ABSTRACTFor many years the hydrostatic pressure test has been

performed as a final integrity check of pipelines. The testinvolves subjecting the pipeline to a hydrostatic pressure that i stypically some specified percentage (125%–150%) of themaximum allowable design pressure or which results in a hoopstress that is a specified percentage (90%–105%) of the specifiedminimum yield stress. The test thus provides a margin of safetyagainst failure under the operational pressure loading. In doingso the test not only demonstrates that the material and geometryare adequate but also provides some confirmation of theworkmanship levels of the welded joints.

However, over recent years the value of the hydrostatic testhas been the subject of a continually broadening debate. It i snow being argued that the information provided by the test canbe obtained by other means. For instance, the quality of thematerial and geometry have improved due to improvementswithin the pipe mill and advances in inspection techniques canlead to higher standards of weld quality.

Whilst the above and other improvements are widelyaccepted it has generally not been possible to quantify theireffect on the structural integrity. This paper describes a studythat focuses on this issue.

The approach adopted here is to quantify the effect of thehydrostatic test on relevant failure modes using structuralreliability analysis. The outcome of the structural reliabilityanalysis is a probability of failure, which is determined from asystematic consideration of the elements of uncertaintyassociated with each failure mode.

The effects of the test are assessed by a detailed comparisonof the failure probabilities resulting from the application of thestructural reliability analysis to a range of scenarios comprising

the effects of workmanship, weld inspection and hydrostatic testpressure.

The results allow a view to be formulated on conditionsunder which it may be possible to forego the test or, conversely,to identify other mitigating factors which may be relaxed in viewof the test

INTRODUCTIONFor many years the hydrostatic pressure test has been

performed as a final check on the structural integrity ofpipelines.

The test involves subjecting the pipeline to a hydrostaticpressure that is typically some specified percentage(125%–150%) of the maximum allowable design pressure orwhich results in a hoop stress that is a specified percentage(90%–105%) of the specified minimum yield stress of thepipeline material. The test thus provides a margin of safetyagainst failure under the operational pressure loading. In doingso the test not only demonstrates that the material and geometryare adequate but also provides some confirmation of theworkmanship levels of the welded joints.

However, over recent years the value of the hydrostatic testhas been the subject of a continually broadening debate [1]. It i snow being argued that some of the information provided by thetest can be obtained by other means. For instance, the quality ofthe material and geometry have improved due to improvementswithin the pipe mill and advances in inspection techniques canlead to higher standards of weld quality.

Whilst the above and other improvements are widelyaccepted it has generally not been possible to quantify theireffect on the structural integrity. Hence, to date it has only been

Proceedings of 20th OMAE Conference3rd - 8th June, 2001

Rio de Janeiro, RJ, Brazil

OMAE01-2120A FUNDAMENTAL INVESTIGATION OF THE EFFECTS OF THE HYDROSTATICPRESSURE TEST ON THE STRUCTURAL INTEGRITY OF

PIPELINES USING STRUCTURAL RELIABILITY ANALYSIS

Andrew Francis, Marcus McCallum & Michael Gardiner Ross MichieAdvantica Technologies BG GroupAshby Road 100 Thames Valley ParkLoughborough ReadingLeicestershire BerkshireLE11 3GR RG6 1PTUnited Kingdom United Kingdom

Tel. +44 (0) 1509 282719Fax. +44 (0) 1509 283118

andrew.francis@advanticatech.com

possible to comment qualitatively or at the most semi-quantitatively on the relative value of the hydrostatic test.However, this situation is now beginning to change due to theapplication of limit state and structural reliability assessments.

Structural Reliability Analysis (SRA) is a technique whichnumerically determines the probability of pipeline failure byusing limit state techniques to analyse the mechanics of failureby the relevant modes and taking account of uncertainty in theparameters which characterise the limit state functions. Recentapplications of these techniques to a range of pipeline operatingscenarios are given in references [2–4]. An important feature ofSRA is the ability to quantify the effects of relevant mitigatingactivities on the probability of failure. Such mitigatingactivities include weld inspection, on-line inspection and, ofparticular relevance to this present study, the hydrostaticpressure test.

