Application of probabilistic methods for calibration of submerine pipeline design criteria

To be printed in the Proceedings of the First European

Offstore Mechanics Symposium,

Trondheim, Norway, 20 - 22 August 3990

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APPLICATION OF PROBABILISTIC METHODS FOR CALIBRATION OF SUBMARINE PIPELINE DESIGN CRITERIA

Torbjrn Sotberg SINTEF Structural Engineering

Trondheim, Norway

ABSTRACT

À method for reliability analysis of submarine pipeli-nes has been developed and applied in a numerical case study addressing three possible failure modes concer-ning on-bottom pipelines excessive displacement, yi-elding and buckling. Different uncertainty sources re-levant for these failure conditions are discussed and included in the analysis. Two alternative approaches for safety assessment are indicated. The reliability calculation procedure can be applied directly repre-senting a full probabilistic design or indirectly through a proposed calibration procedure.

I NTRODUCT I ON

The recent developments related to on-bottom submarine pipelines have lead to a redefinition of the design practice applied. The newly developed design method reported by Sotberg et al. (1988 and 1989), allows for

small movements of the pipeline during the most extreme 'nvironmental conditions in the lifetime. The earlier pipeline stability design procedure for on-bottom pipelines was normally based on a simple

stabi-lity check requiring balance between the hydrodynamic forces end the pipe-soil resistance forces. The new design procedure has the potential to give a more eco-nomic pipeline design, with a prediction of the real safety level against relevant pipeline failure modes. When considering a pipeline design based on a dynamic stability criterion, i. e. allowed movements, the strength limit state needs to be evaluated. Allowing pipeline movements under extreme environmental condi-tronS implies that the stress condition at constrained points along the pipeline has to be checked to verify

a satisfactory design. This means that the dynamic otability design for on-bottom pipeline sections needs

Lo consider several limit states (failure modes) such as pipeline movements, yielding and excessive strai-ning which may cause local buckling or collapse. In this way, the relaxed design criterion with respect to pipeline stability, introduces a need for some addi-tionaL design controLs as compared to the traditional procedure. However, the benefit from this will be a more cost optimal design based on a thorough safety

luat ion

The behaviour of a submarine pipeline on the sea bottom is physically rather complex. Ocean waves must be regarded as stochastic processes and both the hyd-rodynamic forces and the soil reaction are highly non-linear. The numerical modelling of pipeline response is hence a relatively complex task, and assessment of the real safety level against structural failure is rather involved.

In two earlier papers by Sotberg et al.(1989 and 1991), the serviceability Limit state concerning lateral movements of the on-bottom pipeline section due to external wave and Current loading was investi-gated. In this paper, pipeline failure due to excessi-ve bending (yielding and local buckling) is investiga-ted in addition to lateral displacement. A probabilis-tic method has been tailormade to the present applica-tion predicting the probability o! structural failure or exceedence of actual limit state functions. Uncer-tainty analyses related to modelling of the environ-mental processes, soil resistance and hydrodynamic forces and to the prediction of load effects as well as pipeline capacity have been performed. Finally, re-liability calculations have been used to calibrate a proposed design procedure and to quantify the safety

level and sensitivity factors.

UNCERTAINTY ANALYSIS

G en r' cdi.

Submarine pipeline design should be based on a ratio-nal treatment of the uncertainties in the physical qu-antities and models governing the structural behaviour together with methods for predicting the safety of the structural design.

Different uncertainty sources which are relevant for the design of submarine pipelines are discussed briefly in the following. A typical classification of uncertainties is given by Thoft-Ohristensen and Baker

(1982), among others.

The main topic of the uncertainty analysis is to iden-tify and quaniden-tify the different sources of uncertain-ties which are present and to decide how to take them into account in the subsequent reliability analysis.

The performance cf subsiarne pipeline in different areas of interest is a rather complex function of a relatively large number of parameters. Uncertainties -rise from the ocean environmental modelling, from pi-peline, soil and site specific parameters, from model-ling of water kinematids, hydrodynaeic forces and soil resistance descriptions and to the structural model-ling and pipeline cross sectional capacity.

Uncertainties are measured through the variability

(coy,

of the parameters and functional relations. A systematic deviation may often be present which is denoted bias, i.e. ratio of actual to predicted value.

liodelling of the ocean environment

The ocean environment related to submarine pipelines is characterized by wave and current processes, and these represent the major external load condition con-sidered in this study.

The statistical description of the environmental pro-cesses (wave and current) is related to both a short term condition and to the long term variability of the short term Statistical properties.

The short term wave condition is modelled as a Gaussi-an process assuming stationarity within a 3 hour period. fach short term condition is defined through the Jonswap model wave spectrum. The spectral parame-ters, such as the significant wave height, H, and peak wave period, T, are applied deterministicatly for a given short term condition and assumed to be constant during the sea state. Wave directionality and spreading Should in general be accounted for in the short term description. The steady current velocity,

V,

and direction at the sea bed are also applied de-terministically and assumed constant during the short term condition.

The long term variability of the short term sea state parameters needs to be taken into account in the design process. A number cf approaches are possible to adopt for the long term distribution of waves and cur-rent. The method used in the present study is to apply the marginal (one-dimensional) distribution for the significant wave height. H5, and specify the peak wave period, T5, conditional on H5.

An appropriate distribution function should also be adopted for the long term variation of current magni-tude. It is noted that information on directionality of both current and waves is of particular importance for pipeiine design. Any correlation between waves and current should be properly taken into account. The uncertainties related to the different models

applied for short term and long term description cf the ocean environment have to be evaluated on the basis of the data gathering methods. The long term un-certainty in wave and current processes has to be mea-sured through the parameters in the respective long term distributions, while any short term uncertainty is related to the model wave spectrum applied. Uncer-tainties in the spectral form and peakedness have been found to be unimportant for the present application (Sotberg et al. 1990), as the significant flow veloci-ty at the sea bed is almost invariant to the choice of model spectrum (Soulsby, 1987).

The selected modelling of the wave and current envi-ronmental processes is in the present study based on application of the Weibuli distribution for the long

term variability of significant wave height, H, and a lognormal distribution for the peak wave period, T5. conditional on H. In addition to the long term model-ling, the annual maxima distribution of K5 (wave domL-nated), developed on the basis of the long term model-ling, has been utilized. The Weibull probability di-stribution is also adopted for modelling of the long term variability of V.

l'ioeline and soil. earameters

Variability of pipeline properties are in general con-trolled by specified limiting values in guidelines and recommendations. These are related to three categori-es, namely: to the process of manufacturing, to tole-rances on dimensions of the pipeline and to metallur-gical variables.

Variability of cross sectional pipeline data such an diameter, out of roundness (ovality) and pipe wall thickness will mainly affect the cross sectional capa-city against local buckling and collapse failure modes, and is not significant with respect to the global response of the pipeline for external wave and current loading, as noted by Sotberg et al. (1990). Among the metallurgical variables are the yield strength and possible residual stresses which nay be of significance with respect to yielding in the pipe wall.

Bias and statistical variability of these parameters should be taken into consideration in the reliability assessment. Statistical data usid in the present study for pipeline and soil parameters is given in the section on the numerical Study.

Filure modes .- uncertainty in pige strenqth

All relevant failure modes should in general be coen-dered in a reliability assessment of submarine pipeli-nes.

