free sp anning pipelines guidelines

Transcription

GUIDELINES
No.14
FREE SPANNING PIPELINES
JUNE 1998
DETNORSKE VERITAS
Veiitasveien I, N-1322 H0vil<, Norway Tel.: +47 67 57 99 00 Fax: +47 67 57 99 11
FOREWORD
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and the environment at sea and ashore.
DET NORSKE VERITAS AS (DNV AS), a fully owned subsidiary Society of the Foundation, undertakes classification and
certification and ensures the quality of ships, mobile offshore units, fixed offshore strnctures, facilities and systems, and carries
out research in connection with these · functions. The Society operates a world-wide network of survey stations and is
authorised by more than 120 national administrations to carry out surveys and, in most cases, issue certificates on their behalf.
Guidelines
Guidelines are publications which give infonnation and advice on technical and formal matters related to the design, building,
operating, maintenance and repair of vessels and other objects, as well as the services rendered by the Society in this
connection. Aspects concerning classification may be included in the publication.
An updated list of Guidelines is available on request. The list is also given in the Latest edition of the Introduction-booklets to
the ''Rules for Classification of Ships", the "Rules for Classification of Mobile Offshore Units" and the "Rules for
Classification of High Speed and Light Craft".
In "Rules for Classification of Fixed Offshore Installations", only those Guidelines which are relevant for this type of structure
have been listed.
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© Det Norske Veritas AS 1998
Data processed and typeset by Division Technology and Products, Det Norske Veritas AS
Printed in Norway by Det Norske Veritas AS
98-06-05 11:54 -Gul4.doc
6.98.2000
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Ventas.
CONTENTS
1.
1.1
1.2
1.3
1.4
1.5
l .6
2.
2.1
2.2
2.3
3.
3.1
3.2
3.3
3.4
3.5
3 .6
3 .7
4.
4.1
4.2
4.3
4.4
General ..................................................................... 4
Introduction ........................ .................................... ... 4
Scope and Applicability ...... ......................... .............. 4
Structure of Guideline ............................................... S
Relationship to Other Rules ....................................... 6
Safety Philosophy ...... ................................................ 6
Definitions ................................................................. 6
Free Span Classiftcation .......................................... 9
General ...................................................................... 9
Morphological Classification .. ............. .... ................. . 9
Temporal Classification ........................................... I 1
Free Span Analysis ................................................ 11
General .................... ................................................ 11
Structural Modelling ....................... ......................... 11
Loads ....................................................................... 12
Static Analysis .................................. ....................... 12
Eigen-value Analyses ................................ .............. 13
Damping .............................. ........................ .......... .. 13
Approximate Response Quantities ........................ .. . 15
Geotechnical Conditions ....................................... 16
General ........... .............. ......... ... ......... ........ .............. 16
Modelling of Soil Interaction................................... 17
Approximate Soil Stiffness ........................ .............. 18
Artificial Supports ............................. ...................... 20
S.
5.1
5.2
5.3
6.
6.1
6.2
6.3
6.4
7.
7.1
7.2
7.3
7.4
8.
8.1
8.2
8.3
9.
9. I
9.2
9.3
10.
Hydrodynamic Description .................................. 20
Flow Regilnes ......................................................... 20
Hydrodynamic Parameters .......................... .... ........ 22
Sea-bed Proxilnity ................ .. ................................. 22
Environmental conditions..................................... 23
General ................................................ .................... 23
Current Conditions .................................................. 23
Short-tenn Wave Conditions .................. .. ............... 24
Long-Tenn Statistics .. ...... ............ ....... ............. ..... .. 27
Fatigue Analysis .................................................... 28
General .......................................................... .......... 28
Fatigue Criteria ....................................................... 28
SN-Curves ......... .................... .. .. .............................. 29
Safety Factors ........................ .. ................................ 30
Amplitude Response Models ................................ 31
General .................................................................... 31
In-line VIV in Current Dominated Conditions ........ 31
Cross-Flow VIV from Combined Wave and Current34
Force Models ......................................................... 36
General .................................................................... 36
In-line Direction .................................................. .. .. 36
Cross-Flow Direction ............... ................ ............... 38
References .............................................................. 38
DET NORSKE VERJTAS
4
Guidelines No. 14
June 1998
1. General
The flow regimes are discussed in section 5.1.
1.1 Introduction
1.2.3
The present Guideline considers fatigue of free spanning
pipelines subjected to combined wave and current loading.
The premises for the Guideline are based on the technical
development within pipeline free span technology in recent
R&D projects as well as design experience from recent and
ongoing projects, i.e.
The foJlowing soils are considered:
•
1.2.4
•
•
The sections regarding Geotechnical Conditions and part
of the hydrodynamic model are based on the research
perfonned in the GUDESP project, see Tura et al.,
(1994). The GUDESP project is a JIP sponsored by
EEC-General Directorate for Energy, Exxon Production
Research, Statoil and Snam SpA and perfonned by
Danish Hydraulic Institute, Snamprogetti SpA and Det
Norske Veritas.
The sections regarding Free Span Analysis and in-line
VIV fatigue analyses are based on the published results
from the MULTISPAN project, see Merk et al., (1997).
The MUL TISPAN project is a JTP sponsored by Statoil
and Norsk Agip and performed by Snamprogetti SpA,
SINTEF, Danish Hydraulic Institute and Det Norske
Veritas.
Further, recent R&D and design experience e.g. from
Asgard Transport, ZEEPIPE, NORFRA and TROLL
OIL pipeline projects are implemented.
The basic principles applied in this Guideline are in
agreement with most recognised rules and reflect state-ofthe-art industry practice and latest research.
1.2 Scope and applicability
1.2.1
The objective of this Guideline is to provide rational design
criteria and guidance on fatigue analyses of free pipeline
spans subjected to combined wave and current loading.
Detailed design criteria are specified for fatigue analyses due
to in-line and cross-flow Vortex Induced Vibrations (VIV).
Functional requirements are given for direct wave loading.
The following topics are considered:
•
•
•
•
•
•
•
methodologies for free span analysis
requirements for structural modelling
geotechnical conditions
environmental conditions & loads
requirements for fatigue analysis
response and direct wave force analysis models
acceptance criteria.
1.2.2
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.
•
•
cohesive soils (clay)
cohesionless soils (sand).
The geotechnical conditions are discussed in section 4.
The free span analysis may be based on a simple structural
model or a refined FE approach depending on the free span
classification, see section 2. The following cases are
considered:
•
•
single spans
spans interacting with adjacent/side spans.
1.2.5
Free spans may be caused by:
•
•
seabed unevenness
change of seabed topology (e.g. scouring, sand waves).
1.2.6
The following analysis models are considered:
•
•
response models
force models.
An amplitude response model is applicable when the
vibration of the free span is dominated by vortex induced
resonance phenomena. A force model may be used when the
free span response can be found through application of
calibrated hydrodynamic loads. The selection of an
appropriate model may be based on the prevailing flow
regimes, see section 5.1.
t.2.7
The loads to be considered for fatigue analysis of free
spanning pipelines includes:
•
•
functional loads
environmental loads, comprising
direct loads from wave and current
loads induced by hydro-elastic phenomena.
Fatigue loads from trawl impact, cyclic loads during
installation or pressure variations are not considered herein
but must be considered as a part of the integrated fatigue
damage assessment.
1.2.8
An explicit criterion for onset of cross-flow VIV is not
included in this Guideline. Design recommendations in case
of current dominated conditions can be found in
MULTrSPAN ( l 996) and M0rk et al., ( 1997).
DETNORSKE VERITAS
Guidelines No. 14
5
June 1998
1.2.9
1.3 Structure of Guideline
Static design check and combined stress check from static
and dynamic bending moment induced peak stress, axial
force and pressure shall be performed in compliance with the
Rules for Submarine Pipeline Systems, 1996.
1.3.l
The structure of this Guideline illustrating the components
entering the fatigue analyses is given in the figure below.
FLOW CHART FOR FATIGUE ANALYSES
Project Da1a
Free Span Scenario
Design Conditions
DESIGN BASJS
Safety Philosophy
Current Conditions
ENVIRONMENTAL CONDITION
Wave Conditions
Structural Modtlling
Static Analyses
mode shapes
::£---j
-----.....-----------FR.1£E SPAN ANALYSES
Geotechnical Conditions
Full FE-simulation
Eigenvalue
Analyses
Simplified Assessment
frequencies
damping
Hydrodynamic Paramete .
reduced velocity
Keulcgan-Carpenter numbe
Hyd rodynamic Forces
vave velocity
FORCl!:MODEL
RESPONSE MODEL
TIME DOMAIN v~ FREQUENCY DOMAIN
PIPE RESPONSF:
(STRESS RANGES &. CYCLES)
SN CURVF.S
(Tl!ST DATA, LITERATIJRE, l'MA)
SAFETY FACTORS
(SAFETY CLASS. ADD. DATA)
DET NORSKE VERlT AS
Guidelines No. 14
6
June 1998
judgement in order to obtain a safety level equivalent to
modem industry practice.
1.4 Relationship to other Rules
1.4.1
This Guideline formally supports and complies with the
Rules for Submarine Pipeline Systems, 1996, hereafter called
the Rules for Pipelines, and is considered.to be a supplement
to relevant National Rules and Regulations.
1.6 Definitions
The international system of units (ST system) is applied
throughout the Guideline. Further, the following definitions
apply:
external cross-section area
1.4.2
This guideline is supported by other DNV documents as
follows:
•
•
•
Classification Note No. 30.2 "Fatigue Strength Analysis
for Mobile Offshore Units", 1984.
Classification Note No. 30.5 "Environmental Conditions
and Environmental Loads", 1991.
The MUL TISPAN Project: Guideline. VIV of Free
Spanning Pipelines. Part I Steady Current Loading,
1996.
ln case of discrepancies in the recommendation, this
Guideline supersedes the Classification Notes listed above.
1.5 Safety philosophy
A;
internal cross-section area
pipe steel cross section area
(Av/D)
normalised in-line VIV amplitude
(Az/D)
normalised cross-flow VIV amplitude
b
chord corresponding to pipe embedment equal
tov
c
characteristic fatigue strength constant
c.
added mass coefficient
Co
drag coefficient
1.5.1
(C3 +\) is the inertia coefficient
The safety philosophy adopted herein is in full compliance
with section 3 in the Rules for Pipelines.
c(s)
soil dampjng per unit length
Pipeline design is nonnally to be based on Location Class,
Fluid Category and potential failure consequence for each
failure mode, and to be classified into one of the following
Safety Classes:
0
pipe outer diameter (including any coating)
Drat
detenninistic (design) fatigue damage
•
E
Young's modulus
EI
bending stiffuess
e
gap between the pipe bottom and the sea-floor
(e/D)
seabed gap ratio
fo
in-line (fo.W or cross-flow (fo,cr) natural
frequency
•
•
Low Safety Class, where failure implies no risk of
human injury and minor environmental and economic
consequences.
Normal Safety Class, classification for temporary
conditions where failure implies risk of human injury,
significant environmental pollution or very high
economic or political consequences. Normal
classification for Operation.
High Safety Class, classification for operating conditions
where failure implies risk of human injury, significant
environmental pollution or very high economic or
political consequences.
outer steel diameter
S1 U is the vortex shedding frequency
D
For a definition of location class and fluid category, see the
Rules for Pipelines.
(Strouhal frequency)
1.5.2
wave frequency
dominating vibration frequency
The reliability of the pipeline against fatigue failure is
ensured by use of a safety factor fonnat (also known as a
Load and Resistance Factors Design Format (LRFD)).
PO
distribution function
g
gravity
•
G
soil parameter
0(<0)
frequency transfer function
•
For the in-line 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 a "soft calibration" and engineering
DET NORSKE V ERITAS
7
Guidelines No. 14
June 1998
Heir
effective lay tension
Pc
external pressure
Hs
significant wave height
P•
internal pressure
h
water depth, i.e. distance from the mean sea
level to the pipe
.1pi
internal pressure difference relative to laying
Q
deflection load per unit length
le
turbulence intensity over 30 minutes
OCR
over-consolidation ratio (only clays)
Ip
plasticity index, cohesive soils
PE
Euler load
k
wave number
axial soil reaction
soil parameter
R.
kc
Re
current reduction factor
ks
soil parameter
Ro
kw
nonnalisation constant
reduction factor from wave direction and
spreading
KL
lateral (horizontal) dynamic soil stiffness
Rv
vertical soil react1on
Kv
vertical dynamic soil stiffness
Rio
(k/D)
pipe roughness
reduction factor from turbulence and flow
direction
Rt
reduction factor from damping
KC
~;
is the Keulegan Carpenter numper
w
Ks
Re
41tme£;r
pD2
is the stability parameter
UD is the Reynolds number
v
s
abscissa co-ordinate along the pipe axis or
spreading parameter
L
free span length, (apparent)
s
stress range, i.e. double stress amplitude
La
length of adjacent span
Setr
effective axial force
Leff
effectivespanlength
s~~
wave spectral density
Ls
span length with vortex shedding loads
Suu
wave velocity spectra at pipe level
L sh
length of span shoulders
Su
undrained shear strength, cohesive soils
fie
effective mass per unit length
m
fatigue exponent
m(s)
mass per unit length including structural
mass, added mass and mass of internal fluid
Mn
spectral moments of order n
MSL
mean (surface) water level
n·I
number of stress cycles
N
number of cycles to failure
N1r
true steel wall axial force
Ne
soil bearing capacity
Nq
Ny
SA-ID
unit amplitude stress (stress induced by a pipe
(vibration mode) deflection equal to an outer
diameterD)
SCF
Stress Concentration Factor due to geometrical
imperfections in the welded area not
implemented in the applied SN-curve.