This document reports the derivation and application ofstructural reliability based methodologies for quantifying theeffects of the hydrostatic test on failure probability.

The effectiveness and value of the test are assessed by adetailed comparison of the failure probabilities resulting fromthe application of the structural reliability analysis to a range ofscenarios comprising different workmanship, inspection andquality levels within the pipe mill. The effect of different levelsof testing is also investigated. Based on the outcome of theresults, a discussion is presented of the conditions under whichit may be possible to forego the test or under which othermitigating factors which may be relaxed as a result ofconducting the test.

ISSUES AND OBJECTIVESIn general the safe operation of a pipeline is achieved by

ensuring that it is designed, operated and maintained in amanner such that the loading on the pipeline is always less thanthe resistance to the load. Whilst in theory this concept is a verysimple one, in practice, the analysis required to demonstrate thatthis has been achieved can be very complex. This is because,depending on the failure mode under consideration, thequantification of load and resistance can often only be achievedby a detailed consideration of structural mechanics. For instance,in a very simple case, such as failure due to pipewall yielding,the load is readily defined as the hoop stress and the resistanceas the yield stress. However, in practice, pipewall yielding i srarely an issue of concern and attention needs to be focussed onmore realistic causes of failure such as fatigue crack growth. Inthis case a detailed analysis involving elastic-plastic fracturemechanics and significantly more parameters including fracturetoughness, defect depth and growth rate needs to be undertaken.

Traditionally, pipeline design codes have necessarilyavoided such detailed analyses by adopting a generallyconservative approach based on the concept of safety margin.For instance, by prescribing a hoop stress value which i sconsiderably lower than the specified minimum yield stress, notonly will yielding be avoided but also failure by other failuremodes will be unlikely, even though the parameters which canaffect the likelihood of failure by other modes are not explicitlytaken into account. The term safety margin or design factor thusmight be better described by the term ignorance factor/margin.

The same can be said about the specified ratio of thehydrostatic test pressure to the operating pressure. This margin

is applied not only to provide a high level of assurance that thepipeline will not fail during the first pressure raising but also toprovide some assurance that a failure will not occur in for someperiod of time in the future. However, the level of assuranceprovided and for what period of time is not explicitly quantified.This is the root of the growing debate addressed by thisdocument; that is, what does the hydrostatic test contribute tooverall level of structural integrity and how does thiscontribution compare with other forms of mitigation such asweld inspection?

The objectives of this study are therefore to quantify theeffect of the hydrostatic test on the probability of failure, andconsequently to establish the relative important of the testdepending on the level of mitigation provided by other meansand on the particular operating scenario.

INFORMATION PROVIDED BY THE HYDROSTATIC TESTThe survival of the pre-commissioning hydrostatic test

provides a considerable level of assurance that the pipeline willnot fail during the initial pressure raising and during an initialperiod of operation. However, the level of assurance and for whatperiod can only be addressed by making specific reference torelevant failure modes and associated parameters. The effect ofthe test on wall thickness, yield stress and construction defectdepth is investigated below by considering the yielding andfatigue crack growth failure modes. For the purposes ofcomparison the effect of pre-service weld inspection onconstruction defect depth is also considered.

Effect of the Hydrostatic Test on Wall Thickness & YieldStress

A new pipeline is generally hydrostatically tested beforecommissioning, in order to prove the structural integrity at thetime of test. All individual pipe joints are also hydrostaticallytested at the pipe mill, and the pipeline may be tested at intervalsduring its service lifetime.

Prior to the pre-service hydrostatic test some information i savailable regarding the likely values of the yield stress and wallthickness. The variability of these quantities depends on theprocesses which are adopted within the pipemill and thequantification of this variability is dependent on the number ofavailable mill certificates. The information provided on millcertificates can be used to construct independent probabilitydensity functions (PDFs) which describe the variability in eachof these two quantities. In general the extent of the observedvariability depends on the natural variability arising from theprocesses within the mill and on the number of mill certificatesavailable. However, the uncertainty in both quantities can bereduced by taking account of the fact that the hydrostatic testwas survived.

