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International Journal of Pressure Vessels and Piping 85 (2008) 228237

Reliability of pipelines with corrosion defects

A.P. Teixeiraa, C. Guedes Soaresa,, T.A. Nettob, S.F. Estefenb

aUnit of Marine Technology and Engineering, Technical University of Lisbon, Instituto Superior Tecnico, 1096 Lisbon, PortugalbOcean Engineering Department-COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

Received 15 February 2006; received in revised form 3 September 2007; accepted 4 September 2007

Abstract

This paper aims at assessing the reliability of pipelines with corrosion defects subjected to internal pressure using the first-orderreliability method (FORM). The limit-state function is defined based on the results of a series of small-scale experiments and three-

dimensional non-linear finite element analysis of the burst pressure of intact and corroded pipelines. A sensitivity analysis is performed

for different levels of corrosion damage to identify the influence of the various parameters in the probability of burst collapse of corroded

and intact pipes. The Monte Carlo simulation method is used to assess the uncertainty of the estimates of the burst pressure of corroded

pipelines. The results of the reliability, sensitivity and uncertainty analysis are compared with results obtained from codes currently used

in practice.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Pipeline; Corrosion defects; Burst pressure; Reliability assessment

1. Introduction

Offshore and onshore pipelines are one of the safest,

economical and, as a consequence, the most applied means

of transporting oil and gas in the world nowadays.

Unfortunately, the increasing number of aging pipelines in

operation has significantly increased the number of acci-

dents. The major causes of accidents in liquid and natural

gas pipelines are internal and external corrosion defects [1].

As a pipeline ages, it can be affected by a range of corrosion

mechanisms, which may lead to a reduction in its structural

integrity and eventual failure. Clearly, regular inspections of

pipelines with state-of-the-art tools and procedures can

reduce the risk of any undue accident caused by a lack ofunawareness of the integrity of the line [2].

Studies developed by Kiefner[3]and Kiefner and Vieth

[4] resulted in the well-known ASME B31G criterion [5]

and its improved version coded on a computer program

called RSTRENG (Remaining Strength of the Corroded

Pipe) for assessing the detrimental effect of surface

corrosion defects on the burst pressure of pipelines. Later,

DNV [6] published recommended practices for assessing

corroded pipelines under combined internal pressure andlongitudinal compressive stress. Based on both experimen-

tal tests and numerical calculations, the proposed empirical

formulae comprise single and interacting defects, and

complex-shaped defects.

More recent experimental and numerical analyses[713]

indicate that these currently accepted assessment codes

involve safety factors that can occasionally impose costly

and unnecessary repair of defects or replacement of the

affected region.

In the study of Netto et al. [13], the factors governing the

burst capacity of corroded pipelines were investigated

through combined experimental and numerical studies.The residual strength of pipelines with single longitudinal

corrosion defects was initially studied through a series of

small-scale experiments. In parallel, a three-dimensional

nonlinear finite element model was developed to predict the

burst pressure of intact and corroded pipes. After being

validated by reproducing numerically the physical experi-

ments performed, the model was subsequently used to carry

out an extensive parametric study. The data were reduced to

a simple curve that relates the main geometric parameters of

the pipe and defect to its residual pressure capacity.

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0308-0161/$- see front matter r 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijpvp.2007.09.002

Corresponding author. Tel.: +351 1841 7607; fax: +351 1847 4015.

E-mail address: [email protected] (C. Guedes Soares).
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The random characteristics of the governing parameters

in real pipelines have motivated several authors to develop

probabilistic approaches to assess the probability of failure

of pipelines with and without corrosion damages. The firstreliability assessments were based on the modified B31G

criterion and used the first-order second moment formula-

tion (FOSM), and later the first- and second-order

reliability methods (FORM/SORM)[1417].

