RELIABILITY-BASED FATIGUE INSPECTION PLANNING … · ... crack growth model for welded tubular joints available in the literature, which encompasses fracture ... fatigue design of

$Page 1: RELIABILITY-BASED FATIGUE INSPECTION PLANNING … · ... crack growth model for welded tubular joints available in the literature, which encompasses fracture ... fatigue design of$
RELIABILITY-BASED FATIGUE INSPECTION PLANNING

OF FIXED OFFSHORE STRUCTURES

Luis Volnei Sudati Sagrilo,Edison Castro Prates de Lima,COPPE/UFRJ

Carlos Cunha Dias Henriques,Sergio Guillermo Hormazabal Rodriguez,PETROBRAS S.A.

Abstract -This paper proposes the practical application of a reliability-basedprocedure for fatigue inspection planning of fixed offshore structures. Thisprocedure is based on a simplified probabilistic crack growth model for weldedtubular joints available in the literature, which encompasses fracture mechanicsand S-N curves and uses the results of the original fatigue design. Currenttechniques for reliability updating are implemented to re-evaluate the fatiguefailure probability after inspection campaigns. Target reliability values aredefined to be compatible with the simplicity of the procedure. Actualapplications illustrate the inspection costs reduction that can be obtained.

INTRODUCTION

Fatigue is an important limit state in the design and operation of steel offshorestructures. The fatigue design is usually based on Miner's rule and S-N curvesbut alternatively a fracture mechanics approach can be employed. There areseveral uncertainties concerning its evaluation. In-service inspections, usingnondestructive tests, are planned and performed in order to assure an adequatesafety level and to gather more information about the fatigue process. Fatigueinspection results can be basically summarized in detection or no detection ofcracks. Until recently, fatigue inspection planning was based mainly onengineering judgment and usually the results of previous inspections were notaccounted for the next ones. However, since the structural reliability analysishas become a practical and widely spread tool this situation has changed.

Transactions on the Built Environment vol 29, © 1997 WIT Press, www.witpress.com, ISSN 1743-3509

316 Offshore Engineering

Some important works on probabilistic inspection planning of offshorestructures have been published recently*'*'***. These works take into accountinspections results and show that it is possible to establish a rational fatigueinspection planning. Relevant practical results of probabilistic inspectionplanning can be seen also in Ref [11]. Most of these works employ a reliabilitymethod in connection with a fatigue crack growth model, based on linearfracture mechanics, to evaluate and update the probability of getting a through-thickness crack at any time during the field service life of the structure.Inspections are indicated whenever this probability fails above a target value.This target must be established taking into account several issues such asconsequence of failure, cost of repair and so on. Since this task is notstraightforward, this topic has not been clearly defined. As a matter of fact thistarget should be stated by standard codes, but up to now there are few onescovering this topic.

This paper focus on practical inspection planning of fixed offshore structuresusing a probabilistic approach. It describes the theoretical topics employed inthe development of a reliability-based procedure for fatigue inspection planningof fixed offshore structures and illustrates its practical utilization. Thisprocedure uses a probabilistic mixed fracture mechanics/S-N model for crackgrowth in welded tubular joints proposed in Ref. [15] and FORM* to computeand update after inspections the probability of fatigue failure and its associatedreliability index. Due to some approximations involved in the crack growthmodel and uncertainties in statistical data, these results and the target values areseen as qualitative indicators of reliability in the practical inspection schedulingprocess of individual tubular joints. Actual applications show the possibleinspection costs reduction that can be obtained

FATIGUE ANALYSIS

Fatigue analysis can be performed basically by two methods™. 1) Miner's ruleand S-N curves (S-N model); 2) Fracture Mechanics (FM model). Traditionally,the fatigue design of welded offshore structures has been based on S-N modelwhile the FM model has been most used in the maintenance of such structures.These two models and their equivalence will be briefly presented below.

