DNVGL-RP-F105 Free spanning pipelines - Rules and …rules.dnvgl.com/docs/pdf/dnvgl/RP/2017-06/DNVGL-R… · · 2017-06-27Changes - current Recommended practice — DNVGL-RP-F105

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RECOMMENDED PRACTICE

DNVGL-RP-F105 Edition June 2017

Free spanning pipelines

FOREWORD

DNV GL recommended practices contain sound engineering practice and guidance.

© DNV GL AS June 2017

Any comments may be sent by e-mail to [email protected]

This service document has been prepared based on available knowledge, technology and/or information at the time of issuance of thisdocument. The use of this document by others than DNV GL is at the user's sole risk. DNV GL does not accept any liability or responsibilityfor loss or damages resulting from any use of this document.

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Recommended practice — DNVGL-RP-F105. Edition June 2017 Page 3Free spanning pipelines

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CHANGES – CURRENT

This document supersedes the February 2006 edition of DNV-RP-F105.Changes in this document are highlighted in red colour. However, if the changes involve a whole chapter,section or sub-section, normally only the title will be in red colour.

Changes June 2017, entering into force as from date of publicationSome references in this service document may refer to documents in the DNV GL portfolio not yet published(planned published within 2017). In such cases please see the relevant legagy DNV or GL document.

• Sec.1 General— [1.6]: Extended description of the concept of single- vs. multi-spans and addition of new figures to

illustrate the concept have been added.— [1.7]: This section in the previous revision of this RP has been replaced by a new subsection introducing

the novel concepts of active, participating and contributing modes.— [1.10.8]: New paragraph including sensor technology among the listed vortex induced vibration (VIV)

assessment methodologies has been added.— [1.10.8]: Definitions related to new or more comprehensively treated subjects have been added.

• Sec.2 Design criteria— [2.3]: New subsection firmly defining characteristic environmental events and criteria for VIV avoidance

has been added.— [2.5.6]: New paragraph stating that fatigue damage shall be evaluated at inner and outer fibre of steel-

wall has been added.— [2.6]: Definition of characteristic environmental events has been moved to [2.3.2] and an empirical

correction factor to account for stress contributions from higher-order modes has been included in[2.6.10].

— [2.7]: Span classification category for “well to very well defined” spans, and new description ofrelationship to DNVGL-ST-F101 consistent with the new design fatigue factor (DFF) format have beenadded.

• Sec.4 Response models— The single- and multi-mode VIV response algorithms from the previous revision of this RP have been

merged. As a result, Sec.4 has been completely restructured and replaces both Sec.4 and App.A from theprevious revision. Throughout the updated Sec.4, single-mode quantities have therefore been replaced bycorresponding multi-mode quantities.

— [4.1.7]: Note stating that flow shall always be considered as current-dominated for KC > 40 has beenadded.

— [4.3]: New subsection containing important definitions and aspects of the multi-mode calculationprocedure, including how to implement the new concepts of participating and contributing modes havebeen added.

— [4.5]: Description of a new response model to account for cross-flow vibrations in wave-dominatedconditions at low KC has been added.

• Sec.5 Force model— The frequency-domain solution detailed in the previous revision of the RP was limited to single-span/

single-mode response. The method’s applicability is extended in this revision to multi-spans/multi-modeanalyses.

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— [5.1]: Description of applicability to multi-spans using multiple-location analyses and of specialconsiderations for multi-span analyses has been added.

— [5.2.2]: Empirical correction factor to be used for single-span/single-mode analyses has been included.— [5.2.7]: New paragraph describing complete stress response spectrum for multi-mode analyses has been

added.— [5.2.13]: Expression for hydrodynamic modal damping given in [5.2.9] of previous revision of this RP has

been corrected.

• Sec.6 Structural analysis— All comments and requirements pertaining to pipeline characteristics, static analysis, modal analysis and

FE modelling have been collected in subsections [6.3], [6.5], [6.6] and [6.7], respectively.— [6.2]: New subsection introducing important physical aspects pertaining to pipe response in and near free

spans has been added.— [6.4]: New subsection with description of commonly applied approaches for modelling boundary

conditions has been added.— [6.8.1]: Validity range for approximate response quantities in terms of non-dimensional soil stiffness

parameter β has been added.— [6.9]: New subsection describing approximate modal analysis method for very short free spans has been

added.— [6.10]: New subsection outlining a procedure to determine whether adjacent spans dynamically interact

has been added.

• Sec.7 Application of sensors to minitor free span vibrations— New section providing basic guidance for the application of sensors to monitor free span vibrations and on

how the application of sensors influences the safety factor format.

• App.A Application of DNVGL-RP-F105 to jumpers, spoolers, flexible loops and subseapiping— New section providing detailed guidance on how to conservatively apply this RP to fatigue and ultimate

limit state calculations of spools, jumpers, flexible loops and other non-straight piping systems.

• App.D Pipe-soil interaction— App.D has been moved into a new recommended practice, DNVGL-RP-F114 Pipe soil interaction for

submarine pipelines

Editorial correctionsIn addition to the above stated changes, editorial corrections may have been made.

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CONTENTS

Changes – current.................................................................................................. 3

Section 1 General....................................................................................................81.1 Introduction......................................................................................81.2 Scope................................................................................................ 91.3 Application...................................................................................... 101.4 Extended application...................................................................... 111.5 Safety philosophy........................................................................... 121.6 Free span morphological classification........................................... 121.7 Mode classification..........................................................................171.8 Free span response behaviour........................................................191.9 Flow regimes.................................................................................. 191.10 Vortex-induced vibrations assessment methodologies..................211.11 Relationship to other standards....................................................221.12 Definitions.....................................................................................231.13 Abbreviations................................................................................241.14 Symbols........................................................................................ 251.15 Verbal forms................................................................................. 33

Section 2 Design criteria.......................................................................................342.1 General........................................................................................... 342.2 Non-stationarity of spans............................................................... 362.3 VIV avoidance criteria.................................................................... 372.4 Screening fatigue criteria............................................................... 392.5 Fatigue criterion............................................................................. 402.6 ULS criterion...................................................................................442.7 Safety factors................................................................................. 47

Section 3 Environmental conditions...................................................................... 513.1 General........................................................................................... 513.2 Current conditions.......................................................................... 513.3 Short-term wave conditions............................................................553.4 Reduction functions........................................................................ 583.5 Long-term environmental modelling...............................................603.6 Return period values...................................................................... 62

Section 4 Response models...................................................................................634.1 General........................................................................................... 63

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4.2 Marginal fatigue life capacity..........................................................654.3 Aspects of the computational approach..........................................664.4 Cross-flow response model.............................................................694.5 Cross-flow VIV for low KC regimes.................................................764.6 In-line response model...................................................................79

Section 5 Force model...........................................................................................875.1 General........................................................................................... 875.2 Frequency-domain solution for in-line direction............................. 885.3 Simplified fatigue assessment........................................................ 935.4 Force coefficients............................................................................93

Section 6 Structural analysis.................................................................................986.1 General........................................................................................... 986.2 Important physical aspects and effects.......................................... 986.3 Pipeline and material characteristics.............................................. 996.4 Boundary conditions..................................................................... 1016.5 Static analysis...............................................................................1036.6 Eigenvalue analyses......................................................................1056.7 Response quantities based on finite element modelling................1086.8 Approximate response quantities................................................. 1096.9 Special considerations for very short spans..................................1146.10 Interacting multi-spans.............................................................. 117

Section 7 Application of sensors to monitor free span vibrations........................1197.1 General......................................................................................... 1197.2 Practical requirements..................................................................1197.3 Processing sensor data.................................................................120

Section 8 References...........................................................................................1228.1 References.................................................................................... 122

Appendix A Application of DNVGL-RP-F105 to jumpers, spools, flexible loopsand subsea piping.............................................................................................. 125

A.1 General......................................................................................... 125A.2 Applicability and limitations......................................................... 125A.3 Methodology for analysis of non-straight pipes............................ 126A.4 Distinctions between in-line and cross-flow VIV...........................126A.5 Directionality of incoming flow.....................................................128A.6 Hydrodynamic damping considerations........................................ 129A.7 Direct wave loading......................................................................130

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A.8 Modal response quantities............................................................131A.9 Interface loads............................................................................. 131A.10 Mitigation measures................................................................... 132

Appendix B VIV mitigation..................................................................................134B.1 VIV mitigation methods................................................................134B.2 Span rectification methods........................................................... 134

Appendix C VIV in other offshore applications....................................................135C.1 Main application scope................................................................. 135C.2 Riser VIV...................................................................................... 135C.3 VIV in other structural components..............................................136

Changes - historic...............................................................................................137


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SECTION 1 GENERAL

1.1 Introduction

1.1.1 This recommended practice considers free spanning pipelines subjected to combined wave and currentloading. The premises for the document are based on technical development within pipeline free spantechnology in research and development (R&D) projects, as well as design experience from previous andongoing projects, e.g.:

— The sections regarding free span analysis and in-line vortex induced vibrations (VIV) fatigue analyses arebased on the published results from the MULTISPAN project, see Mørk et al. (1997).

— Numerical study based on CFD simulations for vibrations of a pipeline in the vicinity of a trench,performed by Statoil, DHI and DNV, see Hansen et al. (2001).

— Further, R&D and design experience e.g. from Åsgard Transport, ZEEPIPE, TOGI and TROLL OIL pipelineprojects are implemented, see Fyrileiv et al. (2005).

— Ormen Lange tests aimed at moderate and very long spans with multimodal behaviour, see Fyrileiv et al.(2004), Chezhian et al. (2003) and Mørk et al. (2003).

— PhD studies on dynamic response of free spanning pipelines by Sollund (2015).— Important studies on VIV in wave dominated conditions for low Keulegan-Carpenter (KC) regimes, see

Vedeld et al. (2016), which summarizes work by Chioukh and Narayanan (1997), Kozakiewiecz et al(1994; 1995; 1996), Hayashi and Chaplin (1991; 1998), Hayashi et al. (2003), Bearman and Mackwood(1991), Sha et al. (2007), Kaye and Maull (1993), Maull and Kaye (1988), Isaacson and Maull (1981),Slaouti and Stansby (1992), among others.

— Numerous projects on jumpers, spools and piping systems, see for instance Vedeld et al. (2011a, 2011b).

The basic principles applied in this document are in agreement with most recognised standards and reflectstate-of-the-art industry practice and latest research.This document includes a brief introduction to the basic hydrodynamic phenomena, principles and parametersfor dynamic response of pipeline free spans. For more thorough introductions to physical mechanisms andthe theoretical background, see e.g. Sumer and Fredsøe (1997), Blevins (1994) and Zdravkovich (1997,2003).

1.1.2 The main aspects of a free span assessment together with key parameters and main results are illustrated inFigure 1-1.


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Figure 1-1 Overview of main components in a free span assessment

1.2 Scope

1.2.1 The scope of this document is to provide rational design criteria and guidance for assessment of dynamicresponse of pipeline free spans due to combined wave and current loading. Detailed design criteria arespecified for ultimate limit state (ULS) and fatigue limit state (FLS) due to in-line and cross-flow vortexinduced vibrations (VIV) and direct wave loading.Free span design may be performed by conservative avoidance criteria, simplified fatigue criteria or detailedfatigue analyses, all of which are covered in this RP. Whenever fatigue is allowed in design, extremeenvironmental events may cause loading on the structure which, in case, must be accounted for in ULSdesign, and detailed guidance for how to include contributions to ULS calculations due to environmentalloading is also provided in this RP.


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1.3 Application

1.3.1 The following topics are considered:

— methodologies for free span analysis— requirements and guidance for structural and modal response calculations— geotechnical conditions— environmental conditions and loads— requirements for fatigue analysis— VIV response and direct wave force analysis models— acceptance criteria— special considerations for non-straight pipe geometries, including for instance bends— application of sensor technology.

1.3.2 Pipeline free spans can be caused by:

— seabed unevenness— change of seabed topology, e.g. scouring, sand waves— artificial supports/rock beams etc.— crossings and end terminations.

1.3.3 The following environmental flow conditions are described in this document:

— steady flow due to current— oscillatory flow due to waves— combined flow due to current and waves.

The flow regimes are discussed in [1.9].

1.3.4 This recommended practice (RP) is generally only applicable for circular pipe cross sections of steel pipelines.However, it can be applied with care to non-circular cross sections such as piggy-back solutions as long asother hydrodynamic loading phenomena, e.g. galloping, are properly taken into account.Basic principles pertaining to the use of response models and force models may also be applied to morecomplex cross sections such as pipe-in-pipe, bundles, flexible pipes and umbilicals. However, calculationof structural response quantities such as natural frequencies, modal stresses and fatigue damage will bedifferent for the more complex cross-sections.

1.3.5 There are no limitations to pipeline span length and span gap with respect to application of this RP.Both single spans and multi-span scenarios, either in single-mode or multi-mode vibration, can be assessedusing this RP.


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1.3.6 The free span static and modal analyses may be based on approximate response expressions or morerefined approaches, e.g. using the finite element (FE) method, depending on the free span classification andresponse type.The following cases are considered:

— flat span shoulders or span shoulders accounting for seabed topography— single- or interacting multi-spans— distribution of or mean value of effective axial force, i.e. treating the effective axial force as a function of

position along pipe axis or using the mean value in a local span model.

The choice of method for static and dynamic span modelling may have a strong influence on calculatedmodal frequencies and associated stresses. Due to the importance of frequencies and stresses for fatigueand environmental loading calculations, the choice of analysis approach influences the partial safety factorformat.

1.3.7 The following models to estimate the magnitude of dynamic response in a free span are considered:

— Response models (RM), see Sec.4.— Force models (FM), see Sec.5.

An amplitude response model is applicable when the vibration of the free span is dominated by vortexinduced resonance phenomena in the relevant environmental event. A force model may be applied when thefree span response is dominated by direct wave loads. The selection of the appropriate model depends on theflow regime caused by each individual environmental event, see [1.9].

1.3.8 The fatigue criterion is limited to stress cycles within the elastic range. Low cycle fatigue including yielding inthe material is considered outside the scope of this document.

1.4 Extended application

1.4.1 The primary focus of this RP is free spanning subsea pipelines.

1.4.2 The fundamental principles given in this RP may also be applied and extended to other offshore elementssuch as cylindrical structural elements of e.g. jackets, risers on fixed platforms, jumpers and spools, at thedesigner’s discretion. However, some limitations apply and these are discussed in App.A and App.C.

1.4.3 For a more detailed account of riser VIV, see DNVGL-RP-F204 Riser fatigue.


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1.4.4 Recent attention has been given to pipelines emerging in river crossings due to scouring phenomena (Heggenet al, 2014). The fundamental principles of DNVGL-RP-F105 may be applied in such cases. See [6.9] fordetails.

1.5 Safety philosophy

1.5.1 The safety philosophy adopted herein complies with DNVGL-ST-F101 Sec.2.

1.5.2 The reliability of the pipeline against failure is ensured by use of a load and resistance factors design format(LRFD).

— For the in-line and cross-flow VIV acceptance criterion, the set of safety factors is calibrated to acceptabletarget reliability levels using reliability-based methods.

— For all other acceptance criteria, the recommended safety factors are based on engineering judgement inorder to obtain a safety level equivalent to modern industry practice.

— Use of case specific safety factors based on quantification of uncertainty in fatigue damage, can also beconsidered.

1.6 Free span morphological classification

1.6.1 The morphological classification should in general be determined based on detailed static and dynamicanalyses.

1.6.2 The objective of the free span morphological classification is to define free span parameters, typical freespan scenarios and to distinguish between isolated single spans and interacting multi-spans. In Figure 1-2, atypical isolated single span is shown.The gap, e, is the distance between the bottom of the pipe and the seabed as a function of the pipe positionx. More information on how to interpret pipe-to-seabed contact is given in [1.6.5].The free span length, L, is defined as the length of a continuous section with positive gap, e(x) > 0. Sectionsof continuous support on either side of a free span, where e(x) = 0, are defined as span shoulders, withlengths Lsh.


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Figure 1-2 A typical isolated single span, with definition of axes, gap, span, and shoulder

If a particular free span is separated from other spans by considerable stretches of pipe-soil contact, it istermed an isolated single span as illustrated in Figure 1-2. However, on typical rough seabed configurations,as exemplified in Figure 1-3 and Figure 1-4, spans are often in close proximity. A qualitative description ofthe distinction between isolated single spans and interacting multi-spans is given as follows:

— A free span is considered to be an isolated single span if the static and dynamic behaviour is negligiblyaffected by neighbouring spans, if any.

— A sequence of two or more spans is an interacting multi-span if the static and dynamic behaviour of thespans is affected by other spans in the sequence.

Figure 1-3 A typical scenario on a rough seabed where the free spans are still isolated singlespans

In Figure 1-3, two spans are in fairly close proximity to one another. However, if we assume that the threemodes illustrated in the figure are the only active modes for the spans, the spans do not interact since thestatic and dynamic behaviours of the spans are not influenced by each other.For rough sections or free span areas, the shoulders and spans are enumerated from left to right. In otherwords, the lengths of shoulder and span number k, counting from the left, are given symbols Lsh,k and Lkrespectively.


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Figure 1-4 A typical interacting multi-span scenario

In Figure 1-4, three spans are in close proximity. The peak at the second shoulder influences the staticconfiguration, particularly of the second span. Furthermore, if we assume that the two presented modes areamong the active modes in the multi-span, the dynamic behaviour of each individual span is affected by theother spans as observed from the mode shapes. Hence, the multi-span in Figure 1-4 is an interacting multi-span.Interacting multi-spans cannot be assessed using only isolated single span approaches. A precisemathematical formulation to distinguish between isolated single spans and interacting multi-spans ispresented in [6.10].


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Guidance note:When long segments of a pipeline are analysed in automated FE analysis tools, certain limitations can arise for identifyinginteracting spans, as exemplified below.Consider two free spans which are separated by a distance of 1000 m, each with a span length of about 50 m. The FE analysisestimates that some of the response frequencies for these two spans are identical. Due to numerical approximations or due toround-off errors, the results may be presented as one single mode response at these two spans, i.e. as a single interacting mode.In reality, however, these two spans are physically separated by a considerable distance, and not interacting.If isolated spans are incorrectly modelled as interacting multi-spans, it may lead to significant errors in estimating the fatiguedamage. The fatigue damage is dependent on the unit stress amplitudes, as discussed in Sec.4, which in turn are dependent onthe normalised mode shape for the span length over which the normalisation is considered. When long multi-spans are analysed,the normalisation will not be the same as for an isolated single span within the multi-spanning system. This will in turn lead toerrors.Experience has shown that in case of close frequencies for spans, the FE analysis may predict interaction even though thephysical distance between the spans is quite long. In case of mode shapes with deflection in spans that seem to be physicallywell separated, use of appropriate axial pipe-soil stiffness and/or local restraints in between the spans should be considered toseparate individual modes. Particularly, absence of a realistic axial soil stiffness can contribute to excessive unrealistic span modalinteraction.Hence, caution should be exercised when using automated FE tools for identifying interacting spans.

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1.6.3 An isolated single span has a static deflection, modal response frequencies and associated modal stresses,see Sec.6. If a neighbouring span is introduced such that it interacts with the single span, four importanteffects have been demonstrated, see also Sollund et al. (2014) and Sollund (2015):

— modal frequencies decrease— associated maximum modal stresses decrease— static deflection changes— additional modes may respond to VIV or direct wave loading.

Since fatigue and environmental load effect calculations are strongly dependent on the modal response of thepipeline, the consequences of span interaction shall be adequately accounted for.

1.6.4 Span modal interaction generally depends on pipeline bending stiffness, axial stiffness, individual span gaps,tri-axial soil stiffness, effective axial force, span lengths, intermediate shoulder lengths and span shouldergeometries. These effects have been demonstrated by e.g. Sollund et al. (2014) and Sollund and Vedeld(2013; 2015).Tura et al. (1994) developed a simplified model for free span modal interaction classification for doublespans. In the context of preliminary calculations and simplified multi-span assessments this model may beapplied to gain rough estimates of span interaction properties. Based on the approach of Tura et al. (1994),a simplified initial approximation to span interaction, as found in Figure 1-5, may be used to indicate if spansare isolated or interacting depending on soil types, span lengths and span support lengths. Figure 1-5 isprovided only for indicative purposes and is applicable only for straight horizontal supports.Note that Figure 1-5 indicates that for a given span scenario the spans will tend to interact more as the soilbecomes softer. However, for a given seabed profile, a softer soil will tend to have shorter and fewer spansand probably less interacting spans than a harder soil.


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Figure 1-5 Classification of free spans

Sollund and Vedeld (2013) demonstrated that the model of Tura et al. (1994) is only indicative, and may insome cases be substantially inaccurate. For a given pipeline configuration many of the relevant parametersare fixed, such as stiffness of the pipe and soil, and effective axial force. For an individual pipeline it istherefore possible to create a curve such as presented in Figure 1-5 for double span modal interactionclassification. For detailed design and operations management phases it is therefore recommended tocreate curves similar to the ones presented in Figure 1-5, with the exception that correct pipeline bendingstiffness, axial stiffness, representative span gaps, tri-axial soil stiffness, representative effective axial force,representative span lengths and intermediate shoulder lengths are applied. A detailed description of howsuch curves can be developed may be found in Sollund and Vedeld (2013). For systematic analyses in detaildesign or operations management phases, such project specific curves or the method detailed in [6.10] isrecommended.For critical span scenarios and span scenarios where more than two spans can potentially interact, a moredetailed approach is recommended. For such applications, a precise definition of free span modal interactionis described in [6.10]. [6.10] provides an algorithm to classify a span as either a part of an interacting multi-span or an isolated single span. A maximum shoulder length Lsh can be defined depending on soil type,effective axial force and effective mass in order to reduce the number of studied spans in the algorithm.

1.6.5 A definition of the gap between the pipe and the seabed, as a function of position x along the pipe axis, isgiven in [1.6.2]. In the y-z plane, the situations in Figure 1-6 qualify as zero gap.


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Figure 1-6 Two situations where the pipe has contact or partial contact with the seabed – bothsituations should be interpreted as no gap, i.e. e(x) = 0

As long as there is contact between the pipe and the seabed, the gap should be interpreted as zero, even ifthere is only partial contact.

1.6.6 If the pipe has contact with the seabed, as defined in [1.6.5], but the seabed has a severe slope in the y-zplane, special considerations should be made to ensure that the geotechnical properties of the contact areaare appropriately accounted for, particularly in the in-line direction.

1.7 Mode classification

1.7.1 The free span response may generally be calculated as a function of location x (see [4.2.3] for descriptionof multiple-location versus single-location analyses). For each relevant combination of sea state and currentvelocity, a number of modes may be excited by VIV, giving rise to a multi-mode response. However, thenumber of modes that will be responding and the extent to which each particular responding mode willcontribute to fatigue damage will vary depending on flow velocity, position along the x-axis and competitionwith other responding modes. In order to calculate the combined multi-mode response at each location in aconvenient manner, three different sets of modes are introduced:

— Active modes are all the modes in an isolated single-span or interacting multi-span that may be excitedby VIV. A mode that is not active can be disregarded completely in the analyses, for all locations and flowvelocities. The set of active modes is the same for all locations x. A precise definition is given in [1.12].

— Participating modes is the set of all modes that are active and have non-negligible modal curvatureeither at the relevant position x or to each side of x. In an interacting multi-span, some modes willcontribute with damage only in a segment of the whole multi-span section, meaning that the mode can bedisregarded at x-locations where it is not participating. The set of participating modes is always a subsetof the active modes, but will in general vary with position x. A precise definition is given in [4.3.3].

— Contributing modes is the set of all modes that are participating and experience non-negligible VIVexcitation at a particular location and for a particular flow velocity. The contributing modes are mutuallycompeting, in the sense that one of the modes will be dominating and contribute to the combined multi-mode response at full strength, while the contributions from other (weak) modes are reduced. In order tocorrectly identify the dominant mode, it is important to omit modes that are not participating. The set ofcontributing modes is thus always a subset of the participating modes, and will in general vary with bothflow velocity and position x. A precise definition is given in section [4.3.5].


