RECOMMENDED PRACTICE
DNVGL-RP-F105
Edition June 2017
Free spanning pipelines
The electronic pdf version of this document, available free of charge
from http://www.dnvgl.com, is the officially binding version.
DNV GL AS
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 rules@dnvgl.com
This service document has been prepared based on available knowledge, technology and/or information at the time of issuance of this
document. 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 responsibility
for loss or damages resulting from any use of this document.
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 publication
Some 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— [1.7]: This section in the previous revision of this RP has been replaced by a new subsection introducing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 steelwall 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 of
relationship to DNVGL-ST-F101 consistent with the new design fatigue factor (DFF) format have been
added.
• 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 the
previous revision. Throughout the updated Sec.4, single-mode quantities have therefore been replaced by
corresponding multi-mode quantities.
— [4.1.7]: Note stating that flow shall always be considered as current-dominated for KC > 40 has been
added.
— [4.3]: New subsection containing important definitions and aspects of the multi-mode calculation
procedure, including how to implement the new concepts of participating and contributing modes have
been added.
— [4.5]: Description of a new response model to account for cross-flow vibrations in wave-dominated
conditions 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-mode
analyses.
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Changes - current
CHANGES – CURRENT
• 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 subsea
piping
— 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 corrections
In addition to the above stated changes, editorial corrections may have been made.
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Changes - current
— [5.1]: Description of applicability to multi-spans using multiple-location analyses and of special
considerations 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.
Changes – current.................................................................................................. 3
Section 1 General.................................................................................................... 8
1.1 Introduction......................................................................................8
1.2 Scope................................................................................................ 9
1.3 Application...................................................................................... 10
1.4 Extended application...................................................................... 11
1.5 Safety philosophy........................................................................... 12
1.6 Free span morphological classification........................................... 12
1.7 Mode classification..........................................................................17
1.8 Free span response behaviour........................................................ 19
1.9 Flow regimes.................................................................................. 19
1.10 Vortex-induced vibrations assessment methodologies..................21
1.11 Relationship to other standards....................................................22
1.12 Definitions.....................................................................................23
1.13 Abbreviations................................................................................ 24
1.14 Symbols........................................................................................ 25
1.15 Verbal forms................................................................................. 33
Section 2 Design criteria....................................................................................... 34
2.1 General........................................................................................... 34
2.2 Non-stationarity of spans............................................................... 36
2.3 VIV avoidance criteria.................................................................... 37
2.4 Screening fatigue criteria............................................................... 39
2.5 Fatigue criterion............................................................................. 40
2.6 ULS criterion................................................................................... 44
2.7 Safety factors................................................................................. 47
Section 3 Environmental conditions...................................................................... 51
3.1 General........................................................................................... 51
3.2 Current conditions.......................................................................... 51
3.3 Short-term wave conditions............................................................55
3.4 Reduction functions........................................................................ 58
3.5 Long-term environmental modelling............................................... 60
3.6 Return period values...................................................................... 62
Section 4 Response models...................................................................................63
4.1 General........................................................................................... 63
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Contents
CONTENTS
4.3 Aspects of the computational approach.......................................... 66
4.4 Cross-flow response model.............................................................69
4.5 Cross-flow VIV for low KC regimes.................................................76
4.6 In-line response model...................................................................79
Section 5 Force model...........................................................................................87
5.1 General........................................................................................... 87
5.2 Frequency-domain solution for in-line direction............................. 88
5.3 Simplified fatigue assessment........................................................ 93
5.4 Force coefficients............................................................................93
Section 6 Structural analysis.................................................................................98
6.1 General........................................................................................... 98
6.2 Important physical aspects and effects.......................................... 98
6.3 Pipeline and material characteristics.............................................. 99
6.4 Boundary conditions..................................................................... 101
6.5 Static analysis...............................................................................103
6.6 Eigenvalue analyses......................................................................105
6.7 Response quantities based on finite element modelling................108
6.8 Approximate response quantities................................................. 109
6.9 Special considerations for very short spans..................................114
6.10 Interacting multi-spans.............................................................. 117
Section 7 Application of sensors to monitor free span vibrations........................119
7.1 General......................................................................................... 119
7.2 Practical requirements.................................................................. 119
7.3 Processing sensor data................................................................. 120
Section 8 References...........................................................................................122
8.1 References.................................................................................... 122
Appendix A Application of DNVGL-RP-F105 to jumpers, spools, flexible loops
and subsea piping.............................................................................................. 125
A.1 General......................................................................................... 125
A.2 Applicability and limitations......................................................... 125
A.3 Methodology for analysis of non-straight pipes............................ 126
A.4 Distinctions between in-line and cross-flow VIV...........................126
A.5 Directionality of incoming flow..................................................... 128
A.6 Hydrodynamic damping considerations........................................ 129
A.7 Direct wave loading......................................................................130
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Contents
4.2 Marginal fatigue life capacity..........................................................65
A.9 Interface loads............................................................................. 131
A.10 Mitigation measures................................................................... 132
Appendix B VIV mitigation.................................................................................. 134
B.1 VIV mitigation methods................................................................134
B.2 Span rectification methods........................................................... 134
Appendix C VIV in other offshore applications....................................................135
C.1 Main application scope................................................................. 135
C.2 Riser VIV...................................................................................... 135
C.3 VIV in other structural components..............................................136
Changes - historic...............................................................................................137
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Contents
A.8 Modal response quantities............................................................ 131
SECTION 1 GENERAL
1.1 Introduction
1.1.1
This recommended practice considers free spanning pipelines subjected to combined wave and current
loading. The premises for the document are based on technical development within pipeline free span
technology in research and development (R&D) projects, as well as design experience from previous and
ongoing projects, e.g.:
— The sections regarding free span analysis and in-line vortex induced vibrations (VIV) fatigue analyses are
based 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 pipeline
projects 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 reflect
state-of-the-art industry practice and latest research.
This document includes a brief introduction to the basic hydrodynamic phenomena, principles and parameters
for dynamic response of pipeline free spans. For more thorough introductions to physical mechanisms and
the 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 in
Figure 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 dynamic
response of pipeline free spans due to combined wave and current loading. Detailed design criteria are
specified for ultimate limit state (ULS) and fatigue limit state (FLS) due to in-line and cross-flow vortex
induced vibrations (VIV) and direct wave loading.
Free span design may be performed by conservative avoidance criteria, simplified fatigue criteria or detailed
fatigue analyses, all of which are covered in this RP. Whenever fatigue is allowed in design, extreme
environmental events may cause loading on the structure which, in case, must be accounted for in ULS
design, and detailed guidance for how to include contributions to ULS calculations due to environmental
loading 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 as
other 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 more
complex cross sections such as pipe-in-pipe, bundles, flexible pipes and umbilicals. However, calculation
of structural response quantities such as natural frequencies, modal stresses and fatigue damage will be
different 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 assessed
using this RP.
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1.3.6
The free span static and modal analyses may be based on approximate response expressions or more
refined approaches, e.g. using the finite element (FE) method, depending on the free span classification and
response 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 calculated
modal frequencies and associated stresses. Due to the importance of frequencies and stresses for fatigue
and environmental loading calculations, the choice of analysis approach influences the partial safety factor
format.
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 vortex
induced resonance phenomena in the relevant environmental event. A force model may be applied when the
free span response is dominated by direct wave loads. The selection of the appropriate model depends on the
flow 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 in
the 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 elements
such as cylindrical structural elements of e.g. jackets, risers on fixed platforms, jumpers and spools, at the
designer’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 (Heggen
et al, 2014). The fundamental principles of DNVGL-RP-F105 may be applied in such cases. See [6.9] for
details.
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 acceptable
target reliability levels using reliability-based methods.
— For all other acceptance criteria, the recommended safety factors are based on engineering judgement in
order 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 be
considered.
1.6 Free span morphological classification
1.6.1
The morphological classification should in general be determined based on detailed static and dynamic
analyses.
1.6.2
The objective of the free span morphological classification is to define free span parameters, typical free
span scenarios and to distinguish between isolated single spans and interacting multi-spans. In Figure 1-2, a
typical 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 position
x. 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. Sections
of continuous support on either side of a free span, where e(x) = 0, are defined as span shoulders, with
lengths 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 is
termed 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 of
the 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 negligibly
affected by neighbouring spans, if any.
— A sequence of two or more spans is an interacting multi-span if the static and dynamic behaviour of the
spans 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 single
spans
In Figure 1-3, two spans are in fairly close proximity to one another. However, if we assume that the three
modes illustrated in the figure are the only active modes for the spans, the spans do not interact since the
static 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 other
words, the lengths of shoulder and span number k, counting from the left, are given symbols Lsh,k and Lk
respectively.
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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 static
configuration, particularly of the second span. Furthermore, if we assume that the two presented modes are
among the active modes in the multi-span, the dynamic behaviour of each individual span is affected by the
other spans as observed from the mode shapes. Hence, the multi-span in Figure 1-4 is an interacting multispan.
Interacting multi-spans cannot be assessed using only isolated single span approaches. A precise
mathematical formulation to distinguish between isolated single spans and interacting multi-spans is
presented 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 identifying
interacting 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 analysis
estimates that some of the response frequencies for these two spans are identical. Due to numerical approximations or due to
round-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 fatigue
damage. The fatigue damage is dependent on the unit stress amplitudes, as discussed in Sec.4, which in turn are dependent on
the 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 to
errors.
Experience has shown that in case of close frequencies for spans, the FE analysis may predict interaction even though the
physical distance between the spans is quite long. In case of mode shapes with deflection in spans that seem to be physically
well separated, use of appropriate axial pipe-soil stiffness and/or local restraints in between the spans should be considered to
separate individual modes. Particularly, absence of a realistic axial soil stiffness can contribute to excessive unrealistic span modal
interaction.
Hence, caution should be exercised when using automated FE tools for identifying interacting spans.
---e-n-d---o-f---g-u-i-d-a-n-c-e---n-o-t-e---
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 important
effects 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 the
pipeline, 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 shoulder
geometries. 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 double
spans. In the context of preliminary calculations and simplified multi-span assessments this model may be
applied 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 spans
are isolated or interacting depending on soil types, span lengths and span support lengths. Figure 1-5 is
provided 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 soil
becomes softer. However, for a given seabed profile, a softer soil will tend to have shorter and fewer spans
and 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 in
some cases be substantially inaccurate. For a given pipeline configuration many of the relevant parameters
are fixed, such as stiffness of the pipe and soil, and effective axial force. For an individual pipeline it is
therefore possible to create a curve such as presented in Figure 1-5 for double span modal interaction
classification. For detailed design and operations management phases it is therefore recommended to
create curves similar to the ones presented in Figure 1-5, with the exception that correct pipeline bending
stiffness, 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 how
such curves can be developed may be found in Sollund and Vedeld (2013). For systematic analyses in detail
design or operations management phases, such project specific curves or the method detailed in [6.10] is
recommended.
