

T

L

T

L g

T

L

T

L g

T

L

T

L g

a

c

a

c g

109

127449.06430.135411.028639.0,

2

2

g g

T

a

T

a

c

a

c

a

c

a

T

a f

−+

+

+

−=

903.64741.15423.37

0021892.040928.025473.0

2

10

2

9

+

−

=

+

+

−=

c

a

c

a

g

c

a

c

a g

+

=

13

exp,, 12

75429.0

113

g

T

a g

T

a g

T

L

c

a

T

a f




DNV GL AS

M k for crack ends in an as-welded joint subjected to bending loading:

where

(D.12)

51732.0004370.0011411.0

60136.044732.024898.0043891.0

2650.10942.159894.010553.0

2

13

23

12

23

11

+

+

−=

+

+

−

=

−

−

+

−=

c

a

c

a g

T L

T L

T L g

T

L

T

L

T

L g

=

T

L

c

a

T

a f

c

a

T

a f

T

L

a

c

T

a f M kbc ,,,,, 321

9511

87

2

643

2

2

1,, g T

a g

T

a g

T

L

a

c

T

a f

g a

c g

a

c g g

a

c g

a

c g

+

−+

=

+

+

+

+

2302.116086.0082625.0011911.0

026862.00023212.00038508.0

00014693.00025078.000037981.0

4253.527810.0018524.0

16335.0017917.00046169.0

014251.00013715.000039951.0

00086706.000014425.0000044010.0

5985.400037156.00023232.0

23

8

2

7

2

6

2

5

2

4

2

3

2

2

2

1

+

−

+

−=

−

+

−=

+

+

−=

−

+

−=

−

−

=

+

−

=

−

+

−=

+

−

=

T

L

T

L

T

L g

T

L

T

L g

T

L

T

L g

a

c

a

c g

T

L

T

L g

T

L

T

L g

T

L

T

L g

a

c

a

c g

099981.04680.22144.127798.0

23

9 +

−

−

=

T

a

T

a

T

a g




DNV GL AS

D.3 Critical crack size and failure criterion in S-N curve andcriticality of actual details

D.3.1 Jacket structuresD.3.1.1 Simple tubular joints

Effect of cracks in tubular joints on ultimate capacity has been assessed in literature, see reference list. Themain findings from this work have also been included in BS 7910; reference is made to section B.5.5.3.2.The plastic collapse load has been presented as a reduction factor due to the crack size on the ultimatecapacity of the joint.

The braces in T- and Y- type joints do normally not transfer large axial loads due to the transverse flexibilityof the chord. Thus fatigue cracks resulting from bending moment in braces are expected to grow throughthe thickness and still the brace-to-chord connection can transfer so much axial load that the probability ofa failure, given a fatigue crack through the thickness at the hot spot, is small.

T-joints are typically used in conductor frames that are subjected to significant out of plane loading. Here,the cracks in chord members can be longer than through the thickness before the bending capacity is fullylost as some load shedding will also occur during crack growth. An example of fatigue crack growth duringout of plane bending moment in laboratory testing is shown in Figure D-10 and Figure D-11.

For this type of loading a significant crack growth can occur after crack growth through the thickness suchthat FMD can be used for detection for fatigue cracks.

The residual capacity of cracked joints can be assessed based on a reduction factor that accounts forcracked area as shown in Figure D-12.

1110

124988.07053.140768.035006.0,

2

2

g g

T

a

T

a

c

a

c

a

c

a

T

a f

−+

+

+

−=

053.37787.555974.6

011759.039566.025922.0

2

11

2

10

+

+

=

+

+

−=

c

a

c

a g

c

a

c

a g

+

=

14

exp,, 13

94761.0

123

g

T

a g

T

a g

T

L

c

a

T

a f

75939.00066702.001343.0

53433.054154.030180.0055459.0

89808.04795.181526.014895.0

2

14

23

13

23

12

+

−

−=

+

+

−

=

−

−

+

−=

c

a

c

a g

T

L

T

L

T

L g

T

L

T

L

T

L g




DNV GL AS

Figure D-10 Crack development in a T joint with a chord diameter of 457mm under out-of-plane loading(laboratory test)

Figure D-11 Crack development in an overlap K joint under out-of-plane loading (laboratory test)




DNV GL AS

Figure D-12 Normalised ultimate static strength capacity using HSE equations for characteristic strength oftubular joints

D.3.1.2 Simple butt welds

Simple butt welds in tubulars subjected to cyclic axial load shows a rather short fatigue life after a fatiguecrack has grown through most of the thickness.

In general crack growth may be most critical for connections with a low stress concentration and a lowfatigue life that does not show significant possibility for redistribution of stresses during crack growth.

For weld improved butt welds subjected to high tensile loading also the possibility of crack growth frominternal defects should be kept in mind.

D.3.2 SemisubmersiblesFor simple butt welds in semisubmersibles there is a rather short fatigue life after a fatigue crack has grownthrough the thickness. However, this depends also on type of loading.

In general crack growth may be most critical for connections showing a low stress concentration and thatdoes not show significant possibility for redistribution of stresses during crack growth.

Normally there is significant time between a through thickness crack growth before the connection isconsidered to be critical with respect to capacity.

A first estimate of residual capacity can be based on gross yielding of the member with the cracked areaincluded in the analysis model.

