Improved design methods for spanning of pipelines

TECHNISCHE UNIVERSITEIT Laboratorfum voor Scheepshydromechana Archlef Mekefweg 2,2828 CD Deift Tel.: 015- 788813 - Fac 015-781838

IMPROVED DESIGN METHODS FOR SPANNING OF PIPELINES

LB. Bryndum

H.]. Vested

K.G. Nielsen

'f-9 89 Eie an Seminar

IMPROVED DESIGN METHODS'iFOR SPANNING OF PIPELINES

3 :c

-Authors

M.B.

Bryndum

H.J. Vested

K.G. Nielsen

H. Gravesen *)

Danish Hydraulic Institute

Agern Allé 5

DK-2970 HØrsholm

*) Dansk Geoteknik A/S

Granskoven. 6

DK-2600

Glostrup

ABSTRACT

The paper describes a set of rational calculation procedures for

determination

o.

the fatigue damage and niaxirnum stress o

free

spanning pipelines, exposed to wave and current induced

hydrody-nainic loads. The procedures are described in a Project Guideline

or. Pipeline Span

valuation Manual and is supported by aPC-bas

computer programre. The programme handles the extensive and to

some degree tedious

computations required for transformation of

the hydrodynamnic input in terms of waves and current into

hydro-dynamic response of the pipeline span.. Both the response due to

wave action and the hydroelastic vibrations caused by vortex

shedding are included in the assessment of the pipeline

behavi-our.

The structural model deals with a single Span and is based on a

simplified beam-column model associated with elastic foundation

supports. The mddel incorporates the flexural induced normal

for-ces as well as any residual normal force from the lay. profor-cess o

LIST OF CONTENTS

ABS TRACT

INTRODUCTION

1.1 Backgroun4 fQr the Project

1.2 Improvements to Free Span Desi..

PIPELINE SPAN MODEL TESTS 2.1 General oxrtments

2.2 MOdel Tests

DEVELOPMENT OF. COMPUTATIONAL MODEL FOR FATIGUE INVESTIGATIONS 3.1 General Comments 3..2 ydrographic Data 3.3 Soil Interaction 3.4 Structural 4ddel 3.5 Data Base 3.6 Damping 3.7 Real Spans

3..8 Damage Calculation Procedures

4 MODEL FOR EXTREME LOAD CONDITION

4.1 General Comments

4.2 Funcion1 Load

4.3 Extreme Vertical Load

4.4 Extrémé Horizont1 Load

4.5 Voti MisesS tress Check

5. ACKNOWLEDGEMENTS

REFERENCES

APPENDIX A: EXAMPLE OF APPLICATION OFPROGRAMME ...DHISPAN

1. INTRODUCTION

1.1 Background for the. P.roiect.

.Frèe spanning pipelines may develop

for a number of reasons.

Pi-peline spans may be constructed intentionally or. may be the

re-suit of certain activities or natural processes

taking place

af-ter pipelines installation. On purpose built

free spanning

pipe-line Sections can be found within platform areas, at expansion

offsets, at pipeline crossings etc. Natural irregularities

of the

seabed may prevent a continuous contact and thus give

rise to

free

spans.

Furthermore, erosion of the sea bed may lead to

under-scouring of the pipeline and hence to free spans. Finally,

the trenching operation often leads to a

nuirber of free spans

especially if hard bottom or boulder clay are encountered.

The inspection fOr detection of spans and the Subsequent

verifi-cation of critical spans have proven to be very costly.

Therefo-re, a strong incentive exists .to

establish realistic and

practi-cal methodologies for evaluating all risks associated

with

pipe-line spans. The assessment of the risk associated

with flow

indu-ced vibrations have, to great extent been performed

using methods

which have been established for free pipes. Experimental

investi-gations have shown that the rnethçds

o some extent were

inadequa-te when dealing w.it.h the free spans near the sea bed.

..A number of studies have therefore been

initiated with the

purpo-se of improving or developing methods for free span. aspurpo-sessment.

A free spanning pipeline is. a flexible structure

susceptible to

large defornaio,ns..It has in general anui±er.o.well:defined

natural modes and eigenfrequencies. When exposed to

cyclic loads

very large responses may develop when

the frequenc.y of the

At. present such hydroelastic response cannot be. accurately pre-dicted using numerical Or analytia1 methods only,, but have _{to be} determinethusingprocedures' which include the resuits'of model _or

full' scale tests. .

In.l984/85 an extensive model test programme was carried out at

the DanishHydrau1ic nstitute. to determine _{he hydroelastic}

re-sponse of a free spaninq pipeline exposed to a wide range of

environmental conditions. The reslts of the _{programme in terms}

of different amplitude response parameters represent a

comprehen-sive database which not only can be used directly _{to assess the}

hydroelastic response of a free Span, but can also be used to calculate the fatigue damage induced by the environmental loads

However the use of the data. base for practical _{cases generally}

4.nyolves a large number of calculations and a considerably _amount

of work in order to establish the fatigue damage induced _{over a}

longer period of time. A project was therefore formulated with

the purpose pf. developing a PC-based computer _{programme which,}

based on the comprehensive model test results, would _{perfor the}

extensive and somewhat tedious calculations required to establish the fatigue damage. A number of. methods and procedures had _{to be} developed in order the generalize te test results, i.e.

structu-ral model, soil interaction description, damping, fatigue

cal-culation procedure It was. found that _{he most rational procedure}

would be to develop a guideline or a manual for the assessment Of

free spans and to supplement this _{manual with the computer}

pro-gramme.

The project was proposed to and.spported by the industry and the

present. paper gives an , QVerVieW of the manual and the computer

programme and further .illutrates. the use of' the programme by an

1.2 Improvements, to Free Span Design

A uniber. of methods for the design of free pipeline spans have been. presented in project guidelines or in the oen literature,

Ref. 3, 4, 5 and 7. Some of these are based on experimental

in-vestigations in steady current and as. such. operates with distinct fiow.-.regiifléS' in which either in-line or cross flow vibrations

exists. Others operate with application of more extensive data

material and refined numerical modelling.