For critical span scenarios and span scenarios where more than two spans can potentially interact, a more
detailed approach is recommended. For such applications, a precise definition of free span modal interaction
is described in [6.10]. [6.10] provides an algorithm to classify a span as either a part of an interacting multispan 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, is
given 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 – both
situations 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 if
there 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-z
plane, special considerations should be made to ensure that the geotechnical properties of the contact area
are 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 description
of multiple-location versus single-location analyses). For each relevant combination of sea state and current
velocity, a number of modes may be excited by VIV, giving rise to a multi-mode response. However, the
number of modes that will be responding and the extent to which each particular responding mode will
contribute to fatigue damage will vary depending on flow velocity, position along the x-axis and competition
with other responding modes. In order to calculate the combined multi-mode response at each location in a
convenient 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 excited
by VIV. A mode that is not active can be disregarded completely in the analyses, for all locations and flow
velocities. 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 curvature
either at the relevant position x or to each side of x. In an interacting multi-span, some modes will
contribute with damage only in a segment of the whole multi-span section, meaning that the mode can be
disregarded at x-locations where it is not participating. The set of participating modes is always a subset
of 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 VIV
excitation at a particular location and for a particular flow velocity. The contributing modes are mutually
competing, in the sense that one of the modes will be dominating and contribute to the combined multimode response at full strength, while the contributions from other (weak) modes are reduced. In order to
correctly identify the dominant mode, it is important to omit modes that are not participating. The set of
contributing modes is thus always a subset of the participating modes, and will in general vary with both
flow 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 three
spans is shown in the upper part of the figure. The second span, L2, is assumed to be the longest. Modal
deflection of the fundamental mode, mode 1, occurs only in this span as seen to the left in the figure. As a
result, the first mode will only be participating in a restricted x-interval containing the longest span and the
modal 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 response
in all three spans of the interacting multi-span. Hence, mode 2 has a much wider participation interval than
mode 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 VIV
amplitude. Mode 1 will then be the dominant mode (see [4.4.8]) in its participation interval, while mode
2 will be a weak mode in the same interval. The contribution from mode 2 to the combined stressrange 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 nonconservatively underestimated at these locations. Hence, it is important to correctly identify the participating modes at every
location 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 span
length. The ranges indicated for the normalised free span length in terms of (L/D) are tentative and given for
illustration only.
Table 1-1 Free span response characteristics
L/D
Response description
L/D < 30
1)
30 < L/D < 100
Very little dynamic amplification
Normally not required to perform comprehensive fatigue design check. Insignificant dynamic response
from environmental loads expected and unlikely to experience VIV. Natural frequency sensitive to soil
stiffness. Due to high modal stresses, onset criteria for VIV recommended.
Response dominated by beam behaviour
Relevant for free spans at uneven seabed.
Natural frequencies are sensitive to boundary conditions, effective axial force (including initial
deflection, geometric stiffness) and pipe feed in.
100 < L/D <
200
Response dominated by combined beam and cable behaviour
Relevant for free spans at uneven seabed in temporary conditions. Natural frequencies sensitive
to boundary conditions, effective axial force (including initial deflection, geometric stiffness) and
pipe “feed in”. See [1.7] for free span response classification, which provides practical guidance for
engineering applications, with respect to single and multi-mode response.
L/D > 200
Response dominated by cable behaviour
Relevant for small diameter pipes, or pipes exposed to mild environmental conditions, typically in deep
water. 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 Uw
is the significant wave-induced velocity amplitude normal to the pipe, see Sec.4), may be applied to classify
the flow regimes as follows:
α < 0.5
wave dominant – wave superimposed by current
In-line direction: in-line loads may be described according to Morison’s equations, see Sec.5. In-line
VIV due to vortex shedding is negligible.
Cross-flow direction: cross-flow loads are mainly due to asymmetric vortex shedding. Response
models, see Sec.4, are recommended.
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0.5 <
α < 0.8
wave dominant – current superimposed by wave
In-line direction: in-line loads may be described according to Morison’s equations, see Sec.5. In-line
VIV 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 resemble
the current dominated situation. A response model, see Sec.4, is recommended.
α > 0.8
current dominant
In-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’s
equations are normally negligible.
Cross-flow direction: cross-flow loads are cyclic and due to vortex shedding and resembles the pure
current situation. A response model, see Sec.4, is recommended.
Note that α = 0 corresponds to pure oscillatory flow due to waves and
current flow.
α = 1 corresponds to pure (steady)
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 associated
wave 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 a
conservative 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 spanning
pipelines.
1.10.2
This RP applies so-called response models to predict vibration amplitudes in in-line and cross-flow directions
due to vortex shedding. Response models are empirical relations between the reduced velocity, calculated
using the still water natural frequency, and the non-dimensional response amplitude. The stress response is
derived 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, as
a function of non-dimensional response amplitude and non-dimensional vibration frequency, see Larsen and
Koushan (2005).
Guidance note:
For a given flow regime, the response model approach estimates the vibration amplitude directly, whereas the empirical force
coefficient model estimates a balance between excitation and damping. The response model is chosen in this recommended
practice due to its computational efficiency and because it conservatively and conveniently accounts for empirical data from a
large range of experiments and full scale tests. Additionally, effects of combined wave and current, turbulent flow, KC regime and
damping can easily be accounted for in a robust and conservative manner.
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1.10.4
As a third option, computational fluid dynamics (CFD) simulation of the turbulent fluid flow around one- or
several pipes can in principle be applied for VIV assessment to overcome the inherent limitations of the stateof-practice engineering approach. The application of CFD for VIV assessment is at present severely limited by
the computational effort required. In addition, documented work is lacking which shows that the estimated
fatigue damage based on CFD for realistic free span scenarios gives better and satisfactory response, than
the methods described above.
1.10.5
Particularly for VIV of special pipeline designs with limited experience, such as pipe-in-pipe, bundled
pipelines, and piggy back pipelines, experiments should be considered. Experiments should also be
performed 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 as
ordinary pipes as long as changes in structural response, damping and fatigue properties are accurately or
conservatively 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 larger
hydrodynamic 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 sound
understanding of the physical response of the pipe, misinterpretation of sensor readings is a risk. Direct
measurements shall therefore be appropriately combined with one of the above mentioned VIV assessment
methodologies in order to ensure that the physical response of the pipe is well understood. More detailed
guidance 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 is
considered 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 of
the 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, the
requirements of this RP shall prevail.
1.12 Definitions
Table 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 of
natural 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 force
expression.
gap
the distance between the pipe and the seabed.
Note: The gap used in design, as a single representative value, must be characteristic for the
free 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 a
span.
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 significant
wave height, peak period and direction.
multi-mode response
denotes response for a span where several vibration modes may be excited simultaneously
in 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 change
significantly 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 in
section [4.3.3].
response model
is a model where the structural response due to VIV is determined by hydrodynamic
parameters.
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 same
over the design life.
weak cross-flow mode
denotes a participating mode that is not dominant, excited with at least 10% of the
dimensionless 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 stress
range than 10% of the dominant in-line mode at a particular location x, see [4.6.9].
1.13 Abbreviations
Table 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 Latin
characteristic 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 deflection
equal 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
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
CD
0
CM
CM
CL
ρinc to ρw ([A.10.3])
basic drag coefficient ([5.4.4])
inertia coefficient
0
basic inertia coefficient ([5.4.10])
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])
f
LKCR
cyc,CF
cycle counting frequency for the combined CF stress with LKCR response model ([4.5.10])
f
RM
cyc,CF
cycle counting frequency for the combined CF stress with standard response model ([4.4.13])
fcn
concrete construction strength
f
con
f
part
IL.j
IL.j
fIL/CF,j
f
SS
IL/CF,j
natural frequency of the j-th contributing in-line mode ([4.6.10])
natural frequency of the j-th participating in-line mode ([4.6.10])
natural frequency in in-line or cross-flow direction for the j-th single span mode
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])
M
IL/CF
E
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])
SS
n
IL/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-negligible
wave-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)C2π EI/Leff
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])
2
2
LKCR
CF,j
cross-flow VIV stress range for j-th mode, LKCR response model ([4.5.6])
RM
cross-flow VIV stress range for j-th mode, standard reponse model ([4.4.10])
S
S
CF,j
SCF-IL
in-line stress range for candidate mode for cross-flow induced in-line response ([4.6.17])
LKCR
comb,CF
combined stress range from LKCR response model ([4.5.9])
RM
combined stress range from standard cross-flow response model ([4.4.12])
S
S
comb,CF
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])
max
S
IL
SIL,j
P
S
IL,j
RM
S
IL,j
response stress range associated with the dominant in-line mode ([4.6.8])
response stress range associated with j-th contributing in-line mode ([4.6.18], [4.6.19])
preliminary stress range for j-th in-line mode i.e. stress range prior to mode competition ([4.6.6]),
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
FM,IL
T
Hs,Tp,θ
marginal fatigue life capacity against direct wave action ([5.2.2])
RM,CF
Hs,Tp,θ
marginal fatigue life capacity against cross-flow VIV ([4.2.1])
RM,IL
marginal fatigue life capacity against in-line VIV ([4.2.2])
T
T
Hs,Tp,θ
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 velocity
at pipe level ([2.3.2])
v
vertical soil settlement (pipe embedment)
VR
(Uc + Uw)/fwD
V
dec
R
VRd
reduced velocity, decreased due to enlarged diameter ([A.12.3])
reduced velocity (design value) with safety factor ([4.4.3])
V
CF
R,onset
Onset reduced velocity in cross-flow direction ([4.4.4])
V
IL
R,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 Greek
α
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 ratio
or 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])
ψmm
empirical 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 forms
Table 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 necessarily
required
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 to
fatigue (FLS) and local buckling (ULS) shall be performed.
All potential sources of fatigue damage shall be considered as part of the integrated fatigue damage
assessment.
This document only considers fatigue due to environmental loads (VIV and direct wave loads). All other
sources, such as trawl interaction, global buckling cycles, excessive lateral displacements, pressure and
temperature variation, installation etc., shall be accounted for according to the relevant governing design
code, 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 associated
stress concentration factor (SCF).
2.1.2
Vibrations due to vortex shedding and direct wave loads are acceptable provided the fatigue and ULS criteria
specified herein are fulfilled.
2.1.3
All active modes, defined in [1.12], shall be considered in FLS and ULS calculations. Unless otherwise
documented, the damage contribution for each mode should relate to the same critical (weld) location for
FLS calculations.
