guarracino 2008 applied ocean research

8/13/2019 Guarracino 2008 Applied Ocean Research

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Applied Ocean Research 30 (2008) 297304

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Applied Ocean Research

journal homepage:www.elsevier.com/locate/apor

Analysis of testing methods of pipelines for limit state design

F. Guarracino, M. Fraldi, A. GiordanoDipartimento di Ingegneria Strutturale, Universit di Napoli Federico II, 80125 Napoli, Italy

a r t i c l e i n f o

Article history:

Received 19 December 2007

Received in revised form

21 December 2008Accepted 26 December 2008

Available online 4 February 2009

Keywords:Pipelines

Testing arrangement

Limit state

a b s t r a c t

It is well knownthat thedesign of submarine pipelinesrelies on accurate test results forthe local bucklingcollapse of pipes subjected to bending loading. The present paper analyses apparently anomalous valuesof axial tensile and compressivestrains from recent test results in comparison to thevalues that would beexpected on the basis of simple bending theory. This could have important consequences for the efficacyof the design factors derived using these results. The cause of the differences between the strain valuesobtained in the tests and those expected on the basis of simple bending theory are explained using finiteelement modelling.The differences result fromthe typeof collars andsupportscommonlyused in bendingtests, the effects of which persist for a greater length along the test pipe than has hitherto been assumed.In general, it is pointed out that the application of the simplified engineering theory of bending can beerroneous when ovalisation is imposed or, on the contrary, the boundary conditions of the section arerestrained from ovalising deformations. The influence of theD/tratio is also analysed.

The results contribute to the understanding of a crucial limit state for the design of onshore andoffshore pipelines.

2009 Elsevier Ltd. All rights reserved.

1. Introduction

In most modern pipeline designs, the required minimum wallthickness is determined on the basis of a maximum allowablehoop stress under design pressure. Generally, the initial wallthickness design is based on the assumption that pressure willbe the governing load. However, a pipeline may be subjected toadditional loads due to installation, seabed contours, impacts andhigh-pressure/high-temperature operating conditions for whichthe bending moment capacity is often the limiting parameter[1].

The design calculations for pipelines are aimed at providing asafe, robust pipeline with an economical use of expensive materialand installation equipment. Pipeline design has traditionally beenbased on a limiting stress approach but since 1996 a limit statecode has been developed by DNV with the latest version issued

in 2000 [2]. The use of the limit state approach provides a morecomprehensive basis for the calculation of the ultimate conditionsfor pipes subjected simultaneously to pressure and bending loads.One aspect that is incorporated in the code is the concept ofultimate states of pipe with load-controlled and displacement-controlled loading. In the former, the bending deformations aredirectly affected by the variation of the applied moments. Theultimate state thus relates to a maximum moment condition.

Corresponding address: Dipartimento di Ingegneria Strutturale, Universit diNapoli Federico II, via Claudio, 21, 80125 Napoli, Italy. Tel.: +39 081 7683733;

fax: +39 081 7683233.

E-mail address:[email protected](F. Guarracino).

In the displacement controlled condition the deformations are

controlled, say by bending the pipe round a prescribed surface, andonce the pipe is in contact with the surface, additional loading ofwhatever kind, could not increase the local curvature of the pipe.This form of loading is associated with a maximum curvature, i.e. amaximum local axial strain.

In both these cases, the ultimate state of the pipelinedeformation or loading is calculated using a model that describesthe characteristic ultimate moment or strain related to thegeometry and material properties of the pipe. The characteristicvalues are then modified using design factors that produce thedesign values of allowable ultimate moment or strain. The modelsused to determine the characteristic levels of moment or strain aregenerally chosen as those describing as closely as possible meanvalues of these variables measured during tests. The design factors

are calculated using statistical descriptions of the scatter of testresults compared to the mean values together with the statisticaldescriptions of the variables composing the particular model,e.g. material strength, modulus etc. The calculation to determinethe design factors also include a calibration stage in which thevalues of the design factors are adjusted to ensure that the resultsfrom applying the code formulation and factors prescribe levels ofthe ultimate conditions that conform to industry-wide acceptablelevels for the probability of failure of the pipe.