This paper aims at assessing the reliability of pipelines

using a first-order reliability method with corrosion

damage described by the limit-state equation proposed by

Netto et al.[13]. The present study analyses the influence of

the various parameters that compose the failure function

on the probability of burst collapse of either corroded or

intact pipes. A sensitivity analysis is performed for

different levels of corrosion damage to identify theinfluence of the various parameters on the probability of

burst collapse of corroded and intact pipes. The Monte

Carlo simulation method is used to assess the uncertainty

of the estimates of the burst pressure of corroded pipelines.

Finally, the results of the reliability, sensitivity and

uncertainty analysis are compared with these obtained

from codes currently used in practice.

2. Summary of previous experimental and numerical results

Netto et al. [13] conducted a series of seven burst

experiments on small-scale pipes with short, narrow

localized defects with different depths. Discontinuities

were induced in the specimens through the spark erosion

process with customized tools for each size of defect.

Defects were introduced in the mid-section of each pipe.

Additionally, they were positioned so that the minimum

thickness was coincident with the minimum thickness of

the eccentric cross-section.

The tools used to induce the defects on the pipes were

made in circular shapes in both longitudinal and hoop

directions in order to obtain maximum depths (d) of

approximately 0.6t, 0.7t and 0.8t; maximum lengths (l) of

0.5D and 1.0D; and maximum width (c) equal to 0.31D,

where (t) and (D) are the wall thickness and the outside

diameter of the pipe, respectively. These resulted in an

oval-like shape of the defects on the external specimen

surface, as shown inFig. 1.

The specimen was machined from the same long tubemade of AISI 1020 mild steel. Initially, three axial test

coupons were cut from the tube used in the manufacture of

the specimens and tested under uniaxial tension. The

average engineering stressstrain curve calculated from all

test results is shown inFig. 2. In addition, the stressstrain

curve in the hoop direction was determined by internally

pressurizing a 210 mm long piece of tube. Negligible

material anisotropy was observed by comparing the

stressstrain curves in the hoop and axial directions.

Details of the experimental apparatus and procedures

can be found in [13], including typical pressuretime

histories and recorded strains at different points of thespecimens during the experiments. The maximum pressures

attained at each test are listed in Table 1. It is clear that,

among the geometric parameters, the maximum depth of

the defect (d) has the most detrimental effect on the burst

pressure. For instance, one can compare the experimental

results from tubes T2D and T6D. For a defect with l D

andc 0.31D, whendis increased by 0.20t, i.e. from 1.58

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Nomenclature

D outside diameter of the pipe

t wall thickness of the pipe

L length of the pipe

d maximum depth of the defectc maximum width of the defect

l maximum length of the defect

sy yield stress of the material

Pbi burst pressure of intact pipe

Pb burst pressure of the corroded pipe

Po operating internal pressure of the pipe

X random variable (basic variable)

X vector of random variablesX

mX mean value of random variableX

sX standard deviation of random variableX

Xc characteristic value of random variableX

fX (x) probability density function (pdf) ofX

FX (x) cumulative distribution function (CDF) ofXg(.) limit-state (or failure) function

Pf failure probability

b reliability index

F standard normal cumulative distribution func-

tion

ai Sensitivity factor of random variableXi

Fig. 1. Pipe specimen with induced defect.

A.P. Teixeira et al. / International Journal of Pressure Vessels and Piping 85 (2008) 228237 229


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to 2.13 mm, Pb goes from 37.02 to 26.76 MPa (18%

decrease with respect to the burst pressure of the intact

pipe). On the other hand, when l is increased from 0.5Dto

D, i.e. doubled, and the others parameters are kept

constant, Pb decreases on average by only 14%.

In parallel with the experimental program, numerical

models based on the finite-element method incorporating

nonlinear kinematics and J2 flow theory plasticity with

isotropic hardening were developed to simulate the

problem. Numerical and experimental results presented

very good correlation when the exact shape of the defects

was reproduced [13]. A parametric study was then

performed considering different materials and defect

geometries in order to assess their influence on the burst

pressure. Geometries and materials used are listed in

Table 2.