Identification of relevant failure conditions (or limit states) for pipeline spans has been conducted by Walker (1989) based on classification given in the De-partment cf Energy Pipeline Guidance flotes 1987). Three different classes of limit states have been used. Class I is related to a completely unacceptable condition of pipe rupture. Class II concerns the ser-viceability limit state and Class III is related to a

condition which could develop into Class It or t. F.elevant limit states to be considered in the design of submarine pipelines (installation and operation) are also proposed by fIlmas et al. (1987). Three dif-ferent primary limit states have been indicated: The Ultimate Limit State considering the strength of the pipeline for pressure, axial and buckling loadings, the Serviceability Limit State considering excessive deformation of the cross section and loss of on-bottom

stability and the Material Limit State considering fatigue failure or corrosion.

Classification of limit states used in the present work is given in Table 1, This classification follows the same lines as indicated in the references above. The following requirements should be fulfiled for dif-ferent conditions: Serviceability Limit State in which the pipeline must be able to remain in service and operate properly; Fatigue Limit State considering both high cycle and low cycle fatigue damage; Ultimate Limit State in which the pipeline must remain intact

and avoid rupture, but

not

necessarily

be

able

to

operate

and

ProgLessive Limit State considering

pro-gressive collapse of the pipeline

due

to

accidental

Loads

and/or local damage with loss of structural

in-tegr i ty.

Table 1.

Classification of Limit States for submarine

pipeline desig. and related failure modes

Different safety classes should be included to account

for the different consequences

with

respect

to

the

above

failure

conditions.

Typically

three

or four

safety classes are used in codes and

recommendations,

with

failure related to gas leakage near the platform

representing the most severe and exceedence of

opera-tional

criteria being the least severe. Target safety

levels related to different safety classes are

discus-sed later in this paper.

The

failure modes evaluated in this study are failure

related to excessive yielding

and

pipe

displacement

and

failure

caused by local buckling of the pipeline

wall due to large bending curvatures.

Yieldinq

The

onset

of

yielding,

which

should be

checked for the SLS

condition,

represents

a

change

from

elastic

to

plastic

material

behaviour. Yield

strength is typically controlled by application of the

combined stress fcrmulation through the von Mises

cri-t e rio n

(Ci2

I l 0

where

_0eq

is the von Mises equivalent stress. G

and

111

the hoop stress and longitudinal stress,

respecti-vely. n is the utilization factor and

the specified

minimum yield stresS.

Both

the hoop stress and the longitudinal stress

com-ponents are random response variables and the

statis-tical

variabilities

should

be taken into account in

the design calculation. Uncertainties in response

are

modelled

through

uncertainties in the transformation

from loads to load effects and not directly as

coy.

on

the response. In addition, model and parameter

un-certainties in the von Mises yield criterion

as

well

as

the

statistical

variability

of the yield stress

should be included.

3

fice

caoacilfor cure beninq

Information about the

inelastic behaviour and buckling performance

of

sub-marine

pipelines

is

essential

for

the reliability

related to strength limit states. Basically two

diffe-rent

failure modes exist with respect to bending

loa-ding.

mit load type of failure (maximum moment)

Bifurcation failure (local buckling)

The

limit

load

type

of failure (maximum moment) is

controlled by the balance

between

increasing

moment

due

to strain hardening and a reduction of moment due

to increasing circumferential ovalization for

increa-sing

bending

strain

towards

the

critical

bending

strain. Bifurcation refers to a change in the

deforma-tion

pattern

and

thus also the moment capacity. The

bifurcation buckling is caused by the

development

of

local wrinkles axially in the compressed region of the

pipe cross section.

A

variety of design formulae for prediction of

criti-cal bending strain related to locriti-cal buckling

(bifurca-tion) are found in the literature. Characterization cf

bending based on curvature and strain is beneficial as

the

slope

in

moment-strain curve is nearly zero for

large bending strains. Figure 1

presents

experimental

data

for

both the curvature at maximum moment (limit

load) by solid dots, as well as for the buckling

cur-vature (bifurcation) by open circles. For thick-walled

pipes, the maximum moment is seen to occur well before

local buckling, whereas for thin-walled pipes buckling

occurs abruptly at the point of maximum moment or, for

very

high

D/t

ratios,

before

the

development

of

maximum moment. Two different empirical design

formu-lae are given on the figure. These are

0.5

t/D

Murphy and Langner (1985(

(2)

tbl

(4 t/D(2

Marshall (1977)

(3)

where

D

and t are the steel pipe diameter and

thick-ness, respectively.

For

the

description

of bending capacity used in the

present work, the

formula by Murphy and

Laogner

is

applìed

with a measure of bias and coefficient of

va-riation representative for the actual D/t

ratio

Stu-died.

Example

For D/t =

40, the mean bending strain

capaci-ty C5

2.5

s,

with a standard deviation of about

0.6

- 0.7 % according to the experimental data, see Figure

1. Equation 2 gives C5

= 0.5 t/D )= 1.25),

this

re-presents

a

bias of about 2,

and a c,o.v. equal to 25

s,

i.e. design formula

equals to mean value

minus

2

standard deviations, representing the 2

9

fractile,

Structural rsodellinct

Uncertainties

related to the structural modelling for

calculation

of

pìpelirie

displacement,

stress

and

Strain

in

the

pipe wall are discussed in the

follo-wing.

The

load effects, pipeline displacement and stresses,

are calculated by the PIPE computer

program

)Sotberg

et

al. 1988), which is a special purpose design tool.

The PIPE program utilizes a generalized response

data

base

containing information about the lateral

displa-cement of a pipeline section with no boundary

constra-ints

as

well

as

the

bending

stress response at a

clamped end point of the pipeline as in the

model

in

Figure 2. The pipeline model shown here is a

relative-Servicesbility Limit State

)SLS)

- excessive movements (loss of dynamic stability(

- ovalization (flattening)

- yielding

Fatigue Limit State

(FLS)

-

high cyc)e fatigue damage (elastic)

-

_{low cycle fatigue damage (plastic(}

Ultimate Limit State

(IJLS)

-

local buckling failure (bending, pressure, axial)

- hydrostatic collapse due to excessive ovalization

- excessive strains

Progressive Limit State

)PLS)

- progressive buckling

- pipe rupture

ly simple representation of the finite length

pipeli-ne, and will be conservative with respect to the cal-culated stress level at the constrained point. The pipeline response given in the data base is further based on a linear pipeline material model which is not appropriate when considering the local buckling failure mode working with strains far into the plastic range. To handle this Situation a coupling needs to be established between the strain response based on the idealized model in Figure 2 and a more realistic model representing a pipeline constraint due to pipeline burial as shown irr Figure 3. This relati-onship between the linear elastic strain based on the idealized model arid the plastic strain based on a more realistic and comprehensive model is illustrated in

Figure 4. _This curve is representative only for the specific pipeline case which it is generated for. The plastic strain response is generated based on a model-ling of the transition zone between a buried and a free pipeline section using a non-linear pipeline ma-terial formulation as well as modelling the non-linear soil reaction forces. The PONDUS computer program (Uolthe et al. 1987) has been used for these

calcula-t ions.