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1.7.2 The concept of participating modes is illustrated in Figure 1-7. An idealized sketch of a multi-span with threespans is shown in the upper part of the figure. The second span, L2, is assumed to be the longest. Modaldeflection of the fundamental mode, mode 1, occurs only in this span as seen to the left in the figure. As aresult, the first mode will only be participating in a restricted x-interval containing the longest span and themodal stress peaks on the span shoulders (see definition in [4.3.3]).By contrast, the second mode in this example is an interacting mode, with non-negligible modal responsein all three spans of the interacting multi-span. Hence, mode 2 has a much wider participation interval thanmode 1, as indicated to the right in Figure 1-7.Let us further assume that the modes are cross-flow modes and that both modes experience VIV excitation.Because mode 1 has a lower frequency than mode 2, it is likely that mode 1 will have the largest VIVamplitude. Mode 1 will then be the dominant mode (see [4.4.8]) in its participation interval, while mode2 will be a weak mode in the same interval. The contribution from mode 2 to the combined stress-

range is therefore reduced (see [4.4.10]) for . However, for all other locations in the

participation interval of mode 2, i.e. for , mode 2 will be dominating and is

conservatively assumed to respond at full strength.

Figure 1-7 Participating modes for a multi-span with multi-mode response

Guidance note:If mode 1 in the example of [1.7.2] erroneously is considered as participating on the entire length of the multi-span section,the stress-range calculated for mode 2 would be reduced also in the first and third span, and the VIV damage may be non-conservatively underestimated at these locations. Hence, it is important to correctly identify the participating modes at everylocation when calculating the multi-mode response in an interacting multi-span.



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1.8 Free span response behaviour

1.8.1 An overview of typical free span characteristics is given in Table 1-1 below as a function of the free spanlength. The ranges indicated for the normalised free span length in terms of (L/D) are tentative and given forillustration only.

Table 1-1 Free span response characteristics

L/D Response description

L/D < 30 1) Very little dynamic amplificationNormally not required to perform comprehensive fatigue design check. Insignificant dynamic responsefrom environmental loads expected and unlikely to experience VIV. Natural frequency sensitive to soilstiffness. Due to high modal stresses, onset criteria for VIV recommended.

30 < L/D < 100 Response dominated by beam behaviourRelevant for free spans at uneven seabed.

Natural frequencies are sensitive to boundary conditions, effective axial force (including initialdeflection, geometric stiffness) and pipe feed in.

100 < L/D <200

Response dominated by combined beam and cable behaviourRelevant for free spans at uneven seabed in temporary conditions. Natural frequencies sensitiveto boundary conditions, effective axial force (including initial deflection, geometric stiffness) andpipe “feed in”. See [1.7] for free span response classification, which provides practical guidance forengineering applications, with respect to single and multi-mode response.

L/D > 200 Response dominated by cable behaviourRelevant for small diameter pipes, or pipes exposed to mild environmental conditions, typically in deepwater. Natural frequencies governed by deflected shape, span interaction and effective axial force.

1) For hot pipelines (response dominated by the effective axial force) or under extreme current conditions (Uc > 1.0 –2.0 m/s) this L/D limit may be misleading.

1.9 Flow regimes

1.9.1 The current flow velocity ratio, α = Uc/(Uc + Uw) (where Uc is the current velocity normal to the pipe and Uwis the significant wave-induced velocity amplitude normal to the pipe, see Sec.4), may be applied to classifythe flow regimes as follows:

α < 0.5 wave dominant – wave superimposed by currentIn-line direction: in-line loads may be described according to Morison’s equations, see Sec.5. In-lineVIV due to vortex shedding is negligible.

Cross-flow direction: cross-flow loads are mainly due to asymmetric vortex shedding. Responsemodels, see Sec.4, are recommended.


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0.5 < α < 0.8 wave dominant – current superimposed by waveIn-line direction: in-line loads may be described according to Morison’s equations, see Sec.5. In-lineVIV due to vortex shedding is reduced due to the presence of waves.

Cross-flow direction: cross-flow loads are mainly due to asymmetric vortex shedding and resemblethe current dominated situation. A response model, see Sec.4, is recommended.

α > 0.8 current dominantIn-line direction: in-line loads comprises the following components:

— a steady drag dominated component— an oscillatory component due to regular vortex shedding

For fatigue analyses a response model applies, see Sec.4. In-line loads according to Morison’sequations are normally negligible.

Cross-flow direction: cross-flow loads are cyclic and due to vortex shedding and resembles the purecurrent situation. A response model, see Sec.4, is recommended.

Note that α = 0 corresponds to pure oscillatory flow due to waves and α = 1 corresponds to pure (steady)current flow.The flow regimes are illustrated in Figure 1-8.

Figure 1-8 Flow regimes

1.9.2 Oscillatory flow due to waves is stochastic in nature, and a random sequence of wave heights and associatedwave periods generates a random sequence of near seabed horizontal oscillations. For VIV analyses,the significant velocity amplitude, Uw, is assumed to represent a single sea state. This is likely to be aconservative approximation.


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1.10 Vortex-induced vibrations assessment methodologies

1.10.1 Different VIV assessment methodologies exist for assessing cross-flow VIV induced fatigue in free spanningpipelines.

1.10.2 This RP applies so-called response models to predict vibration amplitudes in in-line and cross-flow directionsdue to vortex shedding. Response models are empirical relations between the reduced velocity, calculatedusing the still water natural frequency, and the non-dimensional response amplitude. The stress response isderived from estimated vibration modes with empirical amplitude responses.

1.10.3 Another method is based on empirical lift coefficient and effective added mass coefficient contour plots, asa function of non-dimensional response amplitude and non-dimensional vibration frequency, see Larsen andKoushan (2005).

Guidance note:For a given flow regime, the response model approach estimates the vibration amplitude directly, whereas the empirical forcecoefficient model estimates a balance between excitation and damping. The response model is chosen in this recommendedpractice due to its computational efficiency and because it conservatively and conveniently accounts for empirical data from alarge range of experiments and full scale tests. Additionally, effects of combined wave and current, turbulent flow, KC regime anddamping can easily be accounted for in a robust and conservative manner.


1.10.4 As a third option, computational fluid dynamics (CFD) simulation of the turbulent fluid flow around one- orseveral pipes can in principle be applied for VIV assessment to overcome the inherent limitations of the state-of-practice engineering approach. The application of CFD for VIV assessment is at present severely limited bythe computational effort required. In addition, documented work is lacking which shows that the estimatedfatigue damage based on CFD for realistic free span scenarios gives better and satisfactory response, thanthe methods described above.

1.10.5 Particularly for VIV of special pipeline designs with limited experience, such as pipe-in-pipe, bundledpipelines, and piggy back pipelines, experiments should be considered. Experiments should also beperformed when considering pipelines which use new designs for VIV mitigation devices, see App.B.

1.10.6 Circular and complex cross sections such as pipe-in-pipe, bundles, umbilicals and flexibles may be treated asordinary pipes as long as changes in structural response, damping and fatigue properties are accurately orconservatively accounted for.


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1.10.7 Non-circular bluff-body cross sections such as piggy-back solutions may be considered by applying a largerhydrodynamic diameter and considering the most critical cross-sectional orientation in the calculations.

1.10.8 Sensor technology may be applied to directly estimate fatigue damage in a free span. Without a soundunderstanding of the physical response of the pipe, misinterpretation of sensor readings is a risk. Directmeasurements shall therefore be appropriately combined with one of the above mentioned VIV assessmentmethodologies in order to ensure that the physical response of the pipe is well understood. More detailedguidance for application of sensor technology on free span design is found in Sec.7.

1.11 Relationship to other standards

1.11.1 This document formally supports and complies with DNVGL-ST-F101 Submarine pipeline systems and isconsidered to be a supplement to relevant national rules and regulations.

1.11.2 This document is supported by other DNV GL documents as follows:

Table 1-2 DNV GL references

Document code Title

DNVGL-ST-F101 Submarine pipeline systems

DNVGL-ST-F201 Dynamic risers

DNVGL-RP-C203 Fatigue design of offshore steel structures

DNVGL-RP-C205 Environmental conditions and environmental loads

DNVGL-RP-F109 On-bottom stability design of submarine pipelines

DNVGL-RP-F110 Global buckling of submarine pipelines – structural design due to high temperature/high pressure

DNVGL-RP-F111 Interference between trawl gear and pipelines

DNVGL-RP-F114 Pipe-soil interaction for submarine pipelines

DNVGL-RP-F116 Integrity management of submarine pipeline systems

DNVGL-RP-F204 Riser fatigue

DNVGL-RP-C212 Offshore soil mechanics and geotechnical engineering

In case of conflict between requirements of this RP and a referenced DNV GL document, the requirements ofthe document with the latest revision date shall prevail.

Guidance note:Any conflict is intended to be removed in next revision of that document.



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In case of conflict between requirements of this RP and a referenced document not published by DNV GL, therequirements of this RP shall prevail.

1.12 DefinitionsTable 1-3 Definition of terms

Term Definition

active mode a mode which violates the onset criteria in [2.3]

contributing mode a mode that is either a dominant or a weak mode at a particular location x

dominant cross-flow mode the participating mode with the highest dimensionless amplitude, see [4.4.8]

dominant in-line mode is the participating mode with the highest VIV-induced stress range at a given location x, see[4.6.8].

effective span length is the length of an idealised fixed-fixed span having the same structural response in terms ofnatural frequencies as the real free span supported on soil.

force model is in this document a model where the environmental load is based on Morison’s forceexpression.

gap the distance between the pipe and the seabed.Note: The gap used in design, as a single representative value, must be characteristic for thefree span. The gap may be calculated as the average value over the central third of the span.

interacting multi-spans are spans where the adjacent spans have an influence on the behaviour and response of aspan.

isolated single span is a span that can be assessed independently of the neighbouring spans.

marginal fatigue capacity is defined as the fatigue capacity (life) with respect to one sea state defined by its significantwave height, peak period and direction.

multi-mode response denotes response for a span where several vibration modes may be excited simultaneouslyin the same direction (in-line or cross-flow).

non-stationary span is a span where the main span characteristics such as span length and gap changesignificantly over the design life, e.g. due to scouring of the seabed.

non-straight pipe system is a pipe or system of pipes that has at least one bend.Note: Examples are jumpers, spools and piping systems.

participation interval is the interval of x for which an active mode is a participating mode, see [4.3.3].

participating mode is a mode that has a relevant stress amplitude at or on both sides of a particular location x.Note: The definition of what should be considered a relevant stress amplitude is given insection [4.3.3].

response model is a model where the structural response due to VIV is determined by hydrodynamicparameters.

span length is defined as the length where a continuous gap exists, i.e. as the visual span length.

stationary span is a span where the main span characteristics such as span length and gap remain the sameover the design life.

weak cross-flow mode denotes a participating mode that is not dominant, excited with at least 10% of thedimensionless amplitude of the dominant cross-flow mode, see [4.4.9].


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Term Definition

weak in-line mode denotes a participating mode that is not dominant, and has a higher VIV-induced stressrange than 10% of the dominant in-line mode at a particular location x, see [4.6.9].

1.13 AbbreviationsTable 1-4 Abbreviations

Abbreviation Description

CF cross-flow

CFD computational fluid dynamics

CSF concrete stiffness factor

DFF design fatigue factor

FD frequency domain

FE finite element

FEM finite element method

FLS fatigue limit state

FM force model

IL in-line

KC Keulegan-Carpenter number

LKCR low KC range

LRFD load and resistance factors design format

OCR over-consolidation ratio (only clays)

pdf probability density function

RD response domain

RM response model (VIV)

RMS root-mean square

RP recommended practice

RPV return period values

SCF stress concentration factor

SRSS square root of the sum of squares

TD time domain

ULS ultimate limit state

VIV vortex induced vibrations


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1.14 Symbols

1.14.1 Latincharacteristic fatigue strength constant ([2.5.3])

aA coefficient in expression for gA ([6.9.10])

aκ parameter for rainflow-counting factor ([5.2.5])

Ae external cross-section area

Ai internal cross-section (bore) area

AIL/CF,j in-line or cross-flow unit diameter amplitude stress (stress induced by a maximum modal deflectionequal to an outer diameter D) for the j-th mode ([6.6.2])

maximum unit diameter stress amplitude for the j-th mode ([6.6.3])

Unit diameter stress amplitude for the j-th single span mode

aincr ratio of Dincr to D ([A.10.3])

Ap cross sectional area of penetrated pipe

As pipe steel cross-sectional area

(AY/D)j normalised in-line VIV amplitude for the j-th mode

(AZ/D)j normalised cross-flow VIV amplitude for the j-th mode

(AZ/D)max normalized VIV amplitude for the dominant cross-flow mode

b buoyancy ([4.4.14]) or linearisation constant ([5.2.12])

bA coefficient in expression for gA ([6.9.10])

bincr ratio of ρinc to ρw ([A.10.3])

bκ parameter for rainflow-counting factor ([5.2.5])

B pipe-soil contact width

cA coefficient in expression for gA ([6.9.10])

Ca added mass coefficient =(CM − 1)

Ca,CF-RES added mass coefficient due to cross-flow response ([4.4.15])

CD drag coefficient

CD0 basic drag coefficient ([5.4.4])

CM inertia coefficient

CM0 basic inertia coefficient ([5.4.10])

CL coefficient for lateral soil stiffness


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CT constant for long-term wave period distribution

CV coefficient for vertical soil stiffness

C1-6 boundary condition coefficients

c(s) soil damping per unit length

d trench depth

D hydrodynamic diameter (outer pipe diameter including any coating)

Dexposure deterministic fatigue damage ([2.7.2])

Dfat Accumulated fatigue damage

Dfat,ST-F101 predicted fatigue damage from all sources according to DNVGL-ST-F101 ([2.7.7])

Dfat,RP-F105 Predicted fatigue damage for a particular free span period according to this RP ([2.7.7])

Dincr increased hydrodynamic diameter ([A.10.3])

Ds outer steel diameter

e gap between the bottom of the pipe and the seabed, ([1.6.2] and [1.6.5])

es void ratio

(e/D) seabed gap ratio

E Young's modulus

EI bending stiffness

fBEF frequency of an infinitely long beam on a linear-elastic foundation ([6.9.7])

fCF-RES,j response frequency for dominant cross-flow mode

fcyc,i cycle counting frequency for stress cycle partition i

fcyc,IL/CF cycle counting frequency for in-line or cross-flow stress cycles ([4.3.7], [4.6.20])

fLKCRcyc,CF cycle counting frequency for the combined CF stress with LKCR response model ([4.5.10])

fRMcyc,CF cycle counting frequency for the combined CF stress with standard response model ([4.4.13])

fcn concrete construction strength

fconIL.j natural frequency of the j-th contributing in-line mode ([4.6.10])

fpartIL.j natural frequency of the j-th participating in-line mode ([4.6.10])

fIL/CF,j natural frequency in in-line or cross-flow direction for the j-th single span mode

fSSIL/CF,j natural frequency in in-line or cross-flow direction for the j-th single span mode

fj j-th natural frequency of span in-line (fIL,j) or cross-flow (fCF,j) (determined at no flow around the pipe)

fL lift loading frequency ([4.5.1])

fratio ratio of two consecutive cross-flow modal frequencies ([4.4.4])


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fr,KC KC-dependent coordinate in LKCR response model ([4.5.5])

frd,j design frequency ratio for j-th mode ([4.5.5])

fs vortex shedding frequency(Uc + Uw)/fwD

fw wave frequency

F correction factor for pipe roughness

FL lateral pipe-soil contact force

FV vertical pipe-soil contact force

FX cumulative distribution function

g acceleration of gravity

gA non-dimensional response surface for maximum modal curvature ([6.9.10])

gc correction function due to steady current ([5.4.1])

gD drag force term ([5.4.1])

gI inertia force term ([5.4.1])

G shear modulus of soil or incomplete complementary Gamma function

G(ω) frequency transfer function from wave elevation to flow velocity ([3.3.5])

h water depth, i.e. distance from the mean sea level to the pipe

Heff effective lay tension ([6.5.4])

HS significant wave height

I moment of inertia

Ic turbulence intensity over 30 minutes

Ip plasticity index, cohesive soils

k wave number ([3.3.5]) or depth gradient

kc soil parameter or empirical constant for concrete stiffening

kM non-linear factor for drag loading ([2.6.10])

kp peak factor ([2.6.10])

kw normalisation constant

k1 soil stiffness

k2 soil stiffness

k/D pipe roughness ([5.4.4])

K soil stiffness

KL lateral (horizontal) dynamic soil stiffness

KV vertical dynamic soil stiffness


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KC Uw/fwD

KS stability parameter ([4.1.8])

Ksd Design stability parameter ([4.3.9])

L free span length (apparent, visual) or mode shape length

Leff effective span length

Lk length of span number k in interacting multi-span ([1.6.2])

Lsh length of span shoulder

Lsh,k length of span shoulder number k in interacting multi-span ([1.6.2])

m fatigue exponent ([2.5.3])

m(s) mass per unit length including structural mass, added mass and mass of internal fluid

maug augmented number of contributing modes in case of addition cross-flow induced in-line mode ([4.6.19])

me effective mass per unit length ([6.6.6])

MIL/CFE bending moment in in-line or cross-flow direction due to environmental effects ([2.6.5])

Mstatic static bending moment

Mn spectral moments of order n ([3.3.6], [5.2.6])

n number of participating modes ([4.4.8])

ni number of stress cycles for stress block i

nIL/CF number of participating in-line or cross-flow modes ([6.10.4])

nSSIL/CF number of participating in-line or cross-flow modes in isolated single span ([6.10.4])

N number of independent events in a return period ([3.6.1]) or number of modes with non-negligiblewave-induced damage contributions ([5.2.7])

Nc soil bearing capacity parameter

Ni number of cycles to failure for stress block i

NL integer ratio of lift loading frequency to wave frequency ([4.5.1])

Nq soil bearing capacity parameter

Nsw number of cycles when S-N curve change slope ([2.5.3])

Ntr true steel wall axial force ([6.4.3])

Nγ soil bearing capacity parameter

p() probability density function

pe external pressure

pi internal pressure

P(x,t) hydrodynamic load per unit length ([5.4.1])


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Pcr critical buckling load =(1+CSF)C2π2EI/Leff2

Pi probability of occurrence for i’th stress cycle

q submerged weight of pipe or deflection load per unit length

r radial coordinate of pipe cross-section

Rc current reduction factor ([3.4.1])

RD reduction factor from wave direction and spreading ([3.4.3])

Rv vertical soil reaction (DNVGL-RP-F114)

RIθ reduction factor from turbulence and flow direction ([4.6.5])

Rk reduction factor from damping ([4.4.11])

Re Reynolds number Re = UD/ν

s spreading parameter ([3.4.4])

sg specific gravity ([4.4.14])

su undrained shear strength, cohesive soils

S in-line characteristic stress range for a given sea state ([5.2.2])

SLKCRCF,j cross-flow VIV stress range for j-th mode, LKCR response model ([4.5.6])

SRMCF,j cross-flow VIV stress range for j-th mode, standard reponse model ([4.4.10])

SCF-IL in-line stress range for candidate mode for cross-flow induced in-line response ([4.6.17])

SLKCRcomb,CF combined stress range from LKCR response model ([4.5.9])

SRMcomb,CF combined stress range from standard cross-flow response model ([4.4.12])

Scomb,IL/CF combined stress range for in-line or cross-flow stress cycles ([4.3.7], [4.6.19])

Si the i-th stress range corresponding to ni cycles

Seff effective axial force ([6.5.4])

SmaxIL response stress range associated with the dominant in-line mode ([4.6.8])

SIL,j response stress range associated with j-th contributing in-line mode ([4.6.18], [4.6.19])

SPIL,j preliminary stress range for j-th in-line mode i.e. stress range prior to mode competition ([4.6.6]),

SRMIL,j in-line VIV response model stress range for j-th mode ([4.6.13])

Ssw stress at intersection between two S-N curves ([2.5.3])

SSS one-sided stress response spectral density function ([5.2.7], [5.2.11])

St Strouhal number

SUU wave velocity spectra at pipe level ([3.3.5])

Sηη wave spectral density ([3.3.3])


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t Time

ts pipe wall thickness

Texposure load exposure time

TFM,ILHs,Tp,θ marginal fatigue life capacity against direct wave action ([5.2.2])

TRM,CFHs,Tp,θ marginal fatigue life capacity against cross-flow VIV ([4.2.1])

TRM,ILHs,Tp,θ marginal fatigue life capacity against in-line VIV ([4.2.2])

Tlife fatigue design life capacity

Tp peak period

Tu mean zero up-crossing period of oscillating flow ([3.3.6])

Tw wave period

U total flow velocity normal to the pipe =Uc + Uw

U(z) current velocity at elevation z above seabed ([3.2.6])

Uc current velocity normal to the pipe ([3.4.1])

Uc,i-year i-year return period value for the perpendicular current component at pipe level ([2.3.2])

Uextreme flow condition for characteristic environmental event ([2.3.2])

Us significant wave velocity ([3.3.6])

Uw significant wave-induced flow velocity normal to the pipe, corrected for wave direction and spreading([3.4.3])

Uw,i-year i-year return period value for the perpendicular component of the significant wave induced flow velocityat pipe level ([2.3.2])

v vertical soil settlement (pipe embedment)

VR (Uc + Uw)/fwD

VdecR reduced velocity, decreased due to enlarged diameter ([A.12.3])

VRd reduced velocity (design value) with safety factor ([4.4.3])

VCFR,onset Onset reduced velocity in cross-flow direction ([4.4.4])

VILR,onset Onset reduced velocity in in-line direction ([4.6.4])

w wave energy spreading function ([3.4.4])

x coordinate along pipe axis

xc return period value ([3.6.1], [3.6.2])

xe,j end point of j-th mode shape ([4.3.3])

xend,j end point of participation interval j-th mode shape ([4.3.3])

xstart,j start point of participation interval for j-th mode shape ([4.3.3])


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x0,j start point of j-th mode shape ([4.3.3])

y lateral (in-line) coordinate

z height above seabed or vertical (cross-flow) coordinate

zm macro roughness parameter ([3.2.8])

zr reference (measurement) height ([3.2.6])

z0 sea-bottom roughness ([3.2.6])

1.14.2 Greekα current flow velocity ratio, generalised Phillips’ constant or Weibull scale parameter

αe temperature expansion coefficient ([6.5.4])

αT parameter to determine wave period ([3.5.3])

β Weibull shape parameter and relative soil stiffness parameter ([6.8.8])

βj mode competition reduction exponent for j-th in-line mode ([4.6.12])

Δ/D relative trench depth ([4.4.7])

Δpi internal pressure difference relative to laying ([6.5.4])

ΔT temperature difference relative to laying ([6.5.4]) or storm duration

δ static pipe deflection ([6.8.7]) or statistical skewness (section [3.5.1])

ε band-width parameter ([5.2.5])

Γ gamma function

γ peak-enhancement factor for JONSWAP spectrum ([3.3.3]) or Weibull location parameter

γf,IL/CF safety factor on in-line or cross-flow natural frequency ([2.7.1], [2.7.2])

γk safety factor on stability parameter ([2.7.2])

γon,IL/CF safety factor on onset value for in-line or cross-flow VR ([2.7.2])

γs safety factor on stress amplitude ([2.7.2])

γsoil total unit weight of soil

γsoil’ submerged unit weight of soil

γwater unit weight of water

κRFC rainflow-counting factor ([5.2.5])

κ static curvature

κj modal curvature for the j-th mode


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j mode shape weighting factor for the j-th mode ([5.2.10])

η usage factor

μ mean value

μa axial friction coefficient

μL lateral friction coefficient

ν Poisson's ratioor kinematic viscosity

Φ() cumulative normal distribution function

φ() normal distribution function

φj mode shape of j-th mode

φs angle of friction, cohesionless soils

ψj modal stress for the j-th mode ([5.2.9])

ψKC KC-dependent reduction factor in LKCR response model ([4.5.7])

ψKs Ks-dependent reduction factor in LKCR response model ([4.5.7])

ψmmempirical multi-mode correction factor for single-mode analysis of load effects due to direct wave action([2.6.10], [5.2.2])

correction factor for CM due to pipe roughness ([5.4.11])

correction factor for CM due to effect of pipe in trench ([5.4.13])

reduction factor for CM due to seabed proximity ([5.4.12])

correction factor for CD due to Keulegan-Carpenter number and current flow ratio ([5.4.5])

correction factor for CD due to effect of pipe in trench ([5.4.7])

amplification factor for CD due to cross-flow vibrations ([5.4.8])

reduction factor for CD due to seabed proximity ([5.4.6])

correction factor for onset cross-flow due to seabed proximity ([4.4.6])

reduction factor for onset cross-flow due to the effect of a trench ([4.4.7])

correction factor for onset of in-line due wave ([4.6.7])

ρincr density of material used to increase the hydrodynamic diameter ([A.12.3])


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ρw density of water

ρs/ρ specific mass ratio between the pipe mass (not including added mass) and the displaced water.