2.1.4
Figure 2-1 shows part of a flow chart for a typical pipeline design. After deciding on diameter, material, wall
thickness, potential trenching, and coating for weight and insulation, any global buckling design and release
of effective axial force need to be addressed before the free spans shall be assessed. It is emphasised that
the free span assessment shall be based on a realistic estimate of the effective axial force, and any changes
due to sagging in spans, lateral buckling, end expansion, changes in operational conditions, etc. shall be
properly accounted for.
Note that the sequence in Figure 2-1 is not always followed. Normally an initial routing will be performed
before detailed pipeline design is started. A typical design process follows this flow chart in iterations until a
final, acceptable design is found.
As span lengths/gaps and effective axial force distributions may change significantly for different operational
conditions, it is challenging to identify critical/governing span scenarios, especially for flowlines. This will
also depend on any global buckling or other release of effective axial force by end expansion or sagging into
spans, 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 of
the 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 (span
length, gap ratio, etc.) may change with time.
— Unevenness-induced free spans caused by an irregular seabed profile. Normally the free span scenario is
time 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 expected
span 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 span
length 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 possible
intervention 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 combined
with an inspection strategy may be used to qualify scour induced free spans. These aspects are not covered
in 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 span
characteristics 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 and
lateral 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 cases
the whole range of operational conditions should be checked because the lowest combination may be governing for the free span
design.
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2.2.5
Other changes during the design life such as corrosion shall also be considered in the span assessment where
relevant. Corrosion conditions shall always be accounted for in the estimation of fatigue resistance, e.g. when
choosing an S-N curve.
Guidance note:
For modal reponse calculations, subtracting half the corrosion allowance when performing the span assessment may be applied
in case of no better information. If the fatigue damage is in-line dominated, and corrosion occurs at 6 o’clock and 12 o’clock
respectively, the corrosion can be disregarded in the modal response calculations.
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2.3 VIV avoidance criteria
2.3.1
The avoidance criteria proposed herein can be applied to conservatively determine if VIV must be included
in FLS and ULS calculations for a given free span. If any of the criteria in this [2.3] are violated, either
the fatigue screening criteria in [2.4] may be applied, or full fatigue and extreme environmental loading
calculations 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 environmental
loading 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, shall
reflect the most probable extreme response over a specified exposure period. For permanent operational
conditions and temporary phases with duration in excess of 12 months, a 100-year return period applies, i.e.
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-2
the characteristic environmental condition is the condition with 10 annual exceedance probability. When
detailed information about the joint probability of waves and current is not available, this condition may be
approximated 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 return
period for the actual seasonal environmental condition applies. An approximation to this condition is to use
the most severe condition among the following two combinations:
— The seasonal 10-year return condition for waves combined with the seasonal 1-year return condition for
seasonal current.
— The seasonal 1-year return condition for waves combined with the seasonal 10-year return condition for
current.
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 and
end of the temporary condition to account for e.g. delays. For a temporary phase less than three days an
extreme 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 and
fCF,1. If the following inequalities for the fundamental frequencies are fulfilled, no VIV is expected to occur
during the design exposure period of the span:
where:
Δ
= Outer pipe diameter incl. coating (hydrodynamic diameter)
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= Safety factor on in-line frequency, see [2.7.2]
γf,IL
= Safety factor on cross-flow frequency, see [2.7.2]
γf,CF
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
IL
fCF,j for the j-th mode and by using V R,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 direct
wave loading in combined current and wave loading conditions. The screening criteria have been calibrated
against full fatigue analyses to provide a fatigue life in excess of 50 years. The criteria apply to spans with
st
a response dominated by the 1 symmetric mode (one half-wave) and should preferably be applied for
screening 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 such
these 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 value
for current for the appropriate season, Uc,10year, instead of the 100-year return period value,
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2.4.2
The screening criteria proposed herein are based on the assumption that the current velocity may be
represented by a 3-parameter Weibull distribution. If this is not the case, e.g. for bi-modal current
distributions, care must be taken and the applicability of these screening criteria shall be checked by full
fatigue 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 V R,onset is the cross-flow onset value for the
reduced velocity, see section [4.4.4]. If the above criterion is violated, a full in-line and cross-flow VIV fatigue
analysis is required.
CF
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 fatigue
analyses 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 Texposure
is 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
Ni
Ni
Σ
= Accumulated fatigue damage.
= Total number of stress cycles corresponding to the (inner or outer fibre) stress range Si
= Number of cycles to failure at stress range Si
= 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)
Ssw
= Stress at intersection of the two S-N curves given by:
= Characteristic fatigue strength constant defined as the mean-minus-two-standard-deviation
curve
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 (crack
initiation 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:
= Probability of occurrence for the “i”th stress cycle
Pi
fcyc,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. at
the inner and outer circumference of the pipe steel cross-section respectively. The fatigue stress associated
with VIV and direct wave loading response shall be calculated as the extreme outer fibre stresses, i.e. the
bending stresses at the inner and outer radius of the steel cross-section. Since both the S-N curves and the
stresses are different at each critical location, it is not always obvious which location is more conservative
than the other. Therefore fatigue calculations shall generally be performed at both the weld root and the weld
toe, 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 stress
ranges 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 calculated
in each cell of a scatter diagram in terms of Hs, Tp and θ times the probability of occurrence for the
individual 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 to
Uw and period Tu. The effect of irregularity will reduce the number of large amplitudes. Irregularity may
be accounted for provided it is properly documented.
— Integration over the long-term current velocity distribution for the combined wave and current flow is
performed 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 all
sea states, i.e.
where PHs,Tp,θ is the probability of occurrence of each individual sea state, i.e. the probability of occurrence
reflected by the cell in a scatter diagram. The in-line fatigue life capacity is conservatively taken as the
minimum capacity – corresponding to maximum damage – from VIV (RM) or direct wave loads (FM) in each
sea 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,
current, see [4.2.1].
θ) integrated over long term pdf for the
Marginal fatigue capacity against direct wave actions in a single sea state characterised by (Hs, Tp,
mean value of current, see [5.2.2].
θ) using
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 fatigue
damage) 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 controlled
condition in DNVGL-ST-F101 Sec.5, or similar stress-based criteria in a recognized standard. Environmental
load effects due to VIV and direct wave loading shall be included in the local buckling calculations by means
of an environmental bending moment according to [2.6.6], or relevant bending stresses if another criterion
is 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 with
functional 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 crossflow directions, which are orthogonal. In the local buckling check according to DNVGL-ST-F101, it is therefore
important 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 relevant
characteristic environmental condition. The relevant characteristic environmental condition depends on the
expected 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 extreme
environmental conditions, may be subjected to large lateral displacements on the span shoulders. For
such span conditions, the principles in DNVGL-RP-F109 may be applied to assess the likelihood of large
lateral displacements on span shoulders. Should such considerations imply that lateral displacements on the
shoulders are likely in design conditions, the lateral dynamic soil stiffness should be reduced appropriately to
account for lateral sliding on the span shoulders in ULS calculations.
Note that assuming pinned-pinned boundary conditions as an estimate of reduced shoulder stiffness may
be non-conservative since spans under such conditions are short and therefore have effective lengths which
may 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 current
action may be found from the dynamic stresses. For convenience, these are calculated based on the outer
fibre of the steel cross section, at a distance of Ds/2 from the center of the pipe
σIL/CFE
I
Ds
= Maximum environmental stress given below
= Moment of inertia
= Outer diameter of steel pipe
2.6.6
The maximum environmental stresses are calculated as:
where:
Scomb,IL
Scomb,CF
σFM,max
σCFE
σILE
= In-line stress range, see [4.6]
= Cross-flow stress range, see [4.3]
= Maximum environmental stress due to direct wave loading, see [2.6.10]
= Cross-flow environmental stress
= In-line environmental stress
For the cross-flow direction, the stress simply stems from the VIV induced amplitudes. For the in-line
direction, the dynamic stress range is taken as the sum of the maximum combined stress range from in-line
VIV (incl. potential contribution from cross-flow induced in-line VIV, see [4.6]) and stresses due to direct
wave loading.
2.6.7
Two different methods can be applied to establish the maximum environmental stress,
ST-F201:
σFM,max, see DNVGL-
— 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 in
frequency 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 be
done 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 be
given 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 an
associated period could be used to generate the regular design wave and the corresponding quasi-static response.
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2.6.9
The maximum environmental stress, σFM,max, from direct wave loading can be established using a time
domain design storm approach as follows:
1)
2)
3)
4)
5)
Global time domain response analysis is performed for the actual stationary environmental condition. A
typical storm duration may be taken as 3 hours.
Time histories for the dynamic stress are established.
A 3-parameter Weibull distribution is fitted to the individual stress maxima between successive mean
value crossings σFM(t).
A Gumbel distribution is established for the extreme value for the largest individual maxima of
the 3 hour duration.
σFM(t) for
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 37
th
percentile.
2.6.10
As a simplified alternative
σFM,max may be calculated using:
ΔT is the storm duration equal to 3 hours and fv is the characteristic vibration
σs is the standard deviation of the stress response σFM(t) and σs,I is the standard deviation for the
stress response without drag loading. σs and σs,I may be calculated from a time-domain or frequency-domain
where kp is a peak factor,
frequency.
analysis, 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 isolated
single span, ψmm = 1.07. If σs is obtained from a multi-mode analysis in either an isolated single span or an
interacting 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.
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2.6.11
It is required that the pipe can withstand the fatigue exposure within its characteristic environmental
condition for any relevant design phase, i.e. temporary, water filled, operational and shut-down. The
characteristic 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-STF101 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-flow
frequency, soil and structural damping, onset of in-line VIV and onset of cross-flow VIV and fatigue
utilization, respectively. The partial safety factors apply to both response- and force model calculations, as
detailed in Sec.4 and Sec.5. The values for some of the partial safety factors depend on the safety class and
quality of the analysis input, see Table 2-2 and Table 2-3.
Table 2-2 General safety factors for fatigue
Safety Class
Safety factor
η
Low
Medium
High
1.0
0.5
0.25
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Safety Class
Safety factor
γk
Low
Medium
High
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
Free span classifications
Medium
High
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
1.05
1.05
1.1
1.1
1.15
1.15
1.1
1.1
1.2
1.2
1.3
1.3
Well defined
Not well defined
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 force
are 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 force
are determined/measured. Site-specific soil conditions and a long-term description of the environmental
conditions exist.
Well to very well defined – The same requirements as for very well defined span, with the exception
that 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 the
static 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 axial
force are determined/measured with a high degree of accuracy. The soil conditions and the environmental
conditions 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 in
the 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 be
applied 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 class
concept 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 will
generally have other safety factor formats, or most often an allowable utilization without partial safety
factors. If DNVGL-RP-F105 is applied to calculate partial damage contributions, and these are added to
damage from other sources to adhere to a criterion in a different standard, the damage in DNVGL-RP-F105
shall be normalized in an appropriate manner. A procedure to normalize the damage contribution from this
RP 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 safety
class 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 include
contributions 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 design
phases, and free span morphology will generally be different in all phases after installation. It is required
in DNVGL-ST-F101 that a fatigue utilization distribution shall be developed to define the allowable fatigue
damage in each individual phase, ultimately ensuring that the total damage is less than 1/DFF for the entire
lifetime.