A modei uncertainty factor, has been included to take into account general model uncertainties, and more specifically to model the variability in predic-ted response due to uncertainties in the generalized response data base in addition to uncertainties intro-duced through the transformation from linear elastic to non-linear plastic strain according to Figure 4. Uncertainties in the response data base concerning strain response can represent a variability of up to 25 (Lambrakos et al. 1987), but tends to be lower here as the strain response is tuned to the specific pipeline case through the curve in Figure 4.

The model uncertianty factor n is represented by

adopting a normal distribution function with a

coy.

of 25 9r, which accounts foc all kinds of uncertainties

present in the pipeline modelling. The model 'incerta-inty factor is applied directly to the load effects.

Statistical. uncertainty

À statistical. uncertainty is present in the prediction of pipeline response due to the variability of the wave realization in the time domain. The pipeline re-sponse will be dependent on the actual wave tisi'

series used in the simulation as ilLustrated by Sntberg et al. (1990) where series of 100 simulations .ere performed for wave time series generated based on different seed numbers but wzth identical statistical properties.

There are principally two different ways of including the description of statistical uncertainty into the analysis. One approach is to investigate the variabi-lity in load effects directly based on simulations for different wave realizations, arid use this information to select an appropriate distribution function and c.o.v. This approach was applied by Sotberg et al. (1990) in the prediction of lateral pipeline movement. A second approach, which is used in this study, is to model the effect of statistical uncertainty as a va-riability of sosie characteristic properties of the wave time series relevant for the load effects stu-died, i.e. maximum flow velocity for stress and Signi-ficant velocity for pipeline displacement.

4

The maximum stress during a 3 hour sea state is related to the maximum simultaneous action of lift nd in-line forces, which again is governed by the maximum water velocity cycle during the sea state.

The flow velocity process at the sea bottom is a Gaus-sian narrow banded process with the following extreme value distribution.

F,(y) = esp)-N exp ! (L.)2)1

2 O

where y is the extreme value of the velocity. O is the ritandard deviation in the Gaussian velocity process and N is the number of wave cycles in the sea state.

Asymptotically, based on a lìnearization at the point of maximum likelihood, F(y) is Gumbel, extreme-value type 1 distributed:

F5')y) exp)-N2 exp(-T2lnN

To model the statistical variability of the wave velo-city maxima, the Gumbel distribution (5) has been chosen. It is noted that the Gumbel distribution has a slightly larger probability content in the upper tail than the exact distribution (4) for the typical number of wave cycles in the 3 hours sea state. It is, howe-ver, possibiS to obtain a more accurate fit in the tail by reducing the standard deviation of the extreme value distribution to make the probability content ne representative irr the tail, i.e. at the design point. The significant flow velocity is scaled in the analy-sis to model the statistical variation of the maximum flow velocity. The statistical uncertainty factor is introduced for this purpose, and modelled by the Gumbel distribution with a coy, of il 'is.

RELIABILITY ANALYSIS

Generai.

A variety of procedures representing different levels of sophistication may be used for calculation of failure probabilities. À description of various theo-ries and levels of approximation is given by Thoft-Christensen and Baker (1982) and by Madsen, Krenk and Lind (1986) among others.

Methods of reliability analysis are classified into three main groups by Theft-Christensen and Baker (1982). The most refined methods are the level 3 methods which take into account the exact forre of the failure domain and make use of a complete probabilis-tic description of the random quantities entering the design problem. In level 2 methods some idealizations are introduced commonly related to the failure functi-on (linearization) and the representation of the random quantities, through the distribution functions. Both the level 2 and level 3 methods are siiler in the sense that they give prediction of the structural reliability. The level 1 methods are mainly safety

checking procedures based ori a calibrated set of partial safety factors or partial coefficients arid the use of only one characteristic value of each random quantity.

The classification by Madsen et al. (1986), gives roughly the same overall distinction between the

L))

ci

(4)

classes and adds the level 4 method which includes so-cIoeconomic considerations as welt as failure consequ-onces.

Method of analysis

Characteristic for design of submarine pipelines acc-ording to the present formulation is that application of a standard reliability calculation procedure is difficult. This is partly due to a complex trans-formation from basic load and resistance parameters to the random response quantìties, which means that the failure function is not explicstely defined in terms of the random quantities. It is further not possible to adopt distribution functions to response quantities directly other than by means of simulation, i.e. through the process of transformation from loads to Toad effects. Characteristic for the problem is that the system behaviour is highly non-linear both with respect to loads and resistance, which in turn makes the failure domain complex in terms of the basic vari-ables. These considerations lead to the choice of using a simulation procedure for calculation of the failure probability based on an approximate but very efficient response prediction.

The reliability calculation is for the present study based on an importance sampling procedure by use of the computer code ISPUD (Borgund and Bucher, 1986) combined with application of the semi-probabilistic design tool PIPE for load effect calculation. The com-bination of importance sampling and the response pre-diction based on the generalized response data base provided by PIPE is found to be very efficient for the present application. Totally this procedure combines all the advantages of both exact and approximate met-hods, by first a prediction of the design point and

secondly a rational simulation concentrated around that point.

Taroet Reliability Lvl

When dealing with reliability analysìs of structural systems an appropriate safety or reliability level should be decided, referred to as a target reliability

level. Any evaluation of safety level should be based on information about the safety level implied by past and present design codes and compared with historical data on reported failures.

The safety level of existing pipeline systems designed according to traditional procedures acy be a good re-ference for the target level if the reliability (acc-ording to failure data) is ori average satisfactory. It is important to state that this is related to the average failure rate only, as there is expected to be

a large variability in the real safety from one pipe-line case to another, due to differences and shortco-mings in design practices in the past. The target safety level should further be related to the consequ-ences of different failure modes as well as the nature of failure, and it may be found that the target safety level should be increased or even could be decreased concerning specific failure modes.

In this study, safety classes are used on the basis of the type and the consequencies of failure. This is consistent with the recommendation given by The Nordic Commitee on Building Regulations (NKB, 1978) with annual failure probabilities as given in Table 2.

Table 2 Annual target failure probabilities, NKB

Ellinas et al. 1989 presented some data of historical failure rates for North Sea operating pipelines which is expected to be representative for past design prac-tice and is thus a natural starting point together with recommendations given in relevant codes and gui-delines to decide upon the appropriate target safety level. The annual failure rate for leakage was found to be about 10 and for rupture 10. It is noted that the failure rates for the pipelines, excluding safety zone and riser are given per km pipeline per year.

In the present study, reliability calculations have been performed for three failure modes: excessive displacement and yielding, both considered asservi-ceability limit states and local buckling considered as ultimate limit state. A target failure level (annual failure probability) could be in the range of 10 to for the serviceability conditions and from 1l to 10.6 for the ultimate condition. These ranges of reliability levels have been used in this study, without stating that a certain level is the

correct one.

Load combth&tion - Probbilistr modellino

eased on earlier studies (Sotberg et al. 1990) it is

known that both wave and current loading are of signi-ficance for the extreme load effect on the submarine pipeline system. It is thus clear that the simuLtane-ous action of the combined wave and current loading needs to be considered in the reliability analysis. The main question is thus: Which distribution function for the characteristic wave and current environmental parameters should be used in the reliability calcula-tion? Basically two alternative approaches exist Method 1 Use of the long term distribution of

signi-ficant wave height, H, and current veloci-ty, V. The long term distribution is equi-valent to the instantaneous-point-in-time distribution.