σ stress, spectral width parameter or standard deviation

σc standard deviation of current velocity fluctuations

σIL/CFE environmental stress in in-line or cross-flow direction ([2.6.6])

σFM,max maximum environmental stress due to direct wave loading ([2.6.10])

σs effective soil stress (DNVGL-RP-F114) or standard deviation of wave-induced stress response ([5.2.3])

σs,I standard deviation of wave-induced stress amplitude with no drag effect ([2.6.10])

σU standard deviation of wave-induced flow velocity ([5.2.12])

πSeff non-dimensional effective axial force parameter ([6.9.6])

θ flow direction

θrel relative angle between flow and pipeline direction

ζh hydrodynamic modal damping ratio

ζh,j hydrodynamic modal damping ratio for the j-th mode ([5.2.13])

ζsoil soil modal damping ratio

ζstr structural modal damping ratio

ζT total modal damping ratio

ζT,j total damping ratio for the j-th mode ([5.2.8])

ω angular wave frequency

ωj angular natural frequency for j-th mode

ωp angular spectral peak wave frequency

1.15 Verbal formsTable 1-5 Definition of verbal forms

Term Definition

shall verbal form used to indicate requirements strictly to be followed in order to conform to the document

should verbal form used to indicate that among several possibilities one is recommended as particularly suitable,without mentioning or excluding others, or that a certain course of action is preferred but not necessarilyrequired

may verbal form used to indicate a course of action permissible within the limits of the document


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SECTION 2 DESIGN CRITERIA

2.1 General

2.1.1 For all temporary and permanent free spans a free span assessment addressing the integrity with respect tofatigue (FLS) and local buckling (ULS) shall be performed.All potential sources of fatigue damage shall be considered as part of the integrated fatigue damageassessment.This document only considers fatigue due to environmental loads (VIV and direct wave loads). All othersources, such as trawl interaction, global buckling cycles, excessive lateral displacements, pressure andtemperature variation, installation etc., shall be accounted for according to the relevant governing designcode, for instance DNVGL-ST-F101.Dents or damage which may reduce the fatigue resistance of the pipe are not accounted for in this document,but shall be considered when choosing a relevant fatigue resistance curve, i.e. S-N curve, and the associatedstress concentration factor (SCF).

2.1.2 Vibrations due to vortex shedding and direct wave loads are acceptable provided the fatigue and ULS criteriaspecified herein are fulfilled.

2.1.3 All active modes, defined in [1.12], shall be considered in FLS and ULS calculations. Unless otherwisedocumented, the damage contribution for each mode should relate to the same critical (weld) location forFLS calculations.

2.1.4 Figure 2-1 shows part of a flow chart for a typical pipeline design. After deciding on diameter, material, wallthickness, potential trenching, and coating for weight and insulation, any global buckling design and releaseof effective axial force need to be addressed before the free spans shall be assessed. It is emphasised thatthe free span assessment shall be based on a realistic estimate of the effective axial force, and any changesdue to sagging in spans, lateral buckling, end expansion, changes in operational conditions, etc. shall beproperly accounted for.Note that the sequence in Figure 2-1 is not always followed. Normally an initial routing will be performedbefore detailed pipeline design is started. A typical design process follows this flow chart in iterations until afinal, acceptable design is found.As span lengths/gaps and effective axial force distributions may change significantly for different operationalconditions, it is challenging to identify critical/governing span scenarios, especially for flowlines. This willalso depend on any global buckling or other release of effective axial force by end expansion or sagging intospans, etc.


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Figure 2-1 Flow chart for pipeline design and free span design

2.1.5 The following functional requirements to the fatigue design apply:

— The aim of fatigue design is to ensure an adequate safety against fatigue failure within the design life ofthe pipeline.

— The fatigue analysis should cover a period which is representative for the free span exposure period.— All stress fluctuations imposed during the entire design life of the pipeline capable of causing fatigue

damage shall be accounted for.— The local fatigue design checks shall be performed at all free spanning pipe sections.

2.1.6 Figure 2-2 gives an overview of the required design checks for a free span.


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

2.2 Non-stationarity of spans

2.2.1 Free spans can be divided into the following main categories:

— Scour-induced free spans caused by seabed erosion or bed-form activities. The free span scenarios (spanlength, gap ratio, etc.) may change with time.

— Unevenness-induced free spans caused by an irregular seabed profile. Normally the free span scenario istime invariant unless operational parameters such as pressure and temperature change significantly.

2.2.2 In the case of scour induced spans, where no detailed information is available on the maximum expectedspan length, gap ratio and exposure time, the following apply:


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— Where uniform conditions exist and no large-scale mobile bed forms are present, the maximum spanlength may be taken as the length resulting in a static mid span deflection equal to one external diameter(including any coating).

— The exposure time may be taken as the remaining operational lifetime or the time duration until possibleintervention works will take place. All previous damage accumulation shall be included.

2.2.3 Additional information, such as free span length, gap ratio or natural frequencies, from surveys combinedwith an inspection strategy may be used to qualify scour induced free spans. These aspects are not coveredin this document. Guidance is found in Mørk et al. (1999) and Fyrileiv et al. (2000).

2.2.4 Changes in operational conditions such as pressure and temperature may cause significant changes in spancharacteristics and shall be accounted for in the free span assessment.

Guidance note:One example may be flowlines, installed on uneven seabed, that buckle during operation. The combination of shut-down andlateral buckling may cause tension in the pipeline so several free spans develop.The span length and gap may vary significantly over the range of operational conditions (pressure/temperature). In such casesthe whole range of operational conditions should be checked because the lowest combination may be governing for the free spandesign.


2.2.5 Other changes during the design life such as corrosion shall also be considered in the span assessment whererelevant. Corrosion conditions shall always be accounted for in the estimation of fatigue resistance, e.g. whenchoosing an S-N curve.

Guidance note:For modal reponse calculations, subtracting half the corrosion allowance when performing the span assessment may be appliedin case of no better information. If the fatigue damage is in-line dominated, and corrosion occurs at 6 o’clock and 12 o’clockrespectively, the corrosion can be disregarded in the modal response calculations.


2.3 VIV avoidance criteria

2.3.1 The avoidance criteria proposed herein can be applied to conservatively determine if VIV must be includedin FLS and ULS calculations for a given free span. If any of the criteria in this [2.3] are violated, eitherthe fatigue screening criteria in [2.4] may be applied, or full fatigue and extreme environmental loadingcalculations shall be performed according to [2.5] and [2.6].In the case of wave dominated flow conditions (according to [2.4.5]), full fatigue and extreme environmentalloading calculations shall be performed even if the criteria for VIV avoidance in this section are fulfilled.

2.3.2 The characteristic environmental condition, to be used in the avoidance or ULS (see [2.6.3]) criteria, shallreflect the most probable extreme response over a specified exposure period. For permanent operationalconditions and temporary phases with duration in excess of 12 months, a 100-year return period applies, i.e.


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the characteristic environmental condition is the condition with 10-2 annual exceedance probability. Whendetailed information about the joint probability of waves and current is not available, this condition may beapproximated by the most severe condition among the following two combinations:

— The 100-year return condition for waves combined with the 10-year return condition for current.— The 10-year return condition for waves combined with the 100-year return condition for current.

The representative flow condition Uextreme for the characteristic environmental event is thus given by

where:

Uc,i-year = i-year return period value for the perpendicular current component at pipe level, see [3.4.1]Uw,i-year = i-year return period value for the perpendicular component of the significant wave induced flow

velocity at pipe level, see [3.4.3].

For a temporary phase with duration less than 12 months but in excess of three days, a 10-year returnperiod for the actual seasonal environmental condition applies. An approximation to this condition is to usethe most severe condition among the following two combinations:

— The seasonal 10-year return condition for waves combined with the seasonal 1-year return condition forseasonal current.

— The seasonal 1-year return condition for waves combined with the seasonal 10-year return condition forcurrent.

The representative flow condition Uextreme for the characteristic environmental event in this case becomes

The season covered by the environmental data shall be sufficient to cover uncertainties in the beginning andend of the temporary condition to account for e.g. delays. For a temporary phase less than three days anextreme load condition may be specified based on reliable weather forecasts.

2.3.3 The lowest natural frequencies in in-line and cross-flow directions for a given free span are termed fIL,1 andfCF,1. If the following inequalities for the fundamental frequencies are fulfilled, no VIV is expected to occurduring the design exposure period of the span:

where:

Δ = Outer pipe diameter incl. coating (hydrodynamic diameter)


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γf,IL = Safety factor on in-line frequency, see [2.7.2]

γf,CF = Safety factor on cross-flow frequency, see [2.7.2]

VILR,onset = In-line onset value for the reduced velocity, see [4.6.4]

2.3.4 The avoidance criteria in [2.3.3] may be extended to the j-th in-line or cross-flow mode in the trivial manner,i.e. by replacing the fundamental mode natural frequencies fIL,1 and fCF,1 by the natural frequencies fIL,j and

fCF,j for the j-th mode and by using VILR,onset for the j-th mode. If the inequalities in [2.3.3] then are fulfilled,

the j-th mode is not expected to be excited by VIV during the design exposure period of the span.

2.4 Screening fatigue criteria

2.4.1 The screening criteria proposed herein apply to fatigue caused by vortex induced vibrations (VIV) and directwave loading in combined current and wave loading conditions. The screening criteria have been calibratedagainst full fatigue analyses to provide a fatigue life in excess of 50 years. The criteria apply to spans witha response dominated by the 1st symmetric mode (one half-wave) and should preferably be applied forscreening analyses only. If violated, more detailed fatigue analyses should be performed. The ULS criterion in[2.6] shall always be checked.

Guidance note:The screening criteria as given in [2.4] are calibrated with safety factors to provide a fatigue life in excess of 50 years. As suchthese criteria are intended to be used for the operational phase.The criteria may also be used for the temporary phases (as-laid/empty and flooded) by applying the 10-year return period valuefor current for the appropriate season, Uc,10year, instead of the 100-year return period value,


2.4.2 The screening criteria proposed herein are based on the assumption that the current velocity may berepresented by a 3-parameter Weibull distribution. If this is not the case, e.g. for bi-modal currentdistributions, care must be taken and the applicability of these screening criteria shall be checked by fullfatigue calculations.

2.4.3 The in-line natural frequencies fIL,j must fulfil:

where:

γIL = Screening factor for in-line, see [2.7.1]

=


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Minimum value of 0.6.

L = Free span length

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

2.4.4 The cross-flow natural frequencies fCF,j shall fulfil:

where γCF is a screening factor for cross-flow, see [2.7.1], and VCF

R,onset is the cross-flow onset value for thereduced velocity, see section [4.4.4]. If the above criterion is violated, a full in-line and cross-flow VIV fatigueanalysis is required.

2.4.5 Fatigue analysis due to direct wave action is not required provided that:

and that the above screening criteria for in-line VIV are fulfilled. If this criterion is violated, a full fatigueanalyses due to in-line VIV and direct wave action is required.

2.5 Fatigue criterion

2.5.1 The fatigue criterion is formulated as:

η × Tlife ≥ Texposure

where η is the allowable fatigue damage ratio, see [2.7.2], Tlife is the fatigue design life capacity and Texposureis the design life or load exposure time.

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


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where:

Dfat = Accumulated fatigue damage.Ni = Total number of stress cycles corresponding to the (inner or outer fibre) stress range Si

Ni = Number of cycles to failure at stress range Si

Σ = Implies summation over all stress fluctuations in the design life

2.5.3 The number of cycles to failure at stress range S is defined by the S-N curve of the form:

where:

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

= Characteristic fatigue strength constant defined as the mean-minus-two-standard-deviationcurve

Ssw = Stress at intersection of the two S-N curves given by:

where Nsw is the number of cycles for which change in slope appear. Log Nsw is typically 6 or 7.

A typical two-slope S-N curve is illustrated in Figure 2-3.

Figure 2-3 Typical two-slope S-N curve


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2.5.4 The S-N curve shall be applicable for the material, construction detail, location of the initial defect (crackinitiation point) and corrosive environment. The basic principles in DNVGL-RP-C203 apply.

2.5.5 The fatigue life capacity, Tlife, is formally expressed as:

where:

Pi = Probability of occurrence for the “i”th stress cyclefcyc,I = Cycle counting frequency corresponding to the i-th stress cycle.

2.5.6 According to DNVGL-RP-C203, S-N curves shall be selected for both the weld root and the weld toe, i.e. atthe inner and outer circumference of the pipe steel cross-section respectively. The fatigue stress associatedwith VIV and direct wave loading response shall be calculated as the extreme outer fibre stresses, i.e. thebending stresses at the inner and outer radius of the steel cross-section. Since both the S-N curves and thestresses are different at each critical location, it is not always obvious which location is more conservativethan the other. Therefore fatigue calculations shall generally be performed at both the weld root and the weldtoe, and the fatigue life capacities calculated according to [2.5.9] shall be taken as the minimum of the two.

2.5.7 The concept adopted for the fatigue analysis applies to both response models and force models. The stressranges to be used may be determined by:

— a response model, see Sec.4— a force model, see Sec.5.

2.5.8 The following approach is recommended:

— The fatigue damage is evaluated independently in each sea state, i.e. the fatigue damage is calculatedin each cell of a scatter diagram in terms of Hs, Tp and θ times the probability of occurrence for theindividual sea state.

— In each sea state (Hs, Tp, θ) is transformed into (Uw, Tu) at the pipe level as described in [3.3].— The sea state is represented by a significant short-term flow-induced velocity amplitude Uw with mean

zero up-crossing period Tu, i.e. by a train of regular wave-induced flow velocities with amplitude equal toUw and period Tu. The effect of irregularity will reduce the number of large amplitudes. Irregularity maybe accounted for provided it is properly documented.

— Integration over the long-term current velocity distribution for the combined wave and current flow isperformed in each sea state.


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2.5.9 The total fatigue life capacities in the in-line and cross-flow directions are established by integrating over allsea states, i.e.

where PHs,Tp,θ is the probability of occurrence of each individual sea state, i.e. the probability of occurrencereflected by the cell in a scatter diagram. The in-line fatigue life capacity is conservatively taken as theminimum capacity – corresponding to maximum damage – from VIV (RM) or direct wave loads (FM) in eachsea state.The fatigue life is the minimum of the in-line and the cross-flow fatigue lives.

2.5.10 The following marginal fatigue life capacities are evaluated for (all) sea states characterised by (Hs, Tp, θ).

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

Marginal fatigue capacity against cross-flow VIV in a sea state (Hs, Tp, θ) integrated over long term pdf for thecurrent, see [4.2.1].

Marginal fatigue capacity against direct wave actions in a single sea state characterised by (Hs, Tp, θ) usingmean value of current, see [5.2.2].

2.5.11 Unless otherwise documented, the following assumptions apply:

— The current and wave-induced flow components at the pipe level are statistically independent.— The current and wave-induced flow components are assumed co-linear. This implies that the directional

probability of occurrence data for either waves or current (the most conservative with respect to fatiguedamage) shall be used for both waves and current.


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2.6 ULS criterion

2.6.1 Local buckling calculations shall be in compliance with the combined loading criteria for load controlledcondition in DNVGL-ST-F101 Sec.5, or similar stress-based criteria in a recognized standard. Environmentalload effects due to VIV and direct wave loading shall be included in the local buckling calculations by meansof an environmental bending moment according to [2.6.6], or relevant bending stresses if another criterionis applied. Simplifications are allowed provided that verification is performed by more advanced modelling/analyses in cases where the ULS criteria become governing.In the local buckling check, the environmental bending moment according to [2.6.6] shall be combined withfunctional bending moment, axial force and pressure, as specified in DNVGL-ST-F101.

2.6.2 Typically, the load effects to be considered in the ULS checks shall be:Vertical direction:

— static bending (self weight, seabed profile, etc.)— cross-flow VIV— trawl gear interaction.

Horizontal direction:

— in-line VIV— direct drag and inertia load effects from combined wave and current— trawl gear interaction.

VIV and direct wave loading will generally cause environmental bending moments in both in-line and cross-flow directions, which are orthogonal. In the local buckling check according to DNVGL-ST-F101, it is thereforeimportant to account for the total bending moment vector sum, including contributions from both directions.Note that different soil stiffnesses should be used for different load directions and load rates (static/dynamic).

2.6.3 Environmental bending moments in a span for ULS calculations shall be calculated according to the relevantcharacteristic environmental condition. The relevant characteristic environmental condition depends on theexpected exposure period of the span. How to choose the appropriate condition is described in [2.3.2].

2.6.4 It has been observed that large diameter pipelines in shallow waters experiencing fairly extremeenvironmental conditions, may be subjected to large lateral displacements on the span shoulders. Forsuch span conditions, the principles in DNVGL-RP-F109 may be applied to assess the likelihood of largelateral displacements on span shoulders. Should such considerations imply that lateral displacements on theshoulders are likely in design conditions, the lateral dynamic soil stiffness should be reduced appropriately toaccount for lateral sliding on the span shoulders in ULS calculations.Note that assuming pinned-pinned boundary conditions as an estimate of reduced shoulder stiffness maybe non-conservative since spans under such conditions are short and therefore have effective lengths whichmay be so long that the pinned-pinned boundary is actually stiffer than the real scenario, see Sollund et al.(2015b). This effect may be increased in magnitude by a reduction in stiffness due to sliding.


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2.6.5 The maximum environmental bending moments due to in-line and cross-flow VIV or direct wave and currentaction may be found from the dynamic stresses. For convenience, these are calculated based on the outerfibre of the steel cross section, at a distance of Ds/2 from the center of the pipe

σIL/CFE = Maximum environmental stress given below

I = Moment of inertiaDs = Outer diameter of steel pipe

2.6.6 The maximum environmental stresses are calculated as:

where:

Scomb,IL = In-line stress range, see [4.6]Scomb,CF = Cross-flow stress range, see [4.3]σFM,max = Maximum environmental stress due to direct wave loading, see [2.6.10]

σCFE = Cross-flow environmental stress

σILE = In-line environmental stress

For the cross-flow direction, the stress simply stems from the VIV induced amplitudes. For the in-linedirection, the dynamic stress range is taken as the sum of the maximum combined stress range from in-lineVIV (incl. potential contribution from cross-flow induced in-line VIV, see [4.6]) and stresses due to directwave loading.

2.6.7 Two different methods can be applied to establish the maximum environmental stress, σFM,max, see DNVGL-ST-F201:

— design based on response statistics— design based on environmental statistics.

For free span analysis design based on environmental statistics it is recommended to use:


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— a design storm approach with irregular wave analysis in time domain (TD) or irregular wave analyses infrequency domain (FD), or

— a design wave approach using regular wave analysis in TD with bending moment calculated from Hmax.

2.6.8 The design wave approach may use a set of appropriate design cases in terms of wave height, wave period,current and directionality, likely to produce the extreme response with a chosen return period. This may bedone using a return period value for Hs with a wave period variation covering a realistic variation range, e.g.a 90% confidence interval, or using environmental contours.

Guidance note:Cases with moderate Hs and a large wave period are often governing in the design wave approach. Hence more focus should begiven to large Tp values.In case of a quasi-static and not dynamically sensitive pipeline response for the ULS condition, the 100-year Hmax value with anassociated period could be used to generate the regular design wave and the corresponding quasi-static response.


2.6.9 The maximum environmental stress, σFM,max, from direct wave loading can be established using a timedomain design storm approach as follows:

1) Global time domain response analysis is performed for the actual stationary environmental condition. Atypical storm duration may be taken as 3 hours.

2) Time histories for the dynamic stress are established.3) A 3-parameter Weibull distribution is fitted to the individual stress maxima between successive mean

value crossings σFM(t).4) A Gumbel distribution is established for the extreme value for the largest individual maxima of σFM(t) for

the 3 hour duration.5) σFM,max is estimated as the p-percentile in the Gumbel distribution, i.e., the 57th percentile for the

expected value or the most probable maximum value corresponding to a 37th percentile.

2.6.10 As a simplified alternative σFM,max may be calculated using:

where kp is a peak factor, ΔT is the storm duration equal to 3 hours and fv is the characteristic vibrationfrequency. σs is the standard deviation of the stress response σFM(t) and σs,I is the standard deviation for thestress response without drag loading. σs and σs,I may be calculated from a time-domain or frequency-domainanalysis, see Sec.5. kM is a factor accounting for non-linearity in the drag loading.


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ψmm is an empirical multi-mode correction factor. If σs is obtained from a single mode analysis in an isolatedsingle span, ψmm = 1.07. If σs is obtained from a multi-mode analysis in either an isolated single span or aninteracting multi-span, ψmm =1.0.A static stress component may be added if relevant.

Guidance note:In case the ULS check due to direct wave action is found to be governing, the effect of the axial force should be considered.


2.6.11 It is required that the pipe can withstand the fatigue exposure within its characteristic environmentalcondition for any relevant design phase, i.e. temporary, water filled, operational and shut-down. Thecharacteristic environmental condition is defined in [2.3.2].

2.7 Safety factors

2.7.1 The safety factors to be used with the fatigue screening criteria in [2.4] are listed below.

Table 2-1 Safety factors for screening criteria

γIL 1.4

γCF 1.4

2.7.2 A criterion for fatigue resistance, which is in compliance with the safety class concept specified in DNVGL-ST-F101 Sec.2, is expressed through the following safety factor format:

where γs, γf,IL, γf,CF, γk, γon,IL, γon,CF and η are safety factors on stress, in-line frequency, cross-flowfrequency, soil and structural damping, onset of in-line VIV and onset of cross-flow VIV and fatigueutilization, respectively. The partial safety factors apply to both response- and force model calculations, asdetailed in Sec.4 and Sec.5. The values for some of the partial safety factors depend on the safety class andquality of the analysis input, see Table 2-2 and Table 2-3.

Table 2-2 General safety factors for fatigue

Safety ClassSafety factor

Low Medium High

η 1.0 0.5 0.25


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Safety ClassSafety factor

Low Medium High

γk 1.0 1.15 1.30

γs 1.3

γon,IL 1.1

γon,CF 1.2

Table 2-3 Safety factors for natural frequencies, γf,IL / γf,CF

Safety class

Low Medium HighFree span classifications

γf,IL γf,CF γf,IL γf,CF γf,IL γf,CF

Very well defined 1.0 1.0 1.0 1.0 1.0 1.0

Well to very well defined 1.0 1.05 1.0 1.1 1.0 1.15

Well defined 1.05 1.05 1.1 1.1 1.15 1.15

Not well defined 1.1 1.1 1.2 1.2 1.3 1.3

Comments:

— γs shall be multiplied by the stress range (S ∙ γS)— γf,IL/CF applies to the j-th mode natural frequency (fj/γf,IL/CF)— γon applies to onset values for in-line and cross-flow VIV ( and )

— γk applies to the total damping, i.e. the sum of soil, structural and hydrodynamic damping ratios— for ULS, the calculation of load effects shall be performed without safety factors (γS = γf = γk = γon =

1.0), see also [2.7.5].

2.7.3 The free spans shall be categorised as:Not well defined – spans where important span characteristics like span length, gap and effective axial forceare not accurately determined/measured.Selection criteria for this category are (but not limited to):

— erodible seabed (scouring)— environmental conditions given by extreme values only— operational conditions change the span scenario and these changes are not assessed in detail, or— span assessment in an early stage of a project development.

Well defined – spans where important span characteristics like span length, gap and effective axial forceare determined/measured. Site-specific soil conditions and a long-term description of the environmentalconditions exist.Well to very well defined – The same requirements as for very well defined span, with the exceptionthat the structural response quantities may be calculated by FE analyses using flat span shoulders and


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intermediate shoulders if relevant, and a mean effective axial force can be assumed representative for thestatic equilibrium condition in the isolated single span or interacting multi-span.Very well defined – spans where important span characteristics like span length, gap and effective axialforce are determined/measured with a high degree of accuracy. The soil conditions and the environmentalconditions along the route are well known.Requirements:

— span length/gap actually measured and well defined due to span supports or uneven seabed— structural response quantities determined by detailed FE analyses where accurate seabed topography,

load history, distributed effective axial force and other relevant non-linear effects are accounted for— soil properties assessed by soil samples along route— site-specific long-term distributions of environmental data available— effect of changes in operational conditions evaluated in detail.