S,
Strauhal nwnber
pipe wall thickness or time
T
temperature
Tn
nonnalisation period
T11fe
time of exposure to fatigue load effects
T"
peak period
Tu
mean zero upcrossing period of oscillating
flow
DET NORSKE VERITAS
8
Guidelines No. 14
June 1998
ilT
temperature difference relative to laying
K
von Karmans constant or curvature
u
Uc+Uw is the maximum flow velocity
T]
usage factor
u
mean flow velocity
factor transforming standard deviations to
maximum response
current velocity nonnal to the pipe
axial friction coefficient
significant wave velocity
v
wave induced velocity amplitude
mode shape
significant wave induced flow velocity
corrected for wave direction and spreading
v
Poisson's ratio or kinematic viscosity
vertical soil settlement (pipe embedment)
Uc + U w is the reduced velocity
angle of friction, cohesionless soils
p
density of water
pJp
spedfic mass ratio between the pipe mass (not
including added mass) and the displaced water,
f0 D
7t
02
v•
friction velocity
P4
w
wave energy spreading function
effective soil stress
Wsou
submerged wiit weight of soil
environmental sea state vector E>=[H., Tv, Sw]T
z
height above seabed
Zo
height to the mid pipe
direction perpendicular to the pipeline
sea-bottom roughness
mean/main wave direction
reference (measurement) height
spreading angle measured from the mean
wave direction
z
e
Uc
- ---''--- current flow velocity ratio
Uc + Uw
total modal damping ratio
~voiJ
Weibull distribution parameter
flow angle relative to pipe
soil modal damping ratio
structural modal damping ratio
temperature expansion coefficient
hydrodynamic modal damping ratio
angular wave frequency
soil shear strength.
pipe eccentricity
t
band-width parameter
\f/mod
mode shape parameter
~
reduction factor
r
gamma function
y
peakedness parameter, JONSWAP spectrum
'Ys
safety factor on stress amplitude
Yr
safety factor on natural frequency
'Yk
safety factor on stability parameter
DETNORSKE VERITAS
Guidelines No. 14
9
June 1998
•
scour induced or unevenness induced free span, see 2.3.
2. Free Span Classification
2.1.2
2.1 General
2.1.l
Jn the present chapter the free span scenario in classified into
•
single (isolated) or multi-spanning free spans, see 2.2
ln the table below an overview of typical free span
characteristics are given as a function of the free span length.
The ranges indicated for the normalised free span length in
tenns of (LID) are tentative and given for illustration only.
UD
Response description
Characteristics
< 30
Very little dynamic
amplification. Not
considered a free span
It is nonnally not required to perfonn comprehensive fatigue
design check. Insignificant dynamic response from envirorunental
loads expected and unlikely to experience VIV.
30-lOO
Response dominated by
beam behaviour
Typical span length for operating conditions.
Natural frequencies sensitive to boundary conditions (and
effective axial force). Maximum stress amplitudes normally at
span support.
100-200/250
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" for scour induced free spans in operation.
Maximum stress amplitudes at span support or at mid span
> 200/250
cable behaviour
Relevant for small diameter pipes in temporary conditions.
Natural frequencies governed by detlected shape and effective
axial force. Maximum stress amplillldes at mid span.
2.2 Morphological classification
2.2.l
The objective of the morphological classification is to defme
whether the free span is isolated or interacting. The
morphological classification determines the degree of
complexity required of the free span analysis:
•
•
Two or more consecutive free spans are considered to be
isolated (i.e. single span) if the static and dynamic
behaviour are unaffected by neighbouring spans.
A sequence of free spans is interacting (i.e. multispanning) if the static and dynamic behaviour is affected
by the presence of neighbouring spans. If the free span is
interacting, more than one span must be included in the
pipe/seabed model.
If detailed information is not available Figure 2-1 or figure
2-2 may be used to classify the spans into isolated or
interacting dependent on the soil types and span and support
lengths. The figures are in a narrow sense only valid for the
vertical (in-line) dynamic response but may also be used for
assessment of the horizontal (cross-flow) response. In this
case the effective lateral soil stiffuess should be used to
select the appropriate curve.
2.2.2
The morphological classification should in general be
detennined based on detailed static and dynamic analyses.
The classification may be useful for evaluation of scour
induced free spans or in deriving approximate response
quantities.
DETNORSKE VERITAS
10
Guidelines No. 14
June 1998
1.0 ·c---:----:-:--=:::::;:=~=--:--:---:--:--:----,
lnterac~ng
.
.
0.9
.
.
.
.
.
.
'
o
.
.
... .........:.................;.............. .
...
.
....
.
.... ·······:············...:-·····
.
. ......
............... ·i .. .. ... .... .;. ..............;......... .. .. .;....... . .... ..:........... .
.
0.8
.
.
.
.
I
f
T-.. .:· · · : T:· ::·;:· :::~:.:::.:· . . .. . :. :r.:.· ···-r::· ::·:::: . .......
0.7
0.6
•
~.5 ...........~..........) .......... ) .........1span scenario - Sandi) ..........)...................... .
...J
:
:
.
'
. :
.:
.
.
.•
.
'
.!
•
•
o
o
0.4 . .......·-r···••oo••···~········ ..
o
0.3
..
.
•
•
'
+
o
o
I
I
o
I
t
····r··········--~--
..
I
t
o
~--······-···-~---·-·-·· ---~-·-·····
..
..
o
'
..
o
·. . . . .~ . . . - - l. . .). . . . . ). . . . . . -;10:. . .:-.--. --::'"'
L~·· ~
I Ls~
hl ~~
···········~
0.1
0.0
•
I
. --··-· ·--:··-······
.
.
.
.
········--·:·············:-············:···---·-····
···········?··--·-······~······
0.2
··r·......... r············r-··········-1.. ··········1............1.. ·······
:
:
·(
) ·(
)·(
-1-~~;._.~~~~__;,_.
: ~~~:~~-!;::====::;=============;=======;:=====(
0.0
0.1
0.2
0.3
0.6
0.4
0.7
0.8
0.9
1.0
Figure 2-1 Classification of free spans - sand
0.9
r · v~ry h~rtl -··-··· ; ······ ..
.
'
0.8
.i
.
0.7
. . .+. .
0.6
.
~ 0.5
.J
........ ,.:...
. .. ... ... .. .. . .
.. .... .. .
0.4
.-
0.3
...... ···---~······· .. -~· .. ·····
.
~.
:
0.2 . ········--~--··
:
o
o
o
+. . . . .
t
'
I
o
I
~·
o
o
I
I
'-~
o
o
o
I
I
t
o
f
I
'
o
I
t
j
"'
:
:
:
:
:
:
i
.
•
0.8
0.9
0
o
····f ············~··········--~---······· - ~·-·· ···· ···-~·-·········-~ · -··········~·-·····
o.•···l·· ········+···········+········· -.....,_-~~----:-~
0.1
..
.
-jsp~n scen~rio - Cl.ay j..... .J.-........
.
.
.
.
.
····t···-···-··· ......... ···········1· ......... ··;···-········! ............... .
.
I
I
.
. .:............ .:..............~. ········
..
..
..
....
. ......
.... ·:· ···········!.. . ········. ··t·
.
.
.
... ·: ·········-'"!······ .....
I"". ... I L..hl °''~
L
...a•.-"
(
..
)(
)(
0.0
0.0
0.1
0.2
0.3
0.4
0.6
0.7
Figure 2-2 Classification of free spans - clay
DET NORSKE VERITAS
1.0
11
Guidelines No. 14
June 1998
•
2.3 Temporal classification
Z.3.1
The temporal criterion categorises the free span according to
scour or unevenness induced free spans, i.e.
•
•
Scour induced free spans are 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 are caused by an
irregular seabed profile. Normally the free span scenario
is time invariant unless the operational parameters such
as pressure and temperature change significantly.
2.3.2
The free span analysis shall take due account of the temporal
classification in the application of the load sequence for the
functional loads:
•
•
Scour induced free spans: all loads may be applied in
one step.
Unevenness induced free spans: loading sequence in
steps, see section 3.
•
3.2 Structural modelling
3.2.1
The structural behaviour of the pipeline shall be evaluated by
modelling the pipeline, the seabed and relevant artificial
supports and perfonning static and dynamic analyses. lo this
section requirements to the structural modelling are given.
Soil-pipe interactions are treated in section 4.2.
3.2.2
A realistic characterisation of the cross-sectional behaviour
of a pipeline can be based on the following assumptions:
•
•
2.3.3
•
In case of scour induced spans, where no detailed
infonnation is available on the maximum expected span
length, gap ratio and exposure time, the following apply:
•
•
•
Where unifonn conditions exist and no large-scale
mobile bed-fonns are present the maximum span length
may be taken as the length resulting in a statically 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 must be included.
2.3.4
Additional information (e.g. free span length, gap ratio,
natural frequencies) from surveys combined with an
inspection strategy may be used to qualify scour induced free
spans. These aspects are not covered herein. Guidance may
be found in Fyrileiv et al., (1998).
3. Free Span Analysis
3.1 General
•
•
The pipe cross-sections remain circular and plane.
The two dimensional state of stress (axial and hoop)
should be considered.
The stresses may be assumed constant across the pipewall thickness.
A plasticity model based on the von Mises criterion and
associated flow rule may be adopted.
The internal pressure affects the bending response if
yielding takes place
Load effect calculation is normally to be performed
using nominal un-corroded cross section values.
3.2.3
The pressure differential causes hoop stresses to develop in
the pipeline wall along with axial stresses. In case of yielding
this bi-axial state of stress shall be represented in a consistent
way to allow for a realistic cross-sectional behaviour. In
particular the influence of the hoop stress and Poisson's
effect on the bending stiffness must be considered.
3.2.4
The effect of coating is generally limited to increasing
submerged weight, drag forces, added mass and buoyancy.
The positive effect on the stiffness and strength is normally
to be disregarded. If the contribution of the coating to the
structural response is considered significant, appropriate
models shall be used.
3.2.5
3.1.1
The following tasks normally have to be performed in the
assessment of free spans:
•
•
•
an eigenvalue analysis which provides natural
frequencies and corresponding modal shapes for the inline and cross-flow vibrations of the free spans
a response analysis using a response model or a force
model in order to obtain the stress ranges from
envirorunental actions.
structural modelling
load modelling
a static analysis to obtain the static configuration of the
pipeline
Non-homogeneity of the bending stiffness along the pipe,
due to discontinuities of the coating across field joints or
other effects, may imply strain concentrations that shall be
taken into account.
3.2.6
The boundary conditions at the ends of the pipeline section
modelled shall be able to simulate the pipe-soil interaction
and the continuity of the whole pipeline length.
DET NORSKE VERITAS
l2
Guidelines No. 14
June 1998
3.2.7
3.4 Static analysis
The element length to be used in a finite element model is
dictated by the accuracy required. Typically an element
length of I.120 (L is the span length) is sufficient.
3.3 Loads
3.3.1
The loads to be considered for fatigue analysis of free
spanning pipelines includes:
•
•
The static configuration is to be detennined for different
conditions:
•
•
•
•
as-laid condition
flooded condition
pressure test condition
operating condition.
3.4.2
functional loads
environmental loads, comprising
The static analysis should normally account for non-linear
effects such as:
direct loads from wave and current
loads induced by hydro-elastic phenomena.
Fatigue loads from trawl impact, cyclic loads during
installation or pressure variations are not considered herein
but must be considered as a part of the integrated fatigue
damage assessment.
3.3.2
The functional loads which shall be considered are:
•
•
•
•
•
3.4.1
weight of the pipe and internal fluid
external and internal fluid pressure
soil pressure if the pipe is locaJJy buried
thennal expansion and contraction
installation forces.