Free span design shall include damage contributions from each phase, accounting for differences in pipe
weight, effective axial force distribution, span geometry (lengths, gaps, shoulder lengths, etc.) and phase
duration.
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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 representative
for 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 spanning
pipelines.
3.1.4
The environmental data shall be collected from periods that are representative for the long-term variation
of the wave and current climate. In case of less reliable or limited wave and current data, the statistical
uncertainty 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 measurement
data 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 pipeline
at 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 span
assessment. Internal waves may have high fluid particle velocity which may be modelled as equivalent current distributions.
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3.2.2
For water depths greater than 100 m, the ocean currents can be characterised by the driving and steering
agents:
— The driving agents are tidal forces, pressure gradients due to surface elevation or density changes, wind
and 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 in
the horizontal direction.
— An inner zone where the mean current velocity and turbulence show significant variations in the horizontal
direction 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 a
flat 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 layer
at a level of 1 to 2 seabed form heights above the crest. For large-scale currents, such as wind driven and
tidal currents, the choice of measurement positions may be based on the variations in the bottom topography
assuming that the current is geo-strophic, i.e. mainly running parallel to the large-scale bottom contours.
o
Over smooth hills, flow separation occurs when the hill slope exceeds about 20 . Current data from
measurements in the boundary layer over irregular bed forms are of little practical value when extrapolating
current values to other locations.
3.2.6
In the inner zone the current velocity profile is approximately logarithmic in areas where flow separation does
not occur:
where:
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z
zr
z0
= elevation above the seabed
= reference measurement height (in the outer zone)
= 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 the
values at the nearest suitable measurement point. The flow (and macro-roughness) is normally 3D and
transformation of current characteristics should account for the local bottom topography e.g. be guided by
numerical simulations.
3.2.8
For conditions where the mean current is spread over a small sector, e.g. tide-dominated current, and the
flow condition can be assumed to be bi-directional, the following model may be applied in transforming the
mean 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 with
FLS checks.
3.2.10
For ULS checks, 1-minute average values should be applied. The 1-minute average values may be
established 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 that
the turbulence intensity for macro-roughness areas is from 20% to 40% higher than the intensity over a flat
seabed with the same small-scale seabed roughness. The turbulence intensities in a rough seabed area to be
applied for in-line fatigue assessment may conservatively be taken as typical turbulence intensities over a flat
bottom (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 be
distinguished.
3.2.14
The current speed in the vicinity of a platform may be reduced from the specified free stream velocity, due to
hydrodynamic shielding effects. In absence of a detailed evaluation, the guidance on shielding in DNVGL-RPC205 can be used.
3.2.15
Possible changes in the added mass (and inertia actions) for closely spaced pipelines and pipeline bundles
should 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 or
analytical 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 be
applied. 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 linear
wave theory as a function of the wave conditions and the water depth is given in DNVGL-RP-F109 and
DNVGL-RP-C205. The formulations in [3.3] of this RP only apply for environmental conditions where linear
wave theory is applicable or where linear wave theory has been demonstrated to be conservative. If linear
wave theory is inadequate, significant wave induced flow velocities and mean up-crossing periods shall be
calculated based on an applicable wave theory. If such an approach is not possible, conservative applications
of 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 power
spectral density function of the sea surface elevation. Wave spectra may be given in table form, as measured
spectra, 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
Tw
Tp
ωp
g
= 2π/Tw is the angular wave frequency.
= Wave period.
= Peak period.
= 2π/Tp is the angular spectral peak frequency
= 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 and
swell. 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 spectral
transformation of the waves at sea level using a first order wave theory:
G (ω) is the frequency transfer function from sea surface elevation to wave-induced flow velocities at pipe
level given by:
2
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Where h is the water depth and k is the wave number established by iteration from the transcendental
equation:
Guidance note:
Note that the G (ω) transfer function is valid for Airy wave theory only and is strictly speaking not applicable for shallow water.
2
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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 the
effect 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-linear
interaction between wave and current flow. The modified velocity profile and hereby-introduced reduction
factor 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 is
introduced 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 the
sea state. Normally s is taken as an integer, between 2 and 8, 2 ≤ s ≤ 8. If no information is available, the
most 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 NORSOK
N-003, can also be considered as an alternative to the above approach.
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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 the
current velocity Uc or significant wave height, Hs. The Weibull distribution is given by:
α is the scale parameter, β is the shape parameter and
γ is the location parameter. Note that the Rayleigh distribution is obtained for β = 2 and an exponential
distribution for β = 1.
where FX(x) is the cumulative distribution function,
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 period
values (RPV) are estimated from the corresponding exceedance probability in the histogram or from a
fitted 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 but
engineering judgement applies because defining return period values inappropriately can lead to an
unphysical Weibull pdf.
3.5.3
The wave climate at a given location may be characterised by a series of short-term sea states. Each shortterm sea state may be characterised by Hs, Tp, and the main wave direction θ, measured relative to a given
reference direction.
The directional or omnidirectional significant wave height may be specified as follows:
— A scatter diagram in terms of Hs, Tp,
θ
The fatigue analysis is based on the discrete sea states reflected in the individual cells in the scatter
diagram.
— 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 peak
period 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 and
100 year) with 3 unknowns (α β and γ). This is, in principle, always feasible but engineering judgement
applies 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, N
may 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 is
often taken as 24 hours, whereas the time between independent sea states (described by Hs) normally may
be 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) is
established 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
direction and the flow direction for direction i.
θrel,i is the relative direction between the pipeline
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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 amplitude
response as a function of the basic hydrodynamic and structural parameters. The response models provided
herein have been derived based on available experimental laboratory test data and a limited amount of fullscale 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 from
the first and the second in-line instability regions in current dominated conditions are implicit in the in-line
response model. Cross-flow induced in-line VIV is relevant for all reduced velocity ranges where cross-flow
VIV 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 capacities
according 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 the
environmental 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
Uc
Uw
D
= Natural still-water eigen frequency for the j-th mode
= Mean current velocity normal to the pipe, see [3.4]
= Significant wave-induced flow velocity, see [3.4]
= 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 purpose
of this recommended practice, if KC > 40, the flow shall be considered as current dominant irrespective of
the actual current component. In the response model calculations, this can be implemented by α = 1, when
KC > 40. Importantly, this assumption shall not be used in direct wave action calculations, where the correct
current 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
ζT
me
= Water density
= Total modal damping ratio
= Effective mass, see [6.6.6]
4.1.9
The total modal damping ratio,
— structural damping,
ζT, comprises:
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,
is defined by:
θ)
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
p(Uc)
= Fatigue exponent, depending on the relevant stress range, see [2.5.3].
= 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 calculation
given 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 given
in [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, as
defined 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 distributed
function of x:
— The unit diameter stress amplitudes are calculated per x position according to [6.6.2] for the distributed
damage 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 to
damage 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 are
needed as input to the VIV fatigue and extreme environmental loading calculations. There are several
methods available for calculation of the modal response quantities with varying degree of accuracy and
applicability. A detailed description of the various methods and their suitability for various applications are
given in Sec.6.
4.3.2
For a given sea state, characterized by (Hs,Tp,θ), marginal fatigue life capacities may be calculated according
to [4.2.1] and [4.2.2]. At each location x for a given sea state and current velocity Uc, several vibration
modes may be responding, giving rise to in-line and cross-flow multi-mode responses associated with
combined stress ranges Scomb,IL/CF and cycle-counting frequencies fcyc,IL/CF. Procedures for the calculation of
the in-line and cross-flow equivalent stress ranges, Scomb,IL/CF, and response frequencies, fcyc,IL/CF, are given
in [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 point
x0,j and an end point xe,j, i.e x0,j ≤ x ≤ xe,j, where the modal deflections and curvatures are zero or negligible
at 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:
= Unit diameter stress amplitude for the j-th in-line or cross-flow mode, defined in [6.6.2]
AIL/CF,j(x)
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 defined
as 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 from
lowest 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 the
following 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 (x) is the preliminary response stress range for the j-th in-line mode, see [4.6.6].
IL,j
max
IL(x)
— S
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 KC
regime (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 and
satisfies the following criterion:
4.3.7
The two sets of contributing modes for the standard cross-flow response model and the LKCR response
model are generally different, and shall be determined separately. In other words, while there is only one set
of 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 be
considered, 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 summarized
in 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 VRd
and 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 single
location analyses and all active modes shall be considered. For distributed fatigue damage calculations only
the 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] to
calculate 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-Carpenter
number, KC, the current flow velocity ratio, α, the stability parameter, KS, the seabed gap ratio, (e/D), the
Strouhal number, St and the pipe roughness, (k/D), among others. Note that Reynolds number, Re, is not
explicit in the model.
In wave dominated flow conditions, irrespective of KC regime, cross-flow VIV is strongly related to the
frequency ratio fCF,j/fw, see e.g. Sumer and Fredsøe (1988) and Kozakiewicz et al. (1994). For high
KC numbers, the standard response model calculations based on reduced velocity generally apply with
acceptable accuracy. For wave dominated flow and a low KC number, i.e. KC < 10, a separate response
model 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 typically
at a value of VR between 3.0 and 4.0, whereas the maximum vibration levels occur at larger VR values. For
pipes with low specific mass, wave dominated flow situations or span scenarios with a low gap ratio, crossflow 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 ~2
to ~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 be
taken 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 bending
stiffness dominated lower half-wave symmetric modes, e.g. for single span fundamental mode. For all other current dominated
cases the maximum response amplitude is limited to 0.9 D.
---e-n-d---o-f---g-u-i-d-a-n-c-e---n-o-t-e---
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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 flat
seabed or a pipe located in excess of D/4 above the trench, i.e. the pipe is not affected by the presence of
the 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 the
relation (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 following
criterion:
Modes which are neither weak nor dominant are disregarded in the fatigue and extreme environmental stress
calculations. 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 S
is:
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CF,i
for the dominant cross-flow mode
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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 S
flow modes are:
RM
CF,j
for the contributing, weak cross-
4.4.11
The characteristic amplitude response for cross-flow VIV may be reduced due to the effect of damping. The
reduction 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 is
calculated 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 added
mass coefficient Ca, CF-RES due to the amplitude of cross-flow response using the following equation:
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where:
sg
q
b
= (q+b)/b is the specific gravity of the pipe (often referred to as mass ratio in the context of VIV)
= Submerged weight of the pipe, including content if any
=
πρwgD2/4 is the pipe buoyancy
= Added mass coefficient, according to [6.6.7]
Ca
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 crossflow 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 added
mass built into them, i.e. they are plotted using the reduced velocity calculated with the still water natural
frequency 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 the
initial eigenvalue analysis. The added mass coefficient, Ca,CF-RES, may be taken from Figure 4-5 and is applied
to 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 other
mass ratios if better information is not available.