More detailed guidance on the relationship between free span classifications and the required level of detail inthe structural response quantity calculations is given in section [6.4].

2.7.4 In case several phases with different safety classes shall be accounted for, the highest safety class shall beapplied for all phases as fatigue damage accumulates.

2.7.5 The reliability of the pipeline against local buckling (ULS criterion) is ensured by use of the safety classconcept as implemented by use of safety factors according to DNVGL-ST-F101.

2.7.6 DNVGL-RP-F105 has a partial safety factor format on allowable fatigue damage. Other standards willgenerally have other safety factor formats, or most often an allowable utilization without partial safetyfactors. If DNVGL-RP-F105 is applied to calculate partial damage contributions, and these are added todamage from other sources to adhere to a criterion in a different standard, the damage in DNVGL-RP-F105shall be normalized in an appropriate manner. A procedure to normalize the damage contribution from thisRP for fatigue evaluation according to DNVGL-ST-F101 is shown in [2.7.7].

2.7.7 The normalized damage Dfat,RP-F105 during the exposure period for a particular span is:

Dfat,RP-F105 is the damage in the predicted exposure period according to DNVGL-RP-F105, when the safetyclass has been accounted for. The allowable fatigue damage according to DNVGL-ST-F101 is:

where DFF is the allowable design fatigue factor for the relevant safety class in DNVGL-ST-F101 and


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Dfat,ST-F101 comprises all sources of cyclic fatigue loading in all phases of the pipeline design life. To includecontributions from fatigue damage in free spans to Dfat,ST-F101, Dfat,RP-F105 may be added as follows:

where ni shall be interpreted as all stress cycles which are not included in the calculation of Dfat,RP-F105.

2.7.8 In standard free span design scenarios, the pipeline will undergo different phases, i.e. installation, empty,water-filled, pressure test, operation and shut down phases. Fatigue damage will occur in all pipeline designphases, and free span morphology will generally be different in all phases after installation. It is requiredin DNVGL-ST-F101 that a fatigue utilization distribution shall be developed to define the allowable fatiguedamage in each individual phase, ultimately ensuring that the total damage is less than 1/DFF for the entirelifetime.Free span design shall include damage contributions from each phase, accounting for differences in pipeweight, effective axial force distribution, span geometry (lengths, gaps, shoulder lengths, etc.) and phaseduration.


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SECTION 3 ENVIRONMENTAL CONDITIONS

3.1 General

3.1.1 The objective of the present section is to provide guidance on:

— the long term current velocity distribution— short-term and long-term description of wave-induced flow velocity amplitude and period of oscillating

flow at the pipe level— return period values.

3.1.2 The environmental data to be used in the assessment of the long-term distributions shall be representativefor the particular geographical location of the pipeline free span.

3.1.3 The flow conditions due to current and wave action at the pipe level govern the response of free spanningpipelines.

3.1.4 The environmental data shall be collected from periods that are representative for the long-term variationof the wave and current climate. In case of less reliable or limited wave and current data, the statisticaluncertainty should be assessed and, if significant, included in the analysis.

3.1.5 Preferably, the environmental load conditions should be established near the pipeline using measurementdata of acceptable quality and duration. The wave and current characteristics shall be transferred(extrapolated) to the free span level and location using appropriate conservative assumptions.

3.1.6 The following environmental description may be applied:

— directional information, i.e. flow characteristic versus sector probability, or— omnidirectional statistics if the flow is uniformly distributed.

If no such information is available, the flow should be assumed to act perpendicular to the axis of the pipelineat all times.

3.2 Current conditions

3.2.1 The steady current flow at the free span level may have components from:

— tidal current— wind-induced current


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— storm surge induced current— density driven current.

Guidance note:The effect of internal waves, which are often observed in parts of South East Asia, needs to be taken into account for the free spanassessment. Internal waves may have high fluid particle velocity which may be modelled as equivalent current distributions.


3.2.2 For water depths greater than 100 m, the ocean currents can be characterised by the driving and steeringagents:

— The driving agents are tidal forces, pressure gradients due to surface elevation or density changes, windand storm surge forces.

— The steering agents are topography and the rotation of the earth.

The modelling should adequately account for all agents.

3.2.3 The flow can be divided into two zones:

— An outer zone far from the seabed where the mean current velocity and turbulence vary only slightly inthe horizontal direction.

— An inner zone where the mean current velocity and turbulence show significant variations in the horizontaldirection and the current speed and direction is a function of the local sea bed geometry.

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

3.2.5 Current measurements using a current meter should be made in the outer zone outside the boundary layerat a level of 1 to 2 seabed form heights above the crest. For large-scale currents, such as wind driven andtidal currents, the choice of measurement positions may be based on the variations in the bottom topographyassuming that the current is geo-strophic, i.e. mainly running parallel to the large-scale bottom contours.Over smooth hills, flow separation occurs when the hill slope exceeds about 20o. Current data frommeasurements in the boundary layer over irregular bed forms are of little practical value when extrapolatingcurrent values to other locations.

3.2.6 In the inner zone the current velocity profile is approximately logarithmic in areas where flow separation doesnot occur:

where:


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z = elevation above the seabedzr = reference measurement height (in the outer zone)z0 = bottom roughness parameter to be taken from Table 3-1.

Table 3-1 Seabed roughness

Seabed Roughness z0 (m)

Silt ≈ 5 ×10-6

Fine sand ≈ 1 ×10-5

Medium sand ≈ 4 ×10-5

Coarse sand ≈ 1 ×10-4

Gravel ≈ 3 ×10-4

Pebble ≈ 2 ×10-3

Cobble ≈ 1 ×10-2

Boulder ≈ 4 ×10-2

3.2.7 If no detailed analyses are performed, the mean current values at the free span location may assume thevalues at the nearest suitable measurement point. The flow (and macro-roughness) is normally 3D andtransformation of current characteristics should account for the local bottom topography e.g. be guided bynumerical simulations.

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

The macro-roughness parameter zm is given by:

zm shall be taken less than 0.2.


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Figure 3-1 Definitions for 2D model

3.2.9 It is recommended to perform current measurements with 10 minutes or 30 minutes averages for use withFLS checks.

3.2.10 For ULS checks, 1-minute average values should be applied. The 1-minute average values may beestablished from 10 minutes or 30 minutes average values as follows:

where Ic is the turbulence intensity defined below.

3.2.11 The turbulence intensity, Ic, is defined by:

where σc is the standard deviation of the velocity fluctuations and Uc is the 10 min or 30 min average (mean)velocity at 1 Hz sampling rate.

3.2.12 If no other information is available, the turbulence intensity should be taken as 5%. Experience indicates thatthe turbulence intensity for macro-roughness areas is from 20% to 40% higher than the intensity over a flatseabed with the same small-scale seabed roughness. The turbulence intensities in a rough seabed area to beapplied for in-line fatigue assessment may conservatively be taken as typical turbulence intensities over a flatbottom (at the same height) with similar small-scale seabed roughness.


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3.2.13 Detailed turbulence measurements, if deemed essential, should be made at 1 m and 3 m above the seabed.High frequency turbulence (with periods lower than 1 minute) and low frequency turbulence must bedistinguished.

3.2.14 The current speed in the vicinity of a platform may be reduced from the specified free stream velocity, due tohydrodynamic shielding effects. In absence of a detailed evaluation, the guidance on shielding in DNVGL-RP-C205 can be used.

3.2.15 Possible changes in the added mass (and inertia actions) for closely spaced pipelines and pipeline bundlesshould also be accounted for.

3.3 Short-term wave conditions

3.3.1 The wave-induced oscillatory flow condition at the free span level may be calculated using numerical oranalytical wave theories. The wave theory shall be capable of describing the conditions at the pipe location,including effects due to shallow water, if applicable. For most practical cases, linear wave theory can beapplied. Wave boundary layer effects can normally be neglected.Linear wave theory has been applied for the formulations in this RP. Guidance on the applicability of linearwave theory as a function of the wave conditions and the water depth is given in DNVGL-RP-F109 andDNVGL-RP-C205. The formulations in [3.3] of this RP only apply for environmental conditions where linearwave theory is applicable or where linear wave theory has been demonstrated to be conservative. If linearwave theory is inadequate, significant wave induced flow velocities and mean up-crossing periods shall becalculated based on an applicable wave theory. If such an approach is not possible, conservative applicationsof regular wave theory may be applied.

3.3.2 The short-term, stationary, irregular sea states may be described by a wave spectrum Sηη(ω), i.e. the powerspectral density function of the sea surface elevation. Wave spectra may be given in table form, as measuredspectra, or in an analytical form.

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

where:


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ω = 2π/Tw is the angular wave frequency.Tw = Wave period.Tp = Peak period.ωp = 2π/Tp is the angular spectral peak frequencyg = Gravitational acceleration.

The generalised Phillips’ constant is given by:

The spectral width parameter is given by:

The peak-enhancement factor, if not specified, can be estimated by:

where Hs shall be given in metres and Tp in seconds.

The Pierson-Moskowitz spectrum appears for γ = 1.0.

3.3.4 Both spectra describe wind sea conditions that are reasonable for the most severe sea states. However,moderate and low sea states, not dominated by limited fetch, are often composed of both wind-sea andswell. A two peak (bi-modal) spectrum should be considered to account for swell if considered important.

3.3.5 The wave-induced velocity spectrum at the pipe level SUU(ω) may be obtained through a spectraltransformation of the waves at sea level using a first order wave theory:

G2(ω) is the frequency transfer function from sea surface elevation to wave-induced flow velocities at pipelevel given by:


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Where h is the water depth and k is the wave number established by iteration from the transcendentalequation:

Guidance note:

Note that the G2(ω) transfer function is valid for Airy wave theory only and is strictly speaking not applicable for shallow water.


3.3.6 The spectral moments of order n is defined as:

The following spectrally derived parameters appear:

— Significant flow velocity amplitude at pipe level:

— Mean zero up-crossing period of oscillating flow at pipe level:

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


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Figure 3-2 Significant flow velocity amplitude at pipe level, US

Figure 3-3 Mean zero up-crossing period of oscillating flow at pipe level, Tu

3.4 Reduction functions

3.4.1 The mean current velocity over a pipe diameter, i.e. taken as current at (e + D/2), applies. Introducing theeffect of directionality, the reduction factor, Rc becomes:

where θrel is the relative direction between the pipeline direction and the current flow direction.


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The perpendicular current induced flow velocity component at pipe level may thus be calculated as:

3.4.2 In case of combined wave and current flow the apparent seabed roughness is increased by the non-linearinteraction between wave and current flow. The modified velocity profile and hereby-introduced reductionfactor may be taken from DNVGL-RP-F109.

3.4.3 The effect of wave directionality, i.e. projection onto the velocity normal to the pipe, and wave spreading isintroduced in the form of a reduction factor on the significant flow velocity:

The reduction factor is given by, see Figure 3-4.

where θrel is the relative direction between the pipeline direction and wave direction.

Figure 3-4 Reduction factor due to wave spreading and directionality


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3.4.4 The directional wave energy spreading function given by a frequency independent cosine power function is:

Γ is the gamma function, see [3.5.1], and s is a spreading parameter, typically modelled as a function of thesea state. Normally s is taken as an integer, between 2 and 8, 2 ≤ s ≤ 8. If no information is available, themost conservative value in the range from 2 to 8 shall be selected. For current flow, s > 8.0 may be applied.

Guidance note:Cases with large Hs and large Tp values may have a lower wave spreading. The wave spreading approach, as given in NORSOKN-003, can also be considered as an alternative to the above approach.


3.5 Long-term environmental modelling

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

where FX(x) is the cumulative distribution function, α is the scale parameter, β is the shape parameter andγ is the location parameter. Note that the Rayleigh distribution is obtained for β = 2 and an exponentialdistribution for β = 1.The Weibull distribution parameters are linked to the statistical moments as follows:

where μ is the mean value, σ is the standard deviation and δ is the skewness.Γ is the gamma function defined as:


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3.5.2 The directional or omnidirectional current data can be specified by:

— A histogram in terms of (Uc, θ) versus probability of occurrence.The fatigue analysis is based on the discrete events in the histogram. The corresponding return periodvalues (RPV) are estimated from the corresponding exceedance probability in the histogram or from afitted pdf, see [3.6].

— A long term probability density function (pdf).The corresponding return period values for 1, 10 and 100 years are established from [3.6].

— Return period values.Distribution parameters for an assumed distribution e.g. Weibull, are established using e.g. 3 equations(for 1, 10 and 100 year) with 3 unknowns (α β and γ). This is, in principle, always feasible butengineering judgement applies because defining return period values inappropriately can lead to anunphysical Weibull pdf.

3.5.3 The wave climate at a given location may be characterised by a series of short-term sea states. Each short-term sea state may be characterised by Hs, Tp, and the main wave direction θ, measured relative to a givenreference direction.The directional or omnidirectional significant wave height may be specified as follows:

— A scatter diagram in terms of Hs, Tp, θThe fatigue analysis is based on the discrete sea states reflected in the individual cells in the scatterdiagram.

— A histogram in terms of (Hs, θ) versus probability of occurrence.The fatigue analysis is based on the discrete events for Hs in the histogram. The corresponding peakperiod may be assumed on the form:

where 6 ≤ CT ≤ 8 and 0.3 ≤ αT ≤ 0.5 are location specific.

— A long term probability density function (pdf).The corresponding return period values (RPV) for 1, 10 and 100 year are established from 3.6.

— Based on return period values.The corresponding Weibull distribution is established from [3.6.2] using 3 equations (xc for 1, 10 and100 year) with 3 unknowns (α β and γ). This is, in principle, always feasible but engineering judgementapplies as defining return period values inappropriately can lead to an unphysical Weibull pdf.


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3.6 Return period values

3.6.1 Return period values shall be used for ULS conditions. A return period value (RPV) xc is defined as:

where N is the number of independent events in the return period, e.g. 100 year. For discrete directions, Nmay be taken as the total number of independent events times the sector probability.The time between independent events depends on the environmental condition. For currents, this time isoften taken as 24 hours, whereas the time between independent sea states (described by Hs) normally maybe taken from 3 to 6 hours.

3.6.2 For a Weibull distributed variable the return period value is given by:

3.6.3 In case the statistics are given in terms of a scatter diagram, a long term Weibull distribution (α, β, γ) isestablished from [3.5.1] using statistical moments derived directly from the scatter diagram as follows:

where PHs is the discrete occurrence probability. The same principle applies for current histograms.

3.6.4 The return period value to be used for directional data is taken as the maximum projected flow velocity, i.e.:

where RD is a reduction factor defined in [3.4.3] and θrel,i is the relative direction between the pipelinedirection and the flow direction for direction i.


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SECTION 4 RESPONSE MODELS

4.1 General

4.1.1 Amplitude response models are empirical models providing the maximum steady state VIV amplituderesponse as a function of the basic hydrodynamic and structural parameters. The response models providedherein have been derived based on available experimental laboratory test data and a limited amount of full-scale tests for the following conditions:

— in-line VIV in steady current and current dominated conditions— cross-flow VIV induced in-line motion— cross-flow VIV in steady current and combined wave and current conditions— cross-flow VIV in wave dominated low Keulegan-Carpenter flow regimes.

The response models are in agreement with generally accepted concepts of VIV.

4.1.2 In-line and cross-flow vibrations are considered in separate response models. Damage contributions fromthe first and the second in-line instability regions in current dominated conditions are implicit in the in-lineresponse model. Cross-flow induced in-line VIV is relevant for all reduced velocity ranges where cross-flowVIV occurs, and has been approximately and conservatively accounted for.

4.1.3 All active modes, as defined in[2.1.3], shall be included in the calculation of marginal fatigue life capacitiesaccording to [4.2.1] and [4.2.2].

4.1.4 The amplitude response depends on a set of hydrodynamic parameters constituting the link between theenvironmental data and the response models:

— reduced velocity, VR— Keulegan-Carpenter number, KC— current flow velocity ratio, α,— turbulence intensity, Ic, see [3.2.11]— flow angle, relative to the pipe, θrel— stability parameter, KS.

Note that the Reynolds number, Re, is not explicit in the evaluation of response amplitudes.

4.1.5 The reduced velocity, VR, is defined as:


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where:

fj = Natural still-water eigen frequency for the j-th modeUc = Mean current velocity normal to the pipe, see [3.4]Uw = Significant wave-induced flow velocity, see [3.4]D = Outer pipe diameter.

4.1.6 The Keulegan-Carpenter number is defined as:

where fw = 1/Tu is the significant wave frequency.

4.1.7 The current flow velocity ratio is defined by:

With increasing KC number, the flow regime will eventually resemble pure current conditions. For the purposeof this recommended practice, if KC > 40, the flow shall be considered as current dominant irrespective ofthe actual current component. In the response model calculations, this can be implemented by α = 1, whenKC > 40. Importantly, this assumption shall not be used in direct wave action calculations, where the correctcurrent flow velocity shall be applied regardless of KC regime.

4.1.8 The stability parameter, KS, representing the damping for a given modal shape is given by:

where:

ρw = Water densityζT = Total modal damping ratiome = Effective mass, see [6.6.6]

4.1.9 The total modal damping ratio, ζT, comprises:

— structural damping, ζstr, see [6.3.10].


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— soil damping, ζsoil. For screening purposes ζsoil = 0.01 may be assumed. For details, see DNVGL-RP-F114— hydrodynamic damping, ζh. For VIV within the lock-in region (see [A.6.1]), the hydrodynamic modal

damping ratio is normally taken as zero when using a standard response model. Outside lock-in regions,the hydrodynamic damping may be assessed according to DNVGL-RP-C205.

4.2 Marginal fatigue life capacity

4.2.1 For cross-flow VIV, the marginal fatigue capacity against VIV in a single sea state characterised by (Hs, Tp, θ)is defined by:

where:

Scomb,CF = Cross-flow multi-mode stress range defined in [4.3.8]fcyc,CF = Cross-flow cycle counting frequency, see [4.3.8]

= Fatigue constant, depending on the relevant stress range, see [2.5.3]

m = Fatigue exponent, depending on the relevant stress range, see [2.5.3].p(Uc) = Probability density function for the current velocity, often represented by Weibull or histogram

distributions

The cross-flow marginal fatigue life capacity is applied to the total fatigue damage accumulation calculationgiven in [2.5.9] for each sea state.

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

where:

Scomb,IL= In-line multi-mode stress range defined in [4.6.19]

fcyc,IL = In-line cycle counting frequency, see [4.6.20].

The in-line marginal fatigue life capacity is applied to the total fatigue damage accumulation calculation givenin [2.5.9] for each sea state.


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4.2.3 In both isolated single spans and interacting multi-spans, the marginal fatigue life capacity calculations, asdefined in [4.2.1] and [4.2.2], can either be calculated as functions of x, or for a single critical location.There are two main differences between calculating damage at a single location versus as a distributedfunction of x:

— The unit diameter stress amplitudes are calculated per x position according to [6.6.2] for the distributeddamage calculations and according to [6.6.3] for a critical single location.

— For the distributed damage calculations, only the participating modes (see [4.3.3]) will contribute todamage at a given location. For a critical single location, all active modes (see [4.1.3]) are included.

Generally, it is more accurate and less conservative to calculate fatigue damage as functions of x. It is,however, significantly more computationally efficient to calculate the damage for a single critical location.

4.3 Aspects of the computational approach

4.3.1 Eigen frequencies and associated mode shapes can be defined as modal response quantities and they areneeded as input to the VIV fatigue and extreme environmental loading calculations. There are severalmethods available for calculation of the modal response quantities with varying degree of accuracy andapplicability. A detailed description of the various methods and their suitability for various applications aregiven in Sec.6.

4.3.2 For a given sea state, characterized by (Hs,Tp,θ), marginal fatigue life capacities may be calculated accordingto [4.2.1] and [4.2.2]. At each location x for a given sea state and current velocity Uc, several vibrationmodes may be responding, giving rise to in-line and cross-flow multi-mode responses associated withcombined stress ranges Scomb,IL/CF and cycle-counting frequencies fcyc,IL/CF. Procedures for the calculation ofthe in-line and cross-flow equivalent stress ranges, Scomb,IL/CF, and response frequencies, fcyc,IL/CF, are givenin [4.3] and [4.6] respectively.

4.3.3 It is required that the j-th mode in the calculations has a mode shape with a domain bounded by a start pointx0,j and an end point xe,j, i.e x0,j ≤ x ≤ xe,j, where the modal deflections and curvatures are zero or negligibleat and near the end points. Then, for each mode j, there exists two unique points xstart,j and xend,j such that:

for all x < xstart,j and x > xend,j

where:

AIL/CF,j(x) = Unit diameter stress amplitude for the j-th in-line or cross-flow mode, defined in [6.6.2]AmaxIL/CF,j = Maximum unit diameter stress amplitude for the j-th in-line or cross-flow mode, defined in

[6.6.3]

An active mode is defined as participating on the interval xstart,j ≤ x ≤ xend,j, and the interval itself is definedas the participation interval, see also Figure 1-7. The participation interval is thus a sub-interval of a mode


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shape’s domain, containing all locations where the modal stress exceeds 10% of the maximum modal stress.For single location analyses, all active modes are considered participating.

For a given location, the number of participating modes is denoted n.

4.3.4 The set of n participating modes must be ordered by the magnitude of their individual frequencies fromlowest to highest. This implies that

where fIL/CF,j is the j-th in-line or cross-flow natural frequency.

4.3.5 For a given location x, a mode is defined as contributing if it is participating and satisfies either of thefollowing criteria:

for the cross-flow direction and

for the in-line direction,

where

— (Az/D)j is the normalized cross-flow VIV amplitude for the j-th mode, see [4.4.3].— (Az/D)max is the normalized VIV amplitude for the dominant cross-flow mode, see [4.4.8].— SP

IL,j(x) is the preliminary response stress range for the j-th in-line mode, see [4.6.6].— Smax

IL(x) is the response stress range associated with the dominant in-line mode, see [4.6.8].

4.3.6 Cross-flow VIV may be characterized by two separate response models. The response model described in[4.4] covers current and wave dominated flow conditions. For a given sea state characterized by (Hs,Tp,θ)and current flow velocity Uc, the flow is wave dominated if α ≤ 0.5, and the flow regime is termed a low KCregime (LKCR) if 2 ≤ KC ≤ 10. For wave dominated LKCR, a separate response model is given in [4.5].In a wave dominated LKCR, the j-th cross-flow mode is defined as contributing if it is participating andsatisfies the following criterion:

4.3.7 The two sets of contributing modes for the standard cross-flow response model and the LKCR responsemodel are generally different, and shall be determined separately. In other words, while there is only one setof participating cross-flow modes, there may in general be two sets of contributing cross-flow modes.


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4.3.8 If there are contributing cross-flow modes due to wave dominated LKCR, both response models shall beconsidered, and the highest predicted VIV stress range shall conservatively be applied in design:

The cycle counting frequency shall be determined as follows:

4.3.9 A brief overview of the calculation methodologies for multi-mode response model calculations is summarizedin the flow chart in Figure 4-1.

4.3.10 In all response model calculations, either in-line or cross-flow, the design values for the reduced velocity VRdand the stability parameter Ksd shall be applied as follows:


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(1) For the case of a single critical location, see [4.2.3], only one location needs to be considered.(2) As defined in [4.2.3], the maximum modal stresses according to [6.6.3] shall be applied for singlelocation analyses and all active modes shall be considered. For distributed fatigue damage calculations onlythe participating modes need to be considered, and location specific modal stresses according to [6.6.2]can be applied. Results of Scomb,IL/CF and fcyc,IL/CF calculations can then be applied to [4.2.1] and [4.2.2] tocalculate marginal fatigue life capacities cross-flow and in-line respectively.

Figure 4-1 Calculation process for multi-mode response

4.4 Cross-flow response model

4.4.1 Cross-flow VIV are affected by several parameters, such as the reduced velocity VR, the Keulegan-Carpenternumber, KC, the current flow velocity ratio, α, the stability parameter, KS, the seabed gap ratio, (e/D), theStrouhal number, St and the pipe roughness, (k/D), among others. Note that Reynolds number, Re, is notexplicit in the model.In wave dominated flow conditions, irrespective of KC regime, cross-flow VIV is strongly related to thefrequency ratio fCF,j/fw, see e.g. Sumer and Fredsøe (1988) and Kozakiewicz et al. (1994). For highKC numbers, the standard response model calculations based on reduced velocity generally apply withacceptable accuracy. For wave dominated flow and a low KC number, i.e. KC < 10, a separate responsemodel shall be applied which is based on the frequency ratio, see [4.5].