The present Pipeline Span Evaluation Manual in several ways

re-presents significant improvements to the assessment of free

spans, and as such the Manual is one major step towards the gene--ral' Design Guideline applicable for all span configurations ant environmental conditions. The most important improvements to the

assessment of free pipeline spans 'introduced in the Manual are

listed belOw:

The fatigue a.lcülations are baSed on a database containing experimental results from a large number of model tests

cove-ring a wide range of environmental conditions. The fatigue

damage is thus established through interpolation between ex-perimental results.

Detailed and extensive environmental iiput caxt be handled

efficiently eliminating the need for simplification of the

problem for corputational reasons.

The structural model includes important non-linear effects

such as. the additional axial force induced by the lateral

deflection.

d) The calculationS can be carried out:using a number of

diffe-.rent'SN-curves according tothe users requirements.'

--The-. calculationS are performed,: including the effect of

structural, soil and fluid damping. The vibration amplitudes

of lông flexible spans are found using an energy budget

2. PIPELi SP MODEL TESTS

2.1 GeneraL çprnments

The key element in the Pipeline Span Evaluation Manual is the

data base containing theresults of a large nuther of model tests perorrned in the laboratory. The database contains both response

- amplitude paametes and reference fatigue damage 'parameers. The

laboratory investigations have been perfOrrned using an idealized

model Of the véy complex prototype phenomenae. To fully appraise the procedures and caculations required when, transforming the

test results to protOtype fatigue damage, the model test investi-gations are briefly described.

2.2 Model Tests

The hydroelastic vibrations of a free spanning pipeline exposed

to wave and current action have been investigated in scaled-down

model tests. The objective was to etablish a database containing

high quality data, descri.bin.g response amplitude parameters for free pipeline spans.

The Model

2-i

The model consisted of a spring thounted rigid pipe segment, which

ws 0.74. in long and O.1Oit indiameter. The seabed was modelled

by a flat plate. The pipe axis was vertical and in. this way the spring and daztipthg system could be placed above the water. The

spring system consisted of four flexible steel rods arranged in a

squae configuration.

The "structural damping"

of ,te system

could be varied by apply4ng ar-i external force,., opposing the pipe

movements in phase with the vibration velocity. The principle of

-iO TO R

MOVING CARRIAGE

t.UME BOTTOM

TOWER WITH SUSPENSION

SYSTEM oq MOEI

HORIZONTAL PLATE1

TEST PIPE

PLATE SIMULATING THE SEA BED

Fig. 2.1 Model Set-Up in Flume and Elastic Suspension System Instrumentation

The model was equipped with a

number of force transducers and

motion gauges which measured the following parameters:

- Pipe motions and accelerations in two perpendicular directions. - Reaction forces (total forces on pipe segment) in two

perpendicular directions.

- Damping forces in two perpendicular directions. Scope Of Work

Tests have been performed for the following environmental

condi-tions:

-

Steady Current - Regular Waves

- Combined steady current and regular waves

The four most important non-dimensional parameters in relation to the model tests were identified to be:

The gap ratio

e/D0

The reduced velocity based on the wave induced: flow velocity

Uw,

Vr _{- f D}

no

The reduced velocity based on the steady current

U

r

fD0

The Keulegan-Carpenter number

UT

KC =

D 0

where

S : the distance between the sea bed and the pipe

D0 : the pipe diameter

U : maximum wave velocity

w

T : wave period

natural frequency of the oscillating system steady current velocity

Following ranges of the parameters have been investigated:

- Keu].egan-Carpenter number, KC, from 5 to 120. - Reduced velocity, Vr from 1 to 12

- Reduced velocity, U, four values 1.0, 2.5 and 4.0 - Gap ratio, e/D0, three values 0.0, 0.5 and 1.0.

2-3

TEST MATRIX (GAP/DIAMETER RATIOS, olD 0.0.5.1.0)

O REGULAR WAVES

o REGULAR WAVES STEAOY CURRENT

Fig. 2.2 The test matrix

All tests ifi the matrix have been performed with one damping (K5

= 0.4). A number of tests have been repeated with other values

for the damping in order to quantify the effect of varying this

parameter.

Data Aialysis

The immediate result of each test was a number of time series

describing displacements and forces. Such time series are. imprac-tical for use, and therefore these were analysed in order to

pro-duce parameters which were easy to interprets. Fig. 2.3

illu-strates the parameters derived from the displacement time series

X. NORMALi CIPtACEMENT

_____

LTItiitiLiItMY11TTWi

!1i1III'IIRN

In PEIO0 TEST CUATlON 10.0 20.0 .0 TIME 1

Fig. 2.3 Basic Results of Time Series Ana1yss. Disp1acement

are Normalised with with the Pipe Diameter.

- REDUCE-P VELOCITY, V, 1 2 3 4 5 6 7 B Q '0

ii

12 IL) z U 5 000 -10 o ooO 00 000 -0 0

-15.

0 000

..

0000

. .

.o':---;1-_{. --} -_ -- 000 0000 0000 S 000 0-- -- - -0 00000000000 S

SI

00 0 0

--

- -40.5.14..000ao:0000000eeo 00 oo a 0 0 -U

000000

- 00 00S 0

_

0 S. S - - -80 0 00 00 0 0 0 0 0 0 0 0 - -00 -o 0.3 MAX IX) 0.2

r

2-5

The Results

The parameters found through the analysis are listed below.

1. Mean (x) _{: Mean value of total record}

2.: Max (x) : Maximum value of total recàrd

Mm (x) _{: Minimum value of total record}

Std (x) : Standard deviation of total records

Max(x)

_{Maximum peak to peak value,}

(maximum "wave height")

Min(x)

_{: Minimum peak to peak value}

Mean (x)

: Mean of peak to peak values

Std(x)

: Standard deviation of individual peak to peak

values

Mean (T) : Mean zero up-crossing period

x is the displacement time series (in-line _{or cross-flow)} norma-lized by the diameter of the model pipe.

