Reliability-Based Fatigue Inspection Planning of Fixed Offshore Structures

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-based procedure for fatigue inspection planning of fixed offshore structures. This procedure is based on a simplified probabilistic crack growth model for welded tubular joints available in the literature, which encompasses fracture mechanics

and S-N curves and uses the results of the original fatigue design. Current techniques for reliability updating are implemented to re-evaluate the fatigue failure probability after inspection campaigns. Target reliability values are defined to be compatible with the simplicity of the procedure. Actual

applications illustrate the inspection costs reduction that can be obtained.

INTRODUCTION

Fatigue is an important limit state in the design and operation of steel offshore structures. The fatigue design is usually based on Miner's rule and S-N curves

but alternatively a fracture mechanics approach can be employed. There are several uncertainties concerning its evaluation. In-service inspections, using nondestructive tests, are planned and performed in order to assure an adequate safety level and to gather more information about the fatigue process. Fatigue

inspection results can be basically summarized in detection or no detection of cracks. Until recently, fatigue inspection planning was based mainly on engineering judgment and usually the results of previous inspections were not accounted for the next ones. However, since the structural reliability analysis

has become a practical and widely spread tool this situation has changed.

316 Offshore Engineering

Some important works on probabilistic inspection planning of offshore structures have been published recently*'*'***. These works take into account inspections results and show that it is possible to establish a rational fatigue inspection planning. Relevant practical results of probabilistic inspection planning can be seen also in Ref [11]. Most of these works employ a reliability method in connection with a fatigue crack growth model, based on linear fracture 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 as consequence of failure, cost of repair and so on. Since this task is not straightforward, this topic has not been clearly defined. As a matter of fact this target should be stated by standard codes, but up to now there are few ones covering this topic.

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

FATIGUE ANALYSIS

Fatigue analysis can be performed basically by two methods™. 1) Miner's rule and 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 model while 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 Model

The S-N model uses the well-known S-N curves which are obtained from fatigue 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 loading

S, K and m are material parameters, and So is a threshold level below which no fatigue 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 value of experiments minus two standard deviations^. The Miner's law for fatigue damage is defined as

(S,>S.) (2)

where N is the number of stress cycles in a reference period of time TR and D is the fatigue damage accumulation. Assuming that fatigue failure occurs when D reaches 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, which are computed by multiplying the nominal stresses Sn, obtained from a global deterministic or stochastic structural dynamic analysis of the structure, by the stress concentration factor SCF. The SCF is obtained from standard parametric formulas or through a finite element analysis of the joint. The fatigue design life can thus be rewritten as

AI — (4) I(Sn,SCF)-

Fracture Mechanics Model The most employed FM model is the Paris-Erdogan crack growth equation defined 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 is the number of stress cycles, C and m are material parameters, K(a) is the stress intensity factor obtained from linear elastic fracture mechanics, Y(a) is the geometry function, S is the stress amplitude and AKo is a threshold below which no crack develops. Considering the mean frequency of long term stress cycles process 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 service T and E[ ] is used to express the mean or expected value. The geometry function employed in this work corresponds to one that has been frequently used 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 interval for a crack to grow until a certain size. When using FM model for fatigue design purposes, similarly to S-N model, m is taken as a constant and C as a characteristic value^ (mean value of experiments minus two standard deviations). The fatigue design life is calculated from Equation (6) as the time in service until a critical crack size ac is reached. Usually fatigue failures of tubular joints are defined by a through-thickness crack and in this case the critical crack size ac is the tube wall thickness.

Equivalence between FM and S-N Models A simplified calibration between the FM and S-N models can be obtained by assuming that the fatigue design life predicted by S-N model is the same as the time to obtain a through-thickness crack and the exponent m is the same in both models*'^'". By this calibration it is possible to show that the time in service T(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 uncertainties associated to the parameters of S-N and FM models. The rational way to address the effect of this uncertainties in the fatigue analysis is through structural reliability methods. For this purpose, a failure function or limit state function 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-N fatigue analysis models. As the S-N model does not take into account any parameter related to inspection results, i.e., detection or no detection of cracks, its probabilistic approach has been mainly used in the development of standard

codes for fatigue design™. On the other hand, FM probabilistic model has been widely used to develop rational fatigue inspection planning of offshore structures considering results of previous inspections*'^'*. The probabilistic mixed FM/ S-N model can be used for fatigue design criteria development*'^ or

for probabilistic fatigue inspection planning**. Although some simplifications, the mixed FM/S-N model is attractive for practical purposes since it encompasses fatigue design and fatigue crack growth at same time. For this reason this model has been used in this work and it will be briefly explained in

what follows.

Probabilistic FM/S-N Model

From Equation (8) a failure function for the mixed FM/S-N model can be written 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 a

for the case when inspection results are considered (see next section), the Miner sum parameter A, the stress intensity factor SCF, the S-N curves variability and the uncertainty in the evaluation of the nominal stresses Sn (i.e., structural model idealizations, linearization of drag term in Morison's equation, etc.).

Variability of S-N curves was accounted for by taking K as a random variable and m as a deterministic parameter. All random variables described above, but the 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 many

works*'* by multiplying it by random variable having mean 1.0 and a certain COV, vanishes from Equation (12). Another variable usually considered is the initial crack size ao. In this work it was taken as deterministic and equal to its

mean value because it is assumed that implicitly its variability should be included in the S-N curve uncertainty. When using standard design S-N curves it is necessary 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 mean value.

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) =

where <&(.) is the standard normal probability function. Equation (13) can be evaluated by analytical reliability methods FORM and SORM* or by Monte

Carlo Simulation-based methods. In this work FORM has been used.