Method 2 If the response is wave dominated: tise of the maxima distribution of H5 in the refe-rence period for which the reliability is calculated. toiether with the instantane-ous-point-in-time distribution of V,. If the response is current dominated: Use of the maxima distribution of V in the refe-rence period together with the instantane-ous-point-in-time distribution of H5.

The reference period for which the reliability is cal-culated is set to 1 year, i.e. P refers to the annual

failure probability. 1978) Fa ilure consequence Eailure type I - ductile with

II III reserve capacity II - ductile without lion serious io 10 'I _{reserve capacity}

Ser ious 10-d 10-e III - brittle failure Very serious 10 1O 10 and instability

A Short discussj with respect to the two possible approaches is given below. Differences between relia-bility results by using both of the methods are further commented on the basis of the numerical Study. Method 1: By using the long term distribution function (arbttrary-point-in_timej for both H, sud V in the relsabil ty calculation, no assumption is taken with respect o what is the dominating load type if any. Nowever the result from the reliability calculation gives information as to whether the case is wave domi-nated or current dominated or if the load types are about equally important with respect to the variabili-ty in the load effect. This information is given through the sensìtivity factors.

Method 2: When using this method two design checks are in general necessary, if it rs not known in advance whether the response is wave or current dominated. Re-liability calculation is then performed both with the extreme value distribution of H5 together with the long term distribution of V and vice versa. The case giving the largest failure probability indicates the dominating Load type by its extreme value distributi-on.

This procedure of combining load distributions is ana-logous with application of Turkstras rule (Turkstra, 1970) for predicting the maximum of a Sum of stochas-tic variables, but dealing with distribution functions instead of stochastic variables.

The long term distribution or arbitrary-point-in-time distribution for H5 and V is given by the Weibull di-stribution. Distribution of the maximum value for a given reference period can be derived from this parent distribution.

Parent distribution (Weibull), o and y are distributi-on parameters:

H5

= 1 - exp (-(--)), (6)

The Weibull distribution of both H and V5 is of the form

E(x) i - exp)-g)x)) (7)

where g(x) is an increasing function of the argument x. The extreme value distribution approaches asympto-tically the lumbel extreme value distribution of the following form when assuming independent values from sea state to sea state:

F(yJ exp (-exp

(0)YUv))

(6)

The parameters a and u can be found from the parent (Weibuil) distribution.

xv

9(x) ()

dx x

F(u5) 1 - 1/n, (11)

where u is the characteristic value and n number of independent values during the reference period. This gives for the Weibull distribution:

6 1/Y u,: = O In(n) a o (13) The mean and standard deviation of the Gumbel extreme value distribution are then given as follows:

0.5772

uy

0.5772 ] (14) £(y( u - O[ln)fl) )y-1)/Y a y(ln(n( ITO ₍₁₅₎ [6 y(ln)n) )

The parameters in the extreme value distribution are given in terms of the parameters in the parent distri-bution (Weibull) and as a function of the number of individual sea states, n, in the reference period. It is to be noted that when the reliability is related to

a 1 year reference period the maxima distribution must

be established for the same period, i.e. n N5 2920, This is necessary in order to obtain consistent results when comparing the two approaches outlined. It is noted, however, that this is seen to be used incor-rectly in some cases as the maxima distribution is related to the lifetime or a 100 year period but still used in calculation of the annual failure probability. The failure probability estimated directly when using method 1 refers to the duration of the sea state and

the transition to annual failure probabilities is given by:

(1 year) = i - (i - P1(3 hours)( (16) where l (=2920) is the number of sea states per year. The transition formula is based on independence between excursions from sea state to sea state, which is also assumed in the development of the maxima di-stribution used in method 2, i.e. method 2 performs the transition to annual probabilities indirectly through the distribution function for the dominating load type and the failure probabilities calculated are then given directly as annual probabilities.

Comparison of the two methods: Failure probabilities calculated by method 1 refer to a 3 hours period and

are thus order of magnitudes smaller than those calcu-lated by method 2 (before transformation to the same reference period). The failure probabilities calcula-ted by method i can in some cases be extremely small,

which may be a disadvantage with respect to numerical accuracy.

The calculated reliability level should be comparable from both methods, provided that the reference period for the extreme value distribution of the dominating load type is correct, and that the studied load effect is governed by the extreme values in the di-stribution function for the environmental parameter

(H5 or Ve), i.e. one of the load types dominates the response relative to the other.

In case of any deviations between the calculated failure probabilities, 2, it is expected that method 2 (annual extreme value distribution) yields smaller values. This is the case when mea states with smaller H (or

V)

values than those given in the annual extreme value distribution give some contribution to failure. However, submarine pipeline response for wave and current loading is found to be dominated by the tail in the wave- and current distribution and shows a ay

highly non-linear effect of wave height and current increased beyond a certain threshold value. It is thus expected that the two methods are close with respect to the calculated P1. It j however, noted that for a general linear case, method 2 will give nonconservative Pf values and the above effects should be carefully examined.

Calculations of the design point considering the envi-ronmental parameters may be based on both methods with the same restrictions for method 2 as noted for P1 calculations. Method 2 will of course give a wrong design point location in cases where the true design point is located below the peak point in the annual extreme value distribution, which may be the case for linear systems. This is, however, not relevant for the present application.

The sensitivity factors will be different based on the two methods, as the design point will be about the

saine but the mean value for the dominating Load para-meter (method 2) is increased to the expected 1 year

maximum value. The sensitivity factor isa measure of the location of the design point in terms of number of st. deviations from the mean value. The sensitivity factors have to be discussed on the basis of the refe-rence period for which they are determined.

Method i yields sensitivity factors related to the

du-ration of the sea state and failure probabilities in a single sea state, whereas method 2 gives relevant sen-sitivity factors dependent on a 1 year reference period. The main differences which are related to the length of the reference time period are that the sen-sitivity to the long term environmental data (wave and current) is decreasing for increasing reference time period, and similarly the relative sensitivity to time independent parameters such as pipeline, soil and model parameters is increasing for increasing referen-ce period.

NUMERICAL STUDY

Reliability calculations have been performed for an example pipeline for both 30 si and 80 si water depth. Three limit states have been considered, that is ex-cessive lateral displacement, yielding and local buck-ling failure modes. A relatively comprehensive Struc-turaL model has been used for prediction of bending Strain in the pipeline wall, Fig 3. The submerged pipe weight is the main design parameter as pipeline diameter and thickness have been kept constant. The submerged pipe weight,

W,

has been varied to cover a

certain range of target failure probabilities for the different limit states. Both procedures for reliabili-ty calculations have been applied and compared with respect to the calculated P. sensitivity factors and design point location as well as examination or the effect cf any correlation between wave and current data.

Date basis

Wave and current environmental data for the two loca-tions have been used as described in Table 3 and 4.

Other design data and distribution functions are given in Table 5.

Table 3 Wave environmental data (long ter. distr.)

Table 4 Current data (long term distribution)

The Gumbel maxima distribution of H5 and V for the reference period of 1 year is given based on the

parent Weibull distribution according to Eguations 6 -15. Mean values and standard deviations are given in Table 6. These environmental data are used in the re-liability calculations as described for method 2, whereas the long term wave and current data (Table

3,4( are used for method 1.