Fig. 2.4 shows an example _{on the response amplitudes}

Std(x)/D and Std (y)/D _{for the regular wave tests.}

l.2 I.. 1.1 I.. 3.4 3.2 a.. II 12 3 Vr STD (V ) /

.. RAWDTA

- CALCULATED DATA tI e 12 Vr

Fig. 2.4 _{Std(x)/D and Std(y)/D}

against Vr for KC40 and e/D =

0.5. The calculated _{data are determined}

by

interpolation and extrapolation from the measured

values. STD(X)/D

Ref. 9 presents the results of a similar but less extensive

stu-dy. The results do in general agree with the present.

The tests have been analyzed furthe in. order to pro4uce fatigue damage parameters The analysis comprised peak to peak analysis

according to the rainflow

counting

method and transformation of

these peak to peak values into fatigue damage parameters. In-line and cross-flow fatigue damage parameters

D (x. ./D)

-x N0

-pp,i

a = .2,3,4,8)

(Y/D0)m

(In = 2,3,4,8)

x and y are all peak to peak athplitudes in One test defi-pp,i pp,i

ned according to the rainflow counting methods. N0 is defined as

fITT :natural frequency times test duration) and in principle is

thenu±nber of vibrations in one tet . is oUter pipe diameter.

The calculatio of fatigue damage parameters is described in

3-1

3 DEVELOPMENT O COMPUTTIONAL MODEL FOR FATIGUE INVESTIGATIONS 3. 1 eneral Cornxnents

The Span Evaluation Manual nd the computational model are

struc-tured in the same manner and the calculations perorIned by the

programme can be carried out by hand following the instructions

of the Manual. The key element is the database

contanig the

results of the experimental iivestigations. The database is in

the Manual presented in the form of a series of contour plots of the Vaious'parameters, see example in Fig. 3.5.

The procedures and methods required for transforrnaton of the

en-vironmental input, the soil-, the pipeline- and span data etc.

iflto relevant vibration data and fatigue data are

described

ir

the Manual The same procedures are implemented, in the programme

in a user friendly interOtive menu

driven tructure. The

pro-gramme automatically generates a number of entry. parameters to

the data base, retrieves the appropriate data and calculates the accumulated fatigue damage.

The sequence of ca1cu1tions are illustrated, on Fig. 3.1 next

/SPAN CONF0URATION OAT4 PIPE SYSTEM DATA

SOIL. DATA

STRUCTURAL ENVIRONMENTAL MODEL MODEL

y

RESULTS AND ENTRY

P.RAMETERS FOR DATA BASE:

IcC.Vr.Ur.eic.

DATA BASE FOR OSCILLATIONS AND REFERENCE DAMAGE CALCULATION OF ACCUMULATED REFERENCE DAMAGE DAMAGE

Fig. 3.1 Span Analysis Sequence

3.2 Hydrogaphic Data

The basic hydrographic

data required for

the

span

assessment are

the wave and current condition on the location. These conditions

are required in a forma.t which is commonly used in offshore app-lications.

The waves are given in terms of appropriate long term distributi-ons, e.g. omnidirectional scatter diagram of H, T.

Each seastate can be described by a standard Jonswap or

Pierson-MoskOwitz Spectr1n. The boxes (H5, T) in the scatter diagram can be given a directional distribution. Once the directional

distri-bution has been specified, the surface wave pattern is defined

-for the period ccnsi4ered.

HYOROGRAPPIIC DATA / FATIGUE CRITERIA LEGEND RESPONSE AMPLITUDES INPUT CALCULATIONS PROCEOUE DATA FILE.! RESULT

I

SCALING TO

REAL SPANS /DAMPINGPARAMErERS _-/

/.

-/

DAMAGE RATIO

The surface waves ae transferred to the sea bed using linear

wave theory.

_Thereby

the velocity spectrum at the sea bed is

found. This spectrum is SubSequently decomposed into single waves

assuming a Rayleigh distribution of these The spectral derived

mean period is assignèdl to each wave so that the duration of all waves equals the duratiOn of the original sea States.

The ure

in the. pipe level can be

specified

_{in two independent}

components:

A constant component that is always presert

A cOmponent which may vary in fttaghitude. and direction

The current is combined with the indiiidual waves and each wave

and c'rrent combination defines what is called a "single event". The events are characterized by following parameters:

wave velocity at pipe level. wave period

steady _Cu ent at pipe. level:

TDIJR : duration of event

Only the velocity cotrponent perpendicular to the pipe _{axis iS}

considered in this context The calculation procedure for

S...( r) SU( t) d 11 T _TOUR

T, LJ

TOUR

Uc-Uw SURFACE SPECTRUM H51T,, LINEAR TRANSFORMATION BOTTOM VELOCITY SPECTRUM RAYLEIGH DISTRIBUTION SINGLE WAVES CURRENT DISTRIBUTION DISTRIBUTION OF SINGLE EVENTS

Fig. 3.2 Calculation of Individual Wave and Current situations, "Single Events".

The parameters characterizing the single events are used to

defi-ne a number of non-dimensional parameters which are used as

en-tries to the data base when retrieving amplitude or fatigue data. The parameters are KC, VrF Ur and e/D0.

3.3 Soil Interaction

tnoder. to describe the i

;cioeen. the pipeline and the

surrounding soil, a number of representative, soil parameters has :to be speified. ..

The; strutural model

of the spanning _pipeline requires the

modulus of subgrade reaction and. the axial coefficient of

friction. Further, to include

the effect of soil damping as

described in the QllQwing section, the transverse coefficient of friction and the soil damping ratio must be specified as well. For cases where sufficiently dèt'ailed,inforrnation on soil

charac-teristics is available, the parameters to be specified can be

deducted through analytical and empirical relationships as

de-scribed in the open literature, Ref. 1 and 12, and referenced in the Manual. Alternatively, for cases where only a rough

descrip-tion of the soil can be obtained, guidance can be found in the

estimated soil parameters of Table 3..l below. The table i.s ainly

based on Ref. 7.