When a pipeline or pipe joint has survived a hydrostatictest, this rules out the existence of certain combinations of wallthickness and yield stress in the unit that was tested. Thisinformation can be used to construct a joint probability densitydistribution describing the variability within these twoproperties. It is important to note that on making use of theinformation provided by the hydrostatic test the wall thicknessand yield stress can no longer be regarded as independentquantities

Denoting the event of surviving a hydrostatic test by S, i tcan be shown that the conditional joint pdf, )|,( Swp yσ ,describing the variability in wall thickness and yield stress i sgiven by

( )

( )∫∞

=∫∞

=

−

=

0

|,

w Hy

dwydypwp

HyHypwpSywp

σσσσ

σσσσ (1)

where Hσ is the pipe wall hoop stress, ( )wp and )( yp σ are

respectively the independent distributions of wall thickness andyield stress before the test and H is the Heaviside step function,defined by

( ) 0=xH if 0<x( ) 1=xH if 0≥x

Equation (1) is used to determine the effect of thehydrostatic test on wall thickness and yield stress.

Effect of Inspection and the Hydrostatic Test onConstruction Defect Depth

In this section the effects of weld inspection and thehydrostatic test on the uncertainty in the depth of constructiondefects is considered.

Pre-service weld inspection provides an indication of thelikelihood of defects of a given depth being present. The valueof this information depends on the reliability of the techniqueand the effectiveness and quality of the welding procedure; thatis, if good weld quality is established by the welding procedurethen few defects will be present and therefore a lesser reliance oninspection is required. On the other hand if the weld quality i spoor then greater number of defects would be present and ahighly reliable inspection technique would be required in orderto ensure that any significant defects are detected. In practice i tis the combination of inspection and welding technique whichprimarily determine weld quality, with a greater emphasis on thelatter. The role of the hydrostatic test is to provide a finalassurance that a significant defect introduced duringconstruction and not detected is not present. The relativecontributions of each of these factors are considered below.

Initial distribution of defect depth following weldingSeam welds and girth welds are subjected to well defined

and quality controlled welding procedures. It is this process thatmakes a primary contribution to weld quality. If appropriate carewas not taken at this stage then the increased number of defectswould lead to some defects being missed by the inspection,which would inevitably lead to failures during the hydrostatictest. The use of high quality welding techniques therefore playsa key role in determining structural integrity. However,inspection and hydrostatic testing also contribute to the weldquality and it is the relative contribution of these two activitieswhich are considered in this document. It is therefore assumedhere that the initial welding process has resulted in a probabilitydensity function of defect depth which is denoted here by ( )ap .

The distribution ( )ap is generally derived frommeasurements of defects which have been found in welds made

using similar techniques and in similar geometries to thoseunder consideration. In general the information required is thenumber and size of defects found within a given quantity of weldmetal. The number of defects is used to determine the probabilityp(D) that a defect will be present within a given quantity of weldmetal. The sizes are used to determine the probability that givena defect is present it will have depth a .

It is important to note that sizing errors in non-destructivedefect depth measurements can be significant for some methods,such as manual ultrasonic testing (UT), and may be appreciableeven for the best techniques such as automated time-of-flight UTmeasurement. This effect on )(ap can be accommodated byconsidering the measured depth ma to include an error ε , sothat

aam −=ε (2)

Assuming that the error is normally distributed around a mean ofεm with standard deviation εs , the measurement error can be

represented by distribution

( ) ( )

−−= 2

2

2 2exp

.2

1

ε

ε

ε

ε

πε

sm

sperr (3)

Construction records will allow us to determine a distribution ofmeasured depths ( )apm . Then the pdf for actual depth is

( ) ( ) ( )∫∞

∞−

−= mmerrmm daaapapap (4)

Equation (4) is used to determine the initial distribution ofdefect depths based on measured depths.