Table 5 Design data and distribution function Water

depth

Weibull (

parameters

O Y

Significant wave heights for return periods I - 10000 years

H5

1 10 lOO IODIO

30 si 1.083 1.346 5.1 in 6,1 si 7.1 m 9.0 in

80 si 1.91 1.38 8.7 s 10.4 s 12.0 si 15.1 m 30 m Mean E(HSI = 0.992 rn St. 8ev = 0748 si 80 m Mean E[H5) = 1.74 si, St. 8ev = 1.28 s

see equation 6 Water depth Weibull parameters Current return V velocity for per. i - 100 years VC V Y 1 10 100 30 m/80 si 0.238 2.525 0.54 rn/n 0.60 rn/S 0.65 rn/s Olean value : E[V..J = 0 211 rn/s

St deviation 0 0894 rn/s Parameter Mean value St. dey. Distributionh), comment T5)sec)2) 10/14 1.5/2.0 LW, F(T5185 ), 30780m loo 0.35 0.1 LW, rel. soil density W5(N/m( varied 300 N, submerged weight D (si) 1.25/1.2 .03 0, diameter, 30m /80 m

d rn) 30/80 0.5 N, two sites

D5)m) 1.015 .02 N, steel pipe diameter

t5(m( .0243 .0005 W, wall thickness E (N/rn2) .21E12 .1OSE11 LW, elasticity modulus

1.0 .25 N, model uncertainty 1.0 .10 G, stat, uncertainty 00(13/m2( 463E6 30E6 LW, X60 steel properties

2.0 0.5 LW, buckling capacity uncertainty LW = Lognormal distribution

N = Wormal distribution G Gumbel distribution

Table 6 Cumbel maxima distribution of wave and current

eliabiljty calculation results

ey data from the reliability calculations are given in Table 7 - 12 for all three limit state considered. The design criterion adopted for lateral displacement is 20 rn which is the same as used in the study by Sotberg et al.(1990). The differences between the two methods used for modelling of the environmental loa-ding. method 1: Weibull long term distribution of K and method 2 Cumbel annual maxima distribution for

H5, can be seen from the tables. Reliability data are given for a mean pipe weight of 6225 N/rn and 4000 N/rn

for 30 m and 80 m water depth, respectìvely. The annual failure

probabjlrty

is given versus pipe weight in Figures 5, 6 and 7. Based on these figures, the ap-propriate pipe weight can be found depending on a spe-cific target reliability level. Failure

probabilities

are given for two levels of wave/current correlation, 0HV = 0 and _P55 = 0.3.

Failure rates are usually related to the length of the pipeline section referring to failure rates per km pi-peline. The calculated failure

probabilities

can be given a similar reference for yielding and buckling based on information about the expected number of constrained points along the line. A conservative as-sumption may be one constrained point each km pipeli-ne, which makes the failure

probabilities

equal to the failure rates per cm.

Discussions with respect to differencies between method 1 and method 2 are performed on the basis of

data in tables 7 - 12.

ieldina failu'-e mode Design values are very close for the two methods in particular for the case at 30 m water depth. Failure

probabilities

are almost equal, with method 1 giving 20 - 25 % higher Pf. These results are consistent with the discussions earlier in this paper. The yielding failure mode is dominated by wave loading and combination of the annual maxima di-stribution of 1 with the arbitrary-point-in-time di-stribution for v gives similar results as obtained on the basis of the long term distributions for H5 and

VC.

Method i gives importance factors related to the

re-sponse uncertainty in a short term (3 hours) reference period, while method 2 relates to a 1 year period. It

is seen that the relative uncertainty arising from long term wave loading and model and statistical un-certainty, shiftes from 92 % to 78 c _{and from B to} 22 respectively, when looking at a single storm versus

a 1 year period, i.e. iocreasing refe"ence period makes model and statistical uncertainty more signifi-cant relative to the long term environmental uncerta-inty. However, the variability of wave and current loading is still the major contribution. The above numbers are for the case at 30 is water depth, the same trend is seen for the case at 80 m with a somewhat

higher sensitivity to the peak period due to increased water depth.

s Water depth Wave data Current data

mean st.dev. mean st.dev.

30 is 5.34 m 0.61 s 0.55 m/s 0.09 is,i 80 rs 9.05 ni 1.00 s 0.55 rn/s 0.09 rn/s

I IVI Design values are somewhat

different for this case, It is seen from the sensiti-vity factors that both wave and current loading are important, and the basis for using method 2 is thus not completely satisfied. The failure probability is a factor of 2 to 8 smaller on the basis of method 2. This is due to the sensitivity to current loading as well as the fact that Lower waves than those represen-ted by the annual maxima distribution give rise to failure.

Increasing reference period makes the statistical and model uncertainty as well as other time independent uncertainty sources increasingly important also for this case.

Buckling failure mode: The failure probability calcu-lated on basis of method 2 is larger than from method

1 for this case. This is opposite to what is seen for

the other two failure conditions, due to the follo-wing. The buckling failure probability is very small. The wave loading is dominating and the design wave height is thus located far into the tail of the

di-stribution of H. It is noted that the Gumbel distri-bution overestimates the

probability

in the tail as compared to the exact maxima distribution of H5, see equations B - 15, with n = N5 = 2920. For the case at 30 ni water depth, the probability of exceeding for example H equal to 8 m is 75 % higher based on the Gusbel distribution (method 2) than based on the exact maxima distribution. This effect causes the failure

probability from method 2 to be overestimated.

A general discussion of findings from the reliability calculation is given in the following.

Yielding failure mode: Only a few random parameters give contributions to the variability of bending stress response, Table 7 and 8. Current loading rs in-significant. The long term variability of wave loading represents about 75 - 80 of the total response va-riability, while the model uncertainty and statistical uncertainty give rise to the remaining 20 - 25 i

re-ferred to a 1 year failure

probability.

It is noted that the variability of yield stress is not signifi-cant relative to the other effects.

By comparing the results for 30 rs and 80 is water depth, it is seen that the variability of peak wave period is increasingly important for increasing water depth. This effect is caused by the exponential depth attenuation in which the wave period enters. This result is consistent with discussions by Sotberg et al. 1990).

Dis;lacesent failure mode: From Table 9 and 10 it is seen that current loading is of significance iii addi-tion to wave loading when dealing with displacements. This is irr contrast to the bending stress where the dynamic loading component dominates the response. The long term wave and current variability represents 70 5

of the total variability in displacement response whereas the remaining 30 % is caused by short term

un-certainty represented by soil parameter uncertainty, variabilities in the pipeline properties as well as model uncertainty and statistical uncertainty. These importance factors are representative for the 30 ru

water depth case.

ucklìng failure mode: Sensitivity factors (Table 11 and 12) are very similar to those found when studying the yielding failure, except that current loading is slightly more important due to accumulation of bending strain. It is noted that the uncertainty in the local

buckling capacity, modelled by the factor f, gives a smaller effect on the failure probability than model and statistical uncertainties, representing uncertain-ty on the load effect side.

Pesien oies weicht: The appropriate design pipa weight can be read out of Figures 5, 6 and 7 related to the failure sodes studied and on the basis of a given target probability level. By Setting the target failure probability to 10-2 for the yielding and disp-lacement failure modes and for local buckling the following design weights are found for the two water depths, in Tables 13 and 14.