4.4.2 For steady current dominated flow situations, onset of cross-flow VIV of significant amplitude occurs typicallyat a value of VR between 3.0 and 4.0, whereas the maximum vibration levels occur at larger VR values. Forpipes with low specific mass, wave dominated flow situations or span scenarios with a low gap ratio, cross-flow vibration may be initiated for VR between 2 and 3.


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Only pure cross-flow response is considered, i.e. potential in-line induced cross-flow response at VR from ~2to ~3 is disregarded.

4.4.3 The cross-flow VIV amplitude for the j-th mode (Az/D)j in combined current and wave flow conditions may betaken from Figure 4-2.

Figure 4-2 Basic cross-flow response model

The figure provides characteristic maximum values of normalized response. The corresponding root mean

square (RMS) response amplitudes may be obtained as

4.4.4 The amplitude responses (AZ/D)j as a function of α and KC can be constructed from, see Figure 4-3:


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is the cross-flow frequency ratio for two consecutive (participating) cross-flow modes, taken as the

minimum of and .

Guidance note:The maximum cross-flow response amplitude of 1.3 D is typically only applicable for current-dominated cases with bendingstiffness dominated lower half-wave symmetric modes, e.g. for single span fundamental mode. For all other current dominatedcases the maximum response amplitude is limited to 0.9 D.



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Figure 4-3 Response model generation principle

4.4.5 The reduced onset velocity for cross-flow VIV, depends on the seabed proximity and trench geometry,

whereas the maximum amplitude is a function of α and KC.

4.4.6 ψproxi,onset is a correction factor accounting for the seabed proximity:

4.4.7 ψtrench,onset is a correction factor accounting for the effect of a pipe located in/over a trench:

where Δ/D denotes a relative trench depth given by:


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The trench depth d shall be taken at a width equal to 3 outer diameters. Δ/D = 0 corresponds to a flatseabed or a pipe located in excess of D/4 above the trench, i.e. the pipe is not affected by the presence ofthe trench, see Figure 4-4. The restriction Δ/D < 1.0 is applied in order to limit the relative trench depth.

Figure 4-4 Definition of trench factor

4.4.8 With n participating modes and a given sea state characterized by (Hs,Tp,θ) and a current velocity Uc, (Az/D)j

is determined for each according to the response model in [4.4.4]. The maximum normalized

cross-flow VIV amplitude is defined as:

The i-th mode is the dominant cross-flow mode, when i is the highest integer value which satisfies therelation (Az/D)i = (Az/D)max.

4.4.9 Mode j is a weak cross-flow mode if it is not the dominant cross-flow mode, and satisfies the followingcriterion:

Modes which are neither weak nor dominant are disregarded in the fatigue and extreme environmental stresscalculations. Hence, only dominant and weak modes are defined as contributing, see [4.3.5].

4.4.10 At a given location x, the i-th cross-flow induced VIV stress range SRM

CF,i for the dominant cross-flow modeis:


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where ACF,i is defined in [6.6.2] for multiple location analyses and in [6.6.3] for single location analyses. At

the same location x, the j-th cross-flow induced VIV stress ranges SRMCF,j for the contributing, weak cross-

flow modes are:

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

4.4.12 The combined response model cross-flow induced stress range is given as:

where m is the number of contributing cross-flow modes.

4.4.13 The cycle counting frequency at a given location x, fcyc,CF(x), for the combined cross-flow induced stress iscalculated as follows:

where:

— fj = fCF-RES,j, for j = i when mode i is the dominant cross-flow mode— fj = fCF,j, when j ≠ i.

4.4.14 The cross-flow response frequency fCF-RES,j for the dominant mode is obtained based on the updated addedmass coefficient Ca, CF-RES due to the amplitude of cross-flow response using the following equation:


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where:

sg = (q+b)/b is the specific gravity of the pipe (often referred to as mass ratio in the context of VIV)

q = Submerged weight of the pipe, including content if anyb = πρwgD2/4 is the pipe buoyancy

Ca = Added mass coefficient, according to [6.6.7]

Ca,CF-RES = Added mass coefficient due to cross-flow response, according to [4.4.15] and [4.4.16]

4.4.15 The calculation of the added mass coefficient described in this sub-section is for the calculation of the cross-flow response frequency of the dominant mode only.It should be noted that the response models discussed in this sub-section, have the effect of the addedmass built into them, i.e. they are plotted using the reduced velocity calculated with the still water naturalfrequency and associated added mass.

Figure 4-5 Added mass coefficient Ca, CF-RES as a function of reduced velocity


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4.4.16 The added mass during VIV will be different from the still water added mass, which is applied during theinitial eigenvalue analysis. The added mass coefficient, Ca,CF-RES, may be taken from Figure 4-5 and is appliedto correct the still water cross-flow eigen frequency to the cross-flow response frequency.

Guidance note:This added mass model is in a narrow sense only valid when the mass ratio is in the order of 1.4, but may be used also for othermass ratios if better information is not available.


Guidance note:The added mass coefficient formulation for VR < 2.5 is not important, since the cross-flow response amplitude are very small (A/Dis O (0.1)) in this range.


4.5 Cross-flow VIV for low KC regimes

4.5.1 For a cylinder exposed to pure current conditions, vortices are shed at a regular frequency, and pressureoscillations due to vortex formation and shedding causes oscillating lift and drag forces on the cylinder.Traditionally, VIV response models are based on the concepts of reduced velocity or dimensionless frequency,both of which represent a dimensionless number proportional to the ratio of the loading frequency and theeigen frequency of the cylinder. In wave-dominated conditions, particularly in irregular waves, the lift loadingfrequency may instead be decomposed into a combination of integer multiples of the wave frequency:

where fL is the load frequency, NL is an integer number and fw is the wave frequency. For the present context,

only small KC numbers will be treated and in that case .

4.5.2 When the load frequency fL is sufficiently close to one or more of the natural frequencies of the pipe,vibrations may occur. In the in-line direction, wave loading is treated by Morison’s equation, as statedin [5.4.1]. In cross-flow direction, correlation between the wave load frequency and one or more of thepipe natural frequencies is treated by the response model in [4.5.5], when 2 ≤ KC ≤ 10 and α ≤ 0.5. Ifeither KC or α are higher, experimental results indicate that the response model stated in section [4.4] isconservatively applicable.

4.5.3 For a given modal frequency fCF,j, The relation between the KC number and the reduced velocity is:


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If say KC = 2, α = 0, and fCF,j/fw = 2, then VR = 1. Cross-flow vibrations for these kinds of regimes havebeen recorded in laboratory conditions (Chioukh and Narayanan, 1997; Sha et al., 2007) even thoughtraditional response models predict no onset of cross-flow VIV. As a result, special considerations shall bemade for cross-flow VIV for low KC regimes (LKCR).

4.5.4 The response model for LKCR is based on several studies in regular waves (see Vedeld et al. (2016) andreferences therein), but only corroborated by three experimental data series in irregular waves (Kozakiewieczet al., 1994; Sha et al., 2007). As a result, the model presented herein is limited in accuracy, but stillassumed conservative since irregular wave response amplitudes tend to be smaller and less consistent thanthose achieved in comparative regular wave conditions (Sumer and Fredsøe, 1997). In lieu of more detailedmodel approaches, the response model presented in [4.5.5] may be applied to estimate cross-flow responseamplitudes in wave dominated flow conditions for LKCR.

4.5.5 For a given sea state characterized by (Hs,Tp,θ), and a given current velocity Uc, the response model given inFigure 4-6 applies when KC ≤ 10 and α ≤ 0.5:

Figure 4-6 LKCR Cross-flow response model

4.5.6 In the evaluation of (Az/D) the design values for the frequency ratios shall be applied, i.e.


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4.5.7 Any mode j with a non-zero normalized cross-flow amplitude of response, (Az/D)j, is defined as a contributingmode.For all contributing modes, (Az/D)j may be taken from the response model in [4.5.5]. The associated cross-flow induced stress ranges can be calculated as:

4.5.8 The amplitude of cross-flow motion increases with KC, as is also the case for the response model in higherKC regimes. To account for low amplitude response in the lower regions of the KC range, the followingreduction factor applies:

4.5.9 In LKCR, the amplitude of motion is less affected by the mass damping ratio than standard cross-flow VIVcases. There is, however, still a reduction in the response amplitude as a function of the stability parameter.The following reduction factor applies to the cross-flow amplitude of response:

4.5.10 The combined response model cross-flow induced stress range is given as:

where m is the number of contributing cross-flow modes for the LKCR response model.


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4.5.11 The cycle counting frequency at a given location x, is calculated as follows:

where m is the number of contributing cross-flow modes for the LKCR response model.

4.6 In-line response model

4.6.1 The in-line response of a pipeline span in current-dominated conditions is associated with either alternatingor symmetric vortex shedding. Contributions from both the first in-line instability region and the secondinstability region are included in the model.The in-line response model applies for all in-line vibration modes.

4.6.2 The amplitude response depends mainly on the reduced velocity, VR, the stability parameter, KS, theturbulence intensity, Ic, and the flow angle, θrel relative to the pipe. Mitigation effects from the seabedproximity, (e/D) are conservatively not included.

4.6.3 (Ay/D) is defined as the maximum in-line VIV response amplitude (normalised with D) as a function of VRdand KSd, see Figure 4-7. The corresponding root mean square response may be obtained as (Ay/D)/√2.


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Figure 4-7 Illustration of the in-line VIV Response Amplitude versus VRd and KSd

4.6.4 The response model can be constructed from the co-ordinates in Figure 4-8:


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Figure 4-8 Response model generation principle.

4.6.5 The reduction factors, RIθ,1(Ic,θrel) and RIθ,2(Ic), account for the effect of the turbulence intensity and angleof attack (in radians) for the flow, see Figure 4-9.


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Figure 4-9 Reduction function with respect to turbulence intensity and flow angle

4.6.6 We assume n participating modes, and a given sea state characterized by (Hs,Tp,θ) and current velocity Uc.

(Ay/D)j is determined for each according to the response model in [4.6.3]. For each location

and each mode the preliminary in-line VIV induced stress range, SPIL,j (x), shall be calculated:

where AIL,j(x) is defined in [6.6.2] for multiple location analyses and in section [6.6.3] for single locationanalyses.

4.6.7 ψα,IL is a reduction function to account for reduced in-line VIV in wave dominated conditions:


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Thus, if α < 0.5, in-line VIV may be ignored.

4.6.8 The maximum in-line VIV induced stress range Smax

IL is defined as:

The k-th mode is the dominant in-line mode, when k is an integer value satisfying the relation SP

IL,k = SmaxIL.

4.6.9 Mode j is a weak in-line mode, if it is not the dominant in-line mode and satisfies the following criterion:

Modes which are neither weak nor dominant are disregarded in the fatigue and extreme environmental stresscalculations. Hence, only dominant and weak modes are defined as contributing, see [4.3.5].

4.6.10 The contributing modes are renumbered, excluding inconsequential modes.

For the given location x, sea state characterized by (Hs,Tp,θ) and current velocity Uc, the set of n

participating in-line still-water eigen frequencies fpartIL,j shall be sorted from the lowest to the highest into the

set fconIL,j, where only the m contributing modes shall be included. The m corresponding preliminary in-line

VIV induced stress ranges SPIL,j shall be renumbered in the same order.

4.6.11 Two adjacent contributing modes can either compete with each other, if the ratio of their frequencies is lowerthan 2, or they can act as independent modes if their frequencies are more widely separated. In summary:

Contributing modes j and j+1 are competing

Contributing modes j and j+1 are not competing

Every adjacent contributing mode combination shall be checked.


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4.6.12 For each location x, a mode competition reduction factor βj(x) is defined for each contributing mode, wherej denotes the renumbered mode number. The application of the mode reduction factor is described as analgorithm as follows.

1) set βj(x) = 0 for all

2) for each pair of numbers {j, j+1}, when , check the following criterion:

3) If modes j and j+1 are competing:

Increase βj(x) by one

Increase βj+1 (x) by one.

Since any contributing mode j has a maximum of two adjacent contributing modes, for all j.

Consistent with this algorithm, βj (x) = 0 for the dominant in-line mode.

4.6.13 For each location and each mode, the in-line VIV-induced stress range for the m contributing modes shall becalculated as follows:

4.6.14 It is assumed that only the dominant cross-flow mode can potentially contribute to the cross-flow induced in-line motion.

4.6.15 The participating in-line mode with its eigen frequency closest to twice the dominant cross-flow responsefrequency shall be chosen as the candidate for cross-flow induced in-line VIV. For the dominant cross-flowmode i, the expression:


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will have a minimum for some . The k-th participating mode will then be selected as the

candidate for cross-flow induced in-line VIV.

4.6.16 The in-line stress range corresponding to a figure 8 or half-crescent motion, SCF-IL, excited by the dominantcross-flow mode is calculated as:

4.6.17 If the candidate mode for cross-flow induced in-line is already among the contributing modes, the in-line VIVresponse stress shall be set to:

and the contributing in-line response frequency for the mode undergoing cross-flow induced in-line VIV shallbe set to

4.6.18 If the candidate mode for cross-flow induced in-line is not among the contributing in-line modes, the set ofcontributing stresses and frequencies are expanded by one (to m+1). The in-line VIV response stress shall beset to:

and the (m+1)th contributing in-line response frequency shall be set to:

4.6.19 The combined in-line stress range is given as:


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where maug is equal to m+1 if the cross-flow induced in-line mode is not among the originally contributingmodes. maug is equal to m otherwise.

4.6.20 The in-line cycle counting frequency is given by:


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SECTION 5 FORCE MODEL

5.1 General

5.1.1 In principle, force models may be used for both vortex induced and direct wave and current dominated loadsif appropriate formulations of force models exist and reliable and consistent data are available for calibration.Generally applicable force models for VIV do not exist, and empirical response models presented in Sec.4 isat present superior, reflecting observed pipeline response in a variety of flow conditions.

5.1.2 A force model based on the well-known Morison’s equation for direct in-line loading is considered herein.Both time domain (TD) and frequency domain (FD) solutions are allowed. A time domain solution mayaccount for all significant non-linearities but is in general very time consuming if a large number of sea statesshall be analysed. For fatigue analyses, a frequency domain solution (if thoroughly verified) is more tractablesince it facilitates analyses of a very large number of sea states at a small fraction of the time required for atime domain solution.A linearised FD solution for the Morrison’s equation is given in [5.2]. The method presented in [5.2] appliesto both single- and multi-spans and has been proven to be accurate compared to detailed time domainanalyses, see Sollund (2015). The method is capable of solving the fatigue and extreme environmentalloading problems for a single critical location, or as a distributed function of the position x along the pipeaxis.

5.1.3 In this document, a complete frequency domain approach for short-term fatigue analyses is presented.Recommended procedures for state-of-the-art time domain short-term damage calculation may be found inDNVGL-ST-F201. In some cases, a quasi-static approach to wave loading approximations is sufficient. A shortdescription of how to perform fatigue and extreme environmental loading calculations with a quasi-staticapproach is given in [5.3].

5.1.4 Force model calculations in frequency domain are either based on a single critical location, or alternatively,fatigue and extreme environmental loading may be calculated for densely spaced locations along the spanand respective shoulders. For single isolated free spans, both methods are acceptable, i.e. single or multiplelocations may be considered. For multi-spans, with multiple responding modes, a single critical locationis not readily identifiable, and therefore it is required that all locations along the multi-span section areconservatively accounted for in the analyses.

5.1.5 Force model calculations in interacting multi-spans shall consider response interaction between individualspans. The selection of modes which contribute to fatigue and extreme environmental loading calculationsis not trivial to determine, and depends on a number of different parameters such as soil stiffness, pipedimensions, water depth, environmental conditions, effective axial force and multi-span topography. Anassessment strategy to identify interacting multi-spans is discussed in [6.10]. For interacting multi-spans,force model calculations shall be performed using a multi-mode approach, unless it is documented that asingle mode approach is conservatively applicable.


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5.1.6 In-line modal response is less affected by seabed topography, see Sollund and Vedeld (2015), since axialand bending displacement interaction predominantly influences cross-flow modal response. As a result,simplified modal response calculations, assuming flat span shoulders, are sufficiently accurate for all forcemodel calculations, see [6.4.3].

5.2 Frequency-domain solution for in-line direction

5.2.1 The recommended frequency domain solution for the short term- fatigue damage due to combined currentand direct wave actions in a single sea state is based on:

— Palmgren-Miner approach using S-N curves— linearisation scheme for the drag term in Morison’s equation based on conservation of damage— the effect of co-linear mean current included in linearisation term— narrow-banded fatigue damage with semi-empirical correction to account for wide-band characteristic.

The formulation presented in this document has been successfully verified against comprehensive timedomain simulations using rainflow counting techniques, see e.g. Mørk and Fyrileiv (1998) and Sollund(2015). The formulation is based on the following assumptions:

— the effective mass, me, is invariant over the free span length— the flow velocity, U, and the standard deviation of the flow velocity, σU, are invariant over the free span

length, i.e. the span length is less than the dominant wavelength.

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

where:

σS = Standard deviation of stress amplitudeFv = Vibration frequency

= Fatigue constants, see section [2.5.3]

m1, m2 = Fatigue exponent, see section [2.5.3]Ssw = Stress range, for which change in slope occurs, see [2.5.3]

= is the complementary incomplete gamma function


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= is the incomplete gamma functionγs = Safety factor on stress range, see section [2.7]Ψmm = Empirical multi-mode correction factor. For single mode analyses in isolated

single spans, ψmm = 1.055. In multi-mode analyses, for either isolated singlespans or interacting multi-spans, ψmm = 1.0

5.2.3 The standard deviation of the wave-induced stress amplitude σS is given by the square root of the spectralmoment of the 0-th order defined by [5.2.6].

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

where M0 and M2 is defined in [5.2.6].

5.2.5 The rainflow-counting correction factor, κRFC, accounts for the “exact” wide-banded damage, i.e. correctingthe implicit narrow-banded Rayleigh assumption for the stress amplitudes to provide results similar to thosearising from a state-of-the-art rainflow-counting technique. The Rainflow-counting factor κRFC is given by:

The bandwidth parameter ε is defined as:

The stress process is narrow-banded for ε → 0 and broad banded for ε → 1. In practice the process may beconsidered broad-banded for ε larger than 0.6.


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5.2.6 The n-th response spectral moment (at location x) is given by:

where SSS(x,ω) is the one-sided stress response spectral density function given by [5.2.7] or [5.2.11].

5.2.7 When non-negligible damage contributions from higher order modes cannot be excluded, the one-sidedstress response spectral density function SSS(x,ω) is given by

where:

and

RD = Factor accounting for wave spreading and direction, see [3.4.3]b = Linearisation constant, see [5.2.12]gD = Drag force term, see [5.4.1]gI = Inertia force term, see [5.4.1]G(ω) = Frequency transfer function, see [3.3]Sηη = Single-sided wave elevation spectrum, see [3.3]ωj = 2πfIL,j/γf is the still water angular natural frequency for the j-th mode

me = Effective mass per unit length incl. added mass, see [6.6.6]N = Number of modes with non-negligible damage contribution

5.2.8 ζT,j is the total damping ratio for the j–th mode. The total damping ratio includes contributions from:

— structural damping, see [6.3.10]— soil damping, see DNVGL-RP-F114— hydrodynamic damping, see [5.2.13].


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Guidance note:

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

where ζT,1 and ω1 are the total damping ratio and angular natural frequency, respectively, for the lowest natural mode.


5.2.9 ψj(x) is the modal stress for the j-th mode given by:

Κj = Mode shape curvature, normally calculated as d2φj/dx2

φj = Mode shape for the j-th modeE = Young’s modulusCSF = Concrete stiffness factor, see [6.3.7]r = Radial coordinate. Fatigue stresses shall be calculated at the weld toe and the weld root, i.e. for r =

Ds/2 and r = (Ds-2ts)/2 respectively

Ds = Outer steel pipe diameterts = Pipe steel wall thickness

5.2.10 λj is a mode shape weighting factor for the j-th mode given by:

where L is the length of the mode shape.

Guidance note:The hydrodynamic load P(x,t) will be location invariant, i.e. P(x,t) is assumed equal to P(t) since the flow velocity is assumedlocation invariant, see [5.2.1]. As a consequence, P(t) will be symmetric and modes that are mainly anti-symmetric, i.e. have very

small mode shape weighting factors, will contribute little. The value of λi should therefore be considered when determining the

number of contributing modes N. For example, if the fatigue damage is almost unchanged by increasing N from 3 to 4, the added

damage by increasing N from 3 to 5 may still be non-negligible if λ5/ λ4 > 1.



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5.2.11 When the excitation frequency is far from the natural frequency for the higher order modes, it can beassumed that the main damage contribution comes from the lowest natural mode if the mode has asymmetric mode shape. This is often appropriate for isolated single spans, i.e. when the span’s dynamicbehaviour in the horizontal (in-line) direction is not affected by the presence of neighbouring spans.When only the lowest natural mode needs to be considered, the one-sided stress response spectral densityfunction simplifies to:

The mode shape weighting factor λ1 is typically in the order of 1.3.The location associated with the largest stress response will coincide with the location of maximum (unitdiameter) stress amplitude Amax

IL,1. In lieu of more detailed data, the maximum modal stress ψ1 may betaken as:

where Amax

IL,1 is given by [6.6.3]

Guidance note:Single-mode analyses should not be used if the modal analysis is affected by span interaction. In such cases, the lowest naturalmode may have anti-symmetric properties and not be excited to a significant extent by the presumed symmetric loading, seeSollund (2015).


5.2.12 The linearisation constant b is given by:

where Uc is the mean current and σu = Uw/2 is the standard deviation of the wave-induced flow velocity. Thecorrection function gc accounts for the effect of a steady current by:

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


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5.2.13 The linearised hydrodynamic damping ratio ζh,j for the j-th mode is given by:

where fIL,j is the still-water natural frequency for the j-th mode.

5.3 Simplified fatigue assessment

5.3.1 In situations where quasi-static stress response can be assumed (when the wave period is far larger than thenatural vibration period of the span) a simplified fatigue assessment may be more tractable than a completetime-domain or frequency-domain approach.

5.3.2 In such cases, the short term fatigue capacity against direct wave actions in a single sea state characterisedby (Hs, Tp, θ) may be estimated as follows, see [2.5.5]:

where S is the quasi-static stress range response from a direct regular wave load (Hs and Tu) using Morison’sequation. Tu is the mean zero up-crossing period in [3.3.6].

5.4 Force coefficients

5.4.1 The force P(x,t) per unit length of a pipe free span is represented by Morison’s equation. Assuming that thevelocity of the structure is not negligible compared with the water particle velocity Morison’s equation reads:

Where:

ρw = Water densityD = Outer pipe diameterU = Instantaneous (time dependent) flow velocityy = Pipe lateral displacementgD = 0.5ρwDCD is the drag force term


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gI = is the inertia force term

5.4.2 The added mass term in Morison’s equation

is assumed implicit in the effective mass me, see [6.6.6].

5.4.3 The drag coefficient CD and inertia coefficient CM to be used in Morison’s equation are functions of:

— the Keulegan-Carpenter number, KC— the current flow ratio, α;— the gap ratio, (e/D)— the trench depth, (Δ/D)— the Reynolds number, Re— the pipe roughness, (k/D).

In addition, the cross-flow vibration level, (Ay/D) influences the drag coefficient. Supercritical flow isassumed, hence no further dependency of the Reynolds number is considered.The drag coefficient CD shall be taken as:

5.4.4 is the basic drag coefficient for steady flow as a function of roughness k/D.

In lieu of detailed documentation of the surface roughness the values in Table 5-1 may be applied for theabsolute roughness, k.

Table 5-1 Surface roughness

Pipe surface k [m]

Steel, painted 10-6

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

Concrete 1/300


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Pipe surface k [m]

Marine growth 1/200 → 1/20

Note that the roughness, k/D, to be used in this section is the ratio between the absolute roughness, k, andthe outer diameter, D, of the pipe.