D.3.3 Floating production vesselsIn general crack growth may be most critical for connections showing a low stress concentration that doesnot show significant possibility for redistribution of stresses during crack growth.

For FPSOs, however, there is normally significant time between a crack is grown through the thicknessbefore the connection is considered to be critical with respect to capacity. Such details can be:

— transverse butt welds in the main deck or in the bottom and bilge— attachments and penetrations in main deck




DNV GL AS

The above details are to a large degree exposed to global stresses only. Details exposed to local loads or acombination of local and global loads are normally considered less critical since the loads might beredistributed during crack growth. Local loads may imply plate bending where it is a larger possibility forredistribution of load than for membrane loading; ref. DNVGL-RP-0005 [4.3.6].

For details with low redundancy the time before a through thickness crack becomes critical can be short.Examples of such details are:

— transverse butt welds in flare towers

— transverse butt welds in crane pedestals

— transverse fillet or butt welds in way of the moon pool

— transverse butt weld at thickness transitions in deck and bottom of FPSOs.

D.4 Probabilistic fatigue analysis

D.4.1 System reliability method

D.4.1.1 Purpose of section

Design standards require robustness and capacity in the damaged condition (ALS). This has an effect alsoon requirements to inspection for fatigue cracks as a fatigue crack at a hot spot should normally not leadto a catastrophic failure. If a potential fatigue crack can lead to a catastrophic failure, it should be designedwith a large Design Fatigue Factor; ref. NORSOK N-001. The degree of robustness or redundancy is aparameter that influences requirement to Design Fatigue Factor at the design stage. This also indicates thatthe robustness or redundancy is a significant parameter for planning requirement to in-service inspection.

To assess the consequence of a fatigue crack it is necessary to assess the probability of a further progressivecollapse given the presence of a fatigue crack at a considered location. The probability of a further collapsemay also be denoted as probability of system collapse. The probability of a collapse is an important measurewhen assessing requirement to target reliability.

Thus, the purpose of this section is to describe methods for assessing the probability of a further collapsegiven that there is fatigue crack at a considered hot spot.

D.4.1.2 Assessment of collapse capacity in jacket structures

The structural behaviour near a total collapse failure can be very complex and expensive to fully assess bycomputer analysis. This complexity can be due to the non-linear mechanical behaviour of the structure andthe applied loading and load distribution near failure. The structural behaviour beyond the first member-failure depends not only on the degree of static indeterminacy, but also on the ability of the structure toredistribute the load and on the post-failure behaviour, e.g. the ductility of the individual members and joints.

For jacket structures, collapse is generally load driven; and the variability in the loads is greater than theuncertainties in the collapse capacity.

Simulation studies of jacket structures show that the ultimate structural capacity, or collapse capacity, canbe related directly to the total base-shear force. Also the load pattern has minor effect on the collapsecapacity calculated in a push-over analysis.

A complete reliability analysis of a real multi-leg jacket structure with respect to structural collapse is verycomplicated, and simplifications (approximations) are required. [D.4.1.3] describes a simplifiedmethodology for calculation of the probability of collapse as function of the reserve strength ratio (RSR),which is defined as the ratio between the load carrying capacity and the corresponding load effect, e.g.extreme load effect with known return period. The estimated collapse probability obtained by this simplifiedapproach has been compared to results from more advance models showing acceptable agreement.

D.4.1.3 Simplified method for estimation of probability of system failure

A fatigue crack in a structure does not necessarily imply a significant risk of a collapse of that structure. The

probability of a collapse can be formulated as a probability of a fatigue crack failure times the probability ofa collapse given that there is a fatigue crack present in the structure, PSYS. The calculated resulting




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probability should be lower than a target value Pt:

Some different refinements of this methodology have been presented in literature.

A simplified method for determining PSYS has been used for inspection planning using probabilistic methodssince the 1980ties. For jacket structures a methodology of removing one member has been used to assessthe residual capacity. From this a safety index can be estimated as

where

= Capacity assessed from the analysis of the structure with the considered element removed from theanalysis model

= Load on the structure for the considered environment and return period

= Coefficient of variation for capacity

= Coefficient of variation for load

Ψ = factor accounting for modelling error

It is normal practice to assume input values to this equation to the safe side. Still a rather large PSYS canbe calculated from PSYS = Φ (- β ). It should be noted the calculated probability shown here is related to theprobability level used in the load calculation. Thus, if β is derived based on a 100 year loading, the calculatedPSYS should be multiplied by 10-2 for estimation of annual probability of failure.The following values may be used if not other values are documented:

Proposed value for coefficient of variation for capacity: = 0.10.

Proposed value for coefficients of variation for load: = 0.30.

The uncertainty in a maximum load resulting in structure collapse is considered to be larger than in longterm fatigue loading.

This way of calculating system reliability may be interpreted as system analysis considering failure path witha full correlation with respect to resistance of the remaining elements.

The methodology used here should be seen together with requirements to target safety level of thestructures as this requires that only few fatigue cracks are present in members that are significant for the

integrity.

D.4.2 Effect of correlationD.4.2.1 Definition of correlation

By correlation is understood similarity in parameters involved in a fatigue analysis for different hot spots.For example a full correlation in hot spot stress for two similar details means that the probability of a stressrange in one detail is the same as for the other detail. Reference is made to text books in statistics for amathematical description of correlation.