Details of the numerical model and a thorough discus-

sion of the results are given in[13]. Overall, the depth of the

defect has the strongest detrimental effect on the burst

pressure, but with varied severity depending on the d/t

range. Ford/tless than 0.2, the loss in the burst capacity is

fairly small (within 5%). As the defect grows deeper,

though, this effect becomes much more pronounced.

Conversely, the rate of decay becomes smaller as the

length is increased. When the burst pressure is plotted as a

function ofl/D, a near plateau is formed between 1.5Dand

2.D, showing that the influence of the length of the defect is

negligible forl/D greater than 1.5. The results also showed

that an increase in the circumferential length of the defect,

for c/DX0.0785, has very little influence on the burst

pressure for the material and range of geometric para-

meters analyzed. Thus, the results indicated that it is

possible to estimate two geometric bounds beyond which

small or very little effect is observed in the burst pressure:

c/D 0.0785 and l/D 1.5.

3. Ultimate strength equation

The ultimate strength equation for damaged pipes under

internal pressure has been developed using the experi-

mental data and the numerical results from the parametric

study outlined above. A similar methodology for the design

of pipeline buckle arrestors was proposed in the past by

Kyriakides and Babcock in 1980 [18] and later by Nettoand Estefen [19]. For the present study, it has been

assumed that the burst pressure is dependent on the major

problem parameters, i.e.,

Pb fD; t; d; l; c; Pbi, (1)

wherePbandPbiare the burst pressure of the corroded and

intact pipe, respectively.

Based on the Buckinghams P theorem and assuming

some simplifications supported by both experimental and

numerical results, the ultimate strength equation of

corroded pipes was determined as indicated below:

PbPbi

1 0:9435 dt

1:6l

D

0:4. (2)

According to both experimental and numerical analyses

previously performed, this equation can be used for

c/DX0.0785, 0.1pd/tp0.8 and l/DX0.5. For l/D41.5,

one should set l/D 1.5, since little influence of this

parameter is observed beyond this value, as explained in

Section 2. Care is recommended when extrapolating the

results obtained via the above equation to geometric

parameters and materials not considered in the work of

Netto et al. [13]. Specifically, it should be noted that the

equation is not valid for very narrow and short defects, i.e.,

c/Dp0.0785 and l/Dp0.5.

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500

400

300

200

100

0

0 5 10 15 20 25(%)

(

MPa)

AISI 1020

Fig. 2. Average engineering stressstrain curve of test specimens.

Table 1

Geometric properties and burst pressures of the tested tubes

Tube D (mm) t (mm) d(mm) l(mm) c (mm) Pb (MPa)

T1I 42.06 2.76 57.33

T2D 41.94 2.73 1.58 42.0 13.0 37.02

T3D 41.92 2.73 1.59 21.0 13.0 44.65

T4D 41.95 2.73 1.87 42.0 13.0 32.47

T5D 41.95 2.73 1.91 21.0 13.0 41.28

T6D 41.95 2.73 2.13 42.0 13.0 26.76

T7D 41.95 2.73 2.24 21.0 13.0 34.55

Table 2

Material and geometric parameters of the numerical analyses

Material X-52, X-65, X-77

D (mm) 406.4

t (mm) 6.35, 12.7, 19.05, 25.4

d/t 0.1, 0.2, 0.4, 0.6, 0.7, 0.8

l/D 0.5, 1.0, 1.5, 2.0

c/D 0.0785, 0.1047, 0.1571

A.P. Teixeira et al. / International Journal of Pressure Vessels and Piping 85 (2008) 228237230


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Although this equation has been developed using the

burst pressure of the intact pipe obtained from experi-

mental results, the present study assumes that Pbi is given

by the B31G equation

Pbi 1:1sy2t

D . (3)

This allows a direct comparison of the different models

available to predict the effect of the corrosion defects on

the bust pressure of pipelines. This also needs to be done

because there are no experimental results available of theintact pipes that correspond to the damaged cases tested.