In the process described above, it is generally assumed thatthe scatter of test results arises from minor and usually randomvariations in the variables included in the design model. In the caseof a pipe, these variations would generally relate to differences inmaterial properties and in the geometries of the test pipes (such

0141-1187/$ see front matter 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.apor.2008.12.003
http://www.elsevier.com/locate/aporhttp://www.elsevier.com/locate/apormailto:[email protected]://dx.doi.org/10.1016/j.apor.2008.12.003http://dx.doi.org/10.1016/j.apor.2008.12.003mailto:[email protected]://www.elsevier.com/locate/aporhttp://www.elsevier.com/locate/apor


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298 F. Guarracino et al. / Applied Ocean Research 30 (2008) 297304

Fig. 1. Typical four-point bending test arrangement.

as wall thickness or out-of-roundness) from their correspondingnominal values. The design model is intended to provide adescription of the test conditions that account for systematicdifferences between one test and another.

In the present paper the apparently anomalous results fromtests on pipes, which have been observed, but ignored, in thepast, are analysed and explained with the aid of finite elementsimulations. The influence of theD/tratio is also examined andthe potential influence that these anomalies might have on the

process of providing design calculation guidance using the limitstate method is highlighted.

2. Pipe testing

The pipe cross sectional bending moment is directly propor-tional to the pipe curvature. The moment curvature relationshipprovides information necessary for design against failure due tobending. If the pipe is part of a carrying structure, the elasticlimit may be an obvious choice as the design limit. However,for pipelines and risers where the global shape is less impor-tant, this criterion will be overly conservative due to the signifi-cant resources in the elasticplastic range. Higher design strengthcan therefore be obtained by using design criteria based on thestress/strain levels reached at the point of onset for local bucklingor at the ultimate moment capacity. For displacement-controlledconfigurations, it can even be acceptable to allow the deforma-tion of the pipe to continue into the softening region. Results fromtesting a section of a pipe in purely bending loading has usuallybeen analysed on the basis that simple bending theory can ade-quately describe the behaviour of the test specimen. Primarily thisimplies that while the pipe material remains elastic the applicationof purely bending moment will induce maximum tensile and com-pressive strains that areidentical in magnitude. A typical test rigfora medium diameter pipe, of about 700 mm diameter, is shown inFig. 1.The test rig applies a four-point bending condition with thecentral section of the test pipe assumed to be subjected to bendingaction only, with no, or at most very little, shear or axial forces.

The loading of the section of pipe during a test has slightly

different requirements from that pertaining to a section of a verylong continuous pipe. At the four loading points, see Fig. 1, the pipeis reinforced to avoid the external loads from locally deformingand perhaps crushing the pipe. Since the pipe is assumed to be asimple structural element so that simple beam theory holds true,it has been common practice to assume that the axial strains haveidentical values in tension (top surface) and compression (bottomsurface) and that the strains can be calculated directly from thecurvature or the vertical displacements of the central section ofthe pipe. The ultimate strain values from tests in which the pipehas been loaded to the point of local buckling have usually beeninferred from measurements of the deformations. Only recentlyhave strain gauges been attached to the test pipe to measure axialstrains directly.

Some time ago tests [3] were carried out on 152 mmdiameter pipes to determine the maximum curvature to which

Fig. 2. Results from a 152 mm diameter pipe bend test[3].

the pipe could be deformed prior to local buckling occurring. Anarrangement similar to that inFig. 1was used, although very thicksteel collars were used to protect the pipe at the loading points.The collars were machined to fit very closely around the pipe toensureno localisedloading wasapplied to thepipe wall. As a result,the pipe was fully prevented from ovalising at the loading points.

Strain gauges to measure axial and circumferential strains wereattached at intervalsof 100mm apart along thecentral test section.In the design of the test rig it was assumed that a central testsection of about 5D would suffice to ensure that end effects dueto theloading conditions would diminish to a negligiblelevel alongthemajorpart of that section. Fig.2 shows results of the axial strainvalues along the top and bottom of the pipe section for two levelsof the applied loading.

It is evident the axial strains are fairly uniform along the lengthof the test section but that there are significant differences in theaveraged values of compressive and tensile strains. At the lowerlevel of applied loading, the averaged compressive axial strainsare seen to be about 1.36 times the corresponding values of thetensile strains. The difference between the averaged axial strain

levels increased for the higher level of loading with the averagedcompressive strains being 1.59 times the corresponding tensilestrains.

At that time theevident anomaly between themeasuredstrainswith the expected values vis--vis the simple bending theorywas not followed up, and even after checking that the straingauges were correctly positioned and the instrumentation wasfunctioning properly the cause of the anomaly was not furtherinvestigated.