Frjct.ori Coefficient 3-s

Very seit clay 1-10

Soft cLay 3-33 Aial soil resistance

force is iA the fE

ediu clay 9-33 of adhesion

a.rd clay 30-67

A.xial. (1ongitiidial) Tra.nsverzal (lateral)

Concrete Steel,epoxy Concrete Seel.epoxy

miniu 0.4

- 0.4

- 0.2

- 0.2

Table' 3.1 Soil Parameter Ranges for Various Soil Types Sandy clay! moraine clay 13-140 0.4-L 0.4 to 0.5 t.00se sand 5-13 0.3-0.9 0.2-0.5 0.3-0.7 Dense sand 25-48 0.2-0.5 0.5-0.7 Silt 1-11. 0.4-0.5 Rock 550-52000 0.5-1 0.4-1 0.7-2 0.4-2 Rock dith a.rine growth 550-52000 0-1.0 0-1

3.4 Structural Model

The pipeline span çonfiquatiOnmOde11ed in the. programme

repre-sntsthe common

jÜáiOfl wherë the spañ develops through a

scour process. The pipeline is installed in horizontal position on the sea bed . In this situatiQfl the pipeline is pressure

tes-tèd,an

prior to pipeline commissibfliñg and operation the pipe-line can be trenched or rock covered. A scour hole is formed over a certain length in any of these situations and a free span deve-lops. In addition to the axial forces already present in the pipe

an axial tension component developS in the

span due to

the

deflection and the axial friction along the supported sections.

The situation is illustrated in Fig. 3.3.

SCOUR NOUCED

:..:.:::.::;:::;:;::::::::.;....

-

_..._i-Fig 3.3 Scour Induced Free Span

Static Model

The prototype free span is described through analytical

expressi-ons giving the deflection, the tension and the bending moments.

The analytical expressions are develOped base4 on the idealized

ELASTIc FOUNDATION

3-7

FREE SPAN

Fig. 3.4 Idealized Model of Free Span

The structural model calculates the bending moments,midspan and at the end suppots, as well as the corresponding deflections.

The relationship established, between deflection and. associated stress and strain variation is utilized in the subsequent fatigue dathage and extreme

ipa

lysis. Further the natural frequency

of the pipeline span is calculated.

The interaction between the supporting soil and the pipeline is modelled by application of the Winkler model, assuming that at

any point along the pipeline within the adjacent soil, the

trans-verse reaction forces are prcportional to the beam delection at

that point.

The effect of the axial force on the pipeline .eflection and ben-ding moments

as

well as the influence on the xatural frequency

has been included. The resulting axial force, is composed by the

linear axial force, which is present before the span is formed, and by the non-linear axial force' induced by the deflection of

the pipeline. The lInear axial force is the result of functional

loadings and the poible residual lay tension.

The weight of the spannig prt of the pipeline is supported by

r'eácton forcis,

a

each

end

f the span. 'The flexüral induced

'axial force s gradually t'educed' by axial frictibñ fórcès along

the buried sections of the pipe until the normal forci equals the original value (lInear axial force component).

ELASTIC FOUNDATION

Dynamic Model

The same structural model is used to establish the natural

fre-quency of the pipelIne span for the first sytninetrical vibration

mode together with the second mode. The effect of the axial for-ce, composed of the linear and non-linear components, is included in the formula for eigenfrequencieS.

It has been found that for cases in which the pipespan vibrates

in its symmetrical first mode, the ratio between the maximum dis-placement amplitude at the mnidspan and the corresponding bending

moment respectively at the midspan and at the soil shoulder are

very similar to the ratios found for the case of uniform static

loading acting on the span. The ratio between the dynamic momen

and the deflection at midspan (mode shape factor) is calculated

using the formulas and parameter relationships developed for uni-form static loading.

The theoretical work leading to the various analytical expressi-ons and formulas associated with the established structural model is mainly based on Ref. (8), Hobbs (1987) and Ref. (6), Hetenyi

(1946). Generally the calculations are based on analytical

ex-pressions, but an iterative calculation scheme has been required, because most of the parameters are implicitly given in the

equa-tions.

Fatigue calculation

The accumulated damage and the associated fatigue life, is

calcu-lated using the rule of accumulation

of the partial damages

(Paingren-Miners Law) .

The basic assumption according to this

summation method is that the damage to the structure for each

load cycle is constant for a given stress range. The relationship between the stress range and the corresponding allowed number of

stress cycles (the SN-curve) can be specified by the user prior

'C.>-'

3-9

The fatigue calculation .s performed in two steps. The first step

is bad"on a direct application

of the model test results and

theresult-is.-. a..refereflCe fatigue damage.. The test results

re.-flect the" hydrodyn'amiC response of a spring mounted rigid cylin-der for one p,eci.fic damping and therefore a second step., is

re-quired for converting the. reference damage to prototype value.

The. second. step includes an integrated scaling of the in-line and cross flow vibrations and assdciated fatigue aInages in order to

adjust the results to actual values of damping and incorporate the 3-dimensional effect of the flexibility of the actual span

configuration.

.3.5 Data Ease

The results from the model tests have been used to establish a

data base. The hydrographic 'conditions combined with pipe and

structural data determine values for 'KC, Vrl U and e/D. These

parameters define the

conditions

for the performed model tests

and constitute the key to the da.taase.

The model tests data did. not cover a complete KC', VR range and

were not equally spaced. Therefore the original results were

smoothed and extrapolated by means of a second-order

two-dimen-sional

interpolation/extrapolation

procedure. The resulting data

were plotted as contour plots and visually checked. An example of such a contour plot can be. seen in Fig'. 3.5. In these plots the points for the original data are marked with a cross.

12' 10.2- 4-2- 4. /P#. / I I

Fig. 3.5 Example on contour plot of the hydroelastic Vibration data ontaine in. the data base

Data Base Key Range Parameter interval or actual values

KC

V

r

Ur

e/D0

AssOciated with each set of the key

parameters are 14 seleted

values of the condensed model test results.