Distribution of defect depth following InspectionIn this section a procedure for evaluating the effect of the

hydrostatic test on the prior distribution, ( )ap is derived.

The procedure is based on Bayes’ theorem and the approachadopted is to the determine the probability that a defect of deptha can be present within a weld given that the weld was inspectedand no defect was found.

Let I be the event of a weld inspection detecting nothing, Dbe the event of a construction defect of any size existing in apipe joint and ( )ap be the prior distribution of depths for thosedefects that do exist. Using Bayes’ Theorem, the probability ofthere being a defect of depth a present when nothing has beenfound by inspection is given by

( ) ( ) ( )[ ] ( )( )Ip

aIpDpapIap || = (5)

The probability of nothing being found by an inspection,( )Ip , consists of two parts: the probabilities of finding nothing

when there is, or is not, a defect present. That is,

( ) ( ) ( ) ( ) ( )DpDIpDpDIpIp || += (6)

where D is the event of no defect existing.

By definition ( ) ( )DpDp −= 1 , and we assume that

( ) 1| =DIp . The probability of finding nothing, given that adefect exists, is the integral over all possible depths of theprobability of a given defect depth not being detected:

( ) ( ) ( )daaIpapDIpw

a

||0∫=

= (7)

Denoting the probability of detecting a defect of depth ausing a particular inspection technique by ( )aPoD it follows theprobability of finding nothing given that a defect of depth a i spresent is given by

( ) ( )aPoDaIp −= 1| (8)

Thus, from equations (5) to (8),

( ) ( ) ( ) ( )[ ]

( ) ( ) ( )[ ] ( )( )∫=

−+−

−= w

a

DpdaaPoDapDp

aPoDDpapIap

0

11

1| (9)

Equation (9) is used to determine the likelihood that agiven quantity of weld will contain a defect of size a given thatthe quantity of weld was inspected and no defect was found.

Distribution of defect depth following the hydrostatic testThe hydrostatic test can lead to a further improvement in the

knowledge of the distribution of defect depth since all defectsgreater than some critical value, ( )Hfail Pa , if present, would fail

under the test pressure HP .

Applying Bayes’ theorem in a similar manner to thatdescribed above it is possible to show that theprobability, ),|( HIap , of a defect of depth a being present in aspecified quantity of weld metal, given that the inspection foundnothing, and that the hydrostatic test was survived, is given by

=)(apIH

( ) ( )[ ] ( )( )

( ) ( ) ( )[ ]( )

( )( )DpdaaPoDapDp

aPaHaPoDDpapHfail Pa

Hfail

−+−

−−

∫ 11

1)(

0

(10)

The critical depth ( )Hfail Pa is determined from a detailedconsideration of elastic-plastic fracture mechanics using aprocedure such as BS PD6493 [5].

STRUCTURAL RELIABILITYThe preceding section has described the appropriate

analysis techniques for determining the effect of the hydrostatictest on the distributions of wall thickness, yield stress andconstruction defect depth.

A method for determining the effect of weld inspection onconstruction defect depth was also presented.

In order to establish the relative importance of thehydrostatic test it is necessary to evaluate the effect of thesedistributions on the structural reliability of the pipeline. To thisend it is necessary to consider the relevant failure modes. Thefailure mode which is considered to be most significantlyaffected by the hydrostatic test is fatigue crack growth andtherefore this is the focus of this study.

Fatigue Crack Growth

We postulate a function ( )TaX ,0 — the Paris Law, forexample — to find the depth after time T of a defect subject togrowth by fatigue, given its depth 0a at some initial time 0.