Proving tests were later carried out on several sections of609 mm diameter pipes containing a thin liner made from acorrosion resistant material [4]. The purpose of the tests was todetermine accurately the level of strain to which the pipe couldbe bent before the liner buckled locally. The test arrangement is

shown inFig. 3in which the loading arm is 2 m long to create themoment in the central section of the test pipe. The test section was


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F. Guarracino et al. / Applied Ocean Research 30 (2008) 297304 299

Fig. 3. Test arrangement for lined pipe proving test[4].

Fig. 4. Averaged strain values plotted against corresponding values of applied

loading[4].

Fig. 5. Averaged strain values plotted against corresponding values of appliedloading[4].

Fig. 6. Test arrangement with modified support and load application points.

3.5D long. It may be seen from Fig. 3that the load is applied tothe test pipe using straight bars and loose yokes around part of thepipe circumference. A number of axial strain gauges were attachedalong the top and bottom centre lines of the pipe at intervals fromthe support points. The values of strain were monitored as the load

values were progressively increased and were found to be uniformalong the test section.Figs. 4and5show plots of the variation ofthe values of the top and bottom strain gauges averaged along thetest sections against corresponding values of applied load for twopipes of different wall thickness, respectively. It is evident fromFigs. 4 and5that in both cases there is a systematic differencebetween averaged compressive strains compared to correspondingtensile strains. In one test,Fig. 4,the averaged axial tensile strainswere 1.21 times the corresponding compressive strains and in theother test,Fig. 5,the averaged axial tensile strains were 1.28 timesthe corresponding averaged compressive strains. In view of theimportance of the results of the tests in providing the allowablelevels of strain for the lined pipe an investigation was made withregard to the underlying cause of the anomaly. This is described in

the next section of this paper and some preliminary studies can befound in[5,6].The investigation determined that the cause lay in the effect of

the imposed ovalisation applied by the saddles at the load points.This resultpointed to a proposal for the modification of the loadingapplication in which the loads were applied, not through localstiffening of the pipe wall or saddles, but through the neutral axisof the pipe, as shown inFig. 6.

The test pipe was fitted with strain gauges, as before, and alsogauges to measure the ovality of the pipe. As before, the values ofthe axial strains measured by the gauges along the test section ofthe pipe were very uniform. Fig. 7 shows the result from averagingthe measured values of strain at positions along the test sectionplotted against corresponding values of applied load. It may be

seen that with the modified loading and support arrangement,the averaged measured values of compressive strains agree veryclosely with the corresponding values of the tensile strains.

3. Analysis of the effects of testing arrangement

Following the observation of the apparent anomaly in thevariation of the tensile and compressive strains compared withthe values expected on the basis of the simple theory of bending,analytical [7] and numerical modelling has been carried out toinvestigate the root cause of the anomaly.

Essentially,it wasfound that during thetest of a short section ofpipe, the practical loading and support arrangements can result inboundary conditions that may impose some degree of ovalisation

at the point of load application or, alternatively, decrease thedevelopment of the natural ovalisation [8,9]. It has generally


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Fig. 7. Averaged measured values of strain at positions along the test section with

loads applied through the neutral axis of the pipe.

Fig. 8. Outline of the finite element modelling of a test arranged as inFigs. 1and3.

been assumed that such boundary effects would have a minorconsequence on the deformations of the test pipe and wouldpersist for only a short distance along the test length. However,the investigation has shown a hitherto unsuspected mechanism inwhich the imposition or the prevention of the ovalisation at the

loading point of the test pipe will set up an axial strain system thatis additional to the usual axial strain caused by simple bending.The conjunction of the two strain systems thus causes a differencebetween thevalues of theaxialcompressive andtensile values. Theinteraction between the ovalisation and the axial strain effects isexamined here using finite element modelling.

Fig. 8shows the finite element simulation of a test arranged asinFigs. 1and3on a 609.6 mm diameter pipe (t= 18.9 mm).

For this purpose the commercially available nonlinear finiteelement code, ANSYS r v.11.0, was employed. The case underconsideration was modeled by means of 9000 four-node SHELL63elements for an overall length of 8 m. According to ANSYSdocumentation [10], SHELL63 has both bending and membranecapabilities. Both in-plane and normal loads are permitted. The

element has six degrees of freedom at each node: translations inthe nodal x,y, and z directions and rotations about the nodal x ,

Fig. 9. Finite element simulationof a test arranged as in Figs. 1 and 3: strain values

at the mid-section of the pipe applied load 1 MN.

y,andzaxes. Stress stiffening and large deflection capabilities areincluded. A consistent tangent stiffness matrix option is availablefor use in large deflection (finite rotation) analyses. Both the

loading andthe support zones were supposed to span over a lengthof one fourth of the mean radius of the pipe. In this respect apreliminary mesh refinement sensitivity analysis was carried out.The material properties of a generic isotropic high-grade steel,i.e. E = 2.07 105 N/mm2 and = 0.3, were assumed. Bothlinear and nonlinear elastic analyses were performed and it wasfound that a linear analysis was sufficient to deliver very accurateresults.