The final data base covers following r3nges of the entry

parame-ters: e/Da = 1.0 Ur 0.0 0-120 0-12 0-4 0-1.0 0, 0, 5 0.5 1.0, 2.5, 0.5, 1.0 4.0 0 0 2 4 6 8 10 12 Vr e/Dó t.OUrO.O STD(X)/Do STD(Y)/Do

Contents of data base: Amplitude resp9nse 3-11 peak-peak, in-line low-pass, filtered high-pass, filtered peak-peak, cross-flow

standard deviation inline

standard deviation cross-flow Fatigue damage parameters (see Chapter 2.2)

D (in = 2, 3, 4, 8) : damage. parameters, in-line

D (in = 2, 3, 4,8): damage parameters, cross-flow

The vibration and fatigue parameters stored in the data base can be used for assessing the fatigue damage. The fatigue damage pa-r-ameters can be transfOrmed to represent the relevant stresses,

using the SN-ctrve arid the mo4e shape factor. The damage deterthi!.

ned directly from the data base corresponds to two-dimensional conditions, and a sealing of the model test results to a real

three dimensional span has to be performed in most cases together with an adjustment to the actual darnping conditions.

3.6 Damping

The vibration of a free spanning pipeline is a resonance

phenome-non and as such the damping has a dominating influence on the vibration amplitudes. Traditionally the damping is described by

the, stability parameter, defined.

.2 meo /pD0 Mean (x) /D0 Mean (x) /D0 LP Me an (x) ID0 HP

Mean (Y)

/D0 Std (x)/Do Std (y)/P0

where

me: structural plus hydrodynamic mass per uniElénqth

p : density of water

DO: external pipe diameter logarithmic decrement

The stability parameter is a combined mass ratio and damping

pa-rarneter. The daping is expreSed by the logarithmic decrement,

can be dete*mined from decay tests in air and is the natural

logarithm 9J the ratio between two succeeding vibration

amplitu-des.

The total dampin is basically xtade up of three terms. Structural damping

Soil damping Fluid damping

The structural damping is relatively well known and values based

on measurements áan be found in the open literature.

The soil damping is mOre complex and only limited data are avail-able. The soil damping included in the Manual is therefore partly based on information from foundation theory (Ref, 12) and partly based on calculation of tife soil friction forces when the pip

moves

relativey

to soil. Three physical mechanisms are

considered.

- Hysteretic a!nd radiation damping

- Soil friction along the pipe due to axial movements induced

by

êf1ectins

,.

Soil friction due to transverse movements of the pie at the

Supports.

The fluid damping is closely related to the vibration amplitudes.

Even with very low damping the amplitudes of vortex induced

3-13

due to the fact that the regular _{vortex shedding will.}

Collapse je the amplitudes _{significantly exceeds this limj d thus}

the

fluid damping will reduce the vibrations.

'When exited the .prototpe _{...span will ibrá with cOntinously}

Va-rying amplitudes along the pipe

_and

_{therefore the fluid damping}

and the excitation forces will vary along the pipe. At each sec-tion of the pipe there will, _{be a netto energi}

transfer from the fluid to the pipe or from the pipe to the fluid _{depending on}

whe-ther the excitation forces _{or the damping are dominating.}

This

overall principle is used when the results of the _{2-dimensional}

mOde.1tst _{are transformed to the}

3-dimensional conditions of a

flexible prototype span

The relationship _{between the fluid damp!ng and the vibration}

amplitude has been determined through a nuxtber of tests with

va-rying daiiping conditions. _{Tests have also been made}

for

situati-ons where the pipe has been foced _{to oscillate with athplitudes}

larger tha.n natural undarnped _{vibrations This way the energy}

dis-sipated by damping _{or introduéd by excitation forces}

has been

determined,

3.7 Real Spans

The model tests have _{been performed under strict}

2-dimensional conditions. The flow was uniform along the pipe and the pipe

it-self was a rigid spring _{mounted pipe segment. To be}

applicable under prototype conditions _{the test results had to}

be scaled to compensate . for the differences between _{the model set-up and}

the

flexible pipe span.

This scaling is based on an energy principle. Damping _{reduces the} amplitudes and _{dissipates kinetic energy through}

heat or

turbulence. The excitation forces maintain the vibrations and as

long as a steady state _{condition is present the}

energy supplied by the excitation forces equals the energy dissipated by _damping. This equilibrium may be written

Denominating ELSS to. E a relation between E an4 6, the loga-rithmic decremezt can be established for lightly damped systems

!

-(n)

2.E(n-l)

2 Et

where is the maximum kinetic energy for the vibration consi-deréd. Et0t is proportional to the amplitude squared.

The energy equilibrium is estalishe4 for the flexible span ii

the following way, see Fig. 3.6. The span is divided into a

nuxn-ber of segments, each representing two dimensional conditions.

The energy input or dissiptiç for each segment can be

determi-ned assuming that te effect of structural and soil damping is

identical for all elements and that the fluid damping depends on

the actual amplitude only. By integrating along the span for a

given mid span vibration amplitude and geometry, the energy input and disipation can be determined. This. process is repeated for a

nuin.ber

of midspan

amplitudes

until

the correct energy balance is

found.

CD

\\I

CD

MODELLING OF FLEXIBLE SPAN

NETTO ENERGY TRANSFER

3-15

0

ENERGY TRANSFER,FROM FLUID TO PIPE (DRIVING FORCES) ENERGY TRANSFER,FROM PIPE TO SURROUNDINGS(DAMPING)

Fig. 3.6 Definition sketch for the energy balance for a free

span.

The vortex induced vibrations are scaled according to the

proce-dure described above.

The wave induced in-line movements are

scaled, usin.g the correct value for the cross flow vibrations to determine the effect of the drag forces.

The scaling is performed in three steps. First the cross flow vibrations are scaled, secondly the high frequency part of the

in-line motions (vortex induced) and thirdly these two sets of

vibrations are combined to give the total

in-line

motion

3. 8

Damage Calculation Procedures

The basis for a.l the

fatigue calculation in the Manual is the

?alzngree-MiI1erS Rule

p = Z D

= 1

ALL,i

D is the total 4amage, N

is the number of cy1es with a strain

variation

d NALLi is the allowable number of cycles with

a strain range o,f

The failtiré criterion is D1..

The allowab.e nmer of cycles,

_L

is found from SN-curves c

the general form

NL =

C()m

where C is a cthistant and the exponent in normally

have a value

between 2 and 8.