S-N ModelThe S-N model uses the well-known S-N curves which are obtained fromfatigue experiments of tubular joints. An S-N curve is given by

N(S) = KS- (S>S,) (1)


Offshore Engineering 3 1 7

where N(S) is the number of cycles to failure under constant amplitude loadingS, K and m are material parameters, and So is a threshold level below which nofatigue damage is developed. For design purposes, generally, a characteristic S-N curve is defined by assuming m as a constant and setting K as the mean valueof experiments minus two standard deviations . The Miner's law for fatiguedamage is defined as

(S,>S.) (2)

where N is the number of stress cycles in a reference period of time TR and D isthe fatigue damage accumulation. Assuming that fatigue failure occurs when Dreaches an amount A, the fatigue design life TL is given by

T -31A?L- o (3)

In this procedure the stresses correspond to the local hot spot stresses, whichare computed by multiplying the nominal stresses Sn, obtained from a globaldeterministic or stochastic structural dynamic analysis of the structure, by thestress concentration factor SCF. The SCF is obtained from standard parametricformulas or through a finite element analysis of the joint. The fatigue design lifecan thus be rewritten as

AI —I(Sn,SCF)-

(4)

Fracture Mechanics ModelThe most employed FM model is the Paris-Erdogan crack growth equationdefined by

da- = C(AK(a)f = c(Y(a)S V )" (AK(a) > AK,) (5)

where a is the crack size ( in this paper it will refer to the crack depth only), n isthe number of stress cycles, C and m are material parameters, K(a) is the stressintensity factor obtained from linear elastic fracture mechanics, Y(a) is thegeometry function, S is the stress amplitude and AKo is a threshold below whichno crack develops. Considering the mean frequency of long term stress cyclesprocess equal to v, the integration of Equation (5) gives


3 1 8 Offshore Engineering

(6)

where ao is the initial crack size, a is the crack size associated to time in serviceT and E[ ] is used to express the mean or expected value. The geometryfunction employed in this work corresponds to one that has been frequentlyused in offshore fatigue reliability analysis*'":

Y(a) = 1 1.08 - 0.?Q I! 1.0 + 1.24expf- 22./-11 + 3.17expf- 357 -llj (7)

where a is the crack depth and t is the tube wall thickness.

The FM model can be employed whenever one needs to know the time intervalfor a crack to grow until a certain size. When using FM model for fatiguedesign purposes, similarly to S-N model, m is taken as a constant and C as acharacteristic value^ (mean value of experiments minus two standarddeviations). The fatigue design life is calculated from Equation (6) as the time inservice until a critical crack size ac is reached. Usually fatigue failures of tubularjoints are defined by a through-thickness crack and in this case the critical cracksize ac is the tube wall thickness.

Equivalence between FM and S-N ModelsA simplified calibration between the FM and S-N models can be obtained byassuming that the fatigue design life predicted by S-N model is the same as thetime to obtain a through-thickness crack and the exponent m is the same in bothmodels*' '". By this calibration it is possible to show that the time in serviceT(a) for a crack to grow from ao to a is given by^

where TL is the fatigue life computed by Equation (4) and the function \P(x)

for a particular value x = b is given by

In this paper this calibrated model is identified as mixed FM/S-N model.


Offshore Engineering 3 1 9

PROBABILISTIC FATIGUE ANALYSIS

As pointed out in detail in so many works*'**'**, there are several uncertaintiesassociated to the parameters of S-N and FM models. The rational way toaddress the effect of this uncertainties in the fatigue analysis is throughstructural reliability methods. For this purpose, a failure function or limit statefunction G(X) must be established in such a way that it indicates a failure state

whenever G(X) < 0.0 and a safe state otherwise. X stands for a vector including

all random variables considered in the analysis.

Probabilistic approaches have been developed for S-N, FM and mixed FM/S-Nfatigue analysis models. As the S-N model does not take into account anyparameter related to inspection results, i.e., detection or no detection of cracks,its probabilistic approach has been mainly used in the development of standardcodes for fatigue design™. On the other hand, FM probabilistic model has beenwidely used to develop rational fatigue inspection planning of offshorestructures considering results of previous inspections*' '*. The probabilisticmixed FM/ S-N model can be used for fatigue design criteria development*' orfor probabilistic fatigue inspection planning**. Although some simplifications,the mixed FM/S-N model is attractive for practical purposes since itencompasses fatigue design and fatigue crack growth at same time. For thisreason this model has been used in this work and it will be briefly explained inwhat follows.