Then the inverse function ( )TaX T ,1− gives the depth at time 0

of a crack that will grow to Ta after time T

Taking the time of the initial (proof) hydrostatic test as time0, we have a failure space at this time given by

=),,,(0 aLwU yp σ

( ) ( ) ( ) ( )( ){ }∞∈∞∈∞∈∞∈ ,,,0,,0,,0 Hfaily PaaLwσ (11)

The failure space in normal operation at pressure opP after time Ti s

=),,,( TyNT aLwU σ

( ) ( ) ( ) ( )( ){ }∞∈∞∈∞∈∞∈ ,,,0,,0,,0 opfailTy PaaLwσ (12)

This space can be transformed back to time 0 by using thefunction 1−X to determine the size of construction defect thatwill fatigue to sufficient depth to fail at operating pressure aftertime T. Thus,

=),,,(0 aLwU yN σ

( ) ( ) ( ) ( )( )( ){ }∞∈∞∈∞∈∞∈ − ,,,,0,,0,,0 1 TPaXaLw opfailyσ (13)

Finally, we define the initial properties that would allowfailure by fatigue during the interval (0,T). This is the differencebetween the failure space in normal operation at time T,transformed back to time 0, and the properties that would resultin failure at the initial hydrostatic test:

000 PN UUU −= (14)

That is,

=),,,(0 aLwU yσ (15)

( ) ( ) ( ) ( )( ) ( )( ){ }Hfailopfaily PaTPaXaLw ,,,,0,,0,,0 1−∈∞∈∞∈∞∈σ

Using the failure space 0U , the probability of failure byfatigue growth of construction defects, given that the pipelinehas been inspected and subsequently hydrostatically tested, is

=)(Tp f

( ) ( ) ( )( )( )

( )

y

Pa

TPaX

IHy dadLdwdapLpSwpHfail

opfail

σσ∫ ∫∫∫∞ ∞∞

−0 ,00 1

|, (16)

Substituting from equation (1) for ( )Swp y |,σ this becomes

=)(Tp f

( ) ( ) ( ) ( )( )( )

( )

( ) ( )∫ ∫

∫ ∫ ∫ ∫∞ ∞

∞ ∞ ∞

−

H

H

Hfail

opfail

yy

Pa

TPaX

yIHy

dwdwpp

dadLdwdapLpwpp

σ

σ

σσ

σσ

0

0 0 ,1

(17)

Equation (17) can be evaluated, using equation (10) for( )apIH . Note that for purposes of comparison, the probability of

failure assuming no test was conducted and/or no inspection wasundertaken can be evaluated by equating Hσ and/or PoD(a) tozero, respectively.

NUMERICAL STUDIES

Effect of pre-service inspectionFollowing construction to the appropriate procedure the

occurrence of construction defects in welds is unlikely. Indeed,it is the adherence to the appropriate construction standard by acompetent operator which makes a primary contribution to weldintegrity. However, whilst the likelihood of occurrence of defectsis initially low it is not zero. In view of this all welds areinspected using an appropriate technique in order to detect thepresence of defects that were introduced. It is important to notethat the probability of detecting (PoD) a defect is dependent onthe defect depth. The PoD generally increases as the depthincreases but is generally not greater than 90% even for the mostsophisticated techniques such time of flight (TOF). Theinspection thus further reduces the likelihood of occurrence ofconstruction defects. The results presented below indicate theeffect of inspection numerically.

Prior to the inspection, the probability density function ofdefect depth, )(ap , is obtained from equation (4) and thelikelihood of occurrence of a defect of depth a in a given weld,is given by the product )()( apDp . This product was evaluatedusing representative data in equation (4) with 01.0)( =Dp andthe result is represented graphically by the curve enclosing bothshaded areas in Figure 1. (Note that this curve and the othercurves in Figures 1 and 2 represent the likelihood of occurrenceof defects and not probability density functions; the areaenclosed by these curves is therefore much lower than unity.)

The effect of inspection is dependent on the technique usedand in order to illustrate this effect the radiography techniquewas used for which the PoD curve is given by

aPoD 8326.01−= (18)

This exponential relationship is typical of PoD curves and theabove formulation for the radiography technique wasconstructed to characteristically yield a PoD value of 0.6 for a5mm defect.

Substituting the above expression into equation (9) andperforming the appropriate numerical evaluation results in theprobability of occurrence shown by the curve enclosing thedarker shaded area in Figure 1.