A proper inclusion of correlation in a standard for probabilistic methods for planning inspection for fatiguecracks is considered difficult based on today’s knowledge. The purpose of this section is more to indicatethat there may be significant effect of correlation if there are similar hot spots in the structure (geometry,

fabrication and loading) and that this should be assessed by engineering judgement if analysis advisesextensive inspection of these hot spots. The effect of correlation should also be remembered if fatigue

(D.13)

(D.14)

t SYS F P P P ≤

22

ln

SYS SYS

SYS

SYS

S R

S

R

V V

Q

Q

+

=

ψ

β

SYS RQ

SYS S Q

SYS RV

SYS S V

SYS RV

SYS RV




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cracks are detected; ref. [D.4.3].

When information from inspection of one detail can be utilized to update the prediction of failure of otherdetails, this means that failure probability (or failure rate) of these details are correlated. Such correlationis typically due to the fact that input parameters going in to the different limit states for the details are the

same or has correlated properties. For example the correlation coefficient between two Normal distributedvariables X and Y are defined by:

If the ρ xy = 0.0, the variables X and Y are un-correlated and if the ρ xy = 1.0, the variables X and Y are fullycorrelated.

Two different components Cx and Cy where X and Y are input variables in limit state for components Cx andCy respectively are considered. In the case where uncertainties in X and Y are important for the predictionof the failure probabilities Cx and Cy, and provided there is a correlation between the two components, the

inspection of component Cx may lead to updating of prediction of failure probability of component Cy (andvice-versa).

Now the fatigue crack growth limit states for two different locations are considered. If the correlationbetween failure events of the two different locations is significant, a no-find inspection result for one locationmay update the prediction of failure of the other location detail sufficiently such that the planned inspectionmay be postponed for this detail compared to that otherwise planned. An opposite result may be obtainedin the case that cracks are found, i.e. if a crack is found at one location, inspection of other locations maybe recommended earlier than initially planned. The extent of this effect depends significantly on themagnitude of the correlation, the predicted failure probabilities, the quality of the inspections and thefindings and not least the shape of the fatigue crack growth curve.

D.4.2.2 Example of analysis where correlation was included in assessment of an FPSO

The effect of correlation in parameters has been analysed with respect to inspection for fatigue cracks at

doubling plates in a floating production vessel, ref. Lotsberg et al. (1999). The following assumptions weremade for the analyses:

— The stress range is assumed to be fully correlated between different components. This is considered tobe a reasonable assumption for the actual areas considered in deck and bottom of a floating productionvessel. A long term stress range distribution was established based on the assumption that theproduction vessel is fully loaded 50% of the time and is in ballast the other 50%.

— The material is from the same mill and the same welding procedure is used for the consideredcomponents. Therefore it was assumed that the crack growth parameter is fully correlated. This mightnot be a conservative assumption but was used for the analysis to study the effect of correlation.

— The initial defect distributions were assumed to be without any correlation which was considered to bea conservative assumption.

Analysis of welds that are not ground

From this work it is noted that the effect of correlation is significantly larger for welds that are not groundcompared with those that have been ground to achieve a minimum required fatigue life.

Inspection of more components leads to increased time intervals between the inspections. This result is aneffect of correlation related to the load effect and the crack growth parameters. The required time betweeninspections are increasing significantly by inspecting several components that are equal in geometry withthe same calculated fatigue life.

The effect of correlation also gives some information on calculated fatigue life that does not imply anyinspection requirements at all. If there are a number of hot spots of similar geometry and loading with acalculated fatigue life equal to Lmin , it should not be necessary to perform inspection of hot spots having acalculated fatigue life 3 × Lmin , provided that those components having a fatigue life equal Lmin are

inspected regularly. This information may be used as a screening criterion for selection of hot spots to beanalysed more in detail by probabilistic methods.

(D.15)( )

y x

y x

xy

y x E

σ σ

µ µ ρ

−−=




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Analysis of ground welds at doubling plates and transverse stiffeners in deck structure

The effect of correlation has been analysed with respect to inspection for fatigue cracks at the doublingplates that are ground during fabrication. (The same considerations are also valid for the transversestiffeners below the deck plating.)

The result from this work was that by inspecting one hot spot without finding a crack one may postponeinspection of the neighbouring hot spot for approximately half a year only.

The reason for this is the long initiation time for fatigue cracks in the model. Because the initiation is notconsidered to be correlated, the effect of inspection on one hot spot will have little influence on the reliabilityof the other ground hot spots.

D.4.3 Effect of inspection findingsIf cracks are detected, this may mean that it is also likely that there are fatigue cracks or crack indicationsin other areas in the structure subjected to a similar hot spot stress range. The probability for this may beassessed by probabilistic methods. However, in most cases each fatigue crack is somewhat unique whenone starts to study the real basis for it. Therefore, it is important that the reasons for a crack areinvestigated in detail before further actions are made.