•
•
•
•
large displacements (geometric non·linearity)
soil non·linear response
non-linear behaviour of the pipe cross-section
loading sequence.
3.4.3
The stiffuess of the pipeline consists of material stiffness
plus geometrical stiffness. The effective axial force, Serf,
shall be used to calculate the geometrical stiffness. This force
is the true steel wall axial force, Nir, with corrections for the
effect of external and internal pressures:
3.3.3
Where p; and Pe denotes the internal and external pressure,
respectively and Ai and Ae are the corresponding cross·
section areas.
Weight must account for the weight of the pipe considering
coating and all attachments to the pipe, the weight of the
internal fluid and the buoyancy.
For a completely unrestrained (axially) pipe the effective
axial force becomes:
3.3.4
Soil pressure, if the pipe is locally buried, is normally not
considered explicitly in the free span analyses but rather
implicitly by imposing appropriate soil restraints.
For a totally restrained pipe the following effective axial
force apply:
3.3.5
Thennal expansion and contraction loads and possible other
changes in pipe behaviour caused by temperature differences
shall be accounted for.
where:
effective lay tension
internal pressure difference relative to laying, see
Rules for Pipelines
3.3.6
Installation forces are to include all forces acting on the pipe
during installation . Typical installation forces are applied
tension during laying and forces from the trenching machine
if trenching is carried out after laying. Pre-stressing such as
pennanent curvature or a permanent elongation introduced
during installation must also be taken into account.
pipe steel cross section area
ti.T
temperature difference relative to laying
temperature expansion coefficient.
3.4.4
3.3.7
Response calculations must account for the relevant
sequence of load application if important.
The static environmental loads are in this guideline confined
to those from on bottom current. The load may be
disregarded in the analysis if much smaller than the vertical
DETNORSKE VERITAS
Guidelines No. 14
13
June 1998
functional loads. However, for light pipes it should be
considered.
element modelling. Thus, the element lengths must be short
enough to ensure a sufficient number of elements over the
free spans that are to be assessed.
3.5 Eigen-value analyses
3.6 Damping
3.5.l
The aim of the eigen-value analyses is to calculate the
natural frequencies and corresponding mode shapes. In
general the analysis is complex and depends on
•
•
•
•
•
•
the temporal criterion
the pipeline condition (i.e. as-laid, water-filled, pressure
test and operation)
the pipe and soil properties
the seabed classification, effective free span length and
boundary conditions
the effective axial force and the initial deflected shape
after laying
the loading history and axial displacement ("feed-in") of
the pipe.
Jn general, it is recommended to assess the response
quantities using non-linear FE-analyses conducted over an
appropriate stretch of the pipeline. However, approximate
response quantities may be applied in some cases, see section
3.7.
3.6.l
Response amplitudes are affected by damping. The stability
parameter, Ks, representing the damping for a given modal
shape is given by:
where:
water density
p
total modal damping ratio at a given vibration
mode comprising:
structural damping, (m, see 3.6.4
soil damping, Ssoih see 3.6.5
hydrodynamic damping, Sh, see 3.6.6
•
•
•
specific mass (without added mass)
(psfp)
added mass coefficient.
3.5.2
Using a FE-approach, the follow ing comments apply:
•
•
•
•
•
The eigenvalue analysis shall account for the static
equilibrium configuration.
In the eigenvalue analysis, a consistent linearisation of
the problem must be made.
The pipe-soil linearisation should be validated.
The effect of geometric non-linearity on the dynamic
response should be assessed.
The pipe support points may be assumed not to change
during Vortex-Induced Vibrations (VIV).
3.6.2
The effective mass, me, is defined by
Jm(s)~ 2 (s)dsl
m e-
~
L'--=_
[
_
_
J~ 2 (s)ds
L
m(s) is the mass per unit length including structural mass,
added mass and mass of internal fluid.
3.5.3
For a multi-spanning scenario, special care must be paid to
the determination of the eigenvalues and associated
eigenvectors due to the potential occurrence of very close
eigenvalues, especially as concerns the identification of
con-ect eigenvectors.
3.6.3
The added mass coefficient, Ca, as function of the gap ratio
(e/D) is given by Figure 3-1. It applies for both smooth and
rough pipe surfaces.
3.5.4
The stress ranges are derived from the mode shapes. The
accuracy of the stress ranges is strongly affected by the fmite
DETNORSKE VERITAS
14
Guidelines No. 14
June 1998
·-......... ·: .........··: .................................... ··;· .......... ··1······· ····1········· ·;
.
.
...
...
...
.... .... ...... ·--- ----------·:····-······:·-·-·-·-·· ........... ···········:···········:···········:····· ······:
'
..
....
..
...'
..
.
' ......................
.
................................ ................. ...............................
.....
..
..
.
.'
.'
.
.''
'
'
'
'
.
'
.
'
.
.
................. !' .............:···········
................... ·····:···········1···········1·
---·-····1.
2.00
l.90
~
1.80
..
u
....Q
·o
··········~······
1.70
e
1.60
4J
0
u
"'"'
=
... ·- ----- -··: ........ -·-. !... -- -- .... ;-.......•. ·······--
...... -..... ......... ;· ...........
.
..
...
.
.
.
.
'
.
.
.
.
.
····················-···............... .. ......... . ................. ... ....... .... ... ............
.
.
.
.
.
1.50
'
~ 1.40
""
~-
'
.
.
'
•
'
t
I
'
'
'
·····-··•·i·········-·
~
.
.
t
.
1.10
'
··T···· :· : T·: : : :.:.:. · ;· :::r:· :.L·
'
········ ! ·········
1.20
~
'
~-·······
'
l.30
~
-·~-
'
'
•
4J
"O
t
'
··········t·~ ........ t~ . . . . ·1··--····
.. ·1
... ·····1··········· ..........:~ ........... :...........:... ......
Q,l
~
. .....
•
'
...
········ ···~ ········
'
..
••!
.
..
'
··········-~·· · ·······---~
1.00
0
0.2
0.4
0.6
1.2
0.8
1.6
l.4
1.8
2
Gap Ratio (e/D)
Figure 3-1 Added mass coefficient versus gap ratio
2
3.6.4
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
<'.;,
h
=\jl
pDC 0
4rrf
0 [
jU(s)cjl (s)ds ]
C L-L~l
(s-)$-2-(s-)-ds- -L=-Jm-
where:
Sstr == 0.005
constant to be taken a:> 1.0 for in-line VIV and
0.5 for cross-flow VIV.
can be assumed. If concrete coating is present, the sliding at
the interface between concrete and corrosion coating may
further increase the damping to typically 0.01-0.02.
p
water density
3.6.5
D
outer pipe diameter (including any coating)
For screening purposes the following soil (modal) damping
ratio can be assumed:
Co
drag coefficient
fo
natural frequency
lj>(s)
mode shape
U(s)
mean flow velocity normal to the pipe as a
function of the pipe axis co-ordinate, s.
m(s)
mass per Wlit length incl. structural mass,
added mass and mass of internal tluid
L
free span length
Ls
span length with vortex shedding loads.
~I
=0.01
For a more detailed analysis, see 4.2.
3.6.6
For VIV the hydrodynamic modal damping ratio ~.,is
normally to be taken as zero, i.e.
For VIV the hydrodynamic damping, ~11, is the damping
outside the lock-in region for the pipe. The contribution to
hydrodynamic damping within the lock-in region shall be set
to zero. Thus, ~h. may be taken from:
~his
not to exceed 0.05.
DET NORSKE VERITAS
Guidelines No. 14
15
June 1998
3.7 Approximate response quantities
3.7.1
The approximate response quantities specified in this section
may be applied for free span assessment provided:
•
conservative assumptions are applied with respect to
boundary conditions, span length, effective axial force,
etc.
a sensitivity study is perfonned in order to quantify the
criticality of the assumptions.
•
Approximate response quantities are considered relevant in
performing efficient screening of FE or survey results in
order to identify critical spans to be assessed with methods
that are more accurate, see Fyrileiv & M0rk, (1998).
approximate coefficient related to the deflection (sagging)
tenn. The higher value for C3 typically apply to as-laid
condition and the lower to cases with significant feed-in e.g.
during operation.
If more detailed infonnation is not available the following
values are recommended:
C1~2.0, C2""0.50, C3,..J.0 10·4
for as-laid condition.
C,,.,2.0, Cr:::0.50, C3,.,5.0 10·5
for in-service condition.
The approximate equation for fo normally predicts
frequencies within+/- 30% of the true natural frequency
provided (C 2 S.ffl'PE) > -0.5 and (LID) < 200.
3.7.4
3.7.2
The fundamental natural frequency may be approximated by,
see Bruschi & Vitali, (1991):
The ratio between the effective span length, Leff, and
apparent (visual) span length, L, depend on the soil and
support conditions. If more detailed infonnation is not
available it may be taken as:
L.;:r =
{
where:
E
Youngs modulus
I
moment of inertia
LID < 40
1.12-0.00{~ -40)
40 <UD< l60
1.0
L/D> l60
3.7.5
The unit diameter stress amplitude (stress due to unit outer
diameter mode shape deflection) may be calculated by
effective span length, see 3.7.4
M.
1.12
effective mass, see 3.6.2
steel outer diameter of pipe
Q
deflection load per unit length (submerged
weight for cross-flow or static current loading
for in-line)
s.rr
effective axial force, see section 3.4.3
where ~(s) is the assumed mode shape satisfying the
boundary conditions, D is the outer pipe diameter (including
any coating) and 0 5 is the steel pipe diameter. K is the
curvature of the mode shape ~(s) at the point (s, ~(s)) to be
·
calculated as
3
2
[
2)12
K(s) = .£...1 I+ (ap)
Euler buckling load"" n 2EIIL2.rr.
Bs 2
Os
3.7.3
Alternatively, SA-io, can be calculated as the quasi-static
The coefficients Ci. Cz and C3 are given in the table below
for different idealised boundary conditions:
stress introduced by the inertia load m(s)~(s)(2nf0 r.
Boundary Condition
C1
C2
C3
Pinned - Pinned
1.57
J.00
5.0 10·4 ~ 5.0 10·3
Pinned - Fixed
2.45
0.50
5.0 10· ~ 5.0 10·
Fixed - Fixed
3.56
0.25
5.0 10"6 ~ 5.0 10-5
5
4
3.7.6
Jf detailed infonnation is not available, the (unit diameter)
stress amplitude SA=ID may be taken from Figure 3-2 below.
The figure provides SA=ID divided by the boundary
coefficient C1 squared. Consistent boundary conditions for
evaluation of f0 and SA=ID must be applied.
The coefficients C 1 and C2 relate to the bending stiffness
tenn and axial force tenn in section 3.7.2, respectively. They
are theoretically correct for a rectilinear pipe while C3 is an
DET NORSKE VERIT AS
16
Guidelines No. 14
June 1998
300
.
250
'iO
Cl.
!.
.............. ··········· ····1··
\
200
\
0
150
100
nt
\
'\ \
\
'
..
.. ·. ..
, • • ••
.
__________ _.1 . . . . . . . .-
\..,
'
'
I
·
o,
..
: .............
.
I
~
··- ... :
50
·
. -... fixed ..fixed
- - - pinned-fixed
···--------~~ ---··
·:·..
ame er max mum
ress Ampll u e
scaled wrt boundary coefficient C1 2
-.:·-···---------·-:. .. ···········-:·--r-----.---.--..--'-r-.
.
- - ptnne -ptnn
.. .
:
.. . :: ' ' '' . .
......... : ·....... :
.:..
...
..
:
..:
.
.
.
··········:--··············~···············:············ ··1·············-·r··············
:
............... ,............... .
...\ , ..... ..
N
~
.:..
...
..
·•••••••·•·•·•· ···········---,······································ ······················· ··· ········· ······ · , ••..••..••••••.
..,, ....................... ...'
.. ..................................
...
..
..
'11.... .....
....•..•.•..... ; ....•...••. .•• )::.-:.:::: . •.•
-~.·:·-~-~-~~~+
..:":------....
· - -- ~·-··
... ... .. ..; ... .
-- -:-. ______ _
. ........ .. ·:........... .. ' ... ; .....-: .~.- -
O +----~---~---.-;-----:-----::-----:-----:------l
40
50
60
90
70
100
110
120
Figure 3-2 Unit outer diameter maximum stress amplitude
3.7.7
•
The fatigue damage from higher order modes must be
considered. The following approximate response quantities
may be applied:
4.1.2
f 2 = (2-3)f0
S2 = 2SA=ID
where f2 and S2 is the frequency aud w1it diameter stress
amplitude related to the 2"" mode shape.