---e-n-d---o-f---g-u-i-d-a-n-c-e---n-o-t-e--Guidance note:
The added mass coefficient formulation for VR < 2.5 is not important, since the cross-flow response amplitude are very small (A/D
is O (0.1)) in this range.
---e-n-d---o-f---g-u-i-d-a-n-c-e---n-o-t-e---
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 pressure
oscillations 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 the
eigen frequency of the cylinder. In wave-dominated conditions, particularly in irregular waves, the lift loading
frequency 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 stated
in [5.4.1]. In cross-flow direction, correlation between the wave load frequency and one or more of the
pipe natural frequencies is treated by the response model in [4.5.5], when 2 ≤ KC ≤ 10 and α ≤ 0.5. If
either KC or α are higher, experimental results indicate that the response model stated in section [4.4] is
conservatively 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 have
been recorded in laboratory conditions (Chioukh and Narayanan, 1997; Sha et al., 2007) even though
traditional response models predict no onset of cross-flow VIV. As a result, special considerations shall be
made 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) and
references therein), but only corroborated by three experimental data series in irregular waves (Kozakiewiecz
et al., 1994; Sha et al., 2007). As a result, the model presented herein is limited in accuracy, but still
assumed conservative since irregular wave response amplitudes tend to be smaller and less consistent than
those achieved in comparative regular wave conditions (Sumer and Fredsøe, 1997). In lieu of more detailed
model approaches, the response model presented in [4.5.5] may be applied to estimate cross-flow response
amplitudes 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 in
Figure 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 contributing
mode.
For all contributing modes, (Az/D)j may be taken from the response model in [4.5.5]. The associated crossflow 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 higher
KC regimes. To account for low amplitude response in the lower regions of the KC range, the following
reduction factor applies:
4.5.9
In LKCR, the amplitude of motion is less affected by the mass damping ratio than standard cross-flow VIV
cases. 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 alternating
or symmetric vortex shedding. Contributions from both the first in-line instability region and the second
instability 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, the
turbulence intensity, Ic, and the flow angle, θrel relative to the pipe. Mitigation effects from the seabed
proximity, (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 VRd
and 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 angle
of 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, S
P
IL,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 location
analyses.
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 S
max
IL
is defined as:
P
IL,k
The k-th mode is the dominant in-line mode, when k is an integer value satisfying the relation S
=S
max
IL.
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 stress
calculations. 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
part
IL,j
participating in-line still-water eigen frequencies f
set
con
f IL,j,
shall be sorted from the lowest to the highest into the
where only the m contributing modes shall be included. The m corresponding preliminary in-line
VIV induced stress ranges S
P
IL,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 lower
than 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, where
j denotes the renumbered mode number. The application of the mode reduction factor is described as an
algorithm as follows.
1)
2)
3)
set
βj(x) = 0 for all
for each pair of numbers {j, j+1}, when
, check the following criterion:
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,
Consistent with this algorithm,
for all j.
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 be
calculated as follows:
4.6.14
It is assumed that only the dominant cross-flow mode can potentially contribute to the cross-flow induced inline motion.
4.6.15
The participating in-line mode with its eigen frequency closest to twice the dominant cross-flow response
frequency shall be chosen as the candidate for cross-flow induced in-line VIV. For the dominant cross-flow
mode 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 dominant
cross-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 VIV
response stress shall be set to:
and the contributing in-line response frequency for the mode undergoing cross-flow induced in-line VIV shall
be 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 of
contributing stresses and frequencies are expanded by one (to m+1). The in-line VIV response stress shall be
set 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 contributing
modes. 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 loads
if 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 is
at 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 may
account for all significant non-linearities but is in general very time consuming if a large number of sea states
shall be analysed. For fatigue analyses, a frequency domain solution (if thoroughly verified) is more tractable
since it facilitates analyses of a very large number of sea states at a small fraction of the time required for a
time domain solution.
A linearised FD solution for the Morrison’s equation is given in [5.2]. The method presented in [5.2] applies
to both single- and multi-spans and has been proven to be accurate compared to detailed time domain
analyses, see Sollund (2015). The method is capable of solving the fatigue and extreme environmental
loading problems for a single critical location, or as a distributed function of the position x along the pipe
axis.
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 in
DNVGL-ST-F201. In some cases, a quasi-static approach to wave loading approximations is sufficient. A short
description of how to perform fatigue and extreme environmental loading calculations with a quasi-static
approach 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 span
and respective shoulders. For single isolated free spans, both methods are acceptable, i.e. single or multiple
locations may be considered. For multi-spans, with multiple responding modes, a single critical location
is not readily identifiable, and therefore it is required that all locations along the multi-span section are
conservatively accounted for in the analyses.
5.1.5
Force model calculations in interacting multi-spans shall consider response interaction between individual
spans. The selection of modes which contribute to fatigue and extreme environmental loading calculations
is not trivial to determine, and depends on a number of different parameters such as soil stiffness, pipe
dimensions, water depth, environmental conditions, effective axial force and multi-span topography. An
assessment 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 a
single 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 axial
and 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 force
model 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 current
and 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 time
domain 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,
length, i.e. the span length is less than the dominant wavelength.
σU, are invariant over the free span
5.2.2
The short term fatigue capacity against direct wave actions in a single sea state characterised by (Hs, Tp,
is given in the following form:
θ)
where:
σS
Fv
= Standard deviation of stress amplitude
m1, m2
Ssw
= Fatigue exponent, see section [2.5.3]
= Vibration frequency
= Fatigue constants, see section [2.5.3]
= 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 function
γs
Ψmm
= Safety factor on stress range, see section [2.7]
= Empirical multi-mode correction factor. For single mode analyses in isolated
single spans, ψmm = 1.055. In multi-mode analyses, for either isolated single
spans or interacting multi-spans,
ψmm = 1.0
5.2.3
The standard deviation of the wave-induced stress amplitude
moment of the 0-th order defined by [5.2.6].
σS is given by the square root of the spectral
5.2.4
The characteristic vibration frequency of considered pipe stress response, fv, is taken equal to the mean upcrossing 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. correcting
the implicit narrow-banded Rayleigh assumption for the stress amplitudes to provide results similar to those
arising from a state-of-the-art rainflow-counting technique. The Rainflow-counting factor κRFC is given by:
The bandwidth parameter
ε is defined as:
ε → 0 and broad banded for ε → 1. In practice the process may be
ε larger than 0.6.
The stress process is narrow-banded for
considered broad-banded for
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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-sided
stress response spectral density function SSS(x,ω) is given by
where:
and
RD
b
gD
gI
G(ω)
Sηη
ωj
= Factor accounting for wave spreading and direction, see [3.4.3]
me
N
= Effective mass per unit length incl. added mass, see [6.6.6]
= Linearisation constant, see [5.2.12]
= Drag force term, see [5.4.1]
= Inertia force term, see [5.4.1]
= Frequency transfer function, see [3.3]
= Single-sided wave elevation spectrum, see [3.3]
= 2πfIL,j/γf is the still water angular natural frequency for the j-th mode
= 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
where
ζT,j may be taken as:
ζT,1 and ω1 are the total damping ratio and angular natural frequency, respectively, for the lowest natural mode.
---e-n-d---o-f---g-u-i-d-a-n-c-e---n-o-t-e---
5.2.9
ψj(x) is the modal stress for the j-th mode given by:
Κj
φj
E
CSF
r
Ds
ts
= Mode shape curvature, normally calculated as d2φj/dx2
= Mode shape for the j-th mode
= Young’s modulus
= Concrete stiffness factor, see [6.3.7]
= 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
= Outer steel pipe diameter
= 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 assumed
location 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 be
assumed that the main damage contribution comes from the lowest natural mode if the mode has a
symmetric mode shape. This is often appropriate for isolated single spans, i.e. when the span’s dynamic
behaviour 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 density
function 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 (unit
diameter) stress amplitude A
taken as:
max
IL,1
where A
max
IL,1.
In lieu of more detailed data, the maximum modal stress
ψ1 may be
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 natural
mode may have anti-symmetric properties and not be excited to a significant extent by the presumed symmetric loading, see
Sollund (2015).
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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. The
correction 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 the
natural vibration period of the span) a simplified fatigue assessment may be more tractable than a complete
time-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 characterised
by (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’s
equation. 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 the
velocity of the structure is not negligible compared with the water particle velocity Morison’s equation reads:
Where:
ρw
D
U
y
gD
= Water density
= Outer pipe diameter
= Instantaneous (time dependent) flow velocity
= Pipe lateral displacement
= 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 is
assumed, 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 the
absolute roughness, k.
Table 5-1 Surface roughness
Pipe surface
k [m]
Steel, painted
10
Steel, un-coated (not rusted)
10
Concrete
1/300
-6
-5
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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, and
the outer diameter, D, of the pipe.
5.4.5
is a correction factor accounting for the unsteadiness of the flow, including effects of the KeuleganCarpenter 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
completeness for KC < 5.
may be interpolated for
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 model
response, 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, pressure
test, operating and shut-down conditions. For dynamic loading considerations, the pressure test condition is
normally disregarded.
The distributions of static bending moments Mstatic(x) and effective axial forces Seff(x) are required for the
ULS local buckling check.
Accurate estimations of the static curvature, the effective axial force, span lengths and gaps are required for
the subsequent in-line and cross-flow eigenvalue analyses. The eigenvalue analyses should in turn provide
accurate 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 stress
calculations 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 dynamic
behavior 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 analyses
change accordingly.
Span lengths, gaps and effective axial force distribution depend on functional loads such as pressure and
temperature (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 also
change 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 included
in the total fatigue assessment, see [2.5.2]. Calculation of fatigue damage and maximum environmental load
effects 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 amplitudes
AIL/CF,j(x), is strongly dependent on the preceding static analyses. The modal response quantities are
explicitly dependent on the span length L, effective axial force Seff(x) and static curvature κ(x). The natural
frequencies are also implicitly dependent on the gap e since the added mass and hence also the effective
pipe mass me (see [6.6.6]) are functions of the gap.