However, the results from the experimental tests of the

intact pipe obtained by Netto et al. have shown very good

correlation with the predictions of the B31G equation, as

illustrated in Table 3 for T1I. Additional experimental

results may show the existence of some model uncertainty

in adopting Eq. (3) to represent Pbiin Eq. (2), but then the

reliability formulation may be adjusted to account for this

additional source of uncertainty, which cannot presently be

modeled in view of the lack of the corresponding

experimental data.

For comparison purposes the B31G equation forpredicting the burst pressure of corroded pipelines is also

considered in the reliability and sensitivity analysis:

PB31Gb Pbi1 2=3d=t

1 2=3d=tM1

, (4)

where

M

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi10:8

L

D

2D

t

s . (5)

4. Reliability analysis of pipelines

To assess the probability of burst of a pipe with

corrosion defects, it is necessary to relate the values of

the operating internal pressure with the pipeline burst

pressure. The corresponding limit-state function can be

written as follows:

gX Pb Po, (6)

wherePbis the burst pressure of the corroded pipe and Pois the internal operating pressure.

Thus the limit-state function is given by

gX 1:1sy2t

D Po for intact pipes (7)

and

gX 1:1sy2t

D

10:9435d=t1:6l=D0:4 Po

for corroded pipes. 8

Having defined the limit-state function, the failure

probability can formally be written as

Pf

ZgX

fXxdx, (9)

whereX is the vector of basic random variables and g(X) is

the limit-state (or failure) function for the failure mode

considered,fX(x) is the joint probability density function of

vectorX. A failure domain is defined when g(x)o0, a safe

domain is defined when g(x)40 and a failure surface is

defined when g(x) 0.

The basic random variables comprise physical variables

describing uncertainties in loads, material properties,

geometrical data and calculation modelling. Eq. (9)

requires a multi-dimensional integration, the dimension

of which equals the number of basic random variables.

After calculating Pf, a reliability index may be obtained

from the inverse transformation

b F1Pf, (10)

whereF1 is the inverse of the standard normal cumulative

distribution function.

The difficulty in computing the failure probability Pfdirectly from the integral given by Eq. (9) led to the

development of methods based on approximations of the

failure surface to some simple forms, such as hyperplane orquadratic surfaces, at some locations, which are the so-

called design points. The methods dealing with this

calculation algorithm are called level II methods, in which

the multi-dimensional integral given by Eq. (9) is calculated

after the transformation of the basic random variables (the

vector X) onto a set of independent normal random

variables denoted by the U vector [20,21] and the

approximation of the limit-state (failure) function in the

U space, g(u), to a linear or a second-order (quadratic)

function at the failure surface to form a hyperplane or a

quadratic failure surface.

If a linear approximation of the limit-state function isused, then the method is called the FORM. However, if a

second-order approximation of the limit-state function is

used, then it becomes the SORM.

4.1. Reliability analysis of intact pipelines

The limit-state function defined by Eq. (7) is used in the

reliability analysis of intact pipelines. The probabilistic

models of the basic variables presented in Table 4 are

obtained from the characteristic values of the material and

geometrical parameters used in the numerical analyses

carried out in[13]to derive Eq. (7).

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Table 3

Comparison between the experimental results with the prediction of the

B31G equation for the intact pipe T1I

Pipe Pbi (B31G) Pbi (experiments)

[13]

Pbi (exp.)/Pbi(B31G)

T1I 56.59 MPa 57.33 MPa 1.013



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In accordance with the recommendations in EURO-

CODES EN1990[22], the characteristic value of the yield

stress corresponds to the 5% fractile value. EN1990 also

recommends that for actions, the characteristic value shall

correspond to an upper value with 95% probability of not

being exceeded. With respect to geometrical data, the

characteristic value can be assumed equal to the distribu-

tion mean value. Therefore, having defined the type of

distribution and the coefficient of variation (COV) of the

basic variableX, the mean (mX) and standard deviation (sX)

of each variable are calculated from the characteristic value

(Xc) used in the design and presented in the second column

ofTable 4.