D.5 Assessment of input parameters to probabilistic analysis

D.5.1 Uncertainty in load effectUncertainty in load effect is one of the main reasons why in-service inspection of structures subjected todynamic loading is normally recommended. This uncertainty is of the same magnitude as the uncertaintyin the fatigue capacities as expressed by the S-N data and fabrication. In addition to these two majoruncertainties also the uncertainty in the Palmgren-Miner fatigue damage rule should be mentioned. Inprobabilistic fatigue analysis the uncertainties in the S-N data and in the Palmgren-Miner fatigue damagerule are rather precisely described while the uncertainty in loading can show a wider spread in terms ofpossible bias and variability. This consideration is also a reason for the need for good knowledge of the

fatigue analyses performed for the different structures as presented in App.A, App.B and App.C.

D.5.2 Fatigue loading in jacketsA fatigue analysis of a jacket structure involves a number of uncertainties. A list of some uncertainparameters is presented in App.A, sorted on calculation of i) hydrodynamic loads, ii) stress resultants, iii)hot spot stresses and iv) fatigue damage calculation. The calculated fatigue life is also dependent on theadopted analysis method.

The fatigue load mechanism is extremely complex as the hydrodynamic coefficients are dependent onseveral parameters such as Reynolds number (Re), Keulegan-Carpenter number (KC) and roughness(k/D). The hydrodynamic coefficients will accordingly vary continuously with wave height and position inthe wave etc. The drag and mass terms in Morison’s equation are therefore equally important and need tobe handled consistently. There are also uncertainties associated with marine growth, wave loads on anodes,

shielding effects, short-crestedness etc. The analyst is nevertheless faced with these uncertaintiesindependent of the sophistication of the selected response analysis method (deterministic discrete waveapproach, frequency domain approach or a time domain approach).

Measurements of action effects can significantly reduce the uncertainty related to fatigue loading. Normallyit is easiest to perform a measurement of the nominal stress ranges. The effect of the measurements willbe largest if also the environmental data are collected at same time as the stresses are measured.

Accordingly, measurements of nominal strains and corresponding wave heights/wave directions over acertain period of time are the only means to provide confidence in a response analysis method. Calibrationof the fatigue wave load recipe can thus be done, and improved CoV values can be obtained.

The number of instrumentation projects for jackets reported in the literature is limited, and most of thesereports are focused on storm conditions. Further, it is seen that the instrumentation set-up does often notallow simultaneous records of strains, wave heights and wave directions. It is crucial that the

instrumentation set-up is thoroughly planned for assessing the fatigue loads. For this purpose it is alsoimportant to capture the platform response over the whole wave cycle.




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Such a project has been conducted in the mid-1990s for a North Sea jacket platform in moderate water

depth (~70m), where approximately 400 sea states were selected after a rather extensive quality control

of the wave and response (strain) time series. The wave load recipe used for fatigue (the deterministic

discrete wave approach) was subsequently calibrated with reference to the analysis criteria used (marine

growth, anodes etc.). The work, which is not published, indicates that the standard deterministic fatigueanalysis method normally adopted appears somewhat conservative. The comparison of nominal stresses

also indicates/confirms that it is reasonable to use CoV = 0.15. The same study indicates that care should

be taken in case of a frequency domain analysis, in particular if a stochastic linearization of the drag term

is selected.

It is emphasized that the calibration work referred to above relates to global load effects (including frame

action), and cannot be used to assess the fatigue loading in areas governed by local hydrodynamic loads.

The fatigue load mechanism in the splash zone area is even more complex due to slamming loads, variable

buoyancy loads, water entry loads as well as local Morison loads etc. The CoV for elements in this region

should therefore be higher: CoV = 0.30. It is uncertain if there are successful measurements of strains in

structural members in the splash zone area that can be used as basis for recommendations on uncertainty.

D.5.3 Stress concentration factorsThe bias and uncertainty in calculated SCFs from parametric equations for different simple tubular joints as

presented in Table D-2 should be included in a further assessment of a reliable analysis procedure to

determine best possible estimates of fatigue lives. The uncertainties can be directly accounted for in the

probabilistic analysis. It is more difficult to account for bias as the fatigue damage is derived from fatigue

analysis using influence functions where different SCFs are used in a calculation to derive fatigue damage.

Thus, to account for different bias values associated with the different SCFs, the bias values would have to

be considered before the fatigue damage is calculated.

An assessment of parametric equations for stress concentrations in tubular joints has also been performed

by Fessler et al. (1991). It is concluded that the Efthymiou's equations provide values to the safe side with

a CoV in a region around 0.20.

It should be mentioned that the basis for SCFs in grouted joints are based on a rather limited test database.

Bias is defined as the calculated value divided by the measured value.

Table D-2 Bias and uncertainty in SCF for different simple tubular joints depending on type of loading(Based on assessment of data in HSE (1992))

Joint Loading Hot spot Number of joints Bias CoV (%)

T

axial

chord saddle 28 1.07 11

chord crown 9 1.12 26

brace saddle 8 1.29 25

brace crown 4 1.55 20

OPBchord side 18 1.10 13

brace side 9 1.54 36IPB

chord side 21 1.09 17

brace side 24 1.22 20

X

axial

chord saddle 16 1.15 19

chord crown 3 1.04 6

brace saddle 7 1.22 13

brace crown 3 1.47 9

OPBchord side 6 1.13 20


IPBchord side 12 1.33 38


K axial 1.19 19




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D.5.4 Floating structuresDirect methods based on linear methods in the frequency domain for the computation of hydrodynamicforces and ship motions should be used for fatigue assessment of floating structures. Even though suchprocedures are not the most complete methodologies available, they are considered accurate enough to

capture the main components of fatigue loading for conventional types of displacement ships.The prediction method needs to be capable to calculate with satisfactory accuracy hydrodynamic forces andwave loads for a wide range of wave headings and wave lengths. It is considered necessary to include non-linear phenomena connected with the wet to dry transition in hull portion close to waterline in the analysismodel. The introduction of correction to account for this effect is found essential for the quantification offatigue in this part of the structure.