4. Geotechnical Conditions
4.1 General
4.1.1
The soil is to be classified as cohesive (clays) or cohesion less
(sands). Rocks may be treated as hard clay. As basis for the
evaluations of the pipe-soil interaction the following basic
soil parameters are ofrelevance:
•
•
•
•
•
general soil data as submerged specific weight, void
ratio, water content and plasticity limits.
If the approximate soil stiffness expressions in section 4.3
are to be used the following specific parameters are of
relevance:
•
•
•
•
•
•
•
submerged unit weight of soil (wsoit)
Poisson's ratio (v)
void ratio (e5)
angle of friction, cohesionless soils ( q>5 )
undrained shear strength, cohesive soils (Su)
over-consolidation ratio (OCR)
plasticity index, cohesive soils (ip).
4.1.3
The parameters defined above should preferably be obtained
by means of geotechnica\ tests on undisturbed soil samples,
and be representative for the particular geographical location
of the pipeline. In ·case 110 detailed infonnation is available,
the values given in Table 4-land Table 4-2 may be used.
type of soil
in-situ stress conditions
shear strength parameters for drained or undrained
condition including remoulded shear strength for clays
soil moduli and damping coefficients as function of
cyclic shear strain
soil settlement parameters
DETNORSKE VERITAS
17
Guidelines No. 14
June 1998
Soil type
<p.
Wsoil
[kN/m
4.2.3
es
v
3
The axial and lateral frictional coefficients between the pipe
and the seabed shall reflect the actual seabed condition, the
roughness, the pipe, and the passive soil resistance.
]
Loose
30°
9.1
0.35
0.7
Medium
35"
9.6
0.35
0.5
Dense
40°
10. J
0.35
0.4
Table 4-1 Typical gcotech mcal parameters for sandy
soils
Soil type
Cu
[kN/m3 ]
Wsoil
[kN/m3 ]
v
es
Very soft
5
4.4
0.45
2.0
60
Soft
17
5.4
0.45
1.8
55
Stiff
70
7.4
0.45
J.3
35
Hard
280
9.4
0.45
0.8
20
Ip
l%J
Table 4-2 Typical gcotechnical parameters for clay
(OCR=l).
4.1.4
The uncertainties in the soil data should be co11sidered. lt
may arise from variations in soil conditions along the
pipeline route and difficulties in detennining reliable in-situ
soil characteristics of the upper soil layer, say, 0.02-0.05 m
for small diameter pipelines to 0.2-0.5 m for large diameter
pipelines.
4.2 Modelling of soil interaction
4.2.4
The axial and lateral resistance is not always of a pure
frictional type. Rapid changes in vertical stresses are (in low
permeable soil) reacted by pore water and not by a change in
effective contact sh·csses between the soil and the pipe. In
addition, the lateral resistance will have a contribution due to
the penetration of the pipe into the soil, which need to be
accounted for.
4.2.5
For sands with low content of fines, the frictional component
may be proportional to the vertical force at any time, whereas
for clays the 'frictional' component is more related to the
static vertical force for which the clay is consolidated.
4.2.6
Where linear soil stiffness have to be defined for the
eigenvalue analysis, the soil stiffness should be selected
conside1i11g the actual soil resistance and the amplitude of the
oscillations.
4.2.7
The soil stiffness for vertical loading should be evaluated
differently for static and dynamic analyses. The static soil
response will mainly be governed by the maximum reaction,
including some cyclic effects. Dynamic stiffness will mainly
be characterised by the unloading/re-loading situation.
4.2.1
4.l.8
The pipe-soil interaction is important in the evaluation of the
static equilibrium configuration and the dynamic response of
a free spanning pipeline. The following functional
requirements apply for the modelling of soil resistance:
The soil damping is generally dependent on the dynamic
loads acting on the soil. Two different types of soil damping
mechanisms can be distinguished:
•
•
•
•
•
The seabed topography along the pipeline route must be
represented.
The modelling of soil resistance must account for nonlinear contact forces nonnal to the pipeline and lift off.
The modelling of soil resistance must account for sliding
in the axial direction. For force models this also applies
in the lateral direction.
Appropriate (different) short- and long-tenn
characteristics for stiffness and damping shall be
applied, i.e. static and dynamic stiffiless and damping.
4.2.2
The seabed topography may be defined by a vertical profile
along the pipeline route. The spacing of the data points
characterising t11e profile should relate to the actual
roughness of the seabed.
•
Material damping associated with hysteresis taking place
close to the yield zone in contact with the pipe.
Radiation damping associated with propagation of
elastic waves through the yield zone.
4.2.9
The material damping is dependent on the relative stress
level in the soil, which again depends on the amplitude of the
pipeline oscillations at the contact points with the soil. The
contribution of material damping is more important for inline VIV than for cross-flow VIV, since in-line sliding
between pipe and soil may give larg~ hysteresis effects.
4.2.10
The radiation damping may be evaluated from available
solutions for elastic soils using relevant soil modulus
reflecting the soil stress (or strain) levels. The radiation
damping depends highly on the frequency of the oscillations,
and is more important for high frequency oscillations.
DETNORSKE VERITAS
18
Guidelines No. l4
June 1998
4.2.11
4.2.12
The modal soil damping ratio, ~oil> due to the soil-pipe
interaction may be determined by:
It should be emphasised that the determination of
pipeline/soil interaction effects is encumbered with relatively
large uncertainties stemming from the basic soil parameters
and physical models. It is thus important that a sensitivity
study is performed to investigate the effect of abovementioned uncertainties.
4,3 Approximate Soil Stiffness
where the soil damping per unit length, c(s), may be defined
on the basis of an energy balance between the maximum
elastic energy stored by the soil during an oscillation cycle
and the energy dissipated by a viscous damper in the same
cycle.
4.3.1
The following expressions may be llScd for the static, vertical
soil reaction per unit length as a function of the settlement, v:
Alternatively, the modal soil damping ratio, ~oii. may be
taken from Table 4-4 and Table 4-3. Interpolation is allowed.
LID
Clay
where
Sand
Soft
Medium
Hard
Loose
Medium
Dense
< 40
5.0
2.0
1.4
3.0
1.5
1.5
100
3.5
1.4
1.0
2.0
1.5
1.5
> 160
2.0
0.8
0.6
1.0
1.5
1.5
b
D
D
W 50
Table 4-3 Modal soil damping ratios in[%). Horizontal
(in-line) direction
{2J(D - v)v forv 5 0.5 D
forv >0.5D
n
Su
submerged unit weight of soil
undrained shear strength.
4.3.2
LID
Clay
Sand
Soft
Medium
Hard
Loose
Medium
Dense
< 40
3.0
1.2
0.7
2.0
1.2
1.2
JOO
2.0
1.0
0.6
1.4
1.0
l.O
> 160
1.0
0.8
0.5
0.8
0.8
0.8
The bearing capacity factors Ne. N~ and N.1 versus internal
friction angle cp., may be taken from Figure 4-1. For clayey
soils the friction angle is set equal to O", i.e. N,1 = 1.0 and
N0 =-= 5.l4.
Table 4-4 Modal soil damping ratios in[%]. Vertical
(cross-flow) direction
DETNORSKE VERJTAS
Guidelines No. 14
19
June 1998
100
~~~~~~~~~~~~~~~~~~~~··~~~
···!·.. -:-··"···1·· ·•i .. ..;. ....:.. •..:.•.•...•
•• •:• ••·:• ••i•••
i••• ••·t ·•·f,.. ...
•••j••.,
•1•• • ............ .... ... .
..............
. ....................
,. .. ~o ....................
··~---·~···~---~··· ···!··-~··+ · ..~··· ··-~··· ···~··+-·· ···l···i· .. -: ..
• •
o •
I
1
I
'
~-··
' ' ' .
·f ···r ·1· ··~- ·· ··· ~ - ·· ··-r ·--~- -----T ·-~ - · · ·;~- · ··~- --·(- -~·- -1··---:- ---:----:--·..f··· ···t···!- ···!····'· ··
- ·-;-- ..... - ·-.
: : : : : : : : : : :
: . : ; : : :
· ·1·
4
•
·;-··
~- ~•
•
0
•
•
•
•
·rr-r-r·
.
.
·
r ·-· · · ·
·· ·
..
r·r
··-~··· ··-~--·;.--
1 · · ·r ..:.....; ··
~···;
·r·r~·-·
z. .
'C
c
Ill
D"
'
10
···:---·:·-·-:·--~·-·
=···r
1· ·!· ·...\ ·i ...
?··· ...... T-r·:--·
r.
.. ....
.
.. .
..
.
.. .
. ..
. ..
........ .......
...._.......
..
'
o
o
I
..-
z
0
z
. . .
.
..
.
. .. ..
.
..
..
..
..
. ··.. ··········
. .
. ..
.......
........
..,..
.. .
. .. . .....,. ........
.. ..
... ..
..
I
1
0
20
10
.
.....
.
•
30
I
'
'
..
.
.
..
..
40
50
<p[degreeJ
Figure 4-1 Bearing capacity factors N0 , Nq and N 1 versus the internal friction angle <p1
4.3.3
4.3.4
The ma.'<imum static, axial soil reaction per unit length may
be taken as:
The dynamic soil stiffness in the vertical and horizontal
(lateral) direction may be taken as:
= 0.88-G
K
v
8
- clayey soils: R ~ = min~ ~µ , bTmax }
K1 =0.76 ·G·(l+v)
where:
Rvs
where:
vertical static soil reaction given by 4.3. l.
axial friction coefficient
b
1-v
G
given in section 4.3 . l
s~ -(O.S(l -bk,)R: )' is lhe soil shear strenglh
..fOCR(1-~)+(~)
2.61
200
200
1955-(2.97 -e,)
I +e
2
.Jcr:
sand
$
{kN/m2
2
{ 1300 ·(2.97-e,\ ,fci;(OCR)k,
I +e,
clay
effective soil stress in [kN/rn2] to be calculated as:
cr,= 0.75 WsoH b where b is given in section 4.3.1.
OCR
over-consolidation ratio
void ratio
The coefficient ks, may be taken from Figure 4-2.
D ET NORSKE VERITAS
20
Guidelines No. 14
June 1998
05
_,./
04
/
0.3
,.V
~
/ "'
02
,v
v
01
0
-
i--........
v
/
v
v
/
v
""'"'
-
/
7
-
1-- 1--
/
0
20
60
80
100
120
Plasticity index, ip
Figure 4-2 k. versus plasticity index, ip
CL<
4.3.5
0.5
lfno information is available on the dynamic axial soil
stiffness, it may be taken equal to the dynamic lateral soil
stiffness as described above.
ln-line direct ion: in-line loads may be
described according to Morison's
formulae, see section 9.2. In-line VIV due
to vortex shedding is negligible.
4.4 Artificial supports
Cross-flow direction: cross-flow loads are
mainly due to asymmetric vo1tex shedding.
A response model, see section 8.3, is
recommended. Alternatively a force model
may be applied, see section 9.3.
4.4.J
Gravel sleepers can be modelled by modifying the seabed
profile, considering the rock dump support shape and
applying appropriate stiffness and damping characteristics.
4.4.2
wave dominant - wave superimposed by
current.
0.5 <a < 0.8
The purpose of mechanical supports is generally to impose
locally a pipeline configuration in the vertical and/or
transverse directions. Such supports can be modelled by
concentrated springs having a defi ned stiffness, taking into
account the soil defonnation beneath the support and
disregarding the damping effect.
wave dominant- current superimposed
by wave
In-line direction: in-line loads may be
described according to Morison's
formulae, see section 9.2. In-line VIV due
to vortex shedding is negligible.
Cross-flow direction : cross-flow loads are
mainly due to asymmetric vortex shedding
and resemble the cu1Tent dominated
situation. A response model, see section
8.3, is recommended. Alternatively a for~
model may be applied, see section 9 .3.
5. Hydrodynamic Description
5.1 Flow regimes
5.1.1
The current flow velocity ratio, a=UJ<Uc+Uw}. see 5.2.6,
may be applied to classify the flow regimes as follows:
DETNORSKE V ERITAS
21
Guidelines No. 14
June 1998
current dominant
a.> 0.8
In-line direction: in-line loads comprises
the following components :
a steady drag dominated component
a oscillatory component due to regular
vortex shedding
For fatigue analyses a response model
applies, see section 8.2. In-line loads
according to Morison's formulae may,
however, still be present.
Cross-flow direction: cross-flow loads are
cyclic and due to vortex shedding and
resembles the pure current situation. A
response model, see section 8.3, is
recommended. Alternatively a force model
may be applied, see section 9.3.
Note that a=O correspond to pure oscillatory flow due to
waves and a.=l correspond to pure (steady) current flow.
The flow regimes are illustrated in Figure 5-l.