One should notice that in this probabilistic model, besides the statistics of the biases and crack depth, the only data needed is the fatigue design life. As this is

usually 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 of

fatigue failure at any time T. This probability can be updated by considering new information gathered from in-service inspections, i.e., no crack detection or detection of a crack with a measured size. The updated probability of fatigue failure Pf(T)up is obtained through the Bayesian approach

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 is the minimum crack size detected by the inspection method employed. It is a

random variable modeled by the probability of detection (POD) curve*'^. This formulation can be also extended for the case where a crack is detected and repaired*. The expression (14) is usually evaluated using first order reliability method (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 more information and reduce the uncertainty in the fatigue design. In practice, members whose joints have the lowest calculated fatigue lives are those

selected to be inspected. Until some years ago, the inspection intervals used to be based on engineering judgment and previous inspection results, mainly when no cracks had been found, used not to be accounted for the next ones. This

has changed with the advent of probabilistic fatigue models and reliability updating methods.

Using probabilistic models (before and after updating) the strategy is to inspect

a joint at the time in-service T that its probability of fatigue failure Pf(T) falls above a target value Pfr Using this strategy it is possible to take into account previous inspection results and calculate optimum inspection intervals, so that the number of inspections is minimum.

One of the most important points to elaborate a probabilistic-based fatigue inspection planning is to set up the target failure probability Pfr (or its associated reliability index PT)- Setting up Pfr is not an easy task since it

involves considering consequences of failure, costs of maintenance and so on Other important aspects are the several uncertainties associated to statistical parameters of the random variables involved in fatigue reliability analysis and

simplifications 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. An approach for establishing Pfr for a particular member /, which involves a nonlinear 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 importance when setting up Pfr but it requires besides a nonlinear collapse analysis for each member the setting up of Pf ^ .

In this work a practical approach has been employed to set up the target

probability Pfr. When a joint is inspected at firsttime , according to an existing strategy, it implicitly establishes the target risk that the operator accepts. Therefore, the Pfr for a given joint can be taken as the calculated probability of

failure at the time of itsfirs tinspection . This approach has the advantage of not setting up an absolute target probability of failure. It establishes a qualitative target value that is in accordance with the method of analysis and the statistical description employed.

APPLICATIONS

A computer code called RLINSP, incorporating the topics described above, has been developed to be used in the re-analysis of the inspection plans of the fixed offshore platforms installed in Campos Basin, offshore Brazil. In what follows,

re-evaluation of fatigue inspection planning of two joints belonging to Cheme-2 and Garoupa platforms will be presented. Table (1) shows the statistical data employed in the analyses. Most of them are taken from available literature on fatigue reliability analysis*'"^. Both structures were designed using API X' S-

N curve and statistical bias for the parameter K of this curve was taken from Ref. [13]. The mean initial crack depth ao was assumed to be O.llmm for both joints. Table (2) shows the fatigue design lives and inspections results for both joints. The strategy of PETROBRAS for these joints is to inspect them each %

of their design life. The inspections performed do not correspond exactly to it because the fatigue lives shown in Table (2) are not those obtained in the original design. They were recently re-calculated when these two structures were analyzed considering new SCFs.

Figures (1-2) show the reliability index before and after the inspections for both joints. Through these results it is possible to observe that in order to maintain a reliability level above the target throughout the life time, the Cheme-2 joint

should have been inspected after =13.00 years in-service and the Garoupa joint shall be inspected after =23.00.

Variable Mean Std. Dev. Distributio

n ^SCF LOO 0.2000 Normal LOO 0.3000 Lognormal I* LOO 0.2500 Normal Ssn ad (mm)™ L30<% 1.30 Exponential 2.00^ 2.00 Exponential 6.50<4> 6.50 Exponential 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.

Platfor Brace/ Thickness Fatigue Inspection Results^

m Joint (mm) Design Life (years)™ Cherne- 55047 30.00 22 No cracks.

2 555 Visual Inspection in February, 1989. Garoupa 11023/ 12.70 20 No cracks. 1126 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 future inspections. For this purpose it was assumed that no cracks are found in the inspections 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 the target during the life time of the structures. For the Cherne-2 joint it was assumed that the next inspection will be in the beginning of 1997 (=14.3 years in-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 intervals shown in Table (3) will be enough to maintain the acceptable safety level during the service life of the platforms. It must be also observed that following the standard procedure and under the same conditions, i.e. no crack detection, at least three inspections would be performed in each joint without any sound basis to select the method. A potential inspection costs reduction is evident.

Platform Strategy^ Inspection Years Method in-service A MPI 1"- 23.00 Garoupa B ECI 1*- 23.00 C VI 1*- 23.00 VI 2"* - 28.00

A MPI 1*- 14.30 Cherne-2 B ECI 1*- 14.30 C VI 1*- 14.30 VI 2* - 22.00 Note: (1) Assuming no crack detection Table (3) - Inspection strategies for the joints.

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

2.00 15

1.00 —

N*xt Inspection 0.00 II I I I I I I I I I I I i i | i i i i i i i i i | 20.00 30.00 40.00 50.00 Service life (years) Figure (1) - Fatigue reliability before and after inspection

of the Cherne-2 joint.

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

Figure (2) - Fatigue reliability before and after inspection

of 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 fatigue inspection planning of fixed offshore platforms was presented. This procedure employs some techniques available in the literature in the fields of structural reliability analysis and reliability updating and uses a mixed Fracture Mechanics/SN model for crack growth. It is a very effective and practical procedure since it only needs the calculated fatigue design life of a joint and the inspection results to evaluate and update the probability of fatigue failure. The target probability of failure, which defines inspection intervals, is established by considering 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 be economically planned without any significant computational effort by simply retaining the same risk level of the firstinspection .

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