Mean stress due to cargo gravity loads (still water loads) or to mean values of non-linear hydrodynamicloads have a direct influence on the fatigue behaviour and this influence is accounted for through the meanstress effect for inspection planning of floating production vessels in this RP.

Reference is also made to Special Task Committee VI.1 Fatigue Loading, 15th International Ship andOffshore Structural Congress (ISSC) 2003, San Diego USA for further reading. Even if it is difficult to derive

specific values for uncertainties in fatigue loading from this ISSC report, one may get a sound basis from itfor engineering assessment of uncertainties that can be used for probabilistic fatigue analysis. It is assessedthat the uncertainty related to direct analysis is rather small. The uncertainty depends on the detailconsidered and the uncertainty increases when local effects contribute significantly to the calculated hotspot stress.

For fatigue loading the uncertainties are considered to be rather small as it is the typical scatter diagramsthat can be derived from shorter intervals of measurements that are important. It is assumed that theuncertainty in the scatter diagrams used as basis for structures placed on a specific field is rather smallwhen the load effects from these are integrated to a long-term stress range distribution.

The uncertainty in long term load response derived for fatigue analysis is assessed to be less than a CoV = 0.10.

D.6 Calibration of fracture mechanics models to S-N data

D.6.1 As-welded conditionCalculated fatigue lives based on S-N data are considered to be more reliable than those based on fracturemechanics as S-N data are derived directly from fatigue tests while fracture mechanics is based oncalculations where additional parameters are required as input to the analysis. Thus it is reasonable to makea calibration such that the probability of a fatigue failure based on fracture mechanics follows that of S-Ndata (test data) until first in-service inspection. After the first inspection the results will depend on thefracture mechanics model, the reliability of the inspection method and whether cracks are found or not.

The fatigue initiation time in the model has a significant effect on calculated inspection interval. Thus it isimportant to thoroughly assess the crack growth in order to safely update the probability of fatigue crackingbased on the applied PoD Curves.

Furthermore it is important to include the fatigue initiation time for welded connections where the weldnotch is removed by grinding or machining and for components where the fatigue cracks may initiate in thebase material.

The crack growth from fracture mechanics should be consistent with S-N data for the considered joints.However, it should be kept in mind that crack growth in real structures can be different from that of the testdata (size, residual stresses, and mean stress effect). It is thus important that the fatigue initiation life isdetermined from calibrated models.

D.6.2 Assessment of analysis models

D.6.2.1 General

The modelling of the initial crack depth may have considerable effect on the updating effect from a “no-find”

inspection event. Therefore it is important to include suitable modelling of the crack initiation in theprobabilistic crack growth model.




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— Pure membrane loading and no uncertainty in loading is assumed.

Parameters used in fracture mechanics analysis:

— m = 3.0.

— Mean C: 1.83 · 10-13 (N, mm), Log10(C) = -12.74.— Standard deviation. StD(Log10(C)) = 0.11.

— M k factors calculated by using parametric equation based on Bowness and Lee (2000).

— L = 40 mm.

— Geometry function based on Newman and Raju (1983).

— Initial aspect ratio a0 /c0= 0.2.

— No threshold value for crack growth is assumed (∆Kth = 0).

— The same loading as for derivation of the S-N data was used for calibration.

D.6.2.2 Calibration of initial crack size distribution:

The crack growth is assumed to start from the first stress cycle. Different distribution types for the initial

crack sizes have been studied and the exponential distribution has shown to lead to the most relevantresults.

The exponential distribution is defined by:

— Probability density function:

— Cumulative distribution function:

Both the mean value and the standard deviation for the exponential distribution are equal to 1/l. The medianvalue is given by ln(2)/λ . The best fit to the S-N fatigue data is obtained for median value of a0 equal to0.03 mm i.e. mean value of 0.043 mm. The same magnitude of initial defect was also derived by comparison

with test data for assessment of the size effect based on deterministic analysis, Lotsberg (2014). The 90%fractile level is about 0.1 mm and the probability of an initial crack size larger than say 0.2 mm is very small.

It was not possible to obtain a reasonable fit of the fracture mechanics model to the S-N data, only byassuming a known distribution type of a0; therefore, additional uncertainties in the fracture mechanicsmodel were introduced. The following parameters were included:

— Model uncertainty in the stress intensity range calculation, X ∆K: Modelled as Normal distributed withmean of 1.0 (unbiased) and CoV equal to 5%.

— Model uncertainty in the stress intensity magnification factor, XΜ K: Modelled as Normal distributed withmean of 1.0 (unbiased) and CoV equal to 10%.

By including these additional uncertainties in the crack growth model (X∆K and XΜ K) the tail properties of

the fracture mechanics model were adjusted to the S-N model. Here also an analysis model has beenderived where the initial crack size distribution is in line with that experienced based on test data presentedin literature. Thus a realistic physical analysis model for crack growth has been established. Due to a soundinitial defect distribution this analysis model is considered to be representative for membrane loading aswell as moment loading on the connections. For this reason the Model 2 is the preferred model forprobabilistic analysis.