The FE strain distribution along the mid-section of the pipe foran applied load of 1 MN is shown inFig. 9for elastic conditionsand is in good agreement with the experimental results ofFig. 5.Itis evident that the tensile strains at the top of the pipe are about1.25 times the compressive strains at the bottom of the pipe.

As a matter of fact, the rigid loading yokes at the supportsand at the loading points induce some degree of ovalisation onthe pipe and this results in an increased value of the tensilestrains at the top of the pipe, as confirmed by the finite elementanalysis. This outcome makes it clear that in test design and resultanalysis special attention must be paid to the effects of loading andconstraint arrangement of the pipe being tested.

Fig. 10shows the values along the pipe axis of the longitudinalstrains at the top, at the bottom and at the side of the pipe, asyielded by the finite element analysis.

It may be seen that the effects of the loading and of theconstraints propagate in quite a complex manner along the fulllength. It is also evident in the figure that at the mid-span of themodel,where thebending moment canbe considered constant,theratio of the tensile axial strain to the corresponding compressivestrain is about 1.25 times. Since generally this is the section of pipe

that is assumed to be free from the boundary support effects andto have strain levels pertaining to simple bending theory, it can beseen that the analysis confirms the anomaly observed in the tests,seeFigs. 4and 5,and also confirms that the presence of the testloading conditions will affect the axial strain levels at which localaxial buckling will be initiated in a test pipe.

Finite element modelling has as well been applied to determinethelength over which theeffects of theloadingand of theboundaryconstraints propagate and hence influence the axial strains. Inorder to do so, a very simple modelling was applied to pipes withdifferent diameters and wall thicknesses. The modelling consistedin applying a vertical load of 1 MN exactly on a vertical support. Inthis mannerno bending momentwas expected along theaxis of thepipe and all the strains were due to the imposed ovalisation of the

loaded section. As seen before, these strains are essentially similarto those which, in the case of bending tests, add to the bending


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Fig. 10. Finite element simulation of a test arranged as inFigs. 1and3:strain values along the pipe axis applied load 1 MN.

Fig. 11. FEM simulation for a pipe withD/t= 32 (diameter 609.6 mm, wall thickness 18.9 mm): strain values along the pipe axis applied load 1 MN.

strains and can cause a significant alteration in the symmetry withrespect to the neutral axis of the section. It is worth highlightingthat this effect cannot be seen as a classic local perturbation, as isshown in the next figures.

ThreeD/tratios were taken into consideration, i.e. 16, 32 and

64, obtained by varying either the diameter or the wall thicknessof the pipes. The results are shown in Figs. 1115.On account of

the symmetry, in all the plots the strain values at the top and atthe bottom of the pipe coincide.

First, fromFigs. 1115it is evident that the maximum and theaverage value of the axial strain cannot be directly related to theD/t ratio. In fact, when the D/t ratio increases on account of a

reduction in wall thickness (the diameter D is kept constant at608.6 mm, see Figs. 12, 11 and 13 in sequence), the intensity of the


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strain tends to become greater with theD/tratio. On the contrary,when theD/tratio increases on account of a larger diameter (thewall thickness is kept constant at 18.9 mm, see Figs. 14,11and15in sequence), the intensity of the strain tends to reduce.

Second, it can be noticed that, conversely, the natural wave-length of the solution can be directly related to the D/t ratio. In

fact, fromFigs. 1115it can be seen that when the D/t ratio in-creases (either on account of a reduction in wall thickness or an

increase in diameter), the effects of the loading propagate with awavelength which tends to become greater with the D/tratio.

Largely, it can be affirmed that the effects of loading andconstraint arrangement persist for a greater length along the testpipe than has hitherto been assumed.