6
••••••••••• •• •••• ··-·· •••••••• ··-········ · ••••• .••••• •• ••••••••..•.••••. ••• • •••• ••.••••••••••••••••••••
······1r-··--·······t··· .............. ·t ·····;···-····:: ..
• • ••
4
•• •• •
'
current dominated
••• •
'•.
.. / ··, ·· ·· ·· ······ ········ ..' .-.. .......................
,
,,.,,,,. "
,
. ,• •
J a=-0.s J~
'
: ••••••••••••••••••••• •••,.tl.QW .......... ....
'
+. ..:....
wave dominated llow ' •,.
+······················
,,.
·. ._
.. ·'
. . ·'"~··•<. ....... .
-,<.'. .......................... ........
·1
··········· ·····-············ • • .
·2
............. . . ................. ... ............ .............................. ........... .
time
Figure 5-l Flow regimes
•
5.1.2
Oscillatory flow due to waves is stochastic in nature, and a
random sequence of wave heights and associated wave. .
periods generate a random sequence of near seabed orbital
oscillations. The following definition oftl1e wave induced
flow velocity amplitude, Uw, applies:
•
In case of a fatigue analysis based on decomposition of
sea states into single random waves, Uw corresponds to
each single velocity amplitude at pipe level.
In case of a fatigue analysis based on characteristic
harmonic oscillation representing an entire sea state the
characteristic velocity amplitude, Uw*, applies, see
section 6.3.
DET NORSKE VERITAS
22
Guidelines No. 14
June 1998
5.2 Hydrodynamic parameters
where fw is the wave frequency.
5.2.1
5.2.6
Vortex induced vibrations (VIV) and direct wave actions are
affected by several parameters, such as:
The current flow velocity ratio, a, is defined by:
Reynolds number, Re
Strouhal number, S1
reduced velocity, VR
Keulegan-Carpenter number, KC
current flow velocity ratio, a
flow angle relative to the pipe. Herein, only the
component normal to the pipe axis is to be considered
pipe roughness, (k/D)
gap ratio (seabed proximity), (e!D).
•
•
•
•
•
•
•
•
Herein a brief introduction of the basic hydrodynamic
parameters is given. For a thorough introduction see e.g.
Sumer & Freds0e, (I 997) and Blevins ( 1994).
Vortex shedding from pipe is a function of Reynolds
number:
e
The pipe roughness influences the boundary layer on the pipe
and thereby the vortex shedding. The effect of pipe
roughness in t11e range 0.005 < (k/D) < 0.02 is..implicit in the
response models.
5.3 Seabed proximity
5.3.l
The gap is defmed as the distance between the pipe and the
seabed. The gap used in design, as a single representative
value, must be characteristic for the free span
5.2.2
R
5.2.7
= UD
•
•
v
where U is the flow velocity, Dis the outer pipe diameter of
the pipe (including any coating) and v is the kinematic
viscosity ("'='l.5·10·6 [m2/s] ).
5.2.3
The vortex shedding frequency in steady cun·ent or regular
wave flow with KC numbers greater than 30 is approximated
by:
5.3.2
The presence of a fixed boundary near the pipe (proximity
effect) has a pronounced effect on the response, e.g.:
•
•
where fs is the vortex shedding frequency, Uc is the current
velocity and Uw the wave induced velocity amplitude normal
to the pipe. The Strouhal number, S" is a function of Reynolds
number and other parameters.
For in line VIV the gap may be calculated as the average
value over the central third of the span.
For cross-flow VIV, the gap may be taken as the
maximum modal pipe deflection (vertical) allowed by
the presence of the sea-bottom.
•
•
The physics of pipe vibrations close to a boundary (i.e.
the seabed) is different from the physics of a vibrating
free pipe.
The alternating vortex shedding is suppressed for small
gap ratio (typically for (e/D) < 0.3); however selfexcited vibrations (cross-flow) still take place initiated
by fluctuations in the hydrodynamic lift force.
Significant vertical oscillations exist for (e/D) < l at
oscillatory flow conditions (i.e. a < 0.5) with a vibration
frequency twice the wave frequency.
The drag coefficient C 0 and inertia coefficient CM
increase in the proximity of the boundary.
5.2.4
The reduced velocity, YR, is in the general case with
combined current and wave induced flow, defined as:
V _ Uc+Uw
R -
5.3.3
Details on seabed proximity effect may be found in the
literature, (see Sumer & Freds0e, 1997). Herein, the effect of
the sea-bed proximity is treated conservatively, i.e.:
foD
where f0 is a natural frequency for a given vibration mode.
5.2.5
•
•
For in-line VIV, any mitigation effect is ignored.
For cross-flow VIV the sea-bed effects (for e/D < 0.5) is
introduced conservatively in t~e Response Model using
a simplified approach.
The Keulegan-Carpenter number, KC, is defined as:
DET NORSKE VERIT AS
23
Guidelines No. 14
June 1998
6. Environmental Conditions
6.1 General
6.1.1
The objective of the present section is to provide guidance
on:
•
•
•
the long term current velocity distribution
short-term description of wave induced flow velocity
amplitude and period of oscillating flow at the pipe level
long term statistics
6.2.2
When detailed field measurements are not available, the
tidal, wind and stonn surge driven current velocity
components may be taken from Classification No. 30.5. For
current measurements, data analyses and transfo1mations of
current characteristics reference is given to the MULTIS PAN
Design Guideline, (1996).
6.2.3
For water depths greater than 100 m the ocean currents can
be characterised in tenns of the driving and steering agents:
•
to be applied in fatigue assessment in section 7.
6.1.2
The environmental data to be used in the assessment of the
long-term distributions shall be representative for the
particular geographical location of tl1e pipeline free span.
6.1.3
The fl.ow conditions at the pipe level due to current and wave
action gov em the response behaviour of free spanning
pipelines. The principles and methods as described in
Classification Note No. 30.5 may be used in addition to this
Guideline as a basis when establishing the environmental
load conditions.
6.1.4
Preferably, the environmental load conditions should be
established near the pipeline using measurement data of
acceptable quality and duration. The envirorunental data
must be collected from periods that are representative for the
long-term variation of the wave and current climate,
respectively. In case of less reliable or limited number of,
wave and current data the statistical uncertainty should be
assessed and included in the analysis if significant.
6.1.5
The wave and current characteristics must be transferred
(extrapolated) to the free span level and location using
appropriate conservative assumptions. The level of the free
span is defined relative to the mean water (surface) level
(MSL) by the distance from the top of the pipe to the MSL.
In case of large free span deflection, the top of the pipe
should be taken as the average over the pipe span.
The driving agents are tidal forces, pressure gradients
due to surface elevation or density changes, wind and
sto1m surge forces.
The steering agents are topography and the rotation of
the earth.
•
The modelling should account adequately for all agents.
6.2.4
The distribution type for the long-term current velocity
distribution should be selected based on the physics and
experience. Normally a 3-parameter Weibull distribution is
considered representative:
where F( •) is the cumulative distribution function. a.c, Pc and
Ye are Weibull distribution parameters and U0 is the current
velocity.
6.2.5
Directional infonnation of the current velocity may be used
in the analysis. If no such infonnation is available, the
current should be assumed to act perpendicular to the axis of
the pipeline.
6.2.6
The current velocity profile in the boundary layer in areas
where flow separation does not occur may be taken as:
6.2 Current conditions
6.2.1
The steady current flow at the free span level may be a
compound of:
•
•
•
•
tidal cun-ent
wind induced current
stonn surge induced current
density driven current.
where:
V*
friction velocity
K
von Kannan's constant ( = 0.4)
z
elevation above the seabed
reference measurement height
Zo
DET NO RS KE VERIT AS
bottom roughness parameter to be taken as:
24
Guidelines No. 14
June 1998
Seabed
6.3.3
roughness 7<1 (m)
Silt
: : : 5 10"6
fine sand
<::!
medium sand
::::: 4 10-s
coarse sand
: : : 1 10·4
Gravel
~ 3 10·4
Pebble
-"" 2 10"3
Cobble
:::::: I 10·2
Boulder
""'4 10·2
Directional short-crested wave spectra may be required for a
complete statistical description of the sea. The directional
spectra accounts for the spreading of wave energy by
direction as well as frequency. It may be derived from the
non-directional wave spectra as follows:
l 10·5
S,1,1( (l),O)=S,1,1(co)w(O)
where:
a spreading angle measured from the mean
(main) wave direction, and
the wave energy spreading (directional)
function. A frequency independent cosine
power function is normally applied:
The non-linear interaction between wave and current flow
results in a modification of the steady velocity profile due to
an apparent increase in the seabed roughness. The hereby
introduced reduction factor may be taken from DNV RP
E305, (1988).
6.2.7
The mean current velocity over a pipe diameter (i.e. averaged
over the external pipe diameter, D) should be applied in the
analyses. It may be assessed assuming a logarithmic mean
velocity profile:
6.3.4
e+D
J
The vclocily spcchUm at the pipe level may be obtained
through a spectral transfonnation of the waves at sea level
using a first order wave theory, i.e.
U(z)dz = U(zr)· Re
Uc(z 0 )
=
Re
=a reduction factor
e
=
1
ln(zr I z0 )
r(-) is the gamma function ands is a spreading parameter,
typically modelled as a function of the sea state. Normally s
is lakcn as a real number, SE [2;8]. For larges, the energy is
concentrated around the main wave direction.
for the current
{(..:.+1)1n((e + D)!z0 }-(..:.)1n(e/ zo}-1}
D
D
where e is the gap and z 0 is the height to the mid pipe.
6.3 Short-term wave conditions
6.3.1
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.
6.3.2
The short-term, stationary, irregular sea states may be
described by a wave spectrum S~~(co), i.e. the power spectral
density function of the sea surface elevation. Wave spectra
may be given in table fo1m, as measured spectra, or in an
analytical form. Jn Classification Note No. 30.5, the
commonly used JONSWAP or PM spectra are described in
detail.
'
-
2
-
Suu(co,0) = G ((l))S'1 11 (<o,0)
where:
Suu (co,6)
the wave induced t1ow velocity spet:trum at
pipe level, and
G(ro)
a frequency transfer function given by
G(ro) = oocosh{k(D + e))
sinh(kh)
where:
2nfw is the angular wave frequency and
wave frequency
t~v
is the
k
wave number
D
e
gap between pipeline and sea bed
h
water depth to the sea bottom.
DETNORSKE VERITAS
25
Guidelines No. 14
June 1998
6.3.5
The spectral moments of order n is defined as:
"'
•
M0 = JronSuu(ro)dro
Bandwidth parameter:
f.=~1 - MoM4
M~
0
The following spectrally derived parameters appear:
•
Significant flow velocity amplitude at pipe level:
•
Mean zero upcrossing period of oscillating flow at pipe
level:
The process (spectrum) is narrow-banded fore~ 0 and
broad banded fore ~ l (in practice the process may be
considered broad-banded fore larger than 0.6). Us, Tu and e
may be taken fromFigure 6-1, Figure 6-2 and Figure 6-3
assuming linear wave theory. In the figures, Tn is a
normalisation period and y is the JON SWAP spectrum
peakedness parameter.
0.5 .--·~--~
····--· --- ·····-···· i ··········· · ··· · ··· · · · · ·· ···:·· · ··· · ··· · ··········· · ··· · ·~·-··························:. ······ . . ·····················:
-~~
~:i...
":
;;
1
' ,,-
~
:
0.2
i
:
:
:
:
:
:
.
::
'
......................... , : r=l.0; 3.3; 5.0
'.
I
"\, :
:
rT~-~--·--·-----·--l···
i
~
=
:
.
.
i
.
..................... .
. . . . . . .·-. ····-y---.......................,
:
.
.
...
. -... -.- ....... -... -...............
.................... -·---·---,..-------- ---·-·-·-------·- ·--,·-·-·-·-·---·-·-·
...
....
.
.
.
0.1
o.o
i
:
........ .. .................; ............ '!\, ..... -·~ ···························i············· ···············~·-··· · ·······················i
0.3
~
p
j
:
.........................\..l~----·······-········· ·· ··· l ·· · ··· · ··· · ··· · ··· · ··· · · · · · -~·····························=··········· · ··········· ··· ···=
! ~
l
:
j
!
0 .4
~
;
:
:
~-
-~·......
i
-~
.
L ___j__ _ __J_____i__=::::::l:::::::::::===d
0.0
0.1
0.2
0.3
Figure 6-1 Significant wave induced flow velocity amplitude, Us
DETNORSKE VERrTAS
0.4
0.5
26
Guidelines No. 14
June 1998
-.. -- .......... -.-·-..... ,.........................................
. ---·--·· ..... --.... .. -·--· ... .-.......... ·- -...- ·-.......... ·---·--· ..... -- ....
l.S
....