D.6.2.3 Weibull long term loading and probabilistic analysis

The crack growth model has been compared and calibrated to S-N test data for constant amplitude loadingin [D.6.2.2]. Now a more real application where the long-term distribution of the stress ranges is assumedto be defined by a Weibull distribution with associated uncertainties is considered. Parameters used in S-Nanalysis and growth analysis are the same as above, however now the load is modelled as Weibulldistributed with shape parameter h equal to 0.8 and average cycle rate equal to 0.16. Different fatigue lives

were considered, i.e. an associated Weibull shape parameter is obtained (back calculated) such that the S-N fatigue life becomes equal to given value.

λ e-λ x

; x ≥ 0, 0 ; x < 0

1 - e-λ x

; x ≥ 0, 0 ; x < 0




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D.6.2.4 Stochastic modelling of crack initiation time

The crack growth is assumed to start at first stress cycle using model 2 as described above. The load casesare obtained such that the calculated S-N fatigue life (using design S-N curve) varies from 10 to 60 years.The calculated probabilities of failure for CoV on loading equal 0.25 are shown in Figure D-14. The calculatedprobabilities of failure for CoV on loading equal 0.15 are shown in Figure D-15. Figure D-16 is derived by

presenting the calculated failure probability as function of a normalised time. It is seen that there is goodcorrespondence between that calculated by S-N data with that calculated by fracture mechanics.

Figure D-14 Calculated probability of failure by S-N data (SN) and fracture mechanics (CG) for CoV onloading equal 0.25

Figure D-15 Calculated probability of failure by S-N data and fracture mechanics for CoV on loading equal0.15




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Figure D-16 Calculated probability of failure by S-N data and fracture mechanics for CoV on loading equal0.15

D.6.3 Butt weldThe transition from base material to the weld is smoother in a butt weld than in a cruciform joint. Also theweld attachment length L is shorter in a butt weld than that used in the reported calibration for a cruciform

joint. A butt weld made from both sides is classified as D according to DNVGL-RP-0005 when it is made inflat position or has a weld toe shape similar to such a fabrication. A typical butt weld geometry may havea surface geometry that corresponds to a weld angle approximately equal 15o and with weld attachmentlength L equal half the plate thickness.

Now the validity range for the weld geometry function is between 30o and 60o according to Bowness andLee (2000). Therefore one may question the validity of the geometry function for a weld with angle shapeequal 15o. Therefore to assess this further some different analyses for constant stress ranges have beenperformed for different weld attachment lengths and weld angles. Rather good correspondence between S-N curve D and fracture mechanics crack growth analysis for θ = 15o and attachment length L = 0.5t wasachieved. The analysis was based on the same distribution of parameters as used for calibration of the F-detail in [D.5.2] with respect to initial crack size distribution and uncertainties in the crack growth analysiswith respect to geometry functions.

Then a long term load distribution has been considered like that described in [5.6]. The results arepresented in Figure D-17. An uncertainty in the long term stress range distribution CoV(q) = 0.25 is used.It is observed that there is good correspondence between S-N data and fracture mechanics for weld angleθ = 15o and attachment length L = 0.5t and the uncertainties in initial crack size and geometry functions.Thus these parameters will be used for further probabilistic analysis of fatigue crack growth at weld toes inbutt welds. The same results are presented on a normalised form in Figure D-18. It is seen that there isgood correspondence between the fracture mechanics calculations and the S-N data for different calculatedfatigue lives and different service lives.

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

F a i l u r e p r o b a b i l i t y

Fatigue Utialisation : Service time/Calculated fatigue life

SN - Fatigue Life = 10yr

CG - Fatigue Life = 10yr








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Figure D-17 Calculated probability of failure for butt weld based S-N curve D and calibrated fracture

mechanics model for different calculated fatigue lives

Figure D-18 Calculated probability of failure by S-N data and fracture mechanics for model 2 and CoV onloading equal 0.25

Similar analyses as presented above have also been performed for CoV(q) = 0.15. The results are shownin Figure D-19 and Figure D-20.

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 5 10 15 20


Service time (years)

SN - Fatigue

life = 20 yr

CG - Fatiguelife = 20 yr

SN - Fatigue

life = 60 yr

CG - Fatigue

life = 60 yr

SN - Fatigue

life = 200 yr

CG - Fatigue

life = 200 yr




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D.6.4 Effect of weld improvements on crack initiation based on S-N dataAn alternative to the improvement factors on fatigue life for connections that are improved by grinding orpeening is to use S-N curves with a more correct slope that represents the improved details. An exampleof such S-N curves is shown in Figure D-21.

Characteristic S-N curves for improved details can be found in Table D-3. S-N curve to be selected is linked

to the S-N classification of details shown in DNVGL-RP-0005 App.A. These S-N curves can be used in airand in seawater with cathodic protection.