Probabilistic FM/S-N ModelFrom Equation (8) a failure function for the mixed FM/S-N model can bewritten as

(10)

where P(G(X,T) < 0.0) is the probability of having of crack of size a in T years

in service. The random variables X considered in this work are the crack size afor the case when inspection results are considered (see next section), the Minersum parameter A, the stress intensity factor SCF, the S-N curves variability andthe uncertainty in the evaluation of the nominal stresses Sn (i.e., structuralmodel idealizations, linearization of drag term in Morison's equation, etc.).Variability of S-N curves was accounted for by taking K as a random variableand m as a deterministic parameter. All random variables described above, butthe crack size a, were represented by



where X; stands for any of the parameters A, K, SCF or Sn, X. its mean value

and £„. is a random variable reflecting the bias inherent to it. In summary, for

the present work X* = (a, K scF>£sn) • Substituting Equation (11) into

Equation (10) one obtains

- (12)

Uncertainty in the geometry function, which is usually considered in manyworks*'* by multiplying it by random variable having mean 1.0 and a certainCOV, vanishes from Equation (12). Another variable usually considered is theinitial crack size ao. In this work it was taken as deterministic and equal to itsmean value because it is assumed that implicitly its variability should be includedin the S-N curve uncertainty. When using standard design S-N curves it isnecessary to be careful in the evaluation of the bias %% since generally for this

curves, the parameter K is defined by a characteristic value instead of its meanvalue.

The probability of fatigue failure Pf(T) and its associated reliability index P(T)are defined by

P(G(X,T) < 0.0) = Pf(T) = <D(- P(T)) (13)

where <&(.) is the standard normal probability function. Equation (13) can beevaluated by analytical reliability methods FORM and SORM* or by MonteCarlo Simulation-based methods. In this work FORM has been used.

One should notice that in this probabilistic model, besides the statistics of thebiases and crack depth, the only data needed is the fatigue design life. As this isusually available, no extra fatigue analyses of the structure are necessary.

RELIABILITY UPDATING THROUGH INSPECTION

Setting a = a, into Equation (12), the probabilistic FM/S-N model reduces to

the probabilistic S-N model and it is possible to establish the probability offatigue failure at any time T. This probability can be updated by consideringnew information gathered from in-service inspections, i.e., no crack detection ordetection of a crack with a measured size. The updated probability of fatiguefailure Pf(T)up is obtained through the Bayesian approach


Offshore Engineering 32 1

P(G(X,T) < 0.0/(l,(X,T,)n-oI,(X,T,)))

P((G(X,T) < 0.0)nIt(X,Ti)o.. (Xj;)) (14)

where I,(X,i;) = -G(X,%) < 0.0/a = a^ for no crack detection after T; years in

service, and I.(X,i;) = G(X,%) = 0.0/a = a< when a crack of size a^ is detected

after T; years in service and i = l,--,k refers to the inspections performed, aa isthe minimum crack size detected by the inspection method employed. It is arandom variable modeled by the probability of detection (POD) curve*' . Thisformulation can be also extended for the case where a crack is detected andrepaired*. The expression (14) is usually evaluated using first order reliabilitymethod (FORM) for series systems. Further details can be found in Ref. [3,8].

FATIGUE INSPECTION PLANNING

During their service life, offshore structures are inspected to gather moreinformation and reduce the uncertainty in the fatigue design. In practice,members whose joints have the lowest calculated fatigue lives are thoseselected to be inspected. Until some years ago, the inspection intervals used tobe based on engineering judgment and previous inspection results, mainly whenno cracks had been found, used not to be accounted for the next ones. Thishas changed with the advent of probabilistic fatigue models and reliabilityupdating methods.

Using probabilistic models (before and after updating) the strategy is to inspecta joint at the time in-service T that its probability of fatigue failure Pf(T) fallsabove a target value Pfr Using this strategy it is possible to take into accountprevious inspection results and calculate optimum inspection intervals, so thatthe number of inspections is minimum.

One of the most important points to elaborate a probabilistic-based fatigueinspection planning is to set up the target failure probability Pfr (or itsassociated reliability index PT)- Setting up Pfr is not an easy task since itinvolves considering consequences of failure, costs of maintenance and so onOther important aspects are the several uncertainties associated to statisticalparameters of the random variables involved in fatigue reliability analysis andsimplifications in the methods to evaluate the crack growth in tubular joints.Due to these reasons, the use of an absolute value for Pfr can be doubtful. Anapproach for establishing Pfr for a particular member /, which involves anonlinear collapse analysis of the whole structure, is *



P4 (15)

where Pf . is the probability of structural collapse considering the member

failed and Pf is the target collapse probability for the structure under

consideration. This approach automatically considers the member importancewhen setting up Pfr but it requires besides a nonlinear collapse analysis for eachmember the setting up of Pf .