The last column of Table 4 indicates the actual

probability of the occurrence of values smaller than the

characteristic value (Xc), which defines the constraint

required to establish the probabilistic model of the random

variables,

PXpXc FXXc, (11)

where FXdenotes the probability distribution function of

the basic variable X.According to the current design criteria of undamaged

pipes, the characteristic value of internal operating pressure

(Po) is assumed to be 72% of the burst pressure of an intact

pipe given by Eq. (7) calculated from characteristic values

of the variables presented in Table 4.

The reliability calculations were carried out using the

computer program COMREL [23]. Table 5 shows the

reliability index (b) of intact pipes obtained by FORM and

Monte Carlo simulation with importance sampling. It is

interesting to see that, when using the design factor of 0.72

for internal operating pressure, the reliability index of the

intact pipe is almost identical to the target reliability indexof 3.8 recommended in EN1990 for a reference period of

50 years.

In the following, the results of a sensitivity analysis are

presented. The importance of the contribution of each

variable to the uncertainty of the limit-state function g(x)

can be assessed by the sensitivity factors, which are

determined by

ai 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPn

i1qgx=qxi2

q qgxqxi

. (12)

Fig. 3shows the sensitivities of the failure function for

intact pipelines with respect to changes in the variables. A

positive sensitivity indicates that an increase in a variable

results in an increase in the failure function and positively

contributes to reliability. It can be seen that the operating

pressure and the yield stress of the pipe are by far the most

important variables in the reliability estimates of intact

pipelines.

4.2. Reliability analysis of pipelines with corrosion damage

In addition to the basic variables defined for reliability

analysis of intact pipes, the reliability analysis of corroded

pipes requires the probabilistic specification of the basic

variables d and l, which define the corrosion defect. As

done for the intact condition, the probabilistic models for d

and l are obtained from the characteristic values of the

damage parameters used in the numerical analyses carried

out in [13]. A Weibull distribution with COV of 0.50 is

assumed for both basic variables d and l, which results

directly from the Weibull model usually considered for the

defect depth and length growth rate [24]. The mean value

of the random variables is calculated from the character-

istic value (Xc) of each variable for exceedance probabil-

ities, P(X4Xc), from 0.01 to 0.2. In particular, the mean

value of the depth of corrosion defect that ranges from 2.17

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Table 4

Probabilistic models of the basic variables (intact pipe)

Basic variable Characteristic value (Xc) Distribution Mean Std. dev. COV (%) Fx (Xc)

syYield Stress 359.0 MPa Lognormal 410.7 MPa 32.86 MPa 8.0 0.050

DDiameter 406.4 mm Normal 406.4 mm 0.41 mm 0.1 0.500

tThickness 12.7 mm Normal 12.7 mm 0.13 mm 1.0 0.500

Po (F 0.72) 17.8 Pa Gumbel 17.28 Pa 1.20 mm 7.0 0.950

Table 5

Reliability index of intact pipes

Estimation method b-Value

FORM 3.876

MC with importance sampling 3.862

D- Diameter;

-0.01

t- Thickness; 0.06

yYield Stress;

0.49

Po- Operating

Pressure;-0.87

Fig. 3. Sensitivities of the basic variables (a-values).



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to 3.59 mm reflects the expected loss in 15 years, assuming

medium to high constant corrosion rates of approximately

0.15 and 0.25 mm/yr, respectively.

Table 6 presents the resulting probabilistic models for

the random variableslanddandFigs. 4 and 5illustrate the

probability density functions for different levels of corro-

sion obtained using this approach.

Fig. 6shows the reliability index (b) obtained using the

failure equations for corroded pipelines proposed by Netto

et al. [13] and the B31G code [5] for the different

probabilistic models of the corrosion depth (d) and length

(l). It can be seen that the equation proposed in [13] leads

to lower reliability indices for the higher levels of corrosion.

Only for very small defects (P(d4dc) and P(l4l

c)o0.08)

does the limit-state function defined by the B31G code

result in lower reliability of the corroded pipeline subjected

to the operational pressure Po. This is an interesting result

as the deterministic predictions of the B31G code have

been shown to be over-conservative when compared with

the estimates of the failure equation proposed in [13], as

illustrated in Fig. 7. The figure also shows that the

difference between the predictions of the two models is

almost constant (less than 4%) over the range of variation

of the corrosion damages. Therefore, the behavior of the

reliability indices shown inFig. 6can only be explained by

comparing the relative importance of the variables in both

equations, as will now be shown.