Equally, when theovalisationof thecrosssection under bending

(which takes place on account of the well-known von Krmneffect [8,9]) is restricted by any form of constraint, a marked


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asymmetry between the compressive and tensile strains occurswith a turnround with respect to what has been shown in theprevious finite element analyses. This is the case of the resultsfrom a 152 mm diameter pipe bend test [3], shown in Fig. 2,where the averaged compressive axial strains are seen to be about1.36 times the corresponding values of the tensile strains. Theexplanation of this phenomenon is quite simple: preventing the

natural ovalisation under bending canbe seen as applying a loadingsimilar to those inFigs. 1115,but reversed in sign. The resulting

strains will be reversed in sign, too, and, in the case ofFig. 3,addto the bending strains, causing an increase in the value of thecompressive strains and a reduction in the value of the tensilestrains.

4. Considerations on the limit state design

As said earlier, depending on the function of the pipe, any of thepoints from the moment curvature relationship can be used as the


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Fig. 16. Scatter of experimental strain versus D/t from various reported tests in

the literature [11].

design limit. In certain cases the elastic limit may be an obviouschoice but for pipelines and risers this criterion will be excessivelyconservative due to the significant resources in the elasticplasticrange. Higher design strength can therefore be obtained by using

designcriteriabasedon thestress/strain levelsreached at thepointof onset for local buckling or at the ultimate moment capacity.Thiscan be justified provided the availability of the carrying capacitywith high deformations combined with a precise prediction of thedeformation pattern and its amplitude.

The results from bending tests have shown that depending onthe form of arrangement at the support and at the point where theload is applied tothe pipe, thecompressivestrains might be greateror less than the corresponding tensile strains, by up to 30%. It isalso recognised that the onset of local buckling is instigated by thelevel of compressive axial strainin thepipe wall. Thus, thevariationin the axial compressive strain due to the loading arrangement,i.e. the degree of constraint on the ovalisation at the pipe at thatposition, will affect the level of overall bending that would initiatelocal buckling.

In light of this, it is not unreasonable to expect that acomparison of the values of strains at which buckling has beeninitiated in tests carried out by various researchers, with differenttest arrangement, will show a degree of scatter. This scatter hastended to be assumed to have resulted primarily from variationsin the geometry of the test pipes, usually in the form of out-of-roundness of the pipe wall. However, as a result of the analysis ofeffects due to the test loading conditions, it is now suspected that asignificant component of the scatter could result from differencesin the testing equipment.

Fig. 16shows a few examples from various reported tests inthe literature [11]. These results, together with others, have beenused in the calculations of the appropriate values of design factorsthat are currentlyused in the limit state design of subsea pipelines.

In view of the effects of the test arrangement in increasing or

decreasing the apparent buckling strain in a test it is possible thatthe calculations using the apparent values of buckling strain willresult in factors that do not actually correspond to the intendedlevel of probability of failure.

5. Conclusions

The focus of the present work has been to identify and analysethe effects of the test arrangement on the level of apparent strain,based on the assumption of simple engineering bending theory, atwhich local buckling is initiated. The apparently anomalous valuesof measured axial strain in tests have been explained with theaid of finite element modelling. The length over which the effectsof the loading and of boundary constraints propagate (and henceinfluence the axial strains) has been investigated. Hence it hasbecome evident that the scatter in test results from different typesof testing arrangement could include a systematic error that isinduced by the constraints at the support and loading points inthe test rig. The results contribute to the understanding of a cruciallimit state for the design of onshore and offshore pipelines.

Acknowledgements

The authors wish to express their gratitude to Prof. A.C. Walkerfor providing results and information from the tests describedin [3]. The financial support from ReLUIS (University Networkof Seismic Engineering Laboratories) and from the InternationalMobility Program of the University of Naples Federico II is alsograciously acknowledged from the first author.

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method for laying subsea pipeline. In: Proc. 1st petroleum technologyAustralian conference. 1985.[4] Walker AC, Holt A, Guarracino F, Wilmot D. Test procedure for pipe and

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[6] Guarracino F, Giordano A. Influence of boundary conditions on the instabilityof circular cylindrical shells. In: Proceedings of ASSCCA03. 2003.

[7] Guarracino F. Analytical evaluation of local effects in cylindrical shells testingand design. Strength of Materials 2008 [in press].

[8] von Krmn Th. Ueber die Formnderung dnnwandinger Rohre, insbeson-dere federnder Ausgleichrohre. Zeitschrift des Vereines deutscher Ingenieur1911;45:188995.

[9] Brazier LG. On the flexure of thin cylindrical shells and other thin sections.Proceedings of the Royal Society A 1927;116:10414.

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[11] Gresnigt AM, van Foeken RJ. Local buckling of UOE and seamless steel pipes.

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