5.4.5 is a correction factor accounting for the unsteadiness of the flow, including effects of the Keulegan-

Carpenter number KC and the current flow ratio α:

For KC > 40, the term 6/KC in the formula above shall be substituted by 0.15.

The drag load is often of small practical importance for small KC values and may be interpolated forcompleteness for KC < 5.

Figure 5-1 Correction factor

5.4.6 is a correction factor accounting for the seabed proximity:


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5.4.7 is a correction factor accounting for the effect of a pipe in a trench:

Δ/D is the relative trench depth given by [4.4.7].

5.4.8 is an amplification factor due to cross-flow vibrations, i.e.

5.4.9 The inertia coefficient CM shall be taken as:

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


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Figure 5-2 Basic inertia coefficient CM,0 versus KC and α

5.4.11 is a correction factor accounting for the pipe roughness:

5.4.12 is a correction factor accounting for the seabed proximity:

5.4.13 is a correction factor accounting for the effect of a pipe in a trench:

Δ/D is the relative trench depth given by [4.4.7].


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SECTION 6 STRUCTURAL ANALYSIS

6.1 General

6.1.1 The aim of the structural analysis is to provide the necessary input to the calculations of VIV and force modelresponse, and to provide realistic estimations of static loading from functional loads.

6.1.2 The structural analysis comprises two main steps:

— a static analysis to obtain the static configuration of the pipeline— eigenvalue analyses for both the in-line direction and the cross-flow direction.

The static analysis should provide accurate estimates of:

— the static curvature κ(x) and associated bending moment Mstatic(x)— the effective axial force Seff(x)— the number of free spans and associated span lengths L, if relevant/possible— the gap e(x) between the pipeline and the seabed in free spans, if relevant/possible.

The parameters should be determined for every relevant pipeline condition, i.e. as-laid, flooded, pressuretest, operating and shut-down conditions. For dynamic loading considerations, the pressure test condition isnormally disregarded.The distributions of static bending moments Mstatic(x) and effective axial forces Seff(x) are required for theULS local buckling check.Accurate estimations of the static curvature, the effective axial force, span lengths and gaps are required forthe subsequent in-line and cross-flow eigenvalue analyses. The eigenvalue analyses should in turn provideaccurate estimates of:

— the in-line and cross-flow still-water natural frequencies fIL/CF,j for each mode j— the associated in-line and cross-flow unit diameter stress amplitudes AIL/CF,j(x) for each mode j.

The eigenvalue analyses thus provide the necessary input to fatigue and maximum environmental stresscalculations based on the response models in Sec.4 and the force model in Sec.5.

6.2 Important physical aspects and effects

6.2.1 The overview given in [6.2] provides a brief description of physical aspects of pipeline static and dynamicbehavior that may have a strong influence on the predicted response of the pipe in and near free spans.

6.2.2 Free span response generally changes over time, and the outcomes of the associated eigenvalue analyseschange accordingly.Span lengths, gaps and effective axial force distribution depend on functional loads such as pressure andtemperature (see [6.5.3]) and will therefore vary with the range of temporary and operational conditions(see [6.5.1]) and load history encountered. For scour-induced free spans the span characteristics may alsochange with time due to a mobile seabed.


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Accumulation of damage from all sources and all relevant temporary or operational phases shall be includedin the total fatigue assessment, see [2.5.2]. Calculation of fatigue damage and maximum environmental loadeffects shall therefore be carried out for each expected free span configuration and pipeline condition.

6.2.3 The modal response of a free span, i.e. the natural frequencies fIL/CF,j and unit diameter stress amplitudesAIL/CF,j(x), is strongly dependent on the preceding static analyses. The modal response quantities areexplicitly dependent on the span length L, effective axial force Seff(x) and static curvature κ(x). The naturalfrequencies are also implicitly dependent on the gap e since the added mass and hence also the effectivepipe mass me (see [6.6.6]) are functions of the gap.Because the static analysis directly influences the eigenvalue analyses, every simplification or inaccuracyin the static analysis will also implicitly affect the free span fatigue and maximum environmental stresscalculations. Effects that are important to consider in the static analysis are described in [6.5].

6.2.4 When the pipeline has an initial static curvature, transverse modal displacements will be accompaniedby axial displacements. The frequency and mode shape associated with the first symmetric mode (halfsine wave for an isolated single span) are then strongly affected by the degree of axial restraint on thespan shoulders (Vitali et al., 1993; Kristiansen et al., 1998, Søreide et al., 2001; Forbes and Reda, 2013).Generally, if axial displacements are restrained, the frequency of the symmetric mode will rise significantlywith increasing sag. If the static sag and axial restraint are sufficiently large, the first anti-symmetric mode(full sine wave for isolated single span) attains the lowest frequency and becomes the fundamental mode.

6.2.5 The effective axial force depends on the residual lay tension, pipe temperature and pressure, seabedtopography and any (lateral or vertical) static deformations. The global pipeline static behaviour thereforeinfluences the distribution of effective axial forces. This effect is particularly important for pipes which aredesigned to buckle globally, see DNVGL-RP-F110.

6.2.6 The free span static and dynamic response also depends on the morphological span classification, see[1.6]. Methods intended for isolated single spans are not applicable for interacting multi-spans. Analyzinginteracting multi-spans as isolated single spans does not simply increase the uncertainty in the outcome ofthe analysis, but introduces a non-conservative bias in the estimation of important response quantities suchas the natural frequencies fIL/CF,j (Sollund et al., 2014).An algorithm to quantitatively distinguish between isolated single spans and interacting multi-spans is givenin [6.10].

6.3 Pipeline and material characteristics

6.3.1 The guidance given in [6.3] describes requirements, basic assumptions and empirical relations related topipeline and material modeling that applies to both static and dynamic analyses.


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6.3.2 The static and dynamic structural response of the pipeline shall be evaluated by modelling the pipeline,seabed and relevant artificial supports. This section presents the basic pipe-related behavior and DNVGL-RP-F114presents pipe-soil interaction.

6.3.3 For local and global, static and dynamic analyses of pipelines in free spans, it is considered sufficientlyaccurate to model the pipeline as a beam. Normally, the influence of shear deformation can be disregarded,see e.g. Vedeld et al. (2013). In this RP, it will be assumed that beam theory is applied for static and dynamicanalyses, unless otherwise stated.

6.3.4 A realistic characterisation of the cross-sectional behaviour of a pipeline can be based on the followingassumptions:

— Long-term fatigue damage calculations may be based on actual/anticipated variation in pipe wall thicknessover the design life of the free span (if detailed information is not available the calculation shall beperformed using non-corroded cross section values for effective axial force and corroded cross sectionvalues for stresses).

— The application of this document is limited to elastic response, hence plasticity models and effects of two-dimensional state of stress (axial and hoop) on bending stiffness need not be considered.

6.3.5 The effect of coating is generally limited to increased submerged weight, drag forces, added mass orbuoyancy. The positive effect on the stiffness and strength, see [6.3.7], is normally disregarded. If thecontribution of the coating to the structural response is considered significant, appropriate models shall beused.

6.3.6 Non-homogeneity of the bending stiffness along the pipe, due to nominal discontinuities of the coating acrossfield joints or other effects, may imply strain concentrations that shall be taken into account.

6.3.7 The stiffening effect of concrete coating may be accounted for by:

where CSF denotes the stiffness of concrete coating relative to the steel pipe stiffness and (1 + CSF) is thestress concentration factor due to the concrete coating and localised bending. The empirical constant kcaccounts for the deformation/slippage in the corrosion coating and the cracking of the concrete coating. Thevalue of kc may be taken as 0.33 for asphalt and 0.25 for PP/PE coating.In case the increased stiffness effect is utilised, the increased bending stresses due to field joints shall alsobe accounted for.


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The CSF given above is assumed valid for all relevant pipe diameters, D/t-ratios and concrete strengths,fcn, provided that the pipe joint length exceeds 12 m, the field joint length is from 0.5 m to 1.0 m and theconcrete coating thickness does not exceed 150 mm.

6.3.8 In lieu of detailed data, it is conservative to assume that a girth weld is present in the most heavily loadedcross-section. This is also a basis for the concrete stiffening effect given above.

6.3.9 The cross-sectional bending stiffness of the concrete coating, EIconc, is the initial stiffness representative foruncracked coating. Young’s modulus for concrete may be taken as:

where fcn is the construction strength of the concrete. Both Econc and fcn shall be in N/mm2.

6.3.10 Structural damping is due to internal friction forces of the pipe material and depends on the strain level andassociated deflections. If no information is available, a structural modal damping ratio of

ζstr = 0.005can be assumed. If concrete coating is present, the sliding at the interface between concrete and corrosioncoating may further increase the damping, typically from 0.01 to 0.02

6.4 Boundary conditions

6.4.1 The boundary conditions applied at the ends of the modelled pipeline section shall adequately represent thepipe-soil interaction and the continuity of the pipeline. Sufficient lengths of the pipeline at both sides of thespan shall be included in the model to account for the effects of side spans, if relevant.

6.4.2 Boundary conditions for free span analyses may be represented with varying degree of sophistication. Anappropriate choice of boundary condition will in general depend on the purpose and required accuracy of thefree span analyses and the uncertainty of relevant input parameters such as functional and environmentalloads, soil properties, and seabed topography.

Guidance note:In feasibility studies and early design phases, survey data and accurate estimates of key input parameters are not available orlikely to be changed at a later stage. Detailed non-linear FE models on a rough seabed may then, if at all possible, not reducethe overall model uncertainty compared to a simplified analysis methodology. Due to increased transparency and computationalefficiency, simplified modeling approaches may then be preferred.


6.4.3 Common representations of the boundary conditions include, see Figure 6-1:


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a) realistic seabed model, with seabed topography and all relevant side spans included in the modelb) flat seabed model with interacting multi-spans, where the seabed topography is disregarded, but all

relevant side spans are includedc) flat seabed local model of isolated single-spand) idealized rigid-body constraints, such as pinned-fixed ends.

Figure 6-1 Boundary conditions: a) Multi-span with realistic seabed model, b) multi-span with flatshoulders and intermediate shoulder, c) Single span with flat shoulders, d) Idealized rigid bodyconstraints

6.4.4 Seabed unevenness will have a significant influence on static curvatures, bending moments and effectiveaxial forces, and must be included in the analyses if effects of axial sliding (“feed-in”), relaxation of effectiveaxial force, geometric non-linearity and load history shall be accurately accounted for in the static analysis.For accurate estimation of the static and dynamic response quantities listed in [6.1.2], a realistic seabedmodel is therefore recommended, and it is required for pipe-soil interaction modelling in compliance withDNVGL-RP-F114.A realistic seabed model is also the only boundary condition representation that can be used if the staticanalysis is intended to predict span lengths and gaps.The eigenvalue analysis shall be based on a realistic seabed model in order to warrant the use of safetyfactors for a “very well defined span”, see [2.7.2].


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6.4.5 If accurate estimates for span lengths, gaps and effective axial forces are a priori available, and the spanshoulders are relatively flat, a flat seabed model may be appropriate. Flat seabed models may also beconvenient for screening analyses, sensitivity analyses and verification purposes.If interaction with side spans is relevant, potential side spans shall be included in the model.The model length shall therefore be set such that any interacting side spans are included. In addition, thespan shoulders at the boundaries should be modelled long enough that the outcome of the static analysis andeigenvalue analyses is not sensitive to increasing their lengths further.Note that the natural frequencies and unit diameter stress amplitudes are explicitly dependent on the staticcurvature of the pipeline. Disregarding the seabed unevenness may therefore be a significant source ofinaccuracy in the eigenvalue analyses for the cross-flow direction even if soil stiffness, span lengths, gapsand effective axial forces are accurately represented, see Sollund and Vedeld (2015).

6.4.6 Idealized rigid-body constraints may be convenient for manual calculations and illustration of physicalaspects, but will generally give quite crude estimates of the pipe response. The use of such boundaryconditions is therefore discouraged for quantitative free span assessments.The use of idealized rigid-body constraints requires that span lengths, gaps and effective axial forces are apriori known.

Guidance note:Pinned-pinned boundary conditions have often been considered to be a conservative representation, since the actual spanshoulders would provide at least some rotational stiffness. This assumption is, however, not correct in general. Because of modaldeflections on the span shoulders and potential interacting multi-span effects, pinned-pinned boundary conditions may give non-conservative modal response estimates for a number of scenarios, including spans with soft soils, interacting side spans and inparticular for very short spans.


6.5 Static analysis

6.5.1 The static configuration shall be determined for the following conditions if relevant:

1) as-laid condition2) flooded condition3) pressure-test condition4) operating condition5) shut-down condition.

Guidance note:Effects of alternating operation and shut-down cycles should be assessed if relevant.


Guidance note:The pressure test condition should be included in the static analysis, both for obtaining relevant estimates of Mstatic and Seff to the

ULS check and because the load history may influence the outcome of the analysis for subsequent phases. However, the pressuretest condition may normally be disregarded for fatigue calculations.



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6.5.2 The static analysis should normally account for non-linear effects such as:

— large displacements (geometric non-linearity)— non-linear pipe-soil interaction— loading sequence.

6.5.3 The functional loads which shall be considered are:

— weight of the pipe and internal fluid— external and internal fluid pressure— thermal expansion and contraction— residual installation forces.

6.5.4 The stiffness of the pipeline consists of material stiffness and geometrical stiffness. The geometrical stiffnessis governed by the effective axial force, Seff. This force is equal to the true steel wall axial force, Ntr, withcorrections for the effect of external and internal pressures:

Ntr = True steel wall axial forcePi = Internal pressurePe = External pressureAi = Internal cross-sectional area of the pipeAe = External cross-sectional area of the steel pipe

The effective axial force in a span is difficult to estimate because of uncertainties in operational temperatureand pressure, residual lay tension and axial force relaxation by sagging, axial sliding (feed-in), lateralbuckling, multi-spanning and significant seabed unevenness. All these effects should be considered and takeninto account if relevant. The most reliable method to estimate the effective axial force is use of non-linear FEanalysis.

As boundary values, the effective axial force for a completely unrestrained (axially) pipe becomes:

while for a totally restrained pipe the following effective axial force applies (Fyrileiv and Collberg, 2005;Vedeld et al. 2015):


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Heff = Effective lay tensionΔpi = Internal pressure difference relative to laying, see DNVGL-ST-F101As = Pipe steel cross-sectional areaΔT = Temperature difference relative to layingαe = Temperature expansion coefficient, may be temperature dependent

Using the expression for a totally restrained pipe above may lead to over-conservative fatigue results forpipelines on very uneven seabed with several long spans and for pipelines experiencing lateral buckling/snaking. In such cases the structural response quantities must be based on refined, non-linear FE analyses.

A corresponding expression for pipe cross sections with a liner or clad layer may be found in Vedeld et al.(2014).

6.5.5 In this document, the static environmental loads are confined to those from near bottom current. If the loadis much smaller than the vertical functional loads, then it may be disregarded in the analysis. However, forlight pipes or long span lengths it should be considered if relevant.

6.5.6 Load history effects such as the lay tension and submerged weight during installation will influence the staticdeflection and stresses which are mainly determined by the submerged weight and effective axial force in thephase considered.Furthermore, the span geometry such as inclination of the span shoulders will have a significant influenceon the static stresses and deflection. For this reason, the static response should be based on survey results(measured deflections) and/or FE analysis if considered as critical for the span assessment.

6.5.7 In addition to the static penetration into the soil due to the submerged weight of the pipeline, the penetrationmay increase due to effects from laying, erosion processes and self-burial.

6.5.8 In order to accurately account for all relevant non-linear effects (see [6.5.2]), it is recommended that thestatic analysis is based on a non-linear FE analysis with realistic seabed boundary conditions ([6.4.4]) andwith analysis steps reflecting the appropriate loading sequence.Simplified static analysis approaches accounting predominantly for static deflection due to gravity andeffective axial forces, can be applied in conjunction with flat seabed boundary conditions ([6.4.5]) whenthe intention of the static analysis is to provide input to eigenvalue analyses for screening, sensitivityand verification purposes. In a simplified static analysis, relevant span lengths and gaps and a constantequilibrium level of effective axial force are typically taken as input to the analysis, and linear vertical soilstiffness (DNVGL-RP-F114) is applied.

6.6 Eigenvalue analyses

6.6.1 The aim of the eigenvalue analyses is to calculate still-water natural frequencies fIL/CF,j mode shapes φj andunit diameter stress amplitudes AIL/CF,j for undamped free vibration of the free spanning pipeline.


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An eigenvalue analysis (also referred to as a modal analysis) is a linearised procedure, and a consistentlinearisation of the free span problem must therefore be made. The eigenvalue analysis should account forthe static equilibrium configuration, i.e. the analysis should be based on the tangent stiffness of the staticallydeformed pipe configuration.

6.6.2 The unit diameter stress amplitude is the stress associated with a unit outer diameter mode shape deflection,and shall be calculated for each active mode (see [2.1.3]). The unit diameter stress amplitudes for the j-th modes are termed AIL,j and ACF,j in in-line and cross-flow directions respectively, and may be calculatedaccording to the following equation:

where D is the outer pipe diameter (including any coating), κj(x) is the curvature of the mode shape φj forthe j-th in-line or cross-flow mode and r is the radial coordinate. AIL,j and ACF,j shall be calculated at theweld toe and the weld root, i.e. for r = Ds/2 and r = (Ds-2ts)/2 respectively, where Ds is the outer pipe steeldiameter. In ULS calculations, see [2.6.5], AIL,j and ACF,j need only to be calculated at r = Ds/2.

6.6.3 Each mode shape φj has a starting coordinate x0 and an end coordinate xe. The maximum stress amplitudefor the j-th mode is calculated as:

The maximum unit diameter stress amplitudes are applied for calculations when all damage is conservativelyassumed to be accumulated at a single critical location.

6.6.4 In the eigenvalue analysis, a consistent linearisation of the problem shall be made. In addition to the staticcurvature κ(x), effective axial force Seff(x) and span lengths L provided by the static analysis, the eigenvalueanalyses depend on the following parameters:

— the axial stiffness EA and bending stiffness EI of the pipe— the effective pipe mass me

— the soil stiffness in axial, lateral and vertical directions.

6.6.5 The impact of concrete coating and other coating layers on the axial and bending stiffness of the pipe may beaccounted for as described in [6.3.7].

6.6.6 The effective mass, me, is defined by


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where φ(s) is the assumed mode shape satisfying the boundary conditions and m(s) is the mass per unitlength including structural mass, added mass and mass of internal fluid.

6.6.7 The added mass may be considered as:

The downward arrow symbolises KC approaching 0. Note that the effects of pipe roughness and trench, see[5.4.11] and [5.4.13], are not accounted for.According to section [5.4.9], Ca becomes:

where e/D is the span gap ratio. This expression applies for both smooth and rough pipe surfaces.The added mass coefficient given here is for calculation of still water frequency. The added mass coefficient insection [4.4.15] is for modifying cross-flow response frequency and fatigue calculation only.

6.6.8 The linearised dynamic soil stiffness for the lateral (in-line) direction and the vertical (cross-flow) directionmay be determined according to the guidance in DNVGL-RP-F114. The pipe-soil linearisation should bevalidated.

6.6.9 The linearised axial dynamic stiffness has an important influence on the natural frequency of the firstsymmetric mode (Vitali et al., 1993, Søreide et al., 2001), and shall be appropriately accounted for whenthere is a non-negligible static curvature or span interaction. In lieu of detailed information, the axialdynamic stiffness may be taken equal to the lateral dynamic soil stiffness, see DNVGL-RP-F114.The axial modal response component typically extends much further into the span shoulders than thetransverse component. It is therefore important that the boundary conditions are modelled sufficiently longto provide realistic axial restraints.


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6.6.10 ULS conditions may require a more refined pipe-soil modelling than the linearised eigenvalue analysisbecause of potential sliding at the span supports. In particular, the span supports may change because ofdirect wave loading effects.

6.6.11 The eigenvalue analyses may be performed using either FE approaches or, under certain limitations,analytical or semi-analytical approaches.FE approaches can readily account for any variation of static curvature and effective axial force along thepipe axis, and are thus recommended when the preceding static analysis is based on non-linear FE modellingwith realistic seabed boundary conditions, see [6.4.4]. FE analyses may also be used for other choices ofstatic analysis approaches and boundary conditions.Analytical or semi-analytical approaches are typically based on simplified assumptions, which result inapproximate results and limited validity ranges. Such limitations vary depending on the method, and it isimportant to not use analytical approaches outside their indicated validity range. The methods are normallyrestricted to a relatively flat seabed, and most methods do not account for potential interaction betweenneighbouring spans.An important advantage of analytical and semi-analytical methods is their computational efficiency andtransparency, making them suited to be used in conjunction with simplified static analysis approaches forscreening, sensitivity and verification analyses. A particular analytical approach is described in [6.8], see alsoFyrileiv and Mørk (2002).

6.6.12 For analysis of a pipeline stretch with several spans and especially with interacting spans, special care mustbe paid to the determination of the eigenvalues and associated eigenvectors. This is due to the potentialoccurrence of very close eigenvalues, especially with respect to the identification of correct eigenvectors. Seealso the guidance note in [1.6.2].

6.7 Response quantities based on finite element modelling

6.7.1 FEM approaches can be used for both static analysis and eigenvalue analyses in accordance with theguidance given in [6.4]-[6.6]. Some general remarks pertaining to the analysis of free spanning pipelines aregiven below, but for detailed guidance on the use of FEM one of the many textbooks on the subject should beconsulted.

6.7.2 The element length to be used in a finite element model is dictated by the accuracy required. If the stressranges shall be derived from the mode shapes, see [6.6.2], the accuracy of the stress ranges becomesstrongly affected by the element length, especially at the span shoulders.Ideally the maximum element length should be found by reducing the length until the results (naturalfrequencies and stresses) converge towards constant values. In practice this may be difficult to perform, and,as guidance, the element length should be in the order of the outer diameter of the pipeline (1D). However,higher order modes and/or short spans (L/Ds < 30) may require shorter elements.


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6.7.3 In order to obtain realistic rotational pipe-soil stiffness, contact should be ensured between at least twonodes at each span shoulder, preferably by using a sufficiently short element length.

6.7.4 It is recommended to verify the finite element modelling and post-processing by comparing the results fromthe finite element analysis with the approximate response quantities of [6.8] for a single span with zeroeffective axial force and L/Ds = 60. The in-line and cross-flow natural frequencies and stress ranges shallshow similar values within ±5%.

6.7.5 The problem with identification of correct eigenvectors because of closely spaced eigenvalues, see [6.6.12],is particularly relevant for FEM analyses of long pipeline stretches with several spans.Manual inspection and evaluation of all responding modes are therefore recommended to ensure thatindividual modes are appropriately separated.

6.8 Approximate response quantities

6.8.1 The analytical approach described in this section is based on the assumption of an isolated single span withinfinitely long, flat shoulders with uniform linear soil stiffness, see Figure 6-1 c) and [6.4.5]. The resultingapproximate response quantities may be applied for a free span assessment, provided that (Fyrileiv andMørk, 2002):

— Conservative assumptions are applied with respect to span lengths, soil stiffness and effective axial force.— The span is a single span on a relatively flat seabed, i.e. the span shoulders are almost horizontal and at

the same level.— The symmetrical mode shape dominates the dynamic response (normally relevant for the vertical, cross-

flow response only). Here the following limits apply:L/Ds < 140

δ/D < 2.5Note that these are not absolute limits. The shift in cross-flow response from the symmetrical to theunsymmetrical mode will depend on the sagging and the levelling/inclination of the span shoulders. Incases where a shift in the cross-flow response is considered as likely, the structural response of the spanshould be assessed by using an FE analysis that accurately accounts for these aspects.

— Bar buckling does not influence the response, i.e. thatSeff/Pcr > − 0.5

— A sensitivity study is performed in order to quantify the criticality of the assumptions.— The approach is not applicable for multi-spanning pipelines.— The non-dimensional soil stiffness parameter β, defined in [6.8.8], is limited to the range 2 < β < 8. For

smaller values of β, the method described in [6.9] is recommended instead.

A different approach is described Sollund et al. (2015a), where the accuracy and range of validity forthe approximate response quantities are improved compared to the methods described in this section.Particularly, the predictions for stresses and higher order modal response quantities are improvedsubstantially. However, the method proposed by Sollund et al. (2015a) was considered to be too


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comprehensive to include in the present revision of this recommended practice and is therefore given only inthe referenced publication.