ARTICLE IN PRESS

Table 6

Probabilistic models of the random variables d, l(corrosion damage)

ddepth of the defect (mm) Mean Std. dev. COV d=t P(d4dc)

Characteristic value (dc) 5.08 (0.4 tc) Distribution Weibull 3.59 1.79 0.50 0.28 0.200

3.32 1.66 0.50 0.26 0.150

3.02 1.51 0.50 0.24 0.100

2.67 1.33 0.50 0.21 0.050

2.17 1.09 0.50 0.17 0.010

llength, of the defect (mm) Mean Std. dev. COV l=D P(l4lc)

Characteristic value (lc) 406.4 (1.0Dc) Distribution Weibull 287.0 143.6 0.50 0.71 0.200

265.3 132.7 0.50 0.65 0.150

242.0 121.1 0.50 0.60 0.100

213.5 106.8 0.50 0.53 0.050

173.9 87.0 0.50 0.43 0.010

0 4 8 10 12

pdf

2 6

d (mm)

P (d>dc) = 0.2

P (d>dc) = 0.1

P (d>dc) = 0.05

P (d>dc) = 0.01

Fig. 4. Probability density functions of d for different corrosion levels,P(d4dc).

0 100 300 400 600 800 900

pdf

P (l>lc) = 0.2

P (l>lc) = 0.1

P (l>lc) = 0.05

P (l>lc) = 0.01

200

l (mm)

500 700

Fig. 5. Probability density functions of l for different corrosion levels,

P(l4lc).

0 0.1

Netto et al [13]B31G

4.00

3.50

3.00

2.50

2.00

1.50

1.000.02 0.04 0.06

P (d>dc), P (l>lc)

008 0.12 0.14 0.16 0.18 0.2

Fig. 6. Reliability index for different probabilistic models of the corrosiondepth (d) and length (l).



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Fig. 8 shows the sensitivity factors of the failure

functions defined based on the ultimate strength equations

proposed by Netto et al.[13](Fig. 8a) and the B31G code

(Fig. 8b) for P(d4dc) and P(l4lc) o0.10. It is clear that

the depth of the corrosion defect (d), the operational

internal pressure (Po) and the yield stress (so) are the most

important variables. One can also see that in particular thedepth of the corrosion defect is considerably more

important in the Netto et al. failure model than in the

B31G code. Consequently, a relative reduction of the

importance of the remaining variables in the failure

function of [13] is observed.

The larger importance of the depth of the corrosion

defect in the model proposed in [13] influences the

uncertainty of the predictions of the burst capacity of the

pipe as the corrosion defect depth increases. This effect that

will also influence the reliability of the damaged pipe is

investigated in the Section 5 where the uncertainty of the

burst pressure is assessed by means of Monte Carlo

simulation for different levels of corrosion damage.

Figs. 9 and 10show the sensitivity factors for the failure

equations proposed by Netto et al. and the B31G code,

respectively, for different probabilistic models of corrosion

depth and length. It can be seen that in both cases the

importance of sy and particularly of Po increase to the

values obtained for intact pipes when the level of corrosion

decreases. This effect is balanced with a decrease of

importance of the variables that define the corrosion defect

(dandl). It can also be observed that the importance of the

two dominating variables (i.e. the depth of the corrosion

defect and the internal operating pressure) tend to stabilize

after P(d4dc) and P(l4lc)=0.05 when using the failureequation proposed by Netto et al.[13].

ARTICLE IN PRESS

l

-0.305

d

-0.836

l

-0.212d

-0.671

Po - Operating Pressure0.320

D - Diameter

-0.003

t - thickness

0.070

Yield Stress

0.318

Yield Stress

0.455

t- Thickness

0.082

D - Diameter

-0.006 Po - Operating Pressure-0.540

Fig. 8. Sensitivities factors of the basic variables (a-values) for failure function of Netto et al. [13](a) and the B31G code (b).