In this work a practical approach has been employed to set up the targetprobability Pfr. When a joint is inspected at first time, according to an existingstrategy, it implicitly establishes the target risk that the operator accepts.Therefore, the Pfr for a given joint can be taken as the calculated probability offailure at the time of its first inspection. This approach has the advantage of notsetting up an absolute target probability of failure. It establishes a qualitativetarget value that is in accordance with the method of analysis and the statisticaldescription employed.

APPLICATIONS

A computer code called RLINSP, incorporating the topics described above, hasbeen developed to be used in the re-analysis of the inspection plans of the fixedoffshore platforms installed in Campos Basin, offshore Brazil. In what follows,re-evaluation of fatigue inspection planning of two joints belonging to Cheme-2and Garoupa platforms will be presented. Table (1) shows the statistical dataemployed in the analyses. Most of them are taken from available literature onfatigue reliability analysis*'" . Both structures were designed using API X' S-N curve and statistical bias for the parameter K of this curve was taken fromRef. [13]. The mean initial crack depth ao was assumed to be O.llmm for bothjoints. Table (2) shows the fatigue design lives and inspections results for bothjoints. The strategy of PETROBRAS for these joints is to inspect them each %of their design life. The inspections performed do not correspond exactly to itbecause the fatigue lives shown in Table (2) are not those obtained in theoriginal design. They were recently re-calculated when these two structureswere analyzed considering new SCFs.

Figures (1-2) show the reliability index before and after the inspections for bothjoints. Through these results it is possible to observe that in order to maintain areliability level above the target throughout the life time, the Cheme-2 jointshould have been inspected after =13.00 years in-service and the Garoupa jointshall be inspected after =23.00.


Offshore Engineering 323

Variable

^SCF

I*

Ssnad (mm)™

Mean

LOO

LOO

LOO

L30<%2.006.50<4>

Std. Dev.

0.2000

0.3000

0.2500

1.302.006.50

Distribution

Normal

Lognormal

Normal

ExponentialExponentialExponential

Notes:(1) Minimum detectable crack depth;(2) Underwater Magnetic Particle Inspection (MPI);(3) Underwater Eddie Current Inspection (ECI);(4) Underwater Visual Inspection (VI).

Table (1) - Random variables and their statistical description.

Platform

Cherne-2

Garoupa

Brace/Joint

55047555

11023/1126

Thickness(mm)

30.00

12.70

FatigueDesign Life(years)™

22

20

Inspection Results^

No cracks.Visual Inspection inFebruary, 1989.No cracks.MPI in

March, 1992.Notes:(1) after reanalyzing both platforms using Efthymiou's SCFs.(2) Cherne-2 installed in November, 1982 and Garoupa in May,1980.

Table(2) - Fatigue design lives and inspection results.

The probabilistic approach can also be employed to define strategies for futureinspections. For this purpose it was assumed that no cracks are found in theinspections and the field life time of both structures is 30.00 years. Table (3)shows three strategies for each joint that maintain the reliability level above thetarget during the life time of the structures. For the Cherne-2 joint it wasassumed that the next inspection will be in the beginning of 1997 (=14.3 yearsin-service). Figure (3) illustrates graphically the three strategies for the Cherne-2 joint. It can be observed that, in case of no crack detection, one magnetic



particle/Eddie current inspection or two visual inspections at time intervalsshown in Table (3) will be enough to maintain the acceptable safety level duringthe service life of the platforms. It must be also observed that following thestandard procedure and under the same conditions, i.e. no crack detection, atleast three inspections would be performed in each joint without any soundbasis to select the method. A potential inspection costs reduction is evident.

Platform

Garoupa

Cherne-2

Strategy

ABC

ABC

InspectionMethodMPIECIVIVIMPIECIVIVI

Yearsin-service1"- 23.001*- 23.001*- 23.002"* - 28.00

1*- 14.301*- 14.301*- 14.302* - 22.00

Note: (1) Assuming no crack detectionTable (3) - Inspection strategies for the joints.

2.0015

1.00 —

0.00

CHERNE 2 - Joint 555 / Brace 5504—|— before inspection—£r— after visual inspection (02/89)

target reliability index

N*xt InspectionII I I I I I I I I I I I

20.00 30.00Service life (years)

i i | i i i i i i i i i |40.00 50.00

Figure (1) - Fatigue reliability before and after inspectionof the Cherne-2 joint.