6.8.2 The fundamental natural frequency (first eigen frequency) may be approximated by:

where:

C1, C3 = Boundary condition coefficientsE = Youngs modulus for steelI = Moment of inertia for steelCSF = Concrete stiffness enhancement factorLeff = Effective span length, see [6.8.8]me = Effective mass, see [6.6.6]D = Outer diameter of pipePcr = Critical buckling load = (1+CSF)C2π2EI/Leff

2 (positive sign)δ = Static deflection, normally ignored for in-line direction).Seff = Effective axial force (negative in compression), see [6.5.4]

Guidance note:The correction for static deflection in the expression for the fundamental frequency is independent of the dynamic axial soilstiffness, which causes the expression to become increasingly inaccurate when the static deflection approaches the limit specifiedin [6.8.1]. The correction term is based on a static curvature due to the action of gravity for a free span with flat shoulders, andthe accuracy may therefore also be reduced by seabed unevenness in the vicinity of the span.


6.8.3 In lieu of detailed information, the maximum unit diameter stress amplitudes for the fundamental in-

line and cross-flow modes may be estimated as:

where r = Ds/2 and r = (Ds-2ts)/2 for weld toe and weld root calculations respectively and C4 is a boundarycondition coefficient defined in Table 6-1.

6.8.4 The expression for maximum unit diameter stress amplitudes given in [6.8.3] is independent of the effectiveaxial force Seff. For high compressive values of Seff it is recommended to include the impact of Seff on modalstresses. An analytical method accounting for this effect has been presented by Sollund et al. (2015b).


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6.8.5 The static bending moment may be estimated as:

where q represents the loading, i.e. the submerged weight of the pipe in the vertical (cross-flow) directionand/or the drag loading in the horizontal (in-line) direction, see [5.4.1].Note that:

a) Leff shall be calculated using the static soil stiffness in the Leff/L calculation.b) Because of historical effects and the local seabed geometry, there is a large uncertainty associated with

this simplified expression, see [6.5.6].c) The term Seff/Pcr becomes negative when the effective axial force is in compression since Pcr is defined as

positive.

6.8.6 In case the static deflection is not given by direct measurement (survey) or estimated by accurate analyticaltools, it may be estimated as:

where C6 is a boundary condition coefficient.Note that:

a) Leff shall be calculated using the static soil stiffness in the Leff/L calculation.b) Because of historical effects and the local seabed geometry, there is a large uncertainty associated with

this simplified expression, see [6.4.5].

6.8.7 The boundary condition coefficients C1 to C6 are given in Table 6-1. For multi-spanning scenarios, thesecoefficients should not be used. Instead, a dedicated FE-analysis is recommended.

Table 6-1 Boundary conditions coefficients

Pinned-Pinned 2) Fixed-Fixed 3) Single span on seabed

C1 1.57 3.56 3.56

C2 1.0 4.0 4.0

C3 0.8 1) 0.2 1) 0.4 1)

C4 4.93 14.1 Shoulder: 14.1(L/Leff)2

Mid-span: 8.6


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Pinned-Pinned 2) Fixed-Fixed 3) Single span on seabed

C5 1/8 1/12 Shoulder:4)

Mid-span: 1/24

C6 5/384 1/384 1/384

1) Note that C3 = 0 is normally assumed for in-line direction if the steady current is not accounted for.2) For pinned-pinned boundary condition Leff shall be replaced by L in all expressions, including the expression for Pcr.3) For fixed-fixed boundary conditions, Leff/L = 1 per definition.4) C5 shall be calculated using the static soil stiffness in the Leff/L calculation.

6.8.8 The Leff/L term used throughout [6.8] accounts for the effective span length in order to consider the span asfully fixed. This ratio decreases as the L/Ds ratio and soil stiffness increase.The Leff/L term is given by:

where K is the relevant soil stiffness (vertical or horizontal, static or dynamic). For reference see Hobbs(1986) and Fyrileiv and Mørk (2002). Recommended values for static and dynamic soil stiffness parametersmay be found in DNVGL-RP-F114.

6.8.9 The boundary condition coefficients in Table 6-1 based on the effective span length are found appropriatefor fatigue assessment (FLS) under the assumption of small displacements and an isolated, single span on arelatively flat seabed.In the ULS check of maximum bending moments due to direct wave loading, the potential reduction instiffness due to lateral sliding on the span shoulders should be accounted for, see [2.6.4].

Guidance note:The bending moment due to static deformations may be calculated by use of the boundary condition coefficients in Table 6-1 oralternatively by an FE analysis applying long-term (static) soil stiffness.



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Figure 6-2 Effective span length as a function of β

6.8.10 For long single spans (not multi-spans) in multi-mode vibrations, approximate response quantities forscreening purposes can be estimated based on Table 6-2.

Table 6-2 Approximate conservative higher order mode response quantities

Response 2nd mode 3rd mode 4th mode

Frequency1) 2) 2.7 f1 5.4 f1 8.1 f1

Unit Stress amplitude 3.1 A1 6.2 A1 9.3 A1

1) Note that the sagging term shall be excluded from the f1 estimate for these higher order modes.2) The critical force, Pcr, shall consider the frequency mode, i.e. the buckling length shall reflect the mode number.

6.8.11 This approach is intended to be conservative, because the unit stress amplitudes given for the 2nd, 3rd and4th modes correspond to the maximum values of the unit stress amplitudes, which do not occur at the samelocation of the span.

6.8.12 The approximate conservative response quantities for long spans in multimode are intended for screeningpurposes only.


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6.9 Special considerations for very short spans

6.9.1 Short and very short free spans will not experience onset of VIV for the range of flow velocities normallyencountered (see Table 1-1), but VIV excitation may occur in rare cases, e.g. in spans experiencing floods orerosion processes in rivers, straits and inlets with strong bottom currents that are generally perpendicular tothe pipeline.

6.9.2 Very short spans are often associated with high modal stresses, and fatigue failure will normally occur rapidlyonce a critical span length is reached (Heggen et al., 2014). The use of VIV avoidance criteria, see section[2.3], is therefore appropriate in most cases.

6.9.3 The modal response of very short spans will often be dominated by the dynamic soil stiffness K in therelevant direction (in-line/lateral or cross-flow/vertical). Accurate estimation of the linearised dynamic soilstiffness is therefore important for a reliable eigenvalue analysis.

6.9.4 Short and very short spans relevant for VIV fatigue assessments typically arise as a result of riverbed erosionor other scouring processes, which can be difficult to predict. Span length, soil stiffness, effective pipe massand effective axial force may hence be associated with significant uncertainty, and comprehensive sensitivitymapping shall be performed.

6.9.5 The analytical approach for short free spans described in this section is based on the assumption of anisolated single span with infinitely long, flat shoulders with uniform linear soil stiffness, see Figure 6-1 c) and[6.4.5]. The resulting approximate response quantities may be applied for a free span assessment providedthat (Sollund et al., 2015b):

— Conservative assumptions are applied with respect to span length, soil stiffness, effective pipe mass andeffective axial force.

— A sensitivity study is performed in order to quantify the criticality of the assumptions.— The span is an isolated single span with negligible static curvature, which is likely satisfied by most short

and very short spans. The approach is not applicable for interacting multi-spans or free spans with asignificant curvature κ(x) in or in vicinity of the span.

— The non-dimensional soil stiffness parameter β, defined in [6.8.7], is limited to the range -3 ≤ β ≤ 2.— The non-dimensional effective axial force parameter πSeff, defined in [6.9.6], is limited to the range

-0.8∙10β/2 ≤ πSeff ≤ 0.8∙10β/2.

6.9.6 For short isolated single spans satisfying the requirements specified in section [6.9.5], the fundamentalnatural frequency may be approximated by


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where:

fBEF = Frequency of an infinitely long beam in tension on a continuous linear elastic foundation, seesection [6.9.7]

gf(β,πSeff) = Fitted expression for the non-dimensional frequency response surface, see [6.9.8]

β = Non-dimensional soil stiffness parameter β, defined in [6.8.8]πSeff = Seff∙L

2/EI is the non-dimensional effective axial-force parameter

6.9.7 The frequency of an infinitely long beam on a continuous linear elastic foundation is given by

where:

K = Relevant dynamic soil stiffness (lateral or vertical)me = Effective mass, defined in [6.6.6]

Guidance note:When a span length decreases towards zero, the natural frequency will asymptotically approach the natural frequency fBEF of an

infinitely long beam on a continuous linear elastic foundation. The expression for fBEF will generally be different for a beam in

compression than for a beam in tension. The expression given in [6.9.7] corresponds to fBEF for a beam in tension, see Sollund et

al. (2015a, 2015b). However, for the calculation of short-span fundamental frequencies in [6.9.6], the expression for fBEF in [6.9.7]

should always be used regardless of whether the effective axial force is tensile or compressive. The change in the asymptotic

frequency fBEF due to a potential compressive effective axial force is accounted for by the response surface expression gf(β,πSeff).


6.9.8 The non-dimensional frequency response surface gf(β,πSeff) is given by


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6.9.9

The maximum unit diameter stress amplitudes for the fundamental in-line and cross-flow modes may

be estimated as:

where r = Ds/2 and r = (Ds-2ts)/2 for weld toe and weld root calculations, respectively, and gA(β,πSeff) is afitted expression for the non-dimensional response surface for maximum modal curvatures, see [6.9.10].

6.9.10 The non-dimensional response surface gA(β,πSeff) for maximum modal curvatures is given by

where the coefficients a, b and c are functions of β.

For -3 ≤ β <0, the coefficients may be expressed as

For 0 ≤ β ≤ 2, the coefficients may be expressed as

6.9.11 When the span length becomes very short, all higher-order eigenvalues converge towards the same value,corresponding to the frequency of an infinitely long beam on a continuous linear elastic foundation, seeHobbs (1986) and Sollund et al. (2015b). Without consideration of damping and non-linear pipe-soilinteraction effects, multi-mode response is therefore not relevant for very short spans.


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6.10 Interacting multi-spans

6.10.1 In section [1.6], a typical interacting multi-span is shown in Figure 1-4, and a typical scenario with isolatedsingle spans is shown in Figure 1-3. Characteristic modal behaviour for the two scenarios is illustrated in thesame figures.

6.10.2 The aim of this sub-section is to give a precise mathematical formulation which classifies a sequence of spansas either an interacting multi-span or a series of isolated single spans.

6.10.3 When classifying a sequence of spans as either interacting or as a series of isolated single spans, it isconsidered sufficiently accurate to model shoulders and intermediate shoulders as flat. Note, however, thatsevere seabed unevenness may cause more interaction than predicted by such an approach.The algorithm to distinguish interacting multi-spans from isolated single spans given in [6.10.4] to [6.10.5] isbased on the assumption of flat span shoulders and intermediate shoulders; see Figure 6-1 b).

6.10.4 The following algorithm classifies a span as either an interacting multi-span or an isolated single span:For the potential multi-span:

1) Calculate modal frequencies and associated unit diameter stress amplitudes for the sequence of spans.These frequencies fIL/CF,j and stresses AIL/CF,j will be defined as multi-span frequencies and unit diameterstress amplitudes respectively.For each span:

2) Identify all participating modes (see [4.3.3]) from the multi-span analysis. There will be nIL participatingin-line modes and nCF participating cross-flow modes.

3) Calculate modal frequencies fIL/CF,jSS and associated maximum unit diameter stress amplitudes AIL/CF,j

SS

for each span as an isolated single span. There will be nILSS in-line and nCF

SS cross-flow participatingmodes for the single span.

4) If nIL ≠ nILSS or nCF ≠ nCF

SS, the span is part of an interacting multi-span.5) If nIL = nIL

SS and nCF = nCFSS, compare all participating isolated single span frequencies to their

corresponding multi-span frequencies, as described in [6.10.5].

6.10.5 If the following inequality is fulfilled for any of the nIL participating in-line modes, the span is part of aninteracting multi-span:

where


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Similarly, if the following inequality is fulfilled for any of the nCF participating cross-flow modes, the span ispart of an interacting multi-span:

where


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SECTION 7 APPLICATION OF SENSORS TO MONITOR FREE SPANVIBRATIONS

7.1 General

7.1.1 The aim of span instrumentation is to achieve accurate estimations of fatigue utilization at critical locations,i.e. at girth welds. The damage accumulation principle in Sec.2 therefore still applies. However, uncertaintiesin environmental conditions, span dynamic response, response models, force models and stress estimationgive rise to conservatism in free span design. With span instrumentation, the reliability of span behaviourapproximations is greatly increased and thereby conservatism may be reduced. The safety factor format maytherefore be reassessed to account for the new set of uncertainties compared to the empirically predictedresponse method.

7.1.2 It is particularly relevant to measure dynamic response directly for mobile spans, where actual spancharacteristics during significant environmental events are highly difficult to predict. Operations managementof such pipelines is generally most costly in terms of seabed intervention.

7.1.3 This section is only focused on the fatigue limit state of pipelines in free spans. Ultimate limit stateconsiderations shall not be resolved using sensor technology. Sufficient resistance against the characteristicdesign environmental condition ( [2.3.2]) shall be documented according to [2.5].

7.1.4 If a span is continuously monitored by sensors, the estimated fatigue utilization from the sensor readingsmay replace traditional fatigue estimates based on empirical response or force coefficient models. In thatcase, the safety factor format in this RP is no longer directly applicable. Instead, the designer shall accountfor uncertainties in the sensor measurements and their interpretation such that the overall probability offailure in the governing design code for the pipe is maintained, see DNVGL-RP-F114.

7.2 Practical requirements

7.2.1 Digital data sampling rates shall be high enough to satisfactorily resolve the response frequency rangesfor all relevant modes. Keeping the rate about 10 times higher than the relevant upper frequency range isusually acceptable.

7.2.2 The fundamental in-line mode may be excited at small amplitudes. The associated response occurs at smalldisplacements, curvatures and accelerations. The sensors must be capable of measuring this response with ahigh degree of accuracy.


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7.2.3 Sensors shall be placed such that they can account for simultaneous in-line and cross-flow response atcritical locations from all potentially excited modes in the isolated single span or the interacting multi span.For non-stationary spans, it is generally recommended to place sensors densely, to account for variation inspan length, and span migration along the pipe axis.

7.2.4 Traditional fatigue design, based on the requirements in this RP, may be replaced or supplemented by fatigueestimations from sensor recordings only for time periods with recorded data available.If fatigue estimations from sensor recordings are used to estimate expected fatigue damage outside thetime intervals of available measurements, it shall be documented that the overall probability of failure in thegoverning standard used for design of the pipe is maintained.

7.2.5 If fatigue design is planned to be accounted for by the application of sensor technology, it is recommendedthat sufficient redundancy to sensors and power supplies is ensured, such that failure or malfunction of eitherone does not impair the overall function of the sensor application.In particular, there shall be sufficient redundancy in the number of sensors to ensure that erroneous orflawed output from a malfunctioning sensor is detected. As a consequence, more than one sensor mustalways be placed at each instrumented span.

7.2.6 In most cases, depending on sensor type and setup, it will be necessary to perform simultaneous flow andpipe response measurements in order to sensibly interpret the recorded data.

7.2.7 Sensor measurement uncertainty shall be quantified using controlled laboratory tests. Sensor characteristicsand accuracy, including latency, robustness and sensitivity on response, shall be documented when sensortechnology is applied to estimate free span fatigue exposure.

7.3 Processing sensor data

7.3.1 To estimate stress ranges with sufficient accuracy, interpretation of the sensor readings shall be done inconjunction with an accurate modal analysis of the free span, ensuring that stress contributions from allcontributing modes are accounted for and that all critical locations are identified. For a modal analysis tobe considered sufficiently accurate, a high degree of correspondence between the measured and calculatedfrequencies must be achieved. Calculated mode shapes may be applied to estimate stress response onlyfor results of accurate modal analyses. Furthermore, any analysis method based on simplified boundaryconditions cannot be applied. Unless sensors capable of direct stress or strain measurements are applied ateach girth weld, sensor readings alone should not be applied to estimate stress response between sensors.


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7.3.2 The output from the sensors should be validated using recognized empirical models (such as the responsemodels in Sec.4). The output from the sensors should thus be understood in conjunction with typicalexpected response based on such empirical models.

Guidance note:Empirical response models or force coefficient models are intended to supply conservative predictions for given flow regimes. Itwould therefore be expected that sensor readings record less VIV response than predictions from empirical models. However,important physical aspects such as onset of VIV, cross-flow induced in-line VIV and amplitude to reduced velocity relationshipsshould be possible to interpret from the sensor readings. Considerable deviation between measured response and responsepredicted by empirical models should prompt detailed investigation to identify the causes of such deviations in order to avoidmisinterpretations due to faulty equipment, poorly placed sensors, recording/reading errors or sensor interpretation errors.


7.3.3 Response due to direct wave action will normally not occur at any of the span natural frequencies, butrather be strongly related to wave frequencies. As a result, spectral decomposition of response due to directwave action may be challenging to perform. Signal filtering will generally cause reductions in calculatedamplitudes, which shall be considered when the measured response is estimated.

7.3.4 There are several methods to interpret a sensor signal, and transform it to a format which is readily usable infatigue design. The method will depend on the type of sensor applied.As an example, if accelerations are measured, the signal must be transformed to displacements in orderto utilize calculated mode shapes to estimate stresses. Furthermore, the frequency of response must bewell understood in order to determine the relevant number of stress cycles. There are several importantchallenges related to the transformation of recorded accelerations to fatigue stresses. Direct wave action isdiscussed in [7.3.3]. The effective added mass and the natural frequency of the pipe change with the flowvelocity. Hence, when using spectral decomposition, it may be difficult to distinguish between noise and theactual response. Damping will also change the response frequency depending on the amplitude of vibration,having a similar effect.When a signal is transformed and/or filtered, relevant information will always be lost. This creates ameasurable model uncertainty. This model uncertainty shall be part of the overall reliability assessment, see[7.1.4].


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SECTION 8 REFERENCES

8.1 ReferencesAndersen, K.H., 2004. Cyclic clay data for foundation design of structures subjected to wave loading.International Conference on Cyclic Behaviour of Soils and Liquefaction Phenomena, Bochum, Germany, pp.371-387.

Bearman, P.W. & Mackwood, P.R., 1991. Non-linear vibration characteristics of a cylinder in an oscillatingwater flow. 5th Conference on Flow Induced Vibrations, Brighton, UK, pp. 21-31.

Blevins, R.D., 1994. Flow-Induced Vibrations. Florida: Krieger Publishing Company.

Chezhian, M., Mørk, K.J., Fyrileiv, O., Nielsen, F.G. & Søreide, T., 2003. Assessment of Deepwater Multi-Spanning Pipelines – Ormen Lange Experience.15th Deep Offshore Technology (International Conferenceand Exhibition), Marseille, France, November 19-21.

Chioukh, N. & Narayanan, R., 1997. Oscillations of elastically mounted cylinders over plane beds in waves.Journal of Fluids and Structures, 11, pp. 447-463.

Forbes, G.L. & Reda, A.M., 2013. Influence of axial boundary conditions on free spanning pipeline naturalfrequencies. 32nd International Conference on Ocean, Offshore and Arctic Engineering, OMAE 2013, Nantes,France, June 9-14.

Fyrileiv, O., Chezhian, M. & Mørk, K., 2005. Experiences Using DNV-RP-F105 in Assessment of FreeSpanning Pipelines. 24th International Conference on Offshore Mechanics and Arctic Engineering, OMAE2005, Halkidiki, Greece, June 12-17.

Fyrileiv, O., Chezhian, M., Mørk, K.J., Arnesen, K., Nielsen, F.G., & Søreide, T., 2004. New Free SpanDesign Procedure for Deepwater Pipelines. 16th Deep Offshore Technology (International Conference andExhibition), New Orleans, USA.

Fyrileiv, O. & Collberg, L., 2005. Influence of pressure in pipeline design – effective axial force. 24thInternational Conference on Offshore Mechanics and Arctic Engineering, OMAE 2005, Halkidiki, Greece, June12-17.

Fyrileiv, O. & Mørk, K., 2002. Structural Response of Pipeline Free Spans based on Beam Theory. 21stInternational Conference on Offshore Mechanics and Arctic Engineering, OMAE 2002, Oslo, Norway, June23-28.

Fyrileiv, O., Mørk, K.J. & Rongved, K., 2000. TOGI Pipeline – Assessment of Non-stationary Free Spans, 19thInternational Conference on Offshore Mechanics and Arctic Engineering, OMAE 2000, New Orleans, USA,February 14-17.

Hansen, E.A., Bryndum, M., Mørk, K.J., Verley, R., Sortland, L. & Nes, H., 2001. Vibrations of Free SpanningPipeline Located in the Vicinity of a Trench. 20th International Conference on Offshore Mechanics and ArcticEngineering, OMAE 2001, Rio de Janeiro, Brazil, June 3-8.

Hardin, B.O., 1978. The nature of stress-strain behavior for soils. ASCE Geotech. Engrg. Div. SpecialtyConference on Earthquake Engineering and Soil Dynamics, vol. 1, pp. 3-90.

Hayashi, K. & Chaplin, J.R., 1991. Damping of a vertical cylinder oscillating in still water. 1st InternationalOffshore and Polar Engineering Conference, ISOPE 1991, Edinburgh, UK, August 11-16.

Hayashi, K. & Chaplin, J.R., 1998. Vortex-excited vibration of a circular cylinder in waves. InternationalJournal of Offshore and Polar Engineering, 8(1), pp.66-73.

Hayashi, K., Higaki, F., Shigemura, T. & Chaplin, J.R., 2003. Vortex-excited vibration of a circular cylinder inplanar oscillating flow. International Journal of Offshore and Polar Engineering, 13(4), pp. 266-273.


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Heggen, H.O., Fletcher, R., Fyrileiv, O., Ferris, G. and Ho, M., 2014. Fatigue of pipelines subjected tovortex-induced vibrations at river crossings. The Rio Oil & Gas Expo and Conference, Rio de Janeiro, Brazil,September 15-18.

Hobbs, R.E., 1986. Influence of Structural Boundary Conditions on pipeline Free Span Dynamics. 5thInternational Conference on Offshore Mechanics and Arctic Engineering, OMAE 1986, Tokyo, Japan.

Isaacson, M.Q. & Maull, D.J., 1981. Dynamic response of vertical piles in waves. International Symposiumon Hydrodynamics in Ocean Engineering, The Norwegian Institute of Technology, pp. 887-904.

Kaye, D. & Maull, D.J., 1993. The response of a vertical cylinder in waves. Journal of Fluids and Structures,7, pp. 867-896.

Kozakiewicz, A., Fredsøe, J. & Sumer, B.M., 1995. Force on pipelines in oblique attack: Steady currentand waves. 5th International Offshore and Polar Engineering Conference, ISOPE 1995, The Hague, TheNetherlands, June 11-16.

Kozakiewicz, A., Sumer, B.M. & Fredsøe, J., 1994. Cross-flow vibrations of cylinders in irregular oscillatoryflow. ASCE Journal of Waterway, Port, Coastal and Ocean Engineering, 120(6), pp. 515-534.

Kozakiewicz, A., Sumer, B.M., Fredsøe, J., & Hansen, E.A., 1996. Vortex regimes around a freely vibratingcylinder in oscillatory flow. 6th International Offshore and Polar Engineering Conference, ISOPE 1996, LosAngeles, California, May 26-31.

Kristiansen, N.Ø., Tørnes, K., Nystrøm, P.R. & Damsleth, P., 1998. Structural modelling of multi-span pipeconfigurations subjected to vortex induced vibrations. 8th International Offshore and Polar EngineeringConference, ISOPE 1998, Montreal, Canada, May 24-29.

Larsen, C.M, & Koushan, K., 2005. Emperical model for the analysis of vortex induces vibrations of freespanning pipelines. EURODYN 2005, ISBN 90 5966 033 1.

Maull, D.J. & Kaye, D, 1988. Oscillations of a flexible cylinder in waves. International Conference on theBehaviour of Offshore Structures, BOSS 88, Trondheim, Norway, June, pp. 535-549.

Mørk, K.J. & Fyrileiv, O., 1998. Fatigue Design According to the DNV Guideline for Free Spanning Pipelines.Offshore Pipeline Technology Conference, OPT’98, Oslo, Norway, February 23-24.