Table 13 Design pipe weights, 30 m water depth

Table 14 Design pipe weights, 80 m water depth

The displacement criterion limits the design when for the case at 30 m water depth when p2 = O, requiring a pipe weight of 5100 N/rn. Increasing the correlation between waves and current, to PHV 0.3, increases the design weight to 5900 iS/rn, the design being limited by buckling failure.

Design weight for 80 meter water depth assuming no correlation between waves and current is W5 = 3200 tV/rn, the design being displacement control-led. A pipe weight of W5 = 4400 N/m is needed when

0.3, the design being limited by yielding failure. The yielding criterion governs the design when

increa-sing the reliability level to lO for displacement and yielding failure and to l0- for buckling failu-re. The required pipe weight then becomes W5 = 6200

U/rn at 30 s water depth and W 4000 N/c at 80 m water depth, respectively, when PNV

0.

CALIBRATION OF DESIGN PROCEDURES

General

Two approaches are generally possible in the pipeline design process to obtain a specified and uniform safety level. The presented reliability calculation procedure could be used directly, representing a full probabilistic design or indirectly based on a calibra-ted design check with the main goal of obtaining a

uniform safety level.

From the authors point of view it is clear that, con-sidering design for pipeline dynamic stability, the above procedure based on application of the design tool PIPE together with a generai reliability calcula-tien routine is developed to a satisfactory level of confidence and rationality in order to perform routine probabilistic design calculations.

However, as an alternative tos direct application of

9

the reliability calculation in the design process, the above tools have been used to calibrate design proce-dures. This is briefly outlined below. It is noted that the calibration covers only a few cases and is thus not representative with respect to a final cali-bration, but illustrates the main principles and fea-tures.

Through the calibration procedure, the following ques-tions will be discussed. What should be the selected characteristic wave and current load parameters for the different failure modes? What is the dependence on the wave-current correlation PNV? Will the use of ap-propriate functional and environmental load factors as well as material factors make the reliability level more uniform? In that case, what is the optimal set of partial factors?

Calibration

The same three failure modes as used above have been the basis for the calibration process covering the two water depths, 30 m and 80 rn, respectively.

Calibration is performed considering a limit state design, where yielding and displacement failure modes are related to the serviceability limit state and local buckling to the ultimate limit state. The process of calibration is linked to the use of the se-mi-probabilistic design tool PIPE or related design recommendations as given in RP E305 (1988). The cali-brated design check (safety format) is thus classified as a Level t procedure, characterized by a limit state design and application of partial safety factors on Load effect and resistance and specified characteris-tic values.

Partial design factors are often divided into a func-tional and an environmental load factor, YF and y1, respectively. The material factor Yrn is included to take into account the variability in material strength or pipeline capacity with respect to the different

failure modes.

Environmental loads are considered here which give a basis to evaluate the appropriateness of any environ-mental load effect factor, y1, as well as the charac-teristic environmental load combinations. Functional loads are not included in these example calculations, thus no information about the optimal choice of any functional load factor is given.

For a complete calibration process both functional and environmental loads should of course be considered, both separately and in combination.

With reference to the reliability calculation results given in Table 7 - 12, the following is noted consi-dering the choice of material factor: The variability of yield strength as well as local buckling capacity

is not significant with respect to the failure proba-bility. Calculated design point for yield strength is very close to the mean value. The effect of variabili-ty in the buckling capacity is larger due to the larger c.o.v. and the design point is about one stan-dard deviation on the safe side. i.e. corresponding to

the 15 fractile.

The specified minimum yield strength (SMYS) is used as charactristic yield strength which corresponds to the 5 fractile (1.65 st.dev. from mean). Characteristic local buckling capacity is set equal to the 2 frac-tile, i.e. 2 st. deviations from the mean value. This Failure mode Displacement Buckling Yielding

W,

PNV =

W5, P, =

0 0.3 5100 5600 N/rn U/rn 4800 5900 Ulm N/rn 4100 5100 N/rn N/s

Failure mode Displacement Buckling Yielding

W,

W5, PNV PNV = 0 0.3 3200 4000 U/rn N/c 3100 3600 N/rn N/rn 2700 4400 N/a N/rn

corresponds to application of the design equation E = 0.5 (t/D)2 given by Murphy and Langner (1985). Based on these characteristic values, which aro themselves on the conservative side as compared to the design point, the material factor 9m is set equal to 1.0. The environmental load effect factor y is related to the model uncertainty factor f,, as they both are applied directly to the load effects. Im: the design check y1 should also include the effect of statistical uncertainty, the factor f5, arising from the environ-mental loads.

The load factor y1 is now the only variable partial factor y,, = 1.0), and can then be calculated for a certain characteristic load (wave and current) com-bination and reliability level. The result from such a calibration is illustrated in Figure 8 for all three failure modes. The load combinations used for wave and current loading are indicated on the figures. The cha-racteristic loading has been defined on the basis of the long term distribution functions used in the re-liability analysis for both locations. The numbers in-dicated for the load description refer to the return

periods of occurence, i.e. load a) 100/1 means the combination of 100 years and 1 year return period for

H, and V, respectively.

Characteristics in the findings from this calculation are: YE is seen to be very sensitive to even a small variation of the target probability level. P or con-trary, the effect on F from a variation of y1 is small. This implies that the use of y1 as a load effect parameter is not a stable design factor. This is the case for all load combinations used and is most significant for displacement response. This effect is mainly due to the non-linear response characteristics as well as the high sensitivity to the environmental

loading parameters.

The above observation leads to two alternative soluti-ons for the design strategy:

Select a set of characteristic load combinations for different failure conditions (limit states) which may exclude the use of the environmental

load effect factor, i.e. E equal to 1.0.

Select one specified constant set of characteris-tic load combinations for all failure modes (limit states) and specify individual load fac-tors, y1 s for all lirit states.

Cue to the large variability of y1 for a small varia-tion

of

the reliability level, the first approach (YE

- constant) may be the most appropriate to secure a uniform safety level.

The following characteristic load combinations and partial coefficients, y1's, (Table 15) are found for the two alternative approaches based on the data in Figure 8.

Table 15 Characteristic loads and load factors, YE

111

The notation 100/1 for load combination means the 100 years H value combined with the 1 year V value.

The variation of target probability level for the dif-ferent load combinations and environmental factors is

illustrated in Table 15 above. It is noted that both procedures seem to work for the cases included in this example study. However, it is belived that due to the large variability of y1, alternative 1 is the best with respect to uniformity of the code formulation and closeness to the specified target reliability level. The above calibration is based on a wave dominated si-tuaticn. In general it is necessary to give recommen-dations ccncerning situetions when current loading is more significant and also to take into account the effect of any correlation, pu5, between wave and current loading. if such information exists. A brief discussion is given below.

If no information about the joint probabLlity (or p( of wave and current is given, two design checks are required:

Design check for a wave dominated situation with the load combination and load factors as given n Table 15.

Design check for a current dominated s.tuation with the return period for current loading as given for wave in Table 15 and vice versa. The above design load combinations determined on the basis of probabilistic calculations are corsistent with recommendations given in R? E305, and are found to satisfy the safety requirements if the correlation between wave and curent loading is not too strong. Effect of correlation: In cases where the correlation

p5 is high ( 0.3) for some reason, this can be

handled in two ways. The load combination can be modi-fied, so that the return period used for the less im-portant load type is changed towards the return period used for the dominating load. This corresponds to al-ternative 1 in Table 15. Alternatively, load

com-binations as given in Table 15 alternative 2 can be used, but with an increase of the environmental load factor to account for correlation,

The effect on the design load point from a variation of Pv has been studied by performing actual reliabi-lity calculations for different levels of correlations ammd different target total load probability levels. Findings from this calculations are as

follows:

Increasing reliability level makes the dominatìrmg load (here wave) be even more important with respect to the total load effect for zero or low correlation, i.e.