Because the static analysis directly influences the eigenvalue analyses, every simplification or inaccuracy
in the static analysis will also implicitly affect the free span fatigue and maximum environmental stress
calculations. 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 accompanied
by axial displacements. The frequency and mode shape associated with the first symmetric mode (half
sine wave for an isolated single span) are then strongly affected by the degree of axial restraint on the
span 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 significantly
with 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, seabed
topography and any (lateral or vertical) static deformations. The global pipeline static behaviour therefore
influences the distribution of effective axial forces. This effect is particularly important for pipes which are
designed 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. Analyzing
interacting multi-spans as isolated single spans does not simply increase the uncertainty in the outcome of
the analysis, but introduces a non-conservative bias in the estimation of important response quantities such
as the natural frequencies fIL/CF,j (Sollund et al., 2014).
An algorithm to quantitatively distinguish between isolated single spans and interacting multi-spans is given
in [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 to
pipeline 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-RPF114presents pipe-soil interaction.
6.3.3
For local and global, static and dynamic analyses of pipelines in free spans, it is considered sufficiently
accurate 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 dynamic
analyses, unless otherwise stated.
6.3.4
A realistic characterisation of the cross-sectional behaviour of a pipeline can be based on the following
assumptions:
— Long-term fatigue damage calculations may be based on actual/anticipated variation in pipe wall thickness
over the design life of the free span (if detailed information is not available the calculation shall be
performed using non-corroded cross section values for effective axial force and corroded cross section
values for stresses).
— The application of this document is limited to elastic response, hence plasticity models and effects of twodimensional 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 or
buoyancy. The positive effect on the stiffness and strength, see [6.3.7], is normally disregarded. If the
contribution of the coating to the structural response is considered significant, appropriate models shall be
used.
6.3.6
Non-homogeneity of the bending stiffness along the pipe, due to nominal discontinuities of the coating across
field 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 the
stress concentration factor due to the concrete coating and localised bending. The empirical constant kc
accounts for the deformation/slippage in the corrosion coating and the cracking of the concrete coating. The
value 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 also
be 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 the
concrete 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 loaded
cross-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 for
uncracked coating. Young’s modulus for concrete may be taken as:
2
where fcn is the construction strength of the concrete. Both Econc and fcn shall be in N/mm .
6.3.10
Structural damping is due to internal friction forces of the pipe material and depends on the strain level and
associated deflections. If no information is available, a structural modal damping ratio of
ζstr = 0.005
can be assumed. If concrete coating is present, the sliding at the interface between concrete and corrosion
coating 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 the
pipe-soil interaction and the continuity of the pipeline. Sufficient lengths of the pipeline at both sides of the
span 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. An
appropriate choice of boundary condition will in general depend on the purpose and required accuracy of the
free span analyses and the uncertainty of relevant input parameters such as functional and environmental
loads, 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 or
likely to be changed at a later stage. Detailed non-linear FE models on a rough seabed may then, if at all possible, not reduce
the overall model uncertainty compared to a simplified analysis methodology. Due to increased transparency and computational
efficiency, simplified modeling approaches may then be preferred.
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6.4.3
Common representations of the boundary conditions include, see Figure 6-1:
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a)
b)
c)
d)
realistic seabed model, with seabed topography and all relevant side spans included in the model
flat seabed model with interacting multi-spans, where the seabed topography is disregarded, but all
relevant side spans are included
flat seabed local model of isolated single-span
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 flat
shoulders and intermediate shoulder, c) Single span with flat shoulders, d) Idealized rigid body
constraints
6.4.4
Seabed unevenness will have a significant influence on static curvatures, bending moments and effective
axial forces, and must be included in the analyses if effects of axial sliding (“feed-in”), relaxation of effective
axial 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 seabed
model is therefore recommended, and it is required for pipe-soil interaction modelling in compliance with
DNVGL-RP-F114.
A realistic seabed model is also the only boundary condition representation that can be used if the static
analysis 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 safety
factors 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 span
shoulders are relatively flat, a flat seabed model may be appropriate. Flat seabed models may also be
convenient 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, the
span shoulders at the boundaries should be modelled long enough that the outcome of the static analysis and
eigenvalue analyses is not sensitive to increasing their lengths further.
Note that the natural frequencies and unit diameter stress amplitudes are explicitly dependent on the static
curvature of the pipeline. Disregarding the seabed unevenness may therefore be a significant source of
inaccuracy in the eigenvalue analyses for the cross-flow direction even if soil stiffness, span lengths, gaps
and 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 physical
aspects, but will generally give quite crude estimates of the pipe response. The use of such boundary
conditions 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 a
priori known.
Guidance note:
Pinned-pinned boundary conditions have often been considered to be a conservative representation, since the actual span
shoulders would provide at least some rotational stiffness. This assumption is, however, not correct in general. Because of modal
deflections on the span shoulders and potential interacting multi-span effects, pinned-pinned boundary conditions may give nonconservative modal response estimates for a number of scenarios, including spans with soft soils, interacting side spans and in
particular for very short spans.
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6.5 Static analysis
6.5.1
The static configuration shall be determined for the following conditions if relevant:
1)
2)
3)
4)
5)
as-laid condition
flooded condition
pressure-test condition
operating condition
shut-down condition.
Guidance note:
Effects of alternating operation and shut-down cycles should be assessed if relevant.
---e-n-d---o-f---g-u-i-d-a-n-c-e---n-o-t-e--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 pressure
test 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 stiffness
is governed by the effective axial force, Seff. This force is equal to the true steel wall axial force, Ntr, with
corrections for the effect of external and internal pressures:
Ntr
Pi
Pe
Ai
Ae
= True steel wall axial force
= Internal pressure
= External pressure
= Internal cross-sectional area of the pipe
= External cross-sectional area of the steel pipe
The effective axial force in a span is difficult to estimate because of uncertainties in operational temperature
and pressure, residual lay tension and axial force relaxation by sagging, axial sliding (feed-in), lateral
buckling, multi-spanning and significant seabed unevenness. All these effects should be considered and taken
into account if relevant. The most reliable method to estimate the effective axial force is use of non-linear FE
analysis.
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
Δpi
As
ΔT
αe
= Effective lay tension
= Internal pressure difference relative to laying, see DNVGL-ST-F101
= Pipe steel cross-sectional area
= Temperature difference relative to laying
= Temperature expansion coefficient, may be temperature dependent
Using the expression for a totally restrained pipe above may lead to over-conservative fatigue results for
pipelines 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 load
is much smaller than the vertical functional loads, then it may be disregarded in the analysis. However, for
light 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 static
deflection and stresses which are mainly determined by the submerged weight and effective axial force in the
phase considered.
Furthermore, the span geometry such as inclination of the span shoulders will have a significant influence
on 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 penetration
may 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 the
static analysis is based on a non-linear FE analysis with realistic seabed boundary conditions ([6.4.4]) and
with analysis steps reflecting the appropriate loading sequence.
Simplified static analysis approaches accounting predominantly for static deflection due to gravity and
effective axial forces, can be applied in conjunction with flat seabed boundary conditions ([6.4.5]) when
the intention of the static analysis is to provide input to eigenvalue analyses for screening, sensitivity
and verification purposes. In a simplified static analysis, relevant span lengths and gaps and a constant
equilibrium level of effective axial force are typically taken as input to the analysis, and linear vertical soil
stiffness (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
unit 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 consistent
linearisation of the free span problem must therefore be made. The eigenvalue analysis should account for
the static equilibrium configuration, i.e. the analysis should be based on the tangent stiffness of the statically
deformed 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 jth modes are termed AIL,j and ACF,j in in-line and cross-flow directions respectively, and may be calculated
according to the following equation:
where D is the outer pipe diameter (including any coating), κj(x) is the curvature of the mode shape φj for
the j-th in-line or cross-flow mode and r is the radial coordinate. AIL,j and ACF,j shall be calculated at the
weld toe and the weld root, i.e. for r = Ds/2 and r = (Ds-2ts)/2 respectively, where Ds is the outer pipe steel
diameter. 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 amplitude
for the j-th mode is calculated as:
The maximum unit diameter stress amplitudes are applied for calculations when all damage is conservatively
assumed 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 static
curvature κ(x), effective axial force Seff(x) and span lengths L provided by the static analysis, the eigenvalue
analyses 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 be
accounted 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 unit
length 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 in
section [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) direction
may be determined according to the guidance in DNVGL-RP-F114. The pipe-soil linearisation should be
validated.
6.6.9
The linearised axial dynamic stiffness has an important influence on the natural frequency of the first
symmetric mode (Vitali et al., 1993, Søreide et al., 2001), and shall be appropriately accounted for when
there is a non-negligible static curvature or span interaction. In lieu of detailed information, the axial
dynamic 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 the
transverse component. It is therefore important that the boundary conditions are modelled sufficiently long
to 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 analysis
because of potential sliding at the span supports. In particular, the span supports may change because of
direct 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 the
pipe axis, and are thus recommended when the preceding static analysis is based on non-linear FE modelling
with realistic seabed boundary conditions, see [6.4.4]. FE analyses may also be used for other choices of
static analysis approaches and boundary conditions.
Analytical or semi-analytical approaches are typically based on simplified assumptions, which result in
approximate results and limited validity ranges. Such limitations vary depending on the method, and it is
important to not use analytical approaches outside their indicated validity range. The methods are normally
restricted to a relatively flat seabed, and most methods do not account for potential interaction between
neighbouring spans.
An important advantage of analytical and semi-analytical methods is their computational efficiency and
transparency, making them suited to be used in conjunction with simplified static analysis approaches for
screening, sensitivity and verification analyses. A particular analytical approach is described in [6.8], see also
Fyrileiv and Mørk (2002).
6.6.12
For analysis of a pipeline stretch with several spans and especially with interacting spans, special care must
be paid to the determination of the eigenvalues and associated eigenvectors. This is due to the potential
occurrence of very close eigenvalues, especially with respect to the identification of correct eigenvectors. See
also 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 the
guidance given in [6.4]-[6.6]. Some general remarks pertaining to the analysis of free spanning pipelines are
given below, but for detailed guidance on the use of FEM one of the many textbooks on the subject should be
consulted.
6.7.2
The element length to be used in a finite element model is dictated by the accuracy required. If the stress
ranges shall be derived from the mode shapes, see [6.6.2], the accuracy of the stress ranges becomes
strongly 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 (natural
frequencies 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 two
nodes 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 from
the finite element analysis with the approximate response quantities of [6.8] for a single span with zero
effective axial force and L/Ds = 60. The in-line and cross-flow natural frequencies and stress ranges shall
show 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 that
individual 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 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, provided that (Fyrileiv and
Mørk, 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, crossflow response only). Here the following limits apply:
L/Ds < 140
δ/D < 2.5
Note that these are not absolute limits. The shift in cross-flow response from the symmetrical to the
unsymmetrical mode will depend on the sagging and the levelling/inclination of the span shoulders. In
cases where a shift in the cross-flow response is considered as likely, the structural response of the span
should be assessed by using an FE analysis that accurately accounts for these aspects.