Mørk, K.J., Fyrileiv, O., Chezhian, M., Nielsen, F.G. & Søreide, T., 2003 Assessment of VIV Induced Fatigue inLong Free Spanning Pipelines. 22nd International Conference on Offshore Mechanics and Arctic Engineering,OMAE2003, Cancun, Mexico, June 8-13.

Mørk, K.J., Fyrileiv, O., Nes, H. & Sortland, L., 1999. A Strategy for Assessment of Non-Stationary FreeSpans, 9th International Offshore and Polar Engineering Conference, ISOPE 1999, Brest, France, May 30-June 4.

Mørk K.J., Fyrileiv, O., Verley, R., Bryndum, M. & Bruschi, R., 1998. Introduction to the DNV Guideline forFree Spanning Pipelines. 17th International Conference on Offshore Mechanics and Arctic Engineering,OMAE 1998, Lisbon, Portugal, July 6-9.

Mørk, K.J., Vitali, L. & Verley, R., 1997. The MULTISPAN Project: Design Guideline for Free SpanningPipelines. 16th International Conference on Offshore Mechanics and Arctic Engineering, OMAE 1997,Yokohama, Japan, April 13-17.

NORSOK Standard, 2007. Actions and actions effects, NORSOK N-003, Rev. 2. Oslo: Standard Norge.

Sha, Y., Wang, Y. & Pearson, L.M., 2007. Experimental investigation on dynamic response of submarinepipeline over flat beds in waves. 26th International Conference on Offshore Mechanics and ArcticEngineering, OMAE 2007, San Diego, California, June 10-15.

Slaouti, A. & Stansby, P.K., 1992. Response of a circular cylinder in regular and random oscillatory flow atKC = 10. 6th International Conference on the Behaviour of Offshore Structures, BOSS 92, London, UK, July7-10.


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Sollund, H.A., 2015. Dynamic response of offshore pipelines in free spans. PhD thesis. University of Oslo.ISSN 1501-7710/Nr. 1699.

Sollund, H.A. & Vedeld, K., 2013. A semi-analytical model for structural response calculations of subseapipelines in interacting free spans. Vth International Conference on Computational Methods in MarineEngineering, MARINE 2013, Brinkmann, B. and Wriggers, P. (eds.), Hamburg, Germany, May 29-31.

Sollund, H.A. & Vedeld, K., 2015. Effects of seabed topography on modal analyses of free spanningpipelines. 25th International Ocean and Polar Engineering Conference, ISOPE 2015, Kona, Hawaii, June21-26.

Sollund, H.A., Vedeld, K., Hellesland, J. & Fyrileiv, O., 2014. Dynamic response of multi-span offshorepipelines. Marine Structures, 39, pp. 174-197.

Sollund, H.A., Vedeld, K. & Fyrileiv, O., 2015a. Modal response of free spanning pipelines based ondimensional analysis. Applied Ocean Research, 50, pp. 13-29.

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APPENDIX A APPLICATION OF DNVGL-RP-F105 TO JUMPERS,SPOOLS, FLEXIBLE LOOPS AND SUBSEA PIPING

A.1 General

A.1.1 Jumpers, spools, flexible loops and piping systems have traditionally been designed according to avoidancecriteria for VIV. When avoidance criteria have been difficult to satisfy for a proposed design, environmentalcovers, re-routing or re-design have historically been applied to achieve VIV avoidance. Recently, it hasbecome increasingly common to allow fatigue damage due to VIV and environmental loading on jumpers,spools, flexible loops and subsea piping systems, defined generally here as non-straight geometries. Becauseof lack of specific design guidelines for VIV design of non-straight pipes, this recommended practice hasbecome a common design code for such systems.

A.1.2 Fatigue and extreme environmental design of subsea pipelines and risers have been performed for decades,but non-straight geometries present a new and substantial challenge for conservative and reliable VIV fatigueand extreme environmental loading design. This appendix gives guidance on how to apply this document tosuch systems.

A.2 Applicability and limitations

A.2.1 The following aspects of fatigue and extreme environmental loading due to VIV and direct wave loadingcalculations are no less accurate for non-straight geometries than typical free spans:

— Avoidance criteria, i.e. the formulations in [2.3].— Time domain wave loading calculations, although Morrison load coefficients may vary, (see [A.7]).— Modal analyses, when performed using FE methods (See [A.8]).— Static analyses for non-straight pipe systems are generally part of the design of such systems, and

considered well known. Static analyses of non-straight systems are not covered in this document.— Use of sensors, provided that the effects in this appendix are accounted for in the selection of sensors,

and in the predictions of the resulting fatigue damage.— Damage accumulation principles, i.e. damage from all sources and all relevant temporary or operational

phases shall be accumulated in the total fatigue assessment.— Unless otherwise stated, other calculations will need to be made differently and with respect also to more

variables. Guidance for how the calculations differ is given in this appendix.

A.2.2 The following aspects of fatigue and extreme environmental loading due to VIV have limited empiricalbackground, or are strongly influenced by the geometric properties of the system:

— VIV response models— direct wave loading in frequency domain— modal response quantity calculations— hydrodynamic damping— the effect of directionality on the incoming flow— mitigation measures


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— the notions of in-line and cross-flow VIV.

Therefore, all of the above listed aspects must be treated with care when performing fatigue and extremeenvironmental loading calculations for systems with non-straight geometries. In-lieu of more detail, theresponse models in Sec.4 may be applied for non-straight geometries, provided that appendix [A.4] to[A.9] have been appropriately accounted for. Apart from the VIV response models, guidance is given in thisappendix for how to take the non-straight geometries into consideration in the analyses.

A.2.3 Ultimate limit state calculations for a non-straight pipe system, and any structure which it has an interfaceto (see [A.9]), shall be performed according to its governing design code, and is not directly covered in thisdocument. Note, however, that the extreme environmental loading due to VIV and direct wave loading shallbe included in the ultimate limit state calculations for the relevant design environmental condition. See [A.7]and [A.8] for more details on the kinds of load effects which are expected from VIV and direct wave loadingin non-straight pipe systems.

A.3 Methodology for analysis of non-straight pipes

A.3.1 In lieu of more detail, e.g. experimental verification, the calculation methods in [2.5.9] and Figure 4.1applies, with the following exceptions:

— Modes are no longer classified as strictly in-line or cross-flow. They may instead be in-line, cross-flow orboth (see [A.5]), and the modes may change their classification depending on the direction of incomingflow and the position on the non-straight pipe system. Specifically, classification of modes shall be madefor each flow direction for each leg of the pipe system.

— Reductions in flow velocity due to angle of attack do not apply for modes which may be excited both in-line and cross-flow for the same flow conditions, see [A.6] for more details.

— Multi-mode reductions do not apply, i.e. no modes are considered competing, and all participating modesapply their full stress range as if they were all dominant modes. As such, all participating modes areconsidered contributing modes.

— Main damage contributions from in-line and cross-flow modes are no longer in each other’s respectiveneutral planes and may therefore affect the same hot spots. Damage from in-line and cross-flow VIV isadded at each location, rather than calculated separately.

— Damage shall either conservatively be calculated at one critical location, or at a minimum of 16 differentlocations around the circumference of each girth weld. Local critical locations such as thickness variations(e.g. in bends), thickness transitions or out of roundness shall also be appropriately accounted for. If thelocations of the girth welds are not known, any location along the pipe axis shall be treated as if it has agirth weld.

A.4 Distinctions between in-line and cross-flow VIV

A.4.1 For pipelines and risers, modes can always be categorized in either in-line or cross-flow direction. For non-straight pipe systems, the introduction of bends makes such distinctions more challenging. In some cases,depending on the direction of incoming flow, modes have distinct in-line and cross-flow directionalities. If thedirection of incoming flow is changed, the characterizations may differ.


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A.4.2 A part of a non-straight pipe system is shown in Figure A-1. It is assumed that two modes are active, andthese are given as mode 1 and mode 2 in the figure.

Figure A-1 Part of a non-straight pipe system, including a bend. Two assumed responding VIVmodes are indicated by dashed lines

Which modes act as in-line or cross-flow depend on the direction of the incoming flow. In the figure, flowis directed at the non-straight pipe section in three directions θ1, θ2 and θ3. The two modes are either in-line, cross-flow or both depending on the direction of incoming flow. How the directionality of flow affects themode classification is exemplified by:

— Direction θ1: Mode 1 is cross-flow and mode 2 is in-line for both the horizontal and the vertical legs.— Direction θ2: Modes 1 and 2 are both in-line and cross-flow for the vertical leg. For the horizontal leg

Mode 2 is in-line and mode 1 is cross-flow.— Direction θ3: Mode 1 is in-line and mode 2 is cross-flow on the vertical leg.


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A.4.3 The example in [A.4.2] illustrates that a mode may be classified as in-line or cross-flow or both dependingon the angle of attack of the flow, but also on the position along the pipe axis. A mode could be in-line orcross-flow or both on the vertical leg, but will be either an in-line or a cross-flow mode at the horizontalleg. As a result, all modes shall be classified as in-line or cross-flow or both for each leg of the non-straightpipe system. Furthermore, since the classification depends on the direction of flow, each mode shall be re-classified (for each leg) whenever the direction of flow changes.

A.5 Directionality of incoming flow

A.5.1 Figure A-2 illustrates vortex shedding patters for the non-straight pipe system in Figure A-1.

Figure A-2 Vortex shedding pattern for an incoming flow which is not perpendicular to eitherplanes of motion. Forcing directions are given with double arrows and continuous lines, responsedirections are given with double arrows and dotted lines.

The flow that crosses the horizontal leg will have a smaller angle of attack than 90 degrees, and modes aredistinctly either in-line or cross-flow. Therefore, the flow velocity will be reduced based on this angle, as isnormally done for pipelines according to Sec.3. The in-line and cross-flow force directions are assumed to bein the traditional in-line and cross-flow directions, respectively.


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For the vertical leg, it does not make sense to reduce the flow velocity with respect to the angle of attack,since the perpendicular flow component to the pipe axis will never be at an angle. Due to the mismatchbetween the flow velocity and the two directions of responding modes, the in-line and cross-flow forcing donot match any of the modal directions, as indicated in the figure by dotted double arrows for displacementdirections and whole lines for forcing directions. Conservatively it shall be assumed that both modes actas both in-line and cross-flow modes, and furthermore any reduction in forcing shall conservatively bedisregarded.

A.5.2 The example in [A.5.1] gives rise to the following general requirements:

— On a leg in a non-straight pipe system, if a given flow condition can cause a mode classification to be bothin-line and cross-flow at the same time, that flow velocity shall not be reduced with respect to the angle ofattack.

— On a leg in a non-straight pipe system, for a given flow direction, if a mode can be excited due to cross-flow and in-line VIV at the same time, that mode shall be classified both as an in-line mode and a cross-flow mode.

A.5.3 For a given flow velocity, and a given mode that has been classified as both in-line and cross-flow, if thatmode responds both in-line and cross-flow, the stress contribution to fatigue shall be taken as the maximumof the two response model predictions. Since the shape of, and hence the stresses of, the mode itselfis independent of whether it responds in-line or cross-flow, a direct comparison of the modal responseamplitude is sufficient for the classification for either in-line or cross-flow.

A.5.4 Since modal classification of in-line or cross-flow varies with the direction of incoming flow and each leg ofthe pipe system, it is no longer trivial to determine the most critical flow direction. If the fatigue analysesis based on omnidirectional data, or conservatively simplified to include only one direction of flow, the mostconservative direction shall be chosen.In order to determine the most conservative flow direction, it is considered sufficient to choose the directionthat has the highest fatigue damage and largest extreme environmental load effect when the representativedesign environmental condition is applied. If directions are different for the two results, fatigue damagecalculations and extreme environmental load calculations shall be performed separately with the respectivemost conservative flow direction.

A.6 Hydrodynamic damping considerations

A.6.1 A lock-in region is defined as a region where onset of VIV is predicted according to either of the responsemodels in Sec.4. A region where VIV is not excited is defined as a non-lock-in region.

A.6.2 Lock-in regions will contribute to a VIV response. Non-lock-in regions will contribute with hydrodynamicdamping. Hydrodynamic damping from non-lock-in regions can be calculated according to guidance givenin DNVGL-RP-C205. Hydrodynamic damping from lock-in regions shall be set to zero when using a responsemodel from Sec.4.


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A.6.3 Non-lock-in regions may include attachments to the pipe system, such as buoyancy elements and ROV-plates. Such regions may also contribute to hydrodynamic damping which may be included in the calculationof the stability parameter. Note, however, that such attachments have a reduced velocity of their own (withtheir respective hydrodynamic diameter), and if lock-in is achieved for these regions, hydrodynamic dampingcannot be applied.

A.6.4 In detailed fatigue analyses, the variation in modal response classification can be utilized by accounting forincreased hydrodynamic damping. Two examples are made based on a continuance of the example given in[A.4.2], in relation to Figure A-1.

Example 1 – For a flow with direction θ2, if only mode 1 is excited, it is both in-line and cross-flow on thevertical leg, but strictly cross-flow on the horizontal leg. When mode 1 is excited in-line it has a lock-in regionon the vertical leg, but the horizontal leg is a non-lock on region. For in-line response the horizontal leg willtherefore contribute with hydrodynamic damping.

Example 2 – For a flow with direction θ3, the vertical leg is a lock-in region for both active modes. For thehorizontal leg, the flow is parallel to the pipe and hence the horizontal leg is a non-lock-in region for bothmodes. As a result, modal damping for both modes may be accounted for on the horizontal leg when the flowhas direction θ3.

A.7 Direct wave loading

A.7.1 Time-domain analyses based on Morison’s equation are applicable for non-straight pipe systems. These are,however, time consuming and it may be a challenge to perform a large number of such analyses to accountfor the variation in different sea states and combined current and wave environmental conditions.

A.7.2 Closed form frequency-domain solutions, such as the one presented for free spans in Sec.5, may be appliedin some cases. The requirements for use of such methods (even Sec.5 may be applied) are:

— For the most severe storm conditions, the frequency domain solution shall be verified to be conservativecompared to representative time-domain analyses or appropriate quasi-static solutions.

— Mode shape weighing factors shall be calculated specifically for each relevant mode, i.e. for each modethat may be classified as an in-line mode for the relevant incoming flow direction, along the curved pipeaxis coordinate.

— Extreme environmental loading shall be calculated for the maximum wave and the representative 100-year event. This may be performed using a quasi-static approach.

— Morison load coefficients shall be taken either from Sec.5 or from DNVGL-RP-C205. The load coefficientsshall accurately represent the variation of loading along the pipe axis.


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A.8 Modal response quantities

A.8.1 Modal response quantities include modal frequencies and associated modal stress ranges. Detailedguidance for modal response calculation of straight systems and free spans is given in Sec.6. The analyticalapproaches presented in Sec.6 generally do not apply to non-straight systems.

A.8.2 For systems that include bends, FE methods shall generally be applied to perform modal analyses, unlessthere is a support at each side and in near proximity of all bends, such that the bends do not influence themodal response.

A.8.3 The degree of axial restraint in supports has a strong influence on the predicted modal response. The degreeof restraint in supports shall be conservatively modelled or accurately represented. Idealizations i.e. fixed-fixed or pinned-fixed conditions cannot be applied unless it is documented or otherwise ensured that themodelled conditions accurately represent the realistic constraint conditions in the support.

A.8.4 In a three dimensional pipe structure with bends, a modal displacement will generally be associated with athree-dimensional stress state. As a result, three cross-sectional moments, shear forces along two axes anda change in the true wall axial force must generally be accounted for. The moments comprise bending abouttwo planes and torsion, and the cross-sectional shear forces are directed along the y- and z-axes (assumingx to denote the coordinate along the local pipe axis).

A.8.5 In fatigue analyses, the principal stresses shall apply at all relevant critical weld positions. According toDNVGL-RP-C203, the extreme outer fiber stresses shall apply. The principal stresses shall include the effectsof all cross-sectional moments and forces.

A.8.6 For free spans and risers, the effective axial force has a strong influence on the modal response quantities.For free spans, the static deflection also strongly influences the modal response. For non-straight sections,the effective axial force is generally small and its effect is also generally small. Unless it is documented thatthe effects of effective axial forces and static deflections are negligible, these effects shall still be accountedfor in the modal response calculations.

A.9 Interface loads

A.9.1 Spools are generally connected to pipeline end terminations, jumpers may often connect a pipeline or asubsea structure to another subsea structure, flexible loops are generally connected to christmas trees etc.All non-straight subsea pipe systems are connected to other subsea systems.


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A.9.2 If a non-straight subsea pipe system is exposed to VIV or direct wave loading, the reaction forces due toenvironmental loading will be absorbed by its interface to another structure.

A.9.3 Subsea non-straight pipe systems may have attachments such as buoyancy elements, flanges, ROV-plates,etc. If the system responds to VIV or direct wave loading, this will induce reaction forces in the connectionsbetween the pipe system and the attachment, and sometimes also in the attachment itself.

A.9.4 The fatigue and ultimate limit state checks of any interface structure, such as end connections orattachments along the pipe system, shall include fatigue and extreme environmental loading due to VIV anddirect wave loading.

A.10 Mitigation measures

A.10.1 There exists a range of different mitigation measures for non-straight pipe geometries. Traditional mitigationmeasures are developed based on riser structures, masts, poles and chimneys. A non-straight pipe section,however, is limited in size and mitigation may therefore be considered in different ways compared to largerstructures.

A.10.2 Applications for and types of strakes are discussed in DNVGL-RP-C205. There is, however, a challenge whenapplying strakes to non-straight geometries. Strakes shall generally be the subject of a qualification study.The effect of the strakes, with and without marine growth, shall be well documented. In order to use strakeson systems with non-straight geometries, the strake efficiency shall be documented for application on thespecific system, taking into account the differences in VIV response for non-straight compared to straightsystems.

A.10.3 Onset of VIV is a function of the 100-year environmental condition, the fundamental frequency of the systemand the diameter. With increasing diameter, the onset of VIV will occur for higher flow velocities. Hence, thediameter can be increased until no onset of VIV occurs. For riser systems this is not an attractive option sincethe increased hydrodynamic diameter will often cause considerably higher wave loading. For spools, jumpers,piping systems and flexible loops, wave loading is rarely critical and therefore it is often neither expensivenor a problem for other design aspects to increase the hydrodynamic diameter. The relative decrease inreduced velocity due to an increase in the hydrodynamic diameter is:

where:


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VdecR = Decreased reduced velocity, as a result of a higher hydrodynamic diameter

Sg = Specific gravity of the original configuration, see section [4.4.14]Dincr = aincr·D, new hydrodynamic diameter, after increase

aincr = Ratio between new and old hydrodynamic diameterbincr = ρincr/ρw, ratio between the density of the material causing the diameter increase and the water

densityρincr = Density of the material causing the increase in hydrodynamic diameterCa = Added mass coefficient, see section [6.6.7]

If a given relative decrease in reduced velocity is required, in order to pass the onset criterion in section[2.3.3], the equation can be solved for varying densities and thicknesses of the applied coating until therequired decrease is achieved. Note that lower coating density and higher thickness will be beneficial forachieving lower reduced velocities. Note also that the coating cannot be too lightweight since a negativebuoyancy is not acceptable for most systems.

The principles of using increased hydrodynamic diameters to mitigate VIV for onset may also be appliedto reduce the exposure to VIV for systems which fail the avoidance criteria. Note, however, that increasingthe hydrodynamic diameter will also increase the modal stresses, so the effect of an increased diameter isnot always positive. For long flexible systems, with many responding modes, the effect is likely to be moreadverse. For more rigid systems, where only one or two modes respond to VIV, the effects are more likely tobe beneficial.

Some non-straight pipe systems are designed to cool its content, and will therefore require that externalflow passes the pipe either due to environmental events or due to natural convection. For such systems,increasing the diameter must be done with care, in order to avoid reducing the intended function of the pipesince any added coating will act as thermal insulation.

A.10.4 Environmental covers of e.g. rocks, sand bags or manufactured cover structures, may shield the system fromenvironmental actions. This is a common mitigation technique for flexible non-straight structures in harshenvironments.

A.10.5 Partial supports may be applied to increase the stiffness of the system, and hence the natural frequencies.For spools this may be by sand bags, concrete mattresses or rock dumping to create touchdown points in aspan. For piping systems, it is more relevant to fix the pipes to other more rigid structures at closer intervals.

A.10.6 For systems that pass the avoidance criteria according to section [2.3.3] in cross-flow direction, but not in-line, it may only be necessary to introduce piecewise increases to the hydrodynamic diameter. Buoyancyelements, ROV-plates, or similar structures artificially introduced to mitigate VIV may cause sufficienthydrodynamic damping to mitigate in-line VIV, provided that regions with increased hydrodynamic dampingbecome non-excitation regions (see [A.6]). Hydrodynamic damping will generally not be sufficient to fullymitigate cross-flow VIV, even if the damping is considerable.It should be noted that the principles of utilizing non-excitation regions for VIV mitigation also may beapplied for systems where VIV is allowed, i.e. systems where VIV avoidance is not required, and that suchdamping may have a favorable impact on fatigue and extreme environmental load predictions, particularly in-line but also cross-flow.


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APPENDIX B VIV MITIGATION

B.1 VIV mitigation methods

B.1.1 The most commonly used vortex suppression devices are helical strakes. Their function is to triggerseparation in order to decrease the vortex shedding correlation along the riser. Helical strakes increase thecost of the pipeline and will complicate handling during installation. The in-line drag coefficient is increasedby introducing strakes.

B.1.2 The important parameters for the strake design are the height and pitch of the helical strakes for a givenpipeline diameter. The overall performance characteristics of a given strake design will vary with the currentvelocities.

B.1.3 The effectiveness of VIV suppression devices, such as VIV strakes needs to be qualified. It is recommendedthat an independent verification of the effectiveness of VIV suppression devices is performed by a competentverification body.

B.1.4 A qualification process will typically include the following for a given strake design:

— model test results with and without strakes— effect of hydrodynamic scaling— range of current velocities and associated efficiency— durability and impact assessments— effect of marine growth— effect of surface finish.

B.1.5 More detailed information is given in DNVGL-RP-F204 with respect to qualification of VIV strakes.

B.2 Span rectification methods

B.2.1 See DNVGL-ST-F101 Sec.9 for span rectification procedures and methods.

B.2.2 Survey, follow-up and documentation requirements should follow the principles given in DNVGL-ST-F101Sec.9.


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APPENDIX C VIV IN OTHER OFFSHORE APPLICATIONS

C.1 Main application scope

C.1.1 The primary focus and the main application scope of this RP are free spanning subsea pipelines as describedin [1.3].

C.1.2 The fundamental principles given in this RP may also be applied and extended to other offshore elementssuch as cylindrical structural elements of jackets and risers from fixed platforms, at the designer’s discretion.The limitations that apply are discussed in this appendix.

C.2 Riser VIV

C.2.1 Important differences with respect to the riser VIV as compared to free spanning VIV are listed below:

— The circular particle flow due to waves.— Risers will not experience the uniform currents over the span, as assumed in free span assessments.— Typically for long risers, the higher order modes are excited.— For long span lengths and/or when the flow is sheared, several modes may be excited simultaneously. For

such risers the tension will vary and the response is dominated by loading (power input) in some parts ofthe riser while other parts are contributing to damping of the system (power output). In such cases thisdocument is not applicable.

C.2.2 For short riser span lengths, typical for steel risers supported by a jacket structure and when the currentis uniform, the response models given in Sec.4 of this RP can be applied. For short risers the lowest eigenmodes are typically excited. In such cases this RP will predict both in-line and cross-flow VIV provided thatthe natural frequencies are calculated based on relevant boundary conditions.

C.2.3 If no onset of VIV is allowed, the screening criterion may be applied.

C.2.4 For a detailed account of riser VIV and applicable methodologies, see DNVGL-RP-F204 Riser fatigue.


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C.3 VIV in other structural components

C.3.1 Other subsea cylindrical structural components, such as braces, trusses, etc., can also be evaluated, usingthis RP at the designer’s discretion and judgement. The following conditions should, however, be carefullyevaluated:

— uniform current assumption— frequencies and mode shapes should be based on detailed FE analysis— L/D ratio should be within the RP’s design range— location of the structural element (relevance of wave induced VIV, which is not covered by this RP).

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CHANGES - HISTORICThere are currently no historic changes for this document.

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