GAROUPA - Joint 1126 / Brace 11023before inspectionafter magnetic partde inspection (03/92)target reliability index

Figure (2) - Fatigue reliability before and after inspectionof the Garoupa joint.

Figure (3) - Inspection strategies (no crack detection)for the Cheme-2 joint



CONCLUSIONS

In this paper the utilization of a reliability-based procedure for fatigueinspection planning of fixed offshore platforms was presented. This procedureemploys some techniques available in the literature in the fields of structuralreliability analysis and reliability updating and uses a mixed FractureMechanics/SN model for crack growth. It is a very effective and practicalprocedure since it only needs the calculated fatigue design life of a joint and theinspection results to evaluate and update the probability of fatigue failure. Thetarget probability of failure, which defines inspection intervals, is established byconsidering that the first inspection, according to an existing inspection plan,reflects the risk level that the operator implicitly assumes.

From the results presented it is possible to observe that inspections can beeconomically planned without any significant computational effort by simplyretaining the same risk level of the first inspection.

REFERENCES

1. Bjerager, P., Langen, L, Winterstein, S.R., Marthinsen, T and Karunakaran,D., "Application of Nonlinear Stochastic Mechanics in OffshoreEngineering", Proc. of IUTAM Symposium on Nonlinear StochasticMechanics, Torino, Italy, 1991.

2. DnV (Det Norsk Veritas), "Fatigue Strength Analysis for Mobile OffshoreUnits", Classification Notes, No. 30.2, 1984.

3. Jiao, G, "Reliability Analysis of Crack Growth with Inspection Planning",Proc. of the 11th Int. Conf on Offshore Mechanics and Arctic Engineering(OMAE), Alberta, Canada, 1992.

4. Jiao, G and Moan, T, "Reliability-Based Fatigue and Fracture DesignCriteria for Welded Offshore Structures", Engineering Fracture Mechanics,Vol. 41, No. 2, 1992.

5. Kirkemo, F., "Applications of Probabilistic Fracture Mechanics to OffshoreStructures" Proc. of the 7th Int. Conf. on Offshore Mechanics and ArcticEngineering (OMAE), Houston, USA, 1988.

6. Madsen, HO, Krenk, S. and Lind, N.C., Methods of Structural Safety,Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1986.

7. Madsen, HO., Skjong, R and Kirkemo, F., "Probabilistic Fatigue Analysisof Offshore Structures - Reliability Updating Through Inspection Results",Proc. of Integrity of Offshore Structures Conference (IOS'87), Glasgow,Scotland, 1987.

8. Madsen, HO., Sorensen, J.D and Olesen, R, "Optimal Inspection Planningfor Fatigue Damage of Offshore Structures", Proc. of 5th Int. Conf. onStructural Safety and Reliability (ICOSSAR), San Francisco, USA, 1989.



9. Moan, T., Hovde, G.O. and Blanker, A.M., "Reliability-Based FatigueDesign Criteria for Offshore Structures Considering the Effect of Inspectionand Repair", Proc. of Offshore Technology Conference, OTC Paper 7189,Houston, USA., 1993.

10. Naess, A., Fatigue Handbook, Tapir, Trondheim, 1985ll.Pedersen, C, Nielsen, J.A., Riber, J.P., Madsen, H.O and Krenk, S.,

"Reliability Based Inspection Planning for The Tyra Field", Proc. of thellth Int. Conf. on Offshore Mechanics and Arctic Engineering (OMAE),Alberta, Canada, 1992.

12. Pittaluga, A., Cazzulo, R and Romeo, P., "Uncertainties in the FatigueDesign of Offshore Steel Structure", Marine Structures, Vol. 4, No. 4,1991.

13. Wirshing, P.H., "Fatigue Reliability in Welded Joints of OffshoreStructures", Proc. of the Offshore Technology Conference, Houston, USA,1979.

14. Wirshing, P.H., "Fatigue Reliability for Offshore Structures", Journal ofStructural Engineering (ASCE), Vol. 110, No. 10, 1983.

15.Zimmermann, J.J. and Banon, H., "System Fatigue Reliability andInspection Planning for Offshore Platforms", Proc. of 13th Int. Conf. onOffshore Mechanics and Arctic Engineering (OMAE), Houston, USA,1994.


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RELIABILITY-BASED FATIGUE INSPECTION PLANNING … · ... crack growth model for welded tubular joints available in the literature, which encompasses fracture ... fatigue design of