..
.
..
1.4
1.3
·······-·············--·1················-·--······r··· 1
1.2
.
. .......... ·········I·
...................... ··:··········
.......·········:·····
.
.
:
:
- ~~~~~~~~
~
... ............ ........... ·-~· ..... ...................... . ·-·r.... ···--
..,..,.
........
: _
~-~-~;·:.:·:;~1 -· ·
0.9
,,.,,,
0.8
..-".
'/"
:
o
o
I
···················1·························1·················-······r··· ····················1
:
:
:
:
:
:o
;o
:
0
I
'
+
o
I
0.1
0.2
0.3
····· ..1.....·-· ·············-··r··-······ ····-· ······· i·-·· ·· ·· ·· .. ············-:-·...:.r..;,;c'hi;;)·o:s ..·--1
n
:
~
0.7+-~~~~~~+
· ~~~~~~-+· ~~~~~~~·,__~~~~~--+~~~~~~-i
0.0
0.5
0.4
Figure 6-l Zero-up-crossing period, T"
.·. ·. :... : ': . :· ..·.:.: ·_] ·_· ·:· ·_ · :· :· ·:I :· ... . ..L.· _ : ·_ .
0.8
0.7
\;
I
.
I
I
0
0.6
.......... ~-~~··· .. --·1··········.. -· .. -· ..······r·························1·················· ..·····+········ ·-·-· --· -··· ··-~
0.5
· · · · •· · · • · · · · · ·· ·r~
0.4
········· ··· ···- ····--·-{-·, ., . . . .. ··· ·· ···· ·····:---
.
-~,
-~
:.
'."' · ·· ·· -- -- ·· · · · · - ·-- ··· ~ ·: ·-·· ·· ·· ··· · ·· ·· · · · · ··· · · 1• • ••• • ••• • •• • • • • • • • • ••• • • -:- •• • •• • • •• • • • • • • • • • • ••• • •-~
·~'\
(.I)
...
....
.
l
·1
...
:: Iii'"', ~
'
0.3
y=l.0; ,3 .3;5.0
I
::
:
j
,
.....................; ...............................;.. ---------- .. -- .......... ,.:
::
-.. . . .
~--=---,.~
........... ... ................ ~---········ ·· ·· ·· ··· · ·:- ··--···-··· ···- ···-·· ·--:-· ···- ·· - ···· ····-------·:··· ·
0.2
:
l.
........ ........_.......
- ~-
.
...... . ;-..;,:
I
-
.. ........ ..............l.................···· ··-·1--··-··-··-···········l··-··~-· ··-··-......(.. ·-T~;(higjo.s· ·· ··- ·~
'
0. 1
.
..
.
0.1
0.2
0.3
..
'
0+-~~~~~~~·~~~~~~-+~~~~~~-+' ~~~~~~-t-~~~~~---1·
0.0
Figure 6-3 Bandwidth parameter s
DETNORSKE VERITAS
0.4
0.5
27
Guidelines No. 14
June 1998
where:
6.3.6
The effect of wave directionality and wave spreading may be
introduced in the form of a reduction factor on the significant
flow velocity amplitude, i.e.:
mean (main) wave direction
direction perpendicular to the pipeline
sub-direction around mean wave direction
spreading function, see section 6.3.3.
w
Ro is a reduction factor given by
Values for Ro as a function of directionality and wave
spreading may be taken from Figure 6-4.
l.O
r-"-·-----·-_.._.._
········-·r ·---·---·--·--
-- ·--·.l·-·····-···-···-.. ·-·..r.·············· ..··- .... !. ···-·······-·-· -
_::.:::.:.:-_::+ ....
.. - .. - .. - .. _ - ..::- - ~ .,
:
---·------· - .. ......... -~ .•.: . :. _., . ..-::;.-t; . .
0.8
:
:
.
'
"'' t
....
~
'
o
:
:
~ ~.....
..
I
-- ........................ :···············-·--- ···:··-···-···-···" .......
.... .
~
C'-1
~
:
.................... ·-·: ····· ............ )
:
'
·.:.·:····
,~..... ,
I
:
1
• :.
~ ~~ -
:
=
·~ 0.4
.
:
. .. ~--------··· ............... -~· .............. ·------· ;.......... ---... -- -......... :
...... --:, ~ ·
::; 0.6
:
:
,
:
···········-~---
.......... .
.................. •'
.... ,
:· • • • •
.
"":..._
.....::
.:
.
.
.. -·· .. . . . ... ···· · ·····-~·-···-·
... --·· ··· · ··· ·· ····~·····
. - ·······--· - · ··-·-·· .f ............................:
... · ·-· · ·-··· --·---·--i-...
..
i:z::
0.2
....;
··-s=8
.
0.0
s=2
.... ,
....................... f.........>.~.::;-: .~:~- ~:: .":" . -:-., . ~ .~~
:
...;
'
.
s = 100 :
- 1 - - - - -- - 1 - - - - - -- 1 - -- - - - -1 - - - - - - - l - - - -4.-- - - 4
0
20
60
40
80
100
Figure 6-4 Reduction factor due to wave spreading and directionality
6.3.7
The short-tenn flow velocity may be taken as a narrow
banded stationary Gaussian process. The short-term local
maxima for a given sea state (i.e. conditional on the
environmental sea state vector e, see section 6.4) of the
wave-induced flow velocity amplitude perpendicular to the
pipeline axis, Uw, is then given by the Rayleigh distribution:
may be characterised by an environmental sea state vector
E>=(H., Tp, 9w)T comprising:
Hs
significant wave height defmed as the average of
the upper third of the wave heights
TP
peak period
ew
main (mean) wave direction, measured relative to
a given reference direction
in addition to a selection of a wave spectrum and a
directional spreading function.
6.4.2
6.4 Long-term statistics
e
6.4.1
The wave climate at a given location may be characterised
by a series of short-term sea-states. Each short-term sea state
The long-tenn variation of are normally described in terms
of a scatter diagram. The data sets of wave observations may
be sorted with respect to the main wave directions if
directional buoy or hindcast data are available with statistics
DET NORSKE VERIT AS
28
Guidelines No. 14
June 1998
on the observations for different sectors. Otherwise, the
statistical properties may be assumed identical for aJI sectors.
In some locations also the joint environmental probability
density function providing a continuous representation for
e or ranked sets of wave height and associated periods are
available.
7.1.3
The fatigue acceptance criteria in this guideline are based on
the interaction free Palrngren-Miners damage rule. The
fatigue analysis requires suitable SN-curves for the actual
pipe. The SN- curves must be applicable for the material,
construction detail, state of stress and corrosive environment
7.'1,4
6.4.3
The fatigue analysis is normally most conveniently
performed using a scatter diagram. Thus, the fatigue damage
is evaluated in each cell in a scatter diagram in tenns ofHs,
Tp and 8w times the probability of occurrence of the (shorttenn) sea-state followed by a summation over all sea-states,
see 7.2.5.
6.4.4
Alternatively, the fatigue analysis may be based explicitly on
the long-term wave induced flow velocity at the pipe level,
see 7 .2.4. In this case, the long-tenn wave induced flow
velocity distribution may be derived from a set of stationary
short-term sea states:
The concept adopted for the fatigue analysis applies to both
response models and force models. The stress ranges to be
used may be detennined by:
a response model, see section 8
a force model, see section 9.
•
•
The stress ranges and natural frequencies should nonually be
obtained from a FE-approach. Requirements to the structural
modelling and free span analysis are given in section 3.
7.2 Fatigue criteria
7.2.1
The fatigue damage assessment is to be based on the
accumulation law by Palmgren-Mincr:
fuw(Uw)= Jfuwie(Uw 19)dFe
E>
where
f Uwl0 ( uw I e) is the conditional short tenn
probability density function for Uw defined by 6.3.7 and Fe is
the distribution function for the environmental sea state
vector 0, e.g. represented by a scatter diagram or given
explicitly by a joint envirorunental probability distribution.
7.1 General
Vibrations due to vortex shedding and direct wave loads.are
allowed provided the fatigue criteria specified herein are
fulfilled.
The following functional requirements apply:
•
Tl
a llowable damage ratio
summation over all stress fluctuations in the
design life.
=
Ni is the number of cycles to failure at stress range S; defined
by the SN curve (see section 7.3):
where:
7.1.2
•
accumulated fatigue damage
7.2.2
7.1.l
•
Drai
~
7. Fatigue Analysis
•
where:
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 are to be performed at
all free spanning pipe sections accowiting for damage
contributions from all potential vibration modes related
to the actual and neighbouring spans.
m
fatigue exponent (the inverse slope of the SN curve)
C
characteristic fatigue strength constant.
7.2.3
ni is the number of cycles corresponding to the stress range S;
given by:
where:
DETNORSKE VERITAS
29
Guidelines No. 14
June 1998
probability of a given flow condition
dominating vibration frequency of the considered
pipe response
time of exposure to fatigue load effects (i.e.
design life).
In the analyses, the reduced velocity, VR, the KeuleganCarpenter number, KC, and the current flow velocity ratio,
«, are replaced by "significant" substitutes defined as:
v;
Uc+ U~v
KC*
~
7.2.4
When several potential vibration modes may become active
simultaneously at a given current velocity the mode
associated with the largest contribution to the fatigue damage
must be applied. Formally, the fatigue damage criteria may
be assessed numerically as:
where:
vector of environmental parameters. In the
response model approach it comprises the
non-dimensional hydrodynamic parameters:
A=(VR, KC, o:)
A
S(A)
stress range for a given outcome of A
F,.. (A)
long tenn probability distribution (vector-)
function for A, e.g. derived from section 6.2
and 6.4.
a
Dra1 = T~e ·
L
H,,Tp,9w
u•
fwD
Uc
.
u:v
An asterisk * indicate that the wave induced flow velocity
Uw is represented by the significant flow velocity. Thus,
Kc• is assumed constant in each sea-state while Vi and«•
will vary due to the variability in the current velocity. The
following comments apply:
•
•
•
•
The fatigue damage may be evaluated independently in
each sea-state, i.e., the fatigue damage in each cell in a
scatter diagram in tenns of Hs, Tp and 9w times the
probability of occurrence for the individual sea state.
In each sea-state (Hs, TP• 6w) is transformed into (Uw *,
T 0 , 9w) at the pipe level as described in section 6.3.
The sea state is represented by a significant short-tenn
flow induced velocity amplitude Uw * with mean zero
upcrossing period Tu, i.e. by a train ofregular wave
induced flow velocities with amplitudes equal to Uw *
and period T0 • The effect of irregularity will reduce the
number of large amplitudes. It may be accounted for if
properly docwnented.
Integration over the long-term current velocity
distribution is perfonned in each sea-state.
00
Pr(•)
Jmax(rvs(v~;cx• ;Kc•f }Fuc ~11
O
7.2.6
Unless otherwise documented the following assumptions is
recommended:
where
probability of occurrence for the given sea-state
(Hs, Tp, 9w)·
s
foD
Uc+
7.2.5
For practical applications the following approximate fatigue
damage criterion applicable to both in-line and cross-flow
VIV is recommended:
long-term distribution function for the current
velocity.
dFuc
stress range determined from the response
models given in section 8.
•
•
•
The current and wave induced flow components at the
pipe level are statistically independent.
The current and wave-induced flow is co-linear.
Omni-directional environmental data are considered
appropriate.
dominating vibration frequency to be taken as
(response model):
7.3 SN-curves
fv= 2fw: for (KC< 5) or gap ratio (e/D) < 0.3
The SN-curve is on the form
fv = f0,c,: vortex induced cross-flow motion
N=C
fv= fo,cr: cross-flow induced in-line motion
7.3.l
.s-m
where:
fv= f0,u: vortex induced in-line motion,
where f0,n, fo,cr are the in-line and cross-flow
natural frequencies
DET NORSKE VERIT AS
30
Guidelines No. 14
June J998
N
number of cycles to failure at stress range S
s
stress range, i.e. the double stress amplitude S
= (Smax - Smin) SCF
SCF
Stress Concentration Factor
m
fatigue exponent (the inverse slope of the SN
curve)
C
characteristic fatigue strength constant defined
as the mean-minus-two-standard-deviation
curve.
•
f
•
•
7.3.2
For girth welds that are symmetric with respect to the
weld root the F2 curve, with C=4.3-10 11, m=3.0 and
SCF= l .O is recommended.
For girth welds that are not symmetric with respect to
the weld root the F2 curve with SCF accounting for
(eccentricity) fabrication tolerances is recommended.
The transition of the weld to base material on the outside
of the pipe can normally be classified as E, with
C= l.0·10 12 , m: 3.0 with SCF accounting for
(eccentricity) fabrication tolerances.