The fatigue damge for a certain strain range

A

may thus be

written as

D. N.

'1

iC 'ti

The sréss range

to be used in the fatigue

damage c'aiculation

are found the, following way'..

The environmental conditions

cotnbned with the soil and pipeline

span data defize a sere.s.of "single events".

Each event

is

associated with

a

duration,

TDUR,jl

and

the

fatigue

damage

parameters D

and D

scaled to reflect prototype conditions

The midspan

defiectiofl

and

the

strain

in

the most critical

section is relatéd through the

mode shape factor,

K1,

and the

modulus of elasicitY.

c.

= K. E(Y

./D

Similar expression is valid for the in-line direction.

The fatigue damage induced by each "single event" can then be

calculated: (EK1)m

DAM,

= C f (EK4)m DAM . = y,i where E: Youngs modulus

K1: the mode shape factor

The total damage is

found

adding the effect Of all the single

eVents.

DAM = Z DAM

-. ,xii

DAM = Z DAM

_y,1

DUR,i f D7

4. :MODEL FOR EXTREME LOAD CONDITION

4 1 General Comments

The purpose of the extreme load analysis is to calculate the

ma-mum stzess inuàed by the normal operational loads and the

an-ticipated extreme envirQn±netal load. to unamnbigious efinition of the extreme load is possible and the final acceptance criteri-on for the calculãtéd stresS has to be evaluated accordingly. The

maximum stress fo each load case considered is fOund using von

Mises stress criterion.

Three different lcad cases are considered:

1. Fu±ictional loads.

Analysis of pare functional loads

This analysis defines the properties ofthe span (natural

frequency, an4 axial force) in the static situation.

Extreme vertial load,

Functional anã. environmental loads in the vertical plane. ctreme horizântal load.

Functional and environmental loads in the horizontal plane..

The cothbined

load,

cases 2 and 3 are both investigated assuming

that the naturai frequency is equal to the frequency found in

load condition 11 The tension includes both 'linear"

contribu-tions and the fi ural induced contribution orreSpbnding to

4.2 !uncti9na1oad

The functional lOads .iSa stati load case: and the normal force

and the moments are found using the procedures outlined in

Chap-ter 3. These forceS are used to calculate the stresses in the

pipe wall1, and the maximum conthined stress check can be

perfor-med. '

-in

addition to the moment and nonal force, the natural frequency

is found.

4.3 Extreme Vertical Load

The analysis is carried out usiig the natural frequency deter-mined under operational conditions. The frequency is

_{usd to}

de-terrnine the actual value of _{Vr and Ur corresponding to the}

selec-ted extreme load case. Correspondingly _{a KC.-nunther. is defined.}

These parameters and the gap ratio _{are used as etitries' to the}

response amplitude database

and

_{a maximum peak to peak response} Ypb/DQ

is fOund.'

The response found may be significantly smaller than the posg:ible ma,drnum. If a larger response, can be found for

values of Vr and Ur which are smaller than those found for the

extreme load case it is recommended to select the largest respon-se for the calculations.. It meanS that resonance and synchroniza-tion with vortex shedding takes place for _{Smaller. fiow velocities}

than those. induced by the 'extreme load case. "

The bending moments are found assuming that the maximum amplitude midspan is :.'

4-2

4.4 Extreme Horizonta]. Load

The.-.ana'lysis- is-carried .out::-Similarly to the analysis- in the

vertical plane. . ---'.. . -:.

The actual values of V,tJ,: KC 4nd. e/D0 are used

the response -data base -and

the maximum peak:

response x/D0 is found.. Again, should a larger for -lower .v values than the- extreme,

r

..

-these. The bending moments are amplitude mid spn is

x =

4.5 Von Mises Stress Check

The stresses foufld in the various load cases are combined using

Von Mises Stress, Check. .

Von --Mises stres is usually defined by the stresses in the main

irect--ions of t1e pipewall (resp. hoop and combined longitudinal

stresses)

as entries to

to-. peak ...otal

response occur it is ecothmended to use

found assuming that the maximum

/2

+ 2

- aH(L ±.

The stress condition in the pipe wall can be considered

2-dimen-sional and the fbliowing components are included: Hoop stress : Effect of pressure difference

Normal stress Effect of axial force

Bendiig stress ab Effect of bending thoment fQm.functional and extreme loads

5. _{ACKNOWLEDGEMENTs}

The wok is part of

_a Joint _{Industry Project "Spaiting of}

Pipelines1' sponsored b the fo1löwin _companies: EP thternãtjbnal Ltd. (UK)

CoPoco Inc. (USA)

Department of Energy (UK)

banish Oil & Gas Production _{A/S (DK)} Exxon ProdUction Research Company (USA) Norsk Hydro A/S (N.)

Statojl A/S (N)

The authors iish to thank _{the Companies and}

the members of the

Steering comittee fl1owing

_{the Poject for their encoiraement}

and permission to publish _{the material.}

_{It is noted that}

the

ideas and opinions _{expressed in this}

paper are those of the

authors and have not been _{approved or endorsed}

by any o

the

sponsoring companies

6.

REFEREtiCS

/1/

Audiert & Nyrian (1977), "Soil Restraint against

Horizontal Motion of Pipes", ASCE, VOL. 103, GT1O.

/2/

Blevins, R.D

(1979), "Formulas for Natural Frequency and

Mode Shae", VanNostrand Reinho]4 Company, New York.

/3/

Bruschi,

R.,

Montesi,

K.,

Ragaglia,

R..and Tura,

F.

(1987), "A New Boundary Element for Free Spafl Aflalysis'!

OMAE 1987.

/4/

Bruschi, R. and Vitali, L.

(1988), "Large Amplitude

Os-cillations of. Geometrically Non-Linear Beams Subjected to

Hy4odynamic Excitation",OMAE 88, Additional Paper.

/5/

DetNorske Veritas (1981), "Rules for Submarine Pipeline.

systems.

/6/

Hetény.j. (1946), "Beams on Elastic Foundation", University

of Michigan.

/7/

.

Hinstrup, P0, Coiquhoun,

R.S. and Gravesen,

H.