From Figure 1 it is seen that the effect of inspection for thisexample has a noticeable effect on defect depths within the rangeof approximately 1mm to 4mm. This is because the technique i snot very likely to detect defects less than 1mm deep and defectsgreater than 4mm deep are unlikely to be present prior toinspection.

Effect of pre-service hydrostatic test on constructiondefects

The hydrostatic test would fail any defects greater than thecritical value )( Hfail Pa . The effect of survival of the hydrostatictest is obtained using equation (10) which also includes theeffect of the pre-service inspection. The results obtained byapplying equation (10), for the particular case with mma fail 2= ,is shown in Figure 2. The curve and vertical cut-offencompassing the darkest shaded area illustrates the furtherreduction in the likelihood of occurrence of detects. The effect ofthe cut-off can have a significant effect on the likelihood offailure due to fatigue crack growth as shown later.

Effect of pre-service hydrostatic test on material andgeometrical properties.

Quality and sampling procedures within the pipemilldetermine the initial distribution of material and geometricalproperties of the pipe material. The information is customarilyrecorded on mill certificates and provides useful data for thedetermination of structural reliability. In general the level ofquantification of the natural variability in both wall thicknessand yield stress values improves as the number of available millcertificates increases. However, this quantification is improvedsignificantly following survival of the hydrostatic test.

Prior to the hydrostatic test the wall thickness and yieldstress are generally regarded as two independent quantities.However, the test rules out the likelihood of occurrence ofspecific pairs of the two quantities thus leading to modifiedjoint probability density function describing the relativelikelihood of occurrence of the remaining pairs. Thisinformation can strictly only be described graphically byresorting to three dimensions. However, a two-dimensionalrepresentation can be given by determining marginaldistributions of wall thickness and yield stress by averaging thejoint pdf over yield stress and wall thickness respectively.

The example below involves the production of X60 gradepipes (SMYS of 414 MPa) with an actual wall thicknesscharacterised by a Normal distribution with a mean of 12.8 mmand a standard deviation of 0.304 mm, and a yield strengthcharacterised by a lognormal distribution with a mean of 444MPa and a standard deviation of 12.8 MPa. A direct measurementsample of a certain size is taken from this population and eachpipe is then field hydrostatically tested at 105% SMYS. Theknowledge inferred from this process is shown graphically inFigures 3 and 4 for wall thickness and yield stress respectively.

In each case the solid dark line represents the actual productiondistribution, the ‘light’ dotted line represents the estimate of theproduction distribution inferred from the sampling process andthe dark dotted line represents the marginal distribution afterfield hydrostatic testing.

It can be seen that there are significant differences ininferred estimates between cases with a sample size of 5 and 20.However, the sample size of 20 results in a distribution which i smuch closer to the population distribution. This is because thesample standard deviation rapidly tends to the actual populationstandard deviation as the sample size increases.

On the other hand, the significant effect of the fieldhydrostatic test on estimated wall thickness and yield strengthdistributions is most apparent from Figures 3 and 4. The aboveanalysis shows that the field hydrostatic test is significantlymore useful than a large number of pipe mill certificates.

The purpose of the above study has been to demonstrate howstructural reliability analysis can be used to update the yieldstress and wall thickness distributions based on the yield limitstate function.

It should be noted that some localised gross-section yieldingwould be permitted by the hydrostatic test and therefore that theabove analysis should be regarded as simplistic. Thissimplification could be readily removed by modifying the aboveanalysis to account for net section failure based on strainhardening and the ultimate strength. However, the effect of theyield stress and wall thickness on structural reliability is muchless significant than the effect of construction defects. Moredetailed consideration of the issue is therefore not considered tobe necessary for the illustrative purpose of this paper.

Probability of Failure due to Fatigue Crack GrowthIn order to illustrate the effect of the hydrostatic test and

pre-service inspection on the probability of failure, a number ofscenarios have been examined using equation (17). The examplebelow illustrates the individual and combined effects ofinspection and the hydrostatic test for a grade X60 pipeline witha wall thickness of 14.3mm and diameter of 1067mm operatingat a pressure of 70barg. The pipeline is cycled 80 times a yearthrough a pressure range 125Mpa. Two hydrostatic test pressuresare considered, 90%SMYS and 105%SMYS.