If not implicit in the applied SN-curve, a Stress
Concentration Factor (SCF) due to potential geometrical
imperfections in the welded area must be applied. Stress
concentrations may be due to eccentricities resulting from
different sources:
7.4 Safety factors
•
•
•
The reliability of the pipeline against fatigue loads is ensured
by use of tl1e safety class concept. The safety class concept
accounts for the failure consequences, see the Rules for
Pipelines.
concentricity i.e., difference in diameters of joined pipes
difference in thickness of joined pipes
pipe out of roundness or centre eccentricity.
The resulting eccentricity &may conservatively be evaluated
by a direct summation of the contribution from the different
sources. If no detailed information is available, the following
conservative fonnula may be applied:
SCF = 1+3 . & -e- (D/t)--0
7.4.1
The following safety factor format are used:
5
7.4.2
t
7.3.3
A cut-off (threshold) stress range below which no significant
fatigue damage occurs is normally not to be used in the
fatigue analyses.
Yr, Yt and Ys denote partial safety factors for the natural
frequency, stability parameter and stress range respectively.
The set of partial safety factor to be applied are specified in
the table below for the individual safety classes:
Safety Class
Safety Factor
7.3.4
Low
The SN-curves may be determined from:
•
•
•
dedicated laboratory test data,
fracture mechanics theory, or
accepted literature references, see e.g. NORSOK, (1998)
and Classification Note No. 30.2.
If the SN-curves are detennined by a fracture mechanics
approach an accepted crack growth model with a
conservative initial defect hypotheses must be documented.
Guidelines for conducting an Engineering Criticality
Assessment using a fracture mechanics approach may be
found in BSI PD6493, (1991). Consideration should be given
to the applied welding and Non - Destructive Testing
specifications applicable to the weld.
7.3.5
If detailed infonnation is not available the following apply
for cathodically protected carbon steel pipelines:
l
Normal
11
0.6
"ff
1.3
Yk
1.3
'Ys
l.05
l
1.3
I
High
I
1.55
7.4.3
For the in-line VIV acceptance criterion the above set of
safety factors have been calibrated to specified target
reliability levels in compliance with the Rules for Pipelines
using a reliability based approach, see M0rk et al., (1997).
For the cross-flow VIV acceptance criterion the above set of
safety factors normally apply. However, the applicability
should be evaluated on a case to case basis.
The safety factors ri and Ys are considered to be valid in
general and thus also applies for force models while
appropriate values for Yr and Yk should be evaluated on a case
to case basis.
DET NORSKE VERIT AS
31
Guidelines No. 14
June 1998
7.4.4
8.1.2
\llR is a reduction factor normally to be set to 1.0. It may be
set to 0.9 if the free span is well defined. A well defined free
span may be defined as:
In the response models, in-line and cross-flow vibration are
considered separately. Damage contributions from both first
and second in-line instability regions in current dominated
conditions are included. Cross-flow induced additional inline VIV resulting in possible increased fatigue damage is
considered approximately, see 8.2.2.
•
•
•
A free span scenario with well defined boundary
conditions, i.e. where the free span length (or sequence
of free span lengths) and consequently the natural
frequency is insensitive to changes in the functional
loads.
A free span scenario with high precision artificial
supports.
A free span where a reduced variability (increased
knowledge) can be documented through pre-intervention
(post-operation) frequency measurements.
8.2 In-line VIV in current dominated conditions
8.2.1
The fatigue criterion specified in this section applies to
current dominated situations. In case of a <0.8 or
equivalently a·<o.5 (see 7.2.5) in-line VIV may be ignored.
7.4.5
8.2.2
Comments:
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 (1.0<VR<2.5) and the second instability
region (2.5<V R<4.5) are included in this section. ff no other
information is available the cross-flow induced in-line VIV
should be accounted for approximately by taking the
maximum of the in-line VIV amplitude or 50% of the crossflow VIV amplitude for the given VR· The cross-flow VIV
amplitude may be taken from section 9.
Recent industry practice implies TJorr0.1 in case of no access
and llotd=0.3 in case 9faccess combined with 'YF'Yk=rs=l.O
using somewhat different response models e.g. as reflected in
(DNV, 1981). Usually the case TJord=0.3 is not allowed for
submarine pipelines in practice. Note that the present format
does not explicitly distinguish between access and no access
but rather implicitly using a safety class philosophy.
Detailed studies have revealed that existing practice,
although acceptable on average, provides design with very
varying reliability levels dependent on the stability
p arameter, natural frequency, stress amplitudes, etc.
The design format specified herein applies a set of 4 safety
factors in order to control these dominant uncertainty sources
rather than one usage factor, TJ. Due to this, the proposed
design fonnat is more flexible and provides design with a
more uniform reliability levels compared to industry
practice. On average the difference in the resulting safety
level is minor when applying appropriate response models
for the "old" industry practice and the approach proposed
herein.
8.2.3
The amplitude response depends mainly on the reduced
velocity, VR, the stability parameter, Ks, the turbulence
intensity, I" and the flow angle, 0 relative to the pipe. The
Reynolds number, Re. is not explicit in the evaluation of
response amplitudes. Further, mitigation effects from the
seabed proximity, (e/D) is conservatively not included.
The stress range S is calculated by the In-line VlV
Response Model:
S = 2 · SA~ID · R l6 ·(Ay I D)· A.rnax ·'I' mod · Ys · ljlR
where:
8. Amplitude Response Models
unit stress nmplitLlde (stress due to unit
diameter in-line mode shape deflection)
8.1 General
8.1.1
Amplitude response models are empirical models providing
the maximum steady state 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 full-scale tests for the following flow conditions:
•
~
•
in-line VIV from steady current
cross-flow VIV steady current
cross-flow VIV from combined wave and current.
Rio
amplitude reduction factor accounting for
the turbulence intensity and flow angle
(Av/D)
non-dimensional in-line VIV response
amplitude
'Ys
safety factor to be multiplied on the stress
range, see section 7.4
factor depending on the free span scenario,
see section 7.4
Amax
The response models are in agreement with the generally
accepted concept of VIV.
DET NORSKE VERIT AS
transformation factor to be taken as:
32
Guidelines No. 14
June 1998
. - {I
)..
max -
8.2.S
in case of a constant amplitude response
r(I + m /2)11m in case of a narrow· banded Gaussian process
where m is the fatigue exponent.
vR,d = VR 'Yr
Ks,d =Ks l'Yk
8.2.4
The mode-shape parameter, !fmod, accounting for the
flexibility of the span is defined as:
f~ 2 (s)ds
lj/mod
=~max L.J
where Yr and yk are safety factors related to the natural
frequency and damping respectively, see section 7.4.
1/2
Interpolation for different values of the stability parameter is
allowed. The figure provides maximum values. The
corresponding standard deviation may be obtained as
(Av !D)/-f2.
4
~ (s)ds ]
[
(Av/D) is the in-line VIV response amplitude as a function
of VRand Ks, see Figure 8- l . ln the evaluation of (Av/D) the
design values for the reduced velocity and stability parameter
shall be applied:
L.
Typical mode shape values may be found in Classification
Note No. 30.5. For a simply supported pipe in the first
vibration mode, the mode-shape parameter equals 1.16.
0.20
·········=···········=·········T······ ··i··········l··········1···· ······r··········1··········r·········
.
...
...
-......·· 1·· ......... ....... ·--.. ...... -..... :' ...........
'
~
'
'
.'.
.
... ·····1·· .......
'
-~
J'.''.~.110 I r-r--t-..1!_+-:-.:-:..;:-'·_·-
. ....... -:·. ...... -.. -.. .... .. ... ... ' -.. . ''
..'
'
·~
0.00
~. .
~
-1 -- - - 1 . - --i<--
- - i -'---
0.5
1.5
0.0
l.O
~=1.s
+ - ' - - - - l - - - + --'--+---'----f-L-----ll - -- I
2.0
2.5
3.0
4.0
3.5
4.5
5.0
Reduced Velocity V R,d (=VRYr)
Figure 8-1 In-line VIV response amplitude
l
8.2.6
The characteristic vibration amplitude curves in Figure 8· l
can be constructed as follows:
•
The onset value for the reduced velocity in the 151
instability region is given by:
1.0
VR,oosct = 0. 6 + K s,d
•
2.2
for
Ks,d < 0.4
for
0.4 < K s.,d < 1.6
for
Ks,d > 1.6
The end value of the 2"d instability region is given by:
-{4.5-0.8Ks,d
VR,eod 3.7
DETNORSKE VERITAS
for Ks,d < 0.4
for Ks,d;:::: 1.0
Guidelines No. 14
33
June 1998
•
A slope equal to (l /10) at the start of the 1st instability
region and a slope equal to (- L/2) at the end of the 2nd
instability region applies.
•
The maximum in-line vibration amplitude (AY,ntaxJD) as a
function of the stability parameter is given by (see
Figure 8-2):
(Av.max /D)=
1st inst. region
0.15(1- Ks,d)
i ·2
{ 0.11(1- ~)
1.8
zod
inst. region
i
l l : . l l
l
... ····· ·~········ .... r···· 1;.·i~~~~-~~;;fy· ~~~i~~-· . ··r ···········t··········1 .....······r............ . ·······1
0.14
0.12
0.1
•s 0.08
··········~-..
~
$
The amplitude in the lst instability region for given Ks,d
is not to be taken less than the amplitude in the 2nd
instability region, see Figure 8-2.
.......... .,............. i, ............................
,.............,. ........... .,...................................................
:
:
:
:
;
:
;
0.16
-8,.
•
.
·!. .... ······~·--·······
·- ~------ -----~-----······~·-········ ·-~············~·-·········· ············~
..
..
..
.
..
..
..
....
..
.
.
....................:................ i-··········-~-----·-··---~
..
....
.
.................................
..
..;............ . .................•
.
..
...
o
o
I
o
o
t
o
'
0
... -·:···········;············t······ ····1······ .... ··;· .... ······:············
o
.
.
;
:
.
:
o
o
I
·,
o
Instability Region
............ -:-···········~·-··········~·······., ......
0.06
I
I
' :
'
···········~
.
.
··:· ............ ············:
:
:
:
:
.
............1:................ ::................::. ................. ~'-:.,
.........
[... ..... ..,..........................
t.: ........................;:
:'
"
:'
:
..
.
..
'
'
.
.
'
' '
.
.
'
'
'
~
.
.
........................................................... -· ...... ----- -----..... ,, ___ ...... -... ... .
.
.
.
'
; '
:
:
0.04
0.02
~
-~
-\-
'
'
:
'
0
0.2
0
0.4
0.6
' .:
I
'II
'
'
:
'
'
1.2
0.8
Stability Parameter
l.4
1.6
1.8
2
K s,d
Figure 8-2 Maximum in-line vibration amplitude
8.2.7
Linear interpqlation on 0 is allowed.
R10(Ic,9) is a reduction function accounting for the effect of
the turbulence intensity, le, and angle of attack for the flow.
In the 2nd instability region R16(Jc,0) is independent of 8. It
may be taken as
In the 151 instability region R10(Ic,9) is given by:
R19(Ic ,6) =
l
for
1.0 - ( 36~ 0 )(45 ° -0.7 -0}1c
for
0=90°
30° < 0 <60°
0.0
for
e = 0°
1.0
for
le <5%
for 5% <le <20%
for
le >20%
The reduction functions are illustrated in Figure 8-3 .
DET N ORS KE VERITAS
34
Guidelines No. 14
June 1998
.
.
.
i 9==90° v
14
16
18
.... ) .. --· .....~ .........;........... ~..... .
'
0.7
i..
.s 0.6
t>
r:
§
0.5 .
'£
l=0.4
~
0.3
0.2
0.1
0
2
4
6
8
10
12
20
Turbulence Intensity (%]
Figure 8-3 Reduction function wrt turbulence intensity and flow angle
8.3 Cross-flow VIV from combined wave and
current
8.3.3
8.3.l
Cross-Flow VIV Response Model
The characteristic vortex shedding induced stress range S
due to a combined current and wave flow is calculated by the
The fatigue criterion specified in this section applies to all
flow conditions.
where:
8.3.2
Cross-flow VlV are affected by several parameters, such as
the reduced velocity V R> the Keulegan-Carpenter number,
KC, the current flow velocity ratio, a , the stability
parameter, Ks, the seabed gap ratio, (e/D). the Strouhal
number, Si. and the pipe roughness, (k/D), among others.
Note that Reynolds number, R.,, is not explicit in the model.
For steady current dominated fl ow situations, onset of crossflow VIV of significant amplitude occurs typically at a value
of VRbetween 3.0 and 5.0, whereas maximum vibration
levels occurs at a value between 5 and 7. For wave
dominated flow situations or span scenarios with a low gap
ratio, cross-flow vibration may be initiated for VR between 2
and 3 and are in this region apparently linked to the in-line
motions. For high values of VR the motion are again decoupled.