(1985),

"Danish Submarine Pipeline Guidelines", 1st draft,

prepa-red by

anish Hydraulic Institute and Raxnbl1

&

Hanne

mann.

/8/

Hobbs,

i.E.

(1986), "The Effective Length of a Pipeline

Free

Spain", 5th OMAE, Tokyo.

/9/

JacbbSen, V.,

Bryndum, M.B., Nielsen,

R. and.Fines,

S

"Vibrations of Offshore Pipelines exposed to Current and

Wave Acion., 3rd International Symposium on Offshore

6-2

/10/ Mousselli, A.H. (1977), "Pipe Stresses at the Sea Bed

during Installation and Trenching Operations", OTC 2965, Offshore Tech. Conf. Houston.

/11/ Naess, A.A. (1985), "Fatigue Handbook, Offshore Steel

Structures", Tapir, Trondheim.

/12/ Richard, Hall & Woods (1970), "Vibrations of Soils and Foundations", Prentice-Hall International Inc., London.

/13/ Roark, R.J. and Young, W.C. (1976), "Formulas for Stress

and Strain", 5th ed., McGraw-Hill Book Company, Auckland.

/14/ Tsahalis, D.T. (1983), "The Effect of Seabottom Proximity on the Vortex-Induced Vibrations and Fatigue Life of Of f-shore Pipelines", OMAE and ASM.E Journal of Energy Resour-ces Technology.

/15/ Tsahalis, D.T. and Jones, W.T., "Vortex-Induced Vibrati-ons of a Flexible Cylinder near a Plane Boundary in

Stea-dy Flow", 13th Annual Offshore Technology Conference,

Houston, Texas, OTC 2991, 1981.

/16/ Tsahalis, D.T., "Vortex-Induced Vibrations of a Flexible

Cylinder near a Plane Boundary Exposed to

Steady and

Wave-Induced Currents", ASME Journal of Energy Resources

0tT

na1 (I)

iitess J3

aI1 ()

ijt

t1ni) ()

Extena ixrro,oncotir, )

ciri

ti (/.3)

eigit xating (k/a)

tarna1 orrosiOn tir (kJ3)

Ccnt (k/3) EL4TiCIrf jiu of (PJ ct4Lra1 d31rb]

(1 'i rrt)

SI Rejal (kfl) EffRA11iKflm

dC'ciui

ic1lx3, ZJ1 nr iP,)

('

E:c.!e r'urn 'i,E*iit iu (Cttl 1) h1D

APPENDIX: ExAMPLE. QF APPLICATIQN OF PQRAMMEDHI$ PAN

The methOdology and procedures for, the Oalculation ,Qf the fatigue

damage and maximuth stress of a free spanning

pipeline as

descri-bed in the preet paper have been impl!mented.,i

the PC-based

computer programme DHISPAN.

The DHISPAN programme is a set Qf menu

riven pogramnxnes and

con-tains procedures

catng structural properties,

generati-on of envirgenerati-onrnenal input arid calculatigenerati-on of fatigue damage and

extreme lo4d stresSeS. Options are available for

displaying

ana-lyzed data on the: monitor or on a prthter/p1ottr.

The application of DHISPAN has been illustrated by running th

program with selected inpat data

epresenting pipeline, span and

fatigue parameters a4 environenta

data., Four span lengths have

been considered.

Input Data for Analysis.

Pipe, Span and Faigue Data

The input data for span length equal to 40 m is presented below

Npe }ieru .1 . lri. 9.3

0.73 0.8l3 0J37(3 ti3.i) 65.0 2100 0.uiCi)3 10.0 7.0 1!L1.l

DIRECTIOH n1a relative to nirth (eg)

L;m Span (a)

A-2

o.o

SOIL

Stiffre ()

: 2.SJ)3

DnV 1977 Rules, Appendix C, A stress concentration factor of 2.0

has 'been aliéd.

Environmental Iiiput Data

The input is given as a wave scatter diagram. A directional

dis-tribution is applied fo# each box Of the scatter diagram. For

smaller waves the dominating directions are selected _{as waves}

from SW, W and NW. For increasing wave height the directions W,

NW and. N are dominating.

Axial frictic ccfficiest :

Tr.vse frictic, coefficient :

Ocing ratio th teria r ation)

O.E))

i tO

'.iti ()

0.5I3

AOOED Ccfficient C; : 1.1)3

E3co& reti.rn to Edit ru Itrl

The SN-curve has been chosen as the curve X (Tubular _{Joints) of}

DHI( '

11M Scatt K 8.1 - V.s.

dcWatDth(i)

ati of Eèa

Stata (:)'

Pea¼Periec)

b!o.,.'hn,M:

4,3.33 14.

The current has been specified with directional dStiution and

associated probaiiit-y.

Csrt

eniB.2

58.33

Sig. Wave Hecgtz (:)

59.50.08

4.375 7.125 12.625 1.258 L8 1233.8 158 0.8 2.75 1G.8 333.8 433.13 13.0 4.259 8.8 8.8 33.0 18.8 5.758 8.9 13.9 .8 .9

7.8

8.8 13.0 8.9 .18.9

ria1

-,Aiticn Y

retLrfl to Edit 1erU (Ctrl T> h,io

C4zret (a/z)

:0.3)

Cia-rent ircticfl relative to kcth (deg)

:0.33

t iti,Wtion

IE of Ittterva3, Hr i tax Soe*i (/) I 0.23 OM

Curt t.S3tributin beke Diroticial :ttibition Yj1

C&rent J F'robai1ity I '1 I 1 1 I ;i I I i

0.20 1. L13 0. 3.24 J.30 0.E 0.3 0.f.)) 0.3)0

Results of Analysis Strutural-Aia-iysiS

The results of the structural analysis for the span length of 40

rn is

shown

below

1U T YSIS iDOITIuAL JTP'JT

LC):

(N/ti): 36.57

Vrtica1 Load qv (N/ti): 57

Hi:oiit31 L'i (N/a): I3.3

.:1 PIPE i)IL D:

3(11 (ti) :

ii (a) : 8.7&'3

tri ()

: O.Q19l

El

(2)

4E8E3 TAn3 (N) I 4E+i'J5

-ff (Ks/a) 165 51 Kztt (KS/ti) 2Q ..2

n,1 (N/a. 2 i r'c I)5.