P55 < 0.3 - 0.5. The design point for the dominating load parameter will thus move further out in the tail of the distribution function,

Increasing correlation, P55, reduces the relative dif-ferences between the load importance factors or the respective design return periods, and makes the indi-vidual load return period move towards the target total load effect return period. However. Lt is noted that the correlation needs to be larger than 0.5 before the design value for the less significant load type increases noticeably.

The return period for the dominating load type (here Hj is, for zero nd low correlation, far below the total target return period. This is due to the fact that V in this cose gives some contribution to the Met LimIt SLS State ULS fixed value P SLS ULS

Alt 100/1 10000/10 y1=1 .0 (02_103

1O_5 10

Alt 01=1.0 y1=1 .3 100/10 5- 11r3-5 10

105106

total load effect, i.e. both wave and current loading need to be considered, but wave loading is still the dominating one.

The following design recommendations are given on the basis of the above findings.

If p < 0.5 Use load combinations according to

data in Table 15. Check both wave- and current do-minated situations.

If _QHV > U,5 Increase the design return period

for the less significant load type gradually to the name as for the dominating load type for PHV 1.0, It is, however, believed that the correlation

PHV generally is considerably smaller than 0.5.

The effect of correlation PHV can also be included into the design check based on modification of the y1 factor consistent with alt 2 in Table 15. The effect on y1 due to an increase of PCI is illustrated in

Figure 9. By increasrng p from zero to 0.3 the y1 factor has to be increased by 20 - 30 , on average.

That means the figures given in Table 15 have to be increased similarly to obtain the same safety level. It is, however, as discussed above easier to control the reliability level by using a representative cha-racteristic load combination than relying upon a spe-cific Load effect factor which shows a very large sen-sitivity to small variation of the target reliability level.

CONCLUS iONS

A method for reliability analysis of submarine pipeli-nes has been illustrated. The method is used in a nu-merical case study addressing three possible failure modes concerning an on-bottom pipeline section. Different uncertainty sources relevant for these failure conditions are discussed and included into the analysis.

Two methods have been used for combination of environ-mental wave and current loading in the reliability calculations, i.e. long term distribution for both wave and current or combined maxima distribution for the dominating load type and long term distribution for the less significent load. Both methods can be used, it is however noted that the extreme value di-stribution must be related to the reference period studied (1 year) to obtain consistent results.

From the calculations it is seen that the sensitivity to H and T5 is. in general high and care must be taken when combining these quantities and for the

calibrati-on of these

loads.

A procedure has been developed for calibration of the design criteria related to the failure conditions or limit states studied.

Selection of a set of characteristic loads for each limit state (or failure mcds( may be the bst solution with respect to uniformity and closeness to the speci-fied target reliability level.

The work presented opens for two alternative approa-ches for safety assessment of submarine pipelines. The reliability calculation procedure can be used directly representing a full probabilistic design or indirectly through a calibrated design check.

The principles outlined for reliabìlity calculations and safety assessment are found to be very efficient for the present application and may be used generally for a more thorough calibration of design recommenda-tion for submarine pipelines, covering other failure conditions and technical topics than those included in this study

REFERENCES

Borgund K. and Bucher, C.G.)1986): "Importance

Samp-ling Procedure Using Design Points (ISPUD) - A User's Manual", Institute of Engineering Mechanics, Universi-ty of Innsbruck, Report 8 - 86.

Department of Energy (1987): "Submarine Pipeline Gui-dance Notes", Pipeline Inspectorate DEn, London. Ellinas, C.P. , Raven, P.W.J.. Walker, AC. and Davies, P.(1987): "Limit State Philosophy in Pipeline Design". Journal of Offshore Mechanics and Arctic Enoineerifl Vol. 109, pp. 9-22.

fIlmas, C.P. and Williams, K.A.J.(1989): "Reliability Engineering Techniques in Subies Pipeline Design". Proc. of the Eioht lot. Confetence on Offshore Meche-pics nd Arctic E gn. The Hague, March 19-23, Vol. V. Holthe, K., Sotberg, T. and Chao, J.C.(1987): "An Ef-ficient Computer Model for Predicting Submarine Pipe-line Response to Waves and Current". Froc, of Ninete-enth Offshore Technoloov Conference, Paper 14o. 5502. Houston.

Lambrakos, KF., Remseth, S., Sotberg, T. and Verley, R. (1987) : "General ized Response of Mar me Pipelines". ?roc. of Nineteenth Offshore Technoloov Conference, Paper No. 5507, Houston.

Madsen, HO., Krenk, S. aid Lind, NC. (1986): Methods of Structural Safety. Prentice-Hall.

Marshall, P.W. et al.(1977): "Inelastic Dynamic Analy-sis of Tubular Offshore Structures". Offshore

Techno-lv Confetenc, Paper 2908, pp. 235-246.

Murphy, CE. and Langner, C.G.(1985) "Ultimate Pipe Strength under Bending, Collapse and Fatigue".

s'

I.;

I..

Vol.1, p-p. 467-477. NKB (The Nordic Committee on Building Regulations, 1978): Recommandations for Loading and Safety Regula-tions for Structural Design. 14KB-Report No. 36, Copen-hagen.

Recommended Practice, RP E305 (1988): "On-Bottom Sta-bility Design of Submarine Pipelines". Venteo, Oslo. Sotberg, T., Lambrakos, K.F., Remseth, S., Verley, R.L.P., Wolfram, jr., W.R. (1988): "Stability Design of Marine Pipelines", ¡'roc. BOSS Conference Trond-heim.

Sotberg, T., Lema, B.J. and Verley, R.L.P. (1989): "Probabilistic Stability Design of Submarine Pipeli-nes". proc, of the fleht 1nt. Conference an Offshore lechanic.s and Arctic Epgn

Vol.

V, The Hague.

Sotberg, T., Lema, S.J., Larsen, CM. and Verley, R. L.P.(1990(: "On the Uncertainties related to Stability Design of Submarine Pipelines". 2'roc. of the Nirt.th lot. Coferance on Offshore Mechanics and Arctic lThcsn. \ol. V, Houston.

Soulsby, R.L. (1987): Calculatìng Bottom Orbital Ve-locity Beneath Waves". Coastal Enoineerino 11, _PP

371 -380.

Thoft-Chrjstensen P. and Baker, M. J. (1982) Struc-turAI Eeli4bility Theory and its Aoolications. Sprin-ger-Verlag, Berlin.

Turkstra, C. J. (1970): Theory of Structural Design Decisrons Study . 2'. Solid Mechanics Division, Jrì

versity of Waterloo, Waterloo Ontario.

Walker, A. (1989): 'Assessment of Pipeline Spans' Course in Offshorm Pipeline Enqineering. IBC, London.