S A• ID
unit stress amplitude (stress due to unit
diameter cross-flow mode shape deflection)
~
amplitude reduction factor due to damping
(A2 /D)
cross-flow VIV amplitude
Ys
safety factor to be multiplied on the stress
range, see section 7 .4
factor depending on the free span scenario,
see section 7.4
transformation factor, see section 8.2.3.
The cross-flow VIV amplitude (Az/D) in combined current
and wave flow conditions may be taken from Figure 8-4. The
figure provides characteristic maximum values. The
corresponding standard deviation may be obtained as
(Az /D)/../2.
DET NORSKE VERITAS
Guidelines No. 14
35
June 1998
1.2
l.I
,......
e
0.9
'-'
G>
0.8
~
"'.<::::= 0.7
-a.
~
;;...
-
0.6
~
0.4
~
J,
0.5
..."' 0.3
u
~
0.2
0. 1
6
4
2
8
IO
Reduced Velocity VR.d
12
Figure 8-4 Cross-flow VIV amplitude
forKs,d ~ 4
for Ks,d >- 4
8.3.4
Th e characteristic amplitude response for cross-flow VIV
may be reduced due to the effect of damping. The reduction
factor, Rk is given by, see Figure 8-5.
····· ···.,....... ···:. ·· ········r······ ····: ······· ··;·--·-·····r ·· ················· . . :.. ··· ···-· ···· ······· ··
..
..
~
.
.
·-···r··· . . -··- ·r···-····· ·r ·· ··· -----r-------·-·r· -·-····· ···-·--- -----···· ..........:
.
~
:
:e=0.6
~c:
.
0
-
.Si
j
.
.
o
t
o
o
o
I
0
.
..
o
-~-
-~-
.
.
~-
•
o
.... ......................
..
.
. --·· ........................................................................................................
.
'
I
'
>
I
o
t
0
--- ---- ·: .. .... ·-. ·~-·. -··. -- -~- - -
0.4
.
o
.
o
::I
0.2
0
....
..
...
.....
.
...
..
.
.
o
2
3
4
5
6
I
o
o
.
•
I
o
I
'
I
'
..··--·----:---. --- ·- --:-. ...... -....
·-· -- -:- --· --· ---:- -·-····. --:
.
_________ •
o
0
:
: :
l
:
................. ...... -----------······
.
.
.
... ····-- ·-.. ··-·------ -
c.i
~
.
:
:
i
:
~
~
.................
..
.
7
8
Stability Parameter ~,d
Figure 8-5 Damping reduction function Rk
DETNORSKE VERITAS
0
•
9
10
14
16
36
Guidelines No. 14
June 1998
8.3.5
The normalised amplitude curves in Figure 8-4 to a large
degree embody all available test result. However, the
following comments apply:
•
•
•
The response for (e/D < 0.5) is (in reality) not governed
by vortex shedding and should in a narrow sense not be
characterised by VIV parameters as VR and KC. Tue
indicated response curve is considered conservative in
general.
The response for low KC values is associated with a
large uncertainty and the number of test data is scarce.
For KC< 5 the response is not governed by VIV but
rather linked to wave induced water particle motions,
and one sided vortex shedding. Typical maximum
response at VR between 2.5 and 3 .0 occur at fo/fw.,. 2.
In case f0 < 3fw the criticality should be assessed, e.g.
from dedicated tests or applying a force model.
9. Force Models
applied, the adequacy must be evaluated on a case to case
basis.
9.2 In-line direction
9.2.1
The in-line force per unit length of a pipe free span is
determined using the Morison's equation:
where:
p
water density
D
U
instantaneous (time dependent) flow velocity
y
in-line displacement of the pipe
9.1 General
drag coeffici~nt.
9.1.1
ine11ia coefficient
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.
9.1.2
The well-known Morison's equation is presented herein
while functional requirements are provided for general force
models for combined flow conditions.
Several analytical force models for cross-flow have been
proposed and calibrated using experimental data, see e.g.
Sumer & Freds0e, (1997) and Blevins, (1994) for a detailed
introduction. However, generally applicable force models do
not exist and an empirical response model reflecting
observed pipeline response in a variety of flow conditions is
at present superior.
9.1.3
The stress range to be applied in section 7.2 may be
calculated explicitly introducing the force model as a loading
term in the equation of motion for the free span scenario. The
solution may apply time domain solutions or frequency
domain solution using linearization techniques.
(Ca+ l) where
c. is the added mass coefficient
differentiation with respect to time.
9.2.2
In general, the drag and inertia coefficient is given by:
Co= Cn(Rc,KC,o.,(c/D),(k/D),(Az ID))
CM= CM(Rc,KC,a,(e/D), (klf)))
where Re is the Reynolds number, KC is the Keulegan·
Carpenter number, a is the current velocity ratio, (e/D) is the
gap ratio, (k/D) is the pipe roughness and (Az/D) is the crossflow vibration amplitude. Definitions are given in section 5.
9.2.3
In Figure 9-1 and Figure 9-2 drag and inertia coefficients are
given as function of KC and ex., i.e. CL>(KC,a.) and CM(KC,cx.).
Corrections due to the influence of the seabed may be taken
from Figure 5-1. Fuither, the effect of the pipe roughness and
increase oft11e drag coefficient due to cross-flow vibration
may be taken from Classification Note No. 30.5.
The set of safety factors given in section 7.4 is linked to a
consistent definition of characteristic parameters and models.
They have not been calibrated to the force model, and, if
DET NORSKE VERITAS
Guidelines No. 14
37
June 1998
2.0 ..,....----...·
....................;·····--· .. ···-- ···--1·--... ............. .
1.8
...................... ., ..... ········-·······1·············· ....... .
l.6
····-···············r····················!····-···············
.
1.4
····················t···················-.:····················
1.2
....a ............
... ··············f····················i····················
.
.
0.0
:
Q
I
i
.:
:
.
u
f
c
·o
e
~
;
1.0
~
Q
uOil
0.8
<I'S
N
. ..............................................
.
. ..... .... ......... .
~ 0.6 . .. . ....................... ...... ............. .................
... ........ .................. .............
i.
:
!
gap ratio .e > .
·· roughness (k/D)=l/200 ..
:
i
.
<0.5
i.....................f...................T" ................. T .................
.
.
.
.
0.2 ........................................................
..........
--·- ···-···----.................................. .
..
.
.
.
.
.
o.o ...______,_·.____________,______,_·. __________
0.4
t
o
I
o
t
t
I
I
o
0
0
I
t
--·····--~--·········.-······ -· ·······
~
0
20
10
30
40
60
50
KC
Figure 9-1 Drag coefficient C 0 versus KC and«
2.0 i-----=
··--··~···--····--····------~---------·--·--------:--···---- · ·-- · ·----··;·-- · ·------······--··:··· · · ·· · ·· · · -- · ·--···,
...
.
....
.
;.. ------· ---·---·---- ~-- · --··----------·---r ------------------- --~--- -~- ------------1
1.8
.
.
.
;:oo,.........,..._......._ _ _ _~---.-;:.. !:P....
~ 0.2
1.4
................ .. ................ .
>
•
.
~
1.2 ..............
·u
e
:
t.o -1----~-- ....:~ ................ - ~ - .. -·
~
....
•
0.8
~
=
0.4
.
.
~
:
j.
:
· o.4
---~~~:~~~~~~~~____..:
.........
---:--· ...................................... T..............
----j
.
.
..................... .....................f.................... T.<o:s--· ........ j
•
I
j
•
~
.
'
'
.
---· .....................................................
................ - ..................................
_.............................................
-·····-·······
.............. .
.
'
'
... 0.6
•
: 0.3
. ...... ... ~... ......... ....... ~ .. ...................:... ...................;..................
u
'f
........1
.
. ............... .....P-••·--··""······ ·--··--··' --· --· -- ....... ...
....................................
:
'
---·~· ··
.
~o
'
gap ratio e > .
(k/D)=l/200
.... roughness
.
o
I
•
I
.
'
'
I
o
.
:
:
!
:
:
I
:
:
i
"j"................... ( ...................f................... T................... :j
o
~
.
;
;
:
!
:
o.2 .................... T
....................r··················--1··--··--··---........
f.................... 1··--················~
..
..
+
'
..
o
.
o
..
I
'
0.0 -1------+'-----+------1------i-------'1------~·
0
10
20
30
40
50
60
KC
Figure 9-2 Inertia coefficient CM versus KC and a,
DETNORSKE VERITAS
38
Guidelines No. 14
June 1998
9.2.4
Both time domain and frequency domain 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 are to be analysed.
For fatigue analysis a frequency domain solution (if
thoroughly verified) is more tractable since it facilitate
analyses of a very large number of sea-states at a small
fraction of the time required for a time domain solution, see
M0rk and Fyrileiv (1998).
9.3 Cross-flow direction
9.3.t
Models describing the vortex shedding cross-flow forces are
semi-analytical and include coefficients that are derived from
test data. Generally, the models are limited in tenns of their
physical basis and the range of application. A number of
models can treat steady current conditions, see e.g. Blevins,
(1994). Others have been developed for harmonic flow
(regular waves) conditions see e.g. Bearman, (1984) and
Verley ( 1982). Models, which treat general flow conditions,
are more complex and the wide parameter range and
conditions to be covered makes it necessary to include a
number of different terms each justified by different physical
conditions or parameters.
10. References
Bearman, P. W., Graham, J.M. R, Obasaju, E. D., "A Model
Equation for the Transverse Forces on Cylinders in
Oscillatory Flows", Applied Ocean Research, Vol. 6, No. 3,
pp. 166-172, 1984.
Fyrileiv, 0. & M0rk, K.J., " Assessment of Free Spanning
Pipelines using the DNV Guideline", JSOPE'98, M ontreal,
Canada, May 24-29, 1998.
MULTISPAN Project, "Design Guideline. VIV of Free
Spanning Pipelines. Part I: Steady Current Loading'', DNV
report 95-3 134, H0vik, Norway, 1996.
M0rk, K.J., Vitali, L. & Verley, R., "The l'vfULTISPAN
Project: Design Guideline for Free Spanning Pipelines",
Proc. of OMAE'97 conf., Yokohama, Japan, April 13-17,
1997.
Mmk, K.J. & Fyrileiv, 0. "Fatigue Design According to the
DNV Guideline for Free Spanning Pipelines", OPT'98, Oslo,
Norway, February 23-24, 1998.
M0rk K.J., Fyrileiv, 0., Verley, R., Bryndum, M. & Bruschi,
R. "lntroduction to the DNV Guideline for Free Spanning
Pipelines", OMAE'98, Lisboa, July 6-9, 1998.
NORSOK Standard "Design Principles. Steel Structures.
Armex C: Fatigue Strength Analyses", 1998
Sumer B.M. & Freds0e, J. " Hydrodynamics around
Cylindrical Structures", Advanced Series on Ocean
Engineering - Volume 12, World Scientific, London, 1997.
Tura, F., Dwnitrescu, A., Bryndum, M. B. & Smeed, P.F.
"Guidelines for Free Spanning Pipelines: The GUDESP
Project", OMAE'94, Volume V, pp 247-256, Houston, 1994.
Verley, R., "A Simple Method of Vortex-Induced Forces in
Waves and Oscillating Currents'', Applied Ocean Research,
Volume 4, No. 2, 1982.
Blevins, R.D., "Flow-Induced Vibrations", Krieger
Publishing Company, Florida, 1994
Bruschi, R. & Vitali, L., "Large-Amplitude Oscillations of
Geometrically Non-linear Elastic Beams Subjected to
Hydrodynamic Excitation", JOMAE, Vol. 113, May, 1991.
BSI PD6493, "Guidance on Methods for Assessing the
Acceptability of Flaws in Fusion Welded Structures", British
Standard Code of Practice, 1991
DNV, " Rules for Submarine Pipeline Systems", 1981
DNV, "Rules for Submarine Pipeline Systems", 1996
DNV Classification Note No. 30.2, "Fatigue Strength
Analysis for Mobile Offshore Units", 1984.
DNV Classification Note No. 30.5, "Environmental
Conditions and Environmental Loads", 1991.
DNV RP E305, "On-bottom Stability Design of Submarine
Pipelines", 1988.
Fyrileiv, 0., M0rk, K.J., Kathrud, K., & Sortland, L "Free
Span Assessment of the Zeepipe IIA Pipeline", OMAE'98,
Lisboa, July 6-9, 1998.
DETNORSKE VERITAS

free sp anning pipelines guidelines

Transcription

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