Initially, the ‘baseline’ result was determined by evaluatingequation (17) with both Hσ and )(aPoD taken to be identicallyzero. The purpose of this analysis was to establish the worst-casescenario based on no inspection and no hydrostatic test. Theresults of this analysis are given by the curve annotated with‘diamonds’ in Figures 5 and 6 which shows the probability offailure within the time interval [0,T] for values of T from 0 to 50years. It is seen that the probability of failure is greater than5x10-4 during the first pressure raise, T=0, and that thisprobability increases to 4x10-3 for the 50 year period. Theseprobabilities would generally be considered unacceptably highand this operating scenario would not generally be adopted inpractice.

The curve annotated with ‘dark triangles’ in Figures 5 and 6shows the reduction in failure probability due to the effect ofpre-service inspection using the radiography technique. Theprobability of failure during the first pressure raise is about 1 x

10-4 and the probability of failure within the 50year period i sabout 7x10-4. Whilst this is a clear improvement by a factor ofabout 5 these probabilities would still be regarded as too highand it is unlikely that this scenario would be adopted in practice

The curve annotated with ‘black squares’ in Figure 5 and 6shows the effect of the hydrostatic test without any pre-serviceinspection for the two cases 90%SMYS and 105%SMYSrespectively. The hydrostatic test is seen to have a markedimprovement in both cases. Indeed from Figure 6 it is seen thatthe probability of failure is extremely low for the entire 50 yearperiod. However, from Figure 5 it is seen that the probability offailure begins to rapidly increase for values of T greater thanabout 30 years and the probability of failure within 50 years i sabout 1x10-3. This value would generally be considered too highand it follows that a hydrostatic test pressure greater than 90%SMYS would be required.

The curve annotated with ‘light squares’ shows thecombined effect of the hydrostatic test and inspection. Clearly,this leads to acceptable failure probabilities for the 105%SMYScase. For the 90%SMYS case it is seen that probability of failurewithin a 40 year period is about 10-4. This figure could beaccepted and it follows that a 90% hydrostatic test combinedwith pre-service inspection could be a viable scenario.

The curve annotated with ‘light triangles’ shows the effectof conducting a more sophisticated inspection withoutconducting the test. It is seen that this scenario is comparable tothe 90%SMYS / radiography scenario, for times greater thanabout 30 years, and hence could represent a viable option inpractice.

The above result suggest that the hydrostatic test to apressure resulting in hoop stress equal to 105%SMYS withoutany pre-service inspection is generally sufficient to ensure thatfatigue failure is incredible in a 50 year period. The results alsoindicate that a test pressure resulting in a hoop stress of90%SMYS could be acceptable if used in conjunction with pre-service inspection using radiography. Additionally, it may bepossible to forego the test if a sophisticated inspectiontechnique such as ToF is adopted.

Note that in reality the fatigue crack growth rate will besubject to variability. It is a straight-forward process to modifythe above analysis to take account of this variability but thisaffect has not been considered here in the interest of simplicity.However, whist the inclusion of such variability would havesome effect on the numerical results it is not likely to effect theoverall observations made above.

CONCLUSIONS

A detailed structural reliability based methodology fordetermining the mitigating effects of the pre-service hydrostatictest on the probability of existence of possible combinations ofwall thickness and yield stress has been presented.

A detailed structural reliability based methodology fordetermining the mitigating effects of the pre-service hydrostatictest on the probability of existence of construction defects hasbeen presented.

A detailed structural reliability based methodology fordetermining the mitigating effects of the pre-service weld

inspection on the probability of existence of constructiondefects has been presented.

The above methodologies have been used to determine theprobability of failure due to fatigue crack growth for variouscombinations of the above mitigating effects.