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

0 5 10 15 20 25 30 35 40


Service time (years)

SN Analysis - Fatigue life = 10 yr

CG Analysis - Fatigue life = 10 yr







Fatigue Probability as function of service time (a0_50% = 0.03mm)

Fatigue Life (years) = 10, 20 & 60 yr

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2


Fatigue Utialisation : Service time/Calculated fatigue life

SN - FL=10yr

CG - FL=10yr

SN - FL=20yr

CG - FL=20yr

SN - FL=60yr

CG - FL=60yr

Fatigue Probability as function of service time (a0_50% = 0.03mm)

Fatigue Life (years) = 10, 20 & 60 yr




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The S-N curves for improvement are in line with the recommendations from IIW for increased stress rangesat 2 · 106 cycles (increase in stress range by a factor 1.3 for grinding and a factor 1.5 for hammer peening).For longer calculated fatigue lives the resulting improvement may likely be found to be larger when usingthese S-N curves than using factors on calculated fatigue lives as the main contribution to fatigue damageis accumulated to the right of 2 · 106 cycles in the high cycle range of the S-N curve.

It should be noted that S-N curves above that of D should be used with caution for welded connectionswhere fatigue cracks can initiate from internal defects. In general the selection of appropriate S-N curvedepends on NDT method used and acceptance criteria. This needs to be assessed when improvementmethods are used and corresponding S-N curves selected.

Figure D-21 Example of S-N curves (D-curve) for a butt weld in as-welded condition and improved by grindinorg hammer peening

The magnitude of weld improvement on the fatigue performance can be estimated by comparing thecalculated fatigue life obtained using the S-N curves with the calculated fatigue life obtained using the as-

Table D-3 S-N curves for improved details by grinding or hammer peening

S-N curve Improvement by grinding Improvement by hammerpeening

N ≤ 107 cyclesm1 = 3.5

N > 107 cyclesm2 = 5.0

For all Nm2 = 5.0

D 13.540 16.343 16.953

E 13.360 16.086 16.696

F 13.179 15.828 16.438

F1 12.997 15.568 16.178

F3 12.819 15.313 15.923

G 12.646 15.066 15.676

W1 12.486 14.838 15.448

W2 12.307 14.581 15.191

W3 12.147 14.353 14.963

10

100

1000

100000 1000000 10000000 100000000

S t r e s s r a n g e ( M P a )

Number of cycles

Detail category D Ground

Detail category D Peened

Detail category D As welded

1log a 2alog alog




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welded S-N curves. The improvement factor is defined as:

where FLgrind and FLAs-welded are the calculated fatigue lives obtained using the S-N curves for grinding andas-welded details. The relationship for Weibull long-term fatigue loading is shown in Figure D-22.

Figure D-22 Comparison of calculated fatigue life after grinding for given calculated fatigue life for as-welded condition (D-curve)

Figure D-23 Comparison of “weld improvement factor” as function of calculated as-welded fatigue life forgrinded connections

(D.16)

welded As

grind

imp

FL

FL X

−

=

0

50

100

150

200

250

300

350

400

450

500

0 10 20 30 40 50 60 70 80 90 100

C a l c u l a t e d f a t i g u e l i f e a f t e r g r i n d i n g ( y e a r s )

Calculated fatigue life as-welded detail (years)

Weib h = 1.2

Weib h = 1.0

Weib h = 0.8

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0 10 20 30 40 50 60 70 80 90 100

I m p r o v e m e n t f a c t o r o n f a t i g u e l i f e a f t e r g r i n d i n g

Calculated fatigue life as-welded detail (years)

Weib h = 1.2

Weib h = 1.0

Weib h = 0.8

Weib h = fitted h=1




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reduced M k factor. The model properties for X ini are obtained by calibrating the calculated failure probabilityusing a probabilistic S-N fatigue model and the model outlined above.

In order to calibrate an appropriate model for X ini, a butt weld detail is selected with calculated as-weldedfatigue lives from 5 to 100 years.

X ini is proposed to be modelled as uniformly distributed stochastic variable with lower bound equal to X low and upper bound equal to 1.0.

The lower bound depends on the calculated as-welded fatigue life (i.e. the stress level) where the followingmodel is proposed (see also Figure D-25):

where FLAs-welded is as-welded fatigue life.

The above equation has been validated for calculated as-welded fatigue life up to 100 years (ground fatigue

life about 490 years).The comparison of the probabilistic S-N fatigue analysis for ground details and the probabilistic fracturemechanic analysis is shown in Figure D-26. The S-N lives in as-welded condition from 5 to 100 yearscorresponds to 14 to 480 years in the ground condition.

Figure D-25 Lower bound X low as function of calculated fatigue life

(D.19)

≥−=

−−

−−

years FL for FL

years FL for FL X

welded Aswelded As

welded Aswelded As

low1008.0)log(3316.0

10<025.0

0.25

0.35

0.450.48

0.51

0.53 0.550.57 0.58

Xlow = 0.025 FLAs-welded

Xlow = 0.3316log(FLAs-welded) - 0.08

0

0.1

0.2

0.3

0.4

0.5

0.6

0 10 20 30 40 50 60 70 80 90 100

X l o w

Calculated as-welded fatigue life (years)

Xlow as function of as-welded fatigue life




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Figure D-26 Comparison of calculated fatigue failure probabilities using fracture mechanics and S-N basedfatigue model for a ground butt weld

Here a probabilistic fracture model for a butt weld has been calibrated. The same model is not directlyapplicable for other types of details, e.g. F-details. The main reason for this is that the M k solution for grounddetails with significant attachment length seems to underestimate the effect of the notch stress. Therefore,the model used for butt weld needs to be adjusted. By assuming a bias in the M k for other details than buttweld by 15%, a good correspondence between the probabilistic S-N approach and fracture mechanics isobtained. The comparisons between these two models are shown in Figure D-27.The S-N lives in as-weldedcondition from 5 to 100 years corresponds to 14 to 441 years in the ground condition.