— Bar buckling does not influence the response, i.e. that
Seff/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 <
smaller values of
β, the method described in [6.9] is recommended instead.
β < 8. For
A different approach is described Sollund et al. (2015a), where the accuracy and range of validity for
the 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 improved
substantially. 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 in
the referenced publication.
6.8.2
The fundamental natural frequency (first eigen frequency) may be approximated by:
where:
C1, C3
E
I
CSF
Leff
me
D
Pcr
= Boundary condition coefficients
δ
Seff
= Static deflection, normally ignored for in-line direction).
= Youngs modulus for steel
= Moment of inertia for steel
= Concrete stiffness enhancement factor
= Effective span length, see [6.8.8]
= Effective mass, see [6.6.6]
= Outer diameter of pipe
= Critical buckling load = (1+CSF)C2π2EI/Leff2 (positive sign)
= 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 soil
stiffness, which causes the expression to become increasingly inaccurate when the static deflection approaches the limit specified
in [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, and
the accuracy may therefore also be reduced by seabed unevenness in the vicinity of the span.
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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 boundary
condition 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 effective
axial force Seff. For high compressive values of Seff it is recommended to include the impact of Seff on modal
stresses. 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) direction
and/or the drag loading in the horizontal (in-line) direction, see [5.4.1].
Note that:
a)
b)
c)
Leff shall be calculated using the static soil stiffness in the Leff/L calculation.
Because of historical effects and the local seabed geometry, there is a large uncertainty associated with
this simplified expression, see [6.5.6].
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 analytical
tools, it may be estimated as:
where C6 is a boundary condition coefficient.
Note that:
a)
b)
Leff shall be calculated using the static soil stiffness in the Leff/L calculation.
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, these
coefficients 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
1)
C3
0.8
C4
4.93
0.2
1)
0.4
14.1
1)
Shoulder: 14.1(L/Leff)
Mid-span: 8.6
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Pinned-Pinned
C5
2)
1/8
Fixed-Fixed
3)
Single span on seabed
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 as
fully 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 parameters
may 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 appropriate
for fatigue assessment (FLS) under the assumption of small displacements and an isolated, single span on a
relatively flat seabed.
In the ULS check of maximum bending moments due to direct wave loading, the potential reduction in
stiffness 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 or
alternatively 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 for
screening purposes can be estimated based on Table 6-2.
Table 6-2 Approximate conservative higher order mode response quantities
nd
Response
Frequency
2
1) 2)
Unit Stress amplitude
rd
mode
3
mode
th
4
mode
2.7 f1
5.4 f1
8.1 f1
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
nd
rd
This approach is intended to be conservative, because the unit stress amplitudes given for the 2 , 3 and
th
4 modes correspond to the maximum values of the unit stress amplitudes, which do not occur at the same
location of the span.
6.8.12
The approximate conservative response quantities for long spans in multimode are intended for screening
purposes 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 normally
encountered (see Table 1-1), but VIV excitation may occur in rare cases, e.g. in spans experiencing floods or
erosion processes in rivers, straits and inlets with strong bottom currents that are generally perpendicular to
the pipeline.
6.9.2
Very short spans are often associated with high modal stresses, and fatigue failure will normally occur rapidly
once 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 the
relevant direction (in-line/lateral or cross-flow/vertical). Accurate estimation of the linearised dynamic soil
stiffness 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 erosion
or other scouring processes, which can be difficult to predict. Span length, soil stiffness, effective pipe mass
and effective axial force may hence be associated with significant uncertainty, and comprehensive sensitivity
mapping shall be performed.
6.9.5
The analytical approach for short free spans described in this section is based on the assumption of an
isolated 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 provided
that (Sollund et al., 2015b):
— Conservative assumptions are applied with respect to span length, soil stiffness, effective pipe mass and
effective 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 a
significant 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
-0.8∙10β
/2
≤
πSeff ≤ 0.8∙10β/2.
πSeff, defined in [6.9.6], is limited to the range
6.9.6
For short isolated single spans satisfying the requirements specified in section [6.9.5], the fundamental
natural 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, see
section [6.9.7]
gf(β,πSeff)
β
= Fitted expression for the non-dimensional frequency response surface, see [6.9.8]
πSeff
= Seff∙L /EI is the non-dimensional effective axial-force parameter
= Non-dimensional soil stiffness parameter
2
β, defined in [6.8.8]
6.9.7
The frequency of an infinitely long beam on a continuous linear elastic foundation is given by
where:
K
me
= Relevant dynamic soil stiffness (lateral or vertical)
= 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).
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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 a
fitted 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
β.
where the coefficients a, b and c are functions of
For -3 ≤
For 0 ≤
β <0, the coefficients may be expressed as
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, see
Hobbs (1986) and Sollund et al. (2015b). Without consideration of damping and non-linear pipe-soil
interaction 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 isolated
single spans is shown in Figure 1-3. Characteristic modal behaviour for the two scenarios is illustrated in the
same figures.
6.10.2
The aim of this sub-section is to give a precise mathematical formulation which classifies a sequence of spans
as 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 is
considered sufficiently accurate to model shoulders and intermediate shoulders as flat. Note, however, that
severe 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] is
based 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 diameter
stress amplitudes respectively.
2)
For each span:
Identify all participating modes (see [4.3.3]) from the multi-span analysis. There will be nIL participating
in-line modes and nCF participating cross-flow modes.
3)
Calculate modal frequencies fIL/CF,j
SS
SS
and associated maximum unit diameter stress amplitudes AIL/CF,j
SS
for each span as an isolated single span. There will be nIL
modes for the single span.
4)
5)
SS
If nIL ≠ nIL
cross-flow participating
SS
or nCF ≠ nCF
SS
nIL
SS
in-line and nCF
, the span is part of an interacting multi-span.
SS
nCF ,
If nIL =
and nCF =
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 an
interacting 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 is
part of an interacting multi-span:
where
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SECTION 7 APPLICATION OF SENSORS TO MONITOR FREE SPAN
VIBRATIONS
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, uncertainties
in environmental conditions, span dynamic response, response models, force models and stress estimation
give rise to conservatism in free span design. With span instrumentation, the reliability of span behaviour
approximations is greatly increased and thereby conservatism may be reduced. The safety factor format may
therefore be reassessed to account for the new set of uncertainties compared to the empirically predicted
response method.
7.1.2
It is particularly relevant to measure dynamic response directly for mobile spans, where actual span
characteristics during significant environmental events are highly difficult to predict. Operations management
of 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 state
considerations shall not be resolved using sensor technology. Sufficient resistance against the characteristic
design 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 readings
may replace traditional fatigue estimates based on empirical response or force coefficient models. In that
case, the safety factor format in this RP is no longer directly applicable. Instead, the designer shall account
for uncertainties in the sensor measurements and their interpretation such that the overall probability of
failure 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 ranges
for all relevant modes. Keeping the rate about 10 times higher than the relevant upper frequency range is
usually acceptable.
7.2.2
The fundamental in-line mode may be excited at small amplitudes. The associated response occurs at small
displacements, curvatures and accelerations. The sensors must be capable of measuring this response with a
high 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 at
critical 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 in
span 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 fatigue
estimations 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 the
time intervals of available measurements, it shall be documented that the overall probability of failure in the
governing 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 recommended
that sufficient redundancy to sensors and power supplies is ensured, such that failure or malfunction of either
one 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 or
flawed output from a malfunctioning sensor is detected. As a consequence, more than one sensor must
always 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 and
pipe response measurements in order to sensibly interpret the recorded data.
7.2.7
Sensor measurement uncertainty shall be quantified using controlled laboratory tests. Sensor characteristics
and accuracy, including latency, robustness and sensitivity on response, shall be documented when sensor
technology 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 in
conjunction with an accurate modal analysis of the free span, ensuring that stress contributions from all
contributing modes are accounted for and that all critical locations are identified. For a modal analysis to
be considered sufficiently accurate, a high degree of correspondence between the measured and calculated
frequencies must be achieved. Calculated mode shapes may be applied to estimate stress response only
for results of accurate modal analyses. Furthermore, any analysis method based on simplified boundary
conditions cannot be applied. Unless sensors capable of direct stress or strain measurements are applied at
each 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 response
models in Sec.4). The output from the sensors should thus be understood in conjunction with typical
expected 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. It
would 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 relationships
should be possible to interpret from the sensor readings. Considerable deviation between measured response and response
predicted by empirical models should prompt detailed investigation to identify the causes of such deviations in order to avoid
misinterpretations due to faulty equipment, poorly placed sensors, recording/reading errors or sensor interpretation errors.
---e-n-d---o-f---g-u-i-d-a-n-c-e---n-o-t-e---
7.3.3
Response due to direct wave action will normally not occur at any of the span natural frequencies, but
rather be strongly related to wave frequencies. As a result, spectral decomposition of response due to direct
wave action may be challenging to perform. Signal filtering will generally cause reductions in calculated
amplitudes, 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 in
fatigue 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 order
to utilize calculated mode shapes to estimate stresses. Furthermore, the frequency of response must be
well understood in order to determine the relevant number of stress cycles. There are several important
challenges related to the transformation of recorded accelerations to fatigue stresses. Direct wave action is
discussed in [7.3.3]. The effective added mass and the natural frequency of the pipe change with the flow
velocity. Hence, when using spectral decomposition, it may be difficult to distinguish between noise and the
actual 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 a
measurable 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 References
Andersen, 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 oscillating
water 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 Multith
Spanning Pipelines – Ormen Lange Experience.15 Deep Offshore Technology (International Conference
and 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 natural
frequencies. 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 Free
Spanning Pipelines. 24th International Conference on Offshore Mechanics and Arctic Engineering, OMAE
2005, Halkidiki, Greece, June 12-17.
Fyrileiv, O., Chezhian, M., Mørk, K.J., Arnesen, K., Nielsen, F.G., & Søreide, T., 2004. New Free Span
th
Design Procedure for Deepwater Pipelines. 16 Deep Offshore Technology (International Conference and
Exhibition), New Orleans, USA.
Fyrileiv, O. & Collberg, L., 2005. Influence of pressure in pipeline design – effective axial force. 24th
International Conference on Offshore Mechanics and Arctic Engineering, OMAE 2005, Halkidiki, Greece, June
12-17.
Fyrileiv, O. & Mørk, K., 2002. Structural Response of Pipeline Free Spans based on Beam Theory. 21st
International Conference on Offshore Mechanics and Arctic Engineering, OMAE 2002, Oslo, Norway, June
23-28.
Fyrileiv, O., Mørk, K.J. & Rongved, K., 2000. TOGI Pipeline – Assessment of Non-stationary Free Spans, 19th
International 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 Spanning
Pipeline Located in the Vicinity of a Trench. 20th International Conference on Offshore Mechanics and Arctic
Engineering, 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. Specialty
Conference 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 International
Offshore 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. International
Journal 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 in
planar oscillating flow. International Journal of Offshore and Polar Engineering, 13(4), pp. 266-273.