It has been shown that an acceptable fatigue life can beachieved without any pre-service inspection if a hydrostatic testpressure resulting in a hoop stress of 105%SMYS is used. Notethat a lower test pressure may also result in an acceptable fatiguelife without the requirement for inspection but further analysisis required to confirm this.

It has been shown that if the test pressure only achieves ahoop stress of 90%SMYS then pre-service inspection using atechnique such as radiography is likely to be required.

If a sophisticated inspection technique such as Time ofFlight is used then it may be possible to achieve an acceptablefatigue life without the need for a hydrostatic test.

The above is based on a number of simplifyingassumptions. More detailed calculations will allow firmerconclusions to be drawn leading to more prescriptiverecommendations.

ACKNOWLEDGEMENTThe authors are grateful to BG Group for sponsoring and

granting their permission to publish this work

REFERENCES

1. Kiefner, John F., Maxey, Willard A., Pressure ratioskey to effectiveness, Oil & Gas Journal, 31 July,2000.

2. Francis, A., Edwards, A.M., Espiner, R.J. & Senior,G. ‘Applying structural reliability methods toageing pipelines’, I.Mech.E. ConferenceTransactions, C571/011, 1999.

3. Francis, A., Edwards, A.M., Espiner, R.J. & Senior,G. ‘An Assessment Procedure to Justify Operationof Gas Transmission Pipelines at Design Factorsup to 0.8’, Pipeline Technology, Volume I, Brugge,Belgium, May 21-24, 2000.

4. Francis, A., Espiner, R.J., Edwards, A.M. & Senior,G., ‘The use of reliability based limit statemethods in uprating high pressure pipelines’,International Pipeline Conference, Volume 1,ASME 1998.

5. British Standard, BS PD6393, ‘Guidance onMethods for Assessing the Acceptability of Flawsin Fusion Welded Structures’, BSI, 1991.

Figure 1 Likelihood of occurrence of defect of deptha following inspection

The Effect of Inspection

0.00E+001.00E-032.00E-033.00E-034.00E-035.00E-036.00E-037.00E-038.00E-039.00E-031.00E-02

0 2 4 6

a

p(a)

Figure 2 Likelihood of occurrence of defect of deptha following inspection and hydrostatic test

The Effect of a Hydrotest and a Pre-Service Inspection

0.0E+00

2.0E-03

4.0E-03

6.0E-03

8.0E-03

1.0E-02

0 2 4 6

a

p(a)

pi(a)pii(a)piii(a)

Figure 3a Probability density functions for wallthickness

11.5 12 12.5 13 13.5 14 14.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Wall Thickness (mm)

Probability Density (/mm)

Probability Density Functions for Wall Thickness

Actual Population Population inferred from 5 Samples Population inferred after Hydrotest

Figure 3b Probability density functions for wallthickness

11.5 12 12.5 13 13.5 14 14.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Wall Thickness (mm)

Probability Density (/mm)

Probability Density Functions for Wall Thickness

Actual Population Population inferred from 20 SamplesPopulation inferred after Hydrotest

Figure 4a Probability density functions for yield strength

380 400 420 440 460 480 5000

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

Yield Strength (MPa)

Probability Density (/MPa)

Probability Density Functions for Yield Strength

Actual Population Population inferred from 5 Samples Population inferred after Hydrotest

Figure 4b Probability density functions for yield strength

380 400 420 440 460 480 5000

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

Yield Strength (MPa)

Probability Density (/MPa)

Probability Density Functions for Yield Strength

Actual Population Population inferred from 20 SamplesPopulation inferred after Hydrotest

Figure 5 Probability of failure due to fatigue crackgrowth

Probability of Failure @90% SMYS

1.00E-05

1.00E-04

1.00E-03

1.00E-02

0 10 20 30 40 50

Time

Pf

Figure 6 Probability of failure due to fatigue crackgrowth

Probability of Failure @105% SMYS

1.00E-091.00E-081.00E-071.00E-061.00E-051.00E-041.00E-031.00E-02

0 10 20 30 40 50

Time

Pf