Based on the model calibration, the model parameters shown in Table D-4 are proposed to be used in

probabilistic inspection planning for ground details.




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Figure D-27 Comparison of calculated fatigue failure probabilities using fracture mechanics and S-N basedfatigue model for ground F-detail

D.6.6 Example: Inspection for toe ground butt weldA typical butt weld detail with the following properties is considered:

Table D-4 Proposed parameters for probabilistic analyses for ground details

Parameter Comments

Crack growth fatigue model

m the crack growth parameter m is modelled as deterministic, equal to 3.0

Log10(C) Crack growth parameter C A and C C are assumed to be fully correlated and equally distributed, wherelog10(C ) is modelled as normally distributed with a mean value equal to –12.738 and standard deviationequal to 0.11.

a0 Model 2: a0 is modelled by exponential distribution with medial value of 0.03 mm.

a0 /c0 The initial aspect ratio is modelled fixed value equal to 0.2.

X MK Butt welds: Modelled as Normal distributed with mean value of 1.0 and CoV equal to 0.1.Other details: Modelled as Normal distributed with mean value of 1.15 and CoV equal to 0.1.

X ∆K Modelled as Normal distributed with mean value of 1.0 and CoV equal to 0.1.

T 0

X ini: Modelled as uniformly distributed stochastic variable with lower bound equal to X low and upperbound equal to 1.0.

Modelled as deterministic, equal to 63 Nmm-3/2.

Fatigue loading

Fatigue load The long-term stress range distribution modelled as Weibull distributed with deterministic shapeparameter h.The scale parameter is modelled as normal distributed: The CoV will depend on the analysis methodapplied. In the current example the CoV is equal to 15% and 25%. The mean value depends on thecalculated fatigue life; i.e. the scale parameter is calibrated to the specified calculated fatigue life for adetail with given fatigue life. Different calculated fatigue lives are considered.

Cycle rate The number of stress ranges per sec. is modelled as fixed value.

failure

imp

imp

ini T X

X X T

10

−=

≥−=

−−

−−

years FL for FL

years FL for FL X

welded Aswelded As

welded Aswelded As

low1008.0)log(3316.0

10025.0 <

th K ∆




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— structure: semi-submersible

— thickness: t = 25 mm

— length of attachment, L = 12.5 mm

— assume that the nominal stress ranges is derived from local analyses (CoV(q)= 16%)

— S-N curve: D— environment: air

— DOB= 0% and DOB = 50%

— The consequence of a failure is considered to be small: Target PoF = 10-2

— Good access for NDT inspectionPoD: X0 = 0.16 ; b = 1.0 and X0 = 0.45 ; b = 0.9

— Calculated fatigue life:

As-Welded = 5 years (Weibull parameters; q = 22.01, h = 1.0)

Ground = 13.5 years

As-Welded = 10 years (Weibull parameters; q = 17.89, h = 1.0)

Ground = 30.6 years— Detail was ground from installation

— Planned operation 22 years.

The calculated failure probability as function of time and optimised inspection plans are shown in Figure D-29 to Figure D-32. The POD curve used in this example is very good i.e. 50% POD is equal to 0.16 mm.Figure D-33 exhibits an optimised inspection plan with a case where a less accurate inspection is applied,i.e. X0 = 0.45; b = 0.9. In this example the as-welded fatigue life is equal to 5 years and the detail issubjected to pure membrane stress. By comparing the optimized inspection plans shown in Figure D-29 andFigure D-33, the effect of increased inspection quality can be seen.

Figure D-28 Example of butt weld that is weld toe ground




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Figure D-29 Optimised inspection for ground butt weld for calculated as-welded fatiguelife equal to 5 years and pure membrane stresses (DOB=0) – fatigue life ground condition is equal 13.5 years

Figure D-30 Optimised inspection plan for ground butt weld for calculated as-welded fatigue life equal to 5years and 50% membrane stresses (DOB=0.5) – fatigue life ground condition is equal to 13.5 years




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Figure D-31 Optimised inspection plan for ground butt weld for calculated as-welded fatigue life equal to10 years and pure membrane stresses (DOB=0) – fatigue life ground condition is equal to 31 years

Figure D-32 Optimised inspection plan for ground butt weld for calculated as-welded fatigue life equal to

10 years and 50% membrane stresses (DOB=0.5) – fatigue life ground condition is equal to 31 years




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Figure D-33 Optimised inspection plan for ground butt weld for calculated as-welded fatigue life equal to 5years and pure membrane stresses (DOB=0) using recommended POD curve for above water with goodworking conditions – fatigue life ground condition is equal to 13.5 years




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C h a n g e s

–

h i s t o r i cCHANGES – HISTORIC

Note that historic changes older than the editions shown below have not been included. Older historicchanges (if any) may be retrieved through http://www.dnvgl.com.

May 2015 edition

GeneralThis is a new document.

probabilistic methods for planning inspection for fatigue cracks in offshore structures

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