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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 avoidance
criteria for VIV. When avoidance criteria have been difficult to satisfy for a proposed design, environmental
covers, re-routing or re-design have historically been applied to achieve VIV avoidance. Recently, it has
become 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. Because
of lack of specific design guidelines for VIV design of non-straight pipes, this recommended practice has
become 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 fatigue
and extreme environmental loading design. This appendix gives guidance on how to apply this document to
such systems.
A.2 Applicability and limitations
A.2.1
The following aspects of fatigue and extreme environmental loading due to VIV and direct wave loading
calculations 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 empirical
background, 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 extreme
environmental loading calculations for systems with non-straight geometries. In-lieu of more detail, the
response 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 this
appendix 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 interface
to (see [A.9]), shall be performed according to its governing design code, and is not directly covered in this
document. Note, however, that the extreme environmental loading due to VIV and direct wave loading shall
be 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 loading
in 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 4.1
applies, with the following exceptions:
— Modes are no longer classified as strictly in-line or cross-flow. They may instead be in-line, cross-flow or
both (see [A.5]), and the modes may change their classification depending on the direction of incoming
flow and the position on the non-straight pipe system. Specifically, classification of modes shall be made
for 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 inline 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 modes
apply their full stress range as if they were all dominant modes. As such, all participating modes are
considered contributing modes.
— Main damage contributions from in-line and cross-flow modes are no longer in each other’s respective
neutral planes and may therefore affect the same hot spots. Damage from in-line and cross-flow VIV is
added at each location, rather than calculated separately.
— Damage shall either conservatively be calculated at one critical location, or at a minimum of 16 different
locations 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 the
locations of the girth welds are not known, any location along the pipe axis shall be treated as if it has a
girth 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 nonstraight 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 the
direction 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, and
these 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 VIV
modes 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, flow
is directed at the non-straight pipe section in three directions θ1, θ2 and θ3. The two modes are either inline, cross-flow or both depending on the direction of incoming flow. How the directionality of flow affects the
mode 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 depending
on the angle of attack of the flow, but also on the position along the pipe axis. A mode could be in-line or
cross-flow or both on the vertical leg, but will be either an in-line or a cross-flow mode at the horizontal
leg. As a result, all modes shall be classified as in-line or cross-flow or both for each leg of the non-straight
pipe system. Furthermore, since the classification depends on the direction of flow, each mode shall be reclassified (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 either
planes of motion. Forcing directions are given with double arrows and continuous lines, response
directions 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 are
distinctly either in-line or cross-flow. Therefore, the flow velocity will be reduced based on this angle, as is
normally done for pipelines according to Sec.3. The in-line and cross-flow force directions are assumed to be
in 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 mismatch
between the flow velocity and the two directions of responding modes, the in-line and cross-flow forcing do
not match any of the modal directions, as indicated in the figure by dotted double arrows for displacement
directions and whole lines for forcing directions. Conservatively it shall be assumed that both modes act
as both in-line and cross-flow modes, and furthermore any reduction in forcing shall conservatively be
disregarded.
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 both
in-line and cross-flow at the same time, that flow velocity shall not be reduced with respect to the angle of
attack.
— On a leg in a non-straight pipe system, for a given flow direction, if a mode can be excited due to crossflow and in-line VIV at the same time, that mode shall be classified both as an in-line mode and a crossflow 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 that
mode responds both in-line and cross-flow, the stress contribution to fatigue shall be taken as the maximum
of the two response model predictions. Since the shape of, and hence the stresses of, the mode itself
is independent of whether it responds in-line or cross-flow, a direct comparison of the modal response
amplitude 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 of
the pipe system, it is no longer trivial to determine the most critical flow direction. If the fatigue analyses
is based on omnidirectional data, or conservatively simplified to include only one direction of flow, the most
conservative direction shall be chosen.
In order to determine the most conservative flow direction, it is considered sufficient to choose the direction
that has the highest fatigue damage and largest extreme environmental load effect when the representative
design environmental condition is applied. If directions are different for the two results, fatigue damage
calculations and extreme environmental load calculations shall be performed separately with the respective
most 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 response
models 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 hydrodynamic
damping. Hydrodynamic damping from non-lock-in regions can be calculated according to guidance given
in DNVGL-RP-C205. Hydrodynamic damping from lock-in regions shall be set to zero when using a response
model 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 ROVplates. Such regions may also contribute to hydrodynamic damping which may be included in the calculation
of the stability parameter. Note, however, that such attachments have a reduced velocity of their own (with
their respective hydrodynamic diameter), and if lock-in is achieved for these regions, hydrodynamic damping
cannot be applied.
A.6.4
In detailed fatigue analyses, the variation in modal response classification can be utilized by accounting for
increased 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 the
vertical leg, but strictly cross-flow on the horizontal leg. When mode 1 is excited in-line it has a lock-in region
on the vertical leg, but the horizontal leg is a non-lock on region. For in-line response the horizontal leg will
therefore 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 the
horizontal leg, the flow is parallel to the pipe and hence the horizontal leg is a non-lock-in region for both
modes. As a result, modal damping for both modes may be accounted for on the horizontal leg when the flow
has 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 account
for 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 applied
in 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 conservative
compared 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 mode
that may be classified as an in-line mode for the relevant incoming flow direction, along the curved pipe
axis coordinate.
— Extreme environmental loading shall be calculated for the maximum wave and the representative 100year 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 coefficients
shall 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. Detailed
guidance for modal response calculation of straight systems and free spans is given in Sec.6. The analytical
approaches 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, unless
there is a support at each side and in near proximity of all bends, such that the bends do not influence the
modal response.
A.8.3
The degree of axial restraint in supports has a strong influence on the predicted modal response. The degree
of restraint in supports shall be conservatively modelled or accurately represented. Idealizations i.e. fixedfixed or pinned-fixed conditions cannot be applied unless it is documented or otherwise ensured that the
modelled 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 a
three-dimensional stress state. As a result, three cross-sectional moments, shear forces along two axes and
a change in the true wall axial force must generally be accounted for. The moments comprise bending about
two planes and torsion, and the cross-sectional shear forces are directed along the y- and z-axes (assuming
x 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 to
DNVGL-RP-C203, the extreme outer fiber stresses shall apply. The principal stresses shall include the effects
of 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 that
the effects of effective axial forces and static deflections are negligible, these effects shall still be accounted
for 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 a
subsea 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 to
environmental 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 connections
between 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 or
attachments along the pipe system, shall include fatigue and extreme environmental loading due to VIV and
direct wave loading.
A.10 Mitigation measures
A.10.1
There exists a range of different mitigation measures for non-straight pipe geometries. Traditional mitigation
measures 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 larger
structures.
A.10.2
Applications for and types of strakes are discussed in DNVGL-RP-C205. There is, however, a challenge when
applying 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 strakes
on systems with non-straight geometries, the strake efficiency shall be documented for application on the
specific system, taking into account the differences in VIV response for non-straight compared to straight
systems.
A.10.3
Onset of VIV is a function of the 100-year environmental condition, the fundamental frequency of the system
and the diameter. With increasing diameter, the onset of VIV will occur for higher flow velocities. Hence, the
diameter can be increased until no onset of VIV occurs. For riser systems this is not an attractive option since
the 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 expensive
nor a problem for other design aspects to increase the hydrodynamic diameter. The relative decrease in
reduced velocity due to an increase in the hydrodynamic diameter is:
where:
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VdecR
Sg
Dincr
aincr
bincr
= Decreased reduced velocity, as a result of a higher hydrodynamic diameter
= Specific gravity of the original configuration, see section [4.4.14]
= aincr·D, new hydrodynamic diameter, after increase
= Ratio between new and old hydrodynamic diameter
=
ρincr/ρw, ratio between the density of the material causing the diameter increase and the water
density
ρincr = Density of the material causing the increase in hydrodynamic diameter
= Added mass coefficient, see section [6.6.7]
Ca
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 the
required decrease is achieved. Note that lower coating density and higher thickness will be beneficial for
achieving lower reduced velocities. Note also that the coating cannot be too lightweight since a negative
buoyancy is not acceptable for most systems.
The principles of using increased hydrodynamic diameters to mitigate VIV for onset may also be applied
to reduce the exposure to VIV for systems which fail the avoidance criteria. Note, however, that increasing
the hydrodynamic diameter will also increase the modal stresses, so the effect of an increased diameter is
not always positive. For long flexible systems, with many responding modes, the effect is likely to be more
adverse. For more rigid systems, where only one or two modes respond to VIV, the effects are more likely to
be beneficial.
Some non-straight pipe systems are designed to cool its content, and will therefore require that external
flow 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 pipe
since 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 from
environmental actions. This is a common mitigation technique for flexible non-straight structures in harsh
environments.
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 a
span. 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 inline, it may only be necessary to introduce piecewise increases to the hydrodynamic diameter. Buoyancy
elements, ROV-plates, or similar structures artificially introduced to mitigate VIV may cause sufficient
hydrodynamic damping to mitigate in-line VIV, provided that regions with increased hydrodynamic damping
become non-excitation regions (see [A.6]). Hydrodynamic damping will generally not be sufficient to fully
mitigate 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 be
applied for systems where VIV is allowed, i.e. systems where VIV avoidance is not required, and that such
damping may have a favorable impact on fatigue and extreme environmental load predictions, particularly inline 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 trigger
separation in order to decrease the vortex shedding correlation along the riser. Helical strakes increase the
cost of the pipeline and will complicate handling during installation. The in-line drag coefficient is increased
by introducing strakes.
B.1.2
The important parameters for the strake design are the height and pitch of the helical strakes for a given
pipeline diameter. The overall performance characteristics of a given strake design will vary with the current
velocities.
B.1.3
The effectiveness of VIV suppression devices, such as VIV strakes needs to be qualified. It is recommended
that an independent verification of the effectiveness of VIV suppression devices is performed by a competent
verification 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-F101
Sec.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 described
in [1.3].
C.1.2
The fundamental principles given in this RP may also be applied and extended to other offshore elements
such 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 of
the riser while other parts are contributing to damping of the system (power output). In such cases this
document is not applicable.
C.2.2
For short riser span lengths, typical for steel risers supported by a jacket structure and when the current
is uniform, the response models given in Sec.4 of this RP can be applied. For short risers the lowest eigen
modes are typically excited. In such cases this RP will predict both in-line and cross-flow VIV provided that
the 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, using
this RP at the designer’s discretion and judgement. The following conditions should, however, be carefully
evaluated:
—
—
—
—
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 - historic
CHANGES - HISTORIC
There are currently no historic changes for this document.
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