TAB 1 ES

Table 7 Failure mode yielding, 30 m water depth

Table 8 Failure mode yielding, 80 e water depth

12

Table 9 Failure mode displacement. 30 a water depth

Table 10 Failure mode displacement, 80 a water depth Random variable Importance factor Design value Method: 1 2 1 2 H (in) 86 57 6.59 6.98 T5 (sec) 6 21 12.7 12.4 V. )rn/s) 0 0 0.211 0.211 D,. 1) 0 0.35 0.35 W (N/rn) 0 0 6165 6174 D (in) 0 0 1.26 1.26 d (m) 0 0 29.9 29.9 D (in) O 0 1.014 1,014 t (rs) 0 0 .0243 .0243 E (N/rn2) O O 2.OIE11 2.08E11 f,, f,, 0 (N/rn2) 3 5 0 10 12 3 1.31 '.16 457E6 1.28 1.12 458E6 6225 N/rn D = 1.25 in, , O Method 1 P = 1.2 E - 3 Method 2: p = 1 .0 E - 3 Random variable Importance factor % Design value Method: 1 2 1 2 H5 (rn( 70 37 5.38 6.74 T (Sec) 1 8 10.8 11.6 V, (o/s) 15 25 0.45 0.38 Dr 9 6 0.56 0,43 W5 (N/rn) 1 2 6005 6060 U (in) 1 1 1.27 1.26 d (in) 0 0 29.9 29.9 f,, f,, 1 2 2 19 1.19 1.11 1.11 1.17 = 6225 N/rn, D 1 .25 rn, _PHV Method 1: P1 0.7 E - 3 Method 2: Pf 0.3 E - 3 Random var iable Importance factor 'n Design

value

Method, 1 2 1 2 H (rn( 77 7 9.95 10.04 T5 (sec) 10 0 15.5

1.4

V )rn/S( 3 41 0.33 0.44 D,. 1 31 0.42 0.56 W,, (N/m( 1 11 3835 3604 D (in) 0 4 1.20 1.22

d(m(

0 0 80 80 f,,, f,, 0 8 4 2 1.10 1.20 1.20 1.06 = 4000 N/rn, D 1.20 e, 0 = O Method 1, P5 0.8 E - 3 Method 2, Pf = 0.1 E - 3 Random variable Importance factor 'n Design value Method: 1 2 1 2 H, (sr) 83 43 10.56 11.38 'r5 (sec) 10 37 18.8 18.3 Vr (rn/n) 0 0 0.22 0.22 2 8 1.26 1.23 f,, 5 12 1.16 1.12 W5 = 4000 N/rn, 1.2 m,

_Pv

O Method 1: Pf 1.0 E - 3 Method 2 P5 = 0.8 E - 3

' _{Only the most significant variables are}

in the table

Table 11

_{Failure mode local buckling, 30 te water depth}

o.

o tb u

a..

Fiai St,n.-St,..., .t,6/o, lnt,ot,n.o..,. P. A u U

t

_s

s

_s

£ ê £

s

to.

s

lO 20 20 O 00 00 10) 120 Tlt.ckn. Fwtw Ott

Figure

1

Pipe Bending Tests in Air - Curvature of Buckling

(from Murphy and Langner, 1985)

on-bottom section

13

Table 12

Failure mode local buckling. 80 to water depth

ç

- elastic pipe material

clamped end

Figure 2

_{Simplified structural model of the pipeline}

Figure 3

_{Comprehensive structural model of the pipeline}

_{Figure 4}

Relationship between linear elastic strain (Fig

2)

and plastic strain (Fig 3)

Random

ver jable

Importance

factor

't

Design

value

Method: t 2 1 2 H5

(a)

_{83 3}

_7.98

_8.58

T,

lsecl

6 13

13.9

13.6

V.. _Im/SI 1 2 _{0.31) 0.31)} Dr 0 0

0.38

0.38

W. (N/mI

0 0 6164 6170 D (m( 0 1)

1.26

1.26

d

leI

0 0

29.9

29.9

D.

Ial

0 0

1.013

1.013

t5

O (t

.0243

.0243

E (N/rn2) O O 2.07E11 2.OSE1I

f,,

3 6 5 10

t.39

1.26

1.36

1.20

C (N/rn2) O O 462E6 _462E6 f 1 2

1.56

1.59

= 6225 tI/rn,

fl

1.25 a,

PHV 0

Method 1:

P

1.0 E

6

Method 2:

P1

1.5 E

- 6 Random va r jab! e

Importatice

factor 't

Design

value

Method: t 2 1 2 95 Im) 76 60

11.96

13.75

T1 (Sec)

9 21

19.4

19.6

61 _{5 1}

0.40

0.28

Dl 1 0

0.44

0.37

f,,

f 3 7 5 9

1.37

t.19

1.37

1.17

1 ₂

1.58

1.58

W5

4000 N/tn,

D = 1 .20 m,

P5

0

Method 1:

Pf = 1.7 E - 6

Method 2:

P1 =

2.1 E -

6

Only the most significant

in the table

variables are included

F. 2

r

0.5 Fig. 3 r,

04

03

r, = 7,6 r:"

0.2 r, = 075 r. 0.1

00

v,t70'.

0t,.,ItI. _{on-bottom section}

S,,4I 6.. 1.,tttOlSI

.

o

P,r.musSSlI Data £ A

B.t,.77' Dat. 11671)

_u

- axially free

t

-axially constrained

nonlinear pipe matetal elastoplastic soil reaction

(buried pipe section) 0_5

10

20

3.0

40

E,

o o 'b -4 06 06 A

i,

i 0.2 10' 10-' 10' PI 10' IO" 10'

\\

p,=0.5

\

_\

\1

\2

\

\

\

\

_\

0.5

\

\

\

'I'

\

\

\

\

\

FAILURE MODE: Buc*Jirg

p,,0

80m

p,, 0.3

---30m

3000 4000 5000 6000 7000

W [NIm)

Figure 7

Annual failure probability versus pipe weight

- buckling failure mode

'N N 'S

p,,-0.5

N

\

\l.

\

2\\

S.'

-

\

\

\\

\P,,

\

_\

_\

\

\\

_\

0.9 3,5

FAILURE MODE: Displacement

i) p,,-O

80m

2) p,,2 =0.3 30m

3000 4000 5000 6000 7000 3000 4000 5000 6000 7000

W [NIm]

W, [/m

Fgure 5

Annual failure probability versus pipe weight

Figure 6

Annual failure probability versus pipe weight

- yielding failure mode

- displacement failure mode

1.0 PI 10 10" P, 102 IO' 1 0

Suckling, = O 10" 10" P1

7

7

r

'e Ha/Tp

- - - - 30m

00m

Figure 8

Calibrated environmental load factor for different

load combinations and reliability levels

YE 2.0 1.6 1,2 0.8 0,4 0.0

Figure 9

0 0.3 0.5

Environmental load factor versus correlation coefficient

15 2.8

'a'

2.4

/

/

YE

/

2.0

//

2.0

/

1.6 1.6

/

1.2

-

b 1.2 -a 0.8

-

-

0.8

.-

--04 0.4 0.2 b 0.2

10'

10' P1 Displacement, p =O YE A 2.2 24 ,4E 20

₇

7

7

1.8 -'a. , 1.6

-

a-7

7=

1.4

4*

_...b 1.2

7

a-b 10 08 06 a) 100/1 b) 100/10 c) 10000/1 d) 10000110 e) 10/1 102 10' P1 Yielding. p, = O