ML FRPJ1ETER PJ1O FETM L8Th:

LiO Caa : 4.U3 LabdaL :

of It tio: 33 6Ii*&ES T,I'N 3.4 Bet 0.151 :TTIC O'hTIi: 'aaxt JLT.4 Xaaxfl_ FRIcTtcN AO tffCtt( LE(TH: L3/t i.8 Lo/L : OThNIC FROPTIES:

Fnat (It) : 0.771 hapefa : 0.i118 Lcq :

Generation Of Environméntl Sing].eEvents

A-4

The hydrographic input is transformed into a large number of

sin-gle events at the pipeline level. The distribution o the wave

induced orbital velocitieS at pipelinerlevel, tJ, and the associ-ated periods together with the current

distribution

is shown ver-sus the relative duration for each event on the figure. below. The

velOcities are for each event given as' the component perpendicu-lar to the pipeline.

Uw 1.50 1.25-1.00 0.75- 0.50- 0.25-0.00 1.OE CT Tzu 4 UU 12.00 iaoo 800 0.3 0.30 rim 0.20 0.15 0.10 0.05 0.00 ICE Uc IlIllUlIll i; ii

1.OEG6 1.OELO5 1.CELO4 1.0E1-03 1.0EL ICELCI 1.OE+00

t 111111 I I

6?°OE-0T ICEL05 iDE 05 iCE 04 1.CE-03 iCE ICE

07 iCE 06 iCE 05 i.OE-04 I _{CE-03 ICE} iCE

PcI duration

BPeI duration

01 1.OE+00

Pelduration

01 i.OE'+OO

ing!eeents environment file:IBCEX.LC3T

Damage Calculation

A-6

Example of output for the damage calculation for the length of 40

in is shown below

T0T. E

0age Ca1c1atin Prii (days) Z.5.08

Irrtir 1.059 E-3

Cros-fka ø.18 E3 I 0It? CF SL1E airs DE

2 DISFU? CF SDE EUE{1S JLI} FACT

3 DI1A?CFSflG.E E{rS OATh EAi

4ftOT

5 R1T FtOTS

-..-

ATT OtAGM

toesuit

ri

(Cttl 1> ip

1I4 0aaeRej1t ni 0.2 Vz. 0.i3

cz Daiage atter Nei 0.2.1 s. 0.W

SCATTER DiA1CF

!n-iincross-floi(N):

y Total Dage

Dratiai of the C3lculation Pioi (da)

Oae is 1tipii with 1.EE3 Tp 4. 7.13 9.27 I2.b

1.5 9.::: O. 8.96 8.

2.75 O.3 e.r O.( 8

4. e.a 9.O 9. 9.072

5.75 O.CO3 0.( '3.121 8.E

O. 8. '3.9 8.733

Hs

rtr,iaticn Ratio: 8. Ertrlation Ratio: 9.14

Example of detailed listing of.

40 0.77

50 0.53

60 0.38

65 b.33

N KC

R XI

Ypo YSC?pp 0 C3I KY 1thoX ItnoY

12)112.2 L4 02 0.02 0.01 .3.133 0.01 1.22 1.56 1.42 5 2 .272152 t 0 002001002002 122 155 142 12 15.2 1.5 3.4 0.02 0.01 022 0.01 123 1.56 1.42 1224 15.2 1.6 0.2 022 0.01 022 022 1.20 1.56 1.42 1235 12.2 1.2 0.0 3.2 !).02 823 022 1.22 US 1.42 £225172 12 14002 Out 002302 IJ 158 142 0 1227 172 U 0.3 3.02 0.02 323 13.02 122 1.56 1.42 S

H KO UP UP U W)y Xçç XpoLO Xçã1 Ypp Xstd ?d

122112.2 i 1.4 L -I.62 L 0. 022 UI 022 0.138 12 15.2 1. 2.0 -6223 312 3.07 3.08 022 0.01 322 0.31 1233 15.2 1.5 0.4-62.12 -3I.07 0.16 0. 322 0.01 '322 323 1224 15.2 1.6 3.3 -62.22 -3.) 023 023 1322 0.21 0.02 0.01 1225 17.2 1.2 0.9-6223 .5 0.37 023 0.02 322 022 0.01 i221T2l3 046137 3137 't08 0020.01 302001 123717.2 1.3 3.3 -6L61.-26.72 U? 8.08 U? 1322 022 8.91

Results of al.ysis for Span Lengths: 40, 50, 60 and 65 m

SP.

NATtJBAL

LH FtThCY

(1.st.

rtde)

Cm) _(Ha)

NWSPN

STIC

DLECrION (in) damage calculation: 0JT Ui 0.3 4.1E -13.2 -.8intp .. 0.0 l.OE+0002 -11.8 45.1)intp 0.4 L'i302 -11.5 -260 intp 0.3 1.E0l? -11.5 -26.3 irttp 0.2 ?.'1 -11.5 -26.0 intp 0.4 1.gE431 -11.4 263int U 7.13Ei31S11 -11.4 -.0icltp

L DAGE

FOR 1 YEAR N VE + CURR.

FL.

1 61x103

..oio

6.49x102 1.36x101.

53

58

,J U S 5 0 2.43x1O5 5.95x103 13 COB ES ThG

EATIJE

LIFE CAILIA WI A LflVIIT DAfr RATIO

OF 0.1 IN-LINE CPCSS-FLO1 62 .5 1.5 4120 0.74 17 O.Y- KC 1221 I.-0E U.CE+XO 13.2 1.4 12 4.1E4))35 3.0E'3 15.2 1.5 1 4.E- 9.UE' 15.2 1.6 1224 46E-l3 15.2 1.5 iZ 1.-Th 00C4O) 17.2 1.3 i 2eO35 ojcj 17.2 1.3 1227 1E- 0CE+LL)3 17.2 1.2 0,.10 0.21 0.40 0.53