0 0.1 0.3

Pb

/Pb

i

Netto et al [13]B31G

1.00

0.95

0.90

0.85

0.80

0.75

0.70

0.65

0.60

0.05

P (d>dc), P (l>lc)

0.15 0.2 0.25 0.35

Fig. 7. Comparison between the predictions from[13]and the B31G code.

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0 0.05 0.1 0.15 0.2 0.25

Yield Stress t- Thickness D- Diameter Po- Op. Pressure d l

P (d>dc), P(l>lc)

Fig. 9. Sensitivity factors for the failure function defined based on[13]for

different probabilistic models of the corrosion depth (d) and length (l).

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0 0.05 0.1 0.15 0.2 0.25

Yield Stress t- Thickness D- Diameter Po- Op. Pressure d l

P (d>dc), P(l>lc)

Fig. 10. Sensitivity factors of B31G failure function for different

probabilistic models of the corrosion depth (d) and length (l).



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5. Uncertainty of the burst pressure of corroded pipelines

In the following an uncertainty analysis of the burst

pressure (Pb) of corroded pipelines is carried out using the

Monte Carlo simulation method. This study aims at

verifying whether the lower reliability obtained for the

failure function defined in[13]is due to a larger uncertaintyassociated with the predictions of this model when

compared with the B31G code, as the corrosion level

increases. Table 7 presents the stochastic models of the

basic variables used in this analysis.

Table 8shows the results of the uncertainty analysis of

the burst pressure of the corroded pipe estimated by the

failure equation proposed by Netto et al. and the B31G

code. One can see that, at a corrosion level characterized byd=t 0:24, l=D 0:60, both models lead to identicalCOVs. However, while the probability density function is

almost symmetrical for the B31G code, the Netto et al.[13]

failure equation results in a higher coefficient of asymmetry

(0.265).

Table 9shows that both the COV and asymmetry of the

values of the burst pressure calculated from the equation

proposed by Netto et al. increase as the level of corrosion

increases. Fig. 11 illustrates the probability density func-tions ofPbobtained from[13]for two probabilistic models

of the corrosion depth and length. The increasing

uncertainty associated with the predictions of the equation

proposed in[13], mainly due to the increase of importance

of the depth of the corrosion defect, is therefore responsible

for the lower reliability indices of pipes with large corrosion

defects. This aspect is particularly interesting as the B31G

code tends to underestimate the burst capacity of the

corroded pipe, showing the importance of the reliability

methods in comparing different design equations used to

predict the burst capacity of pipelines with corrosion

defects.

6. Conclusions

This paper has presented a complete reliability analysis

of pipelines with corrosion defects in which the failure

function was defined in terms of the burst pressure of the

corroded pipe obtained using both experimental data and

numerical results.

Based on the probabilistic models defined from the

characteristic values of the material and geometrical

parameters used in the numerical analyses carried out in

[13] and assuming the characteristic value of internal

operating pressure as 72% of the burst pressure of theintact pipe, the reliability index obtained for the intact

pipe is almost identical to the target reliability index

of 3.8 recommended in EN1990 for a reference period of

50 years.

It was shown that although the deterministic predictions

of the B31G code are over-conservative when compared

with the estimates of the failure equation proposed by

Netto et al.[13], this latter results in lower reliability indices

for larger corrosion defects.

A sensitivity analysis showed that the depth of the

corrosion defect and the operational internal pressure are

the most important variables in both models. The analysis

also showed that the depth of the corrosion defect is

considerably more important in the Netto et al. failure

model than in the B31G code.

ARTICLE IN PRESS

Table 9

Statistical moments of the bust pressure Pb, calculated from[13]

Probabilistic model P(X4Xc)o0.05d=t 0:22; l=D 0:22

P(X4Xc)o0.1d=t 0:22; l=D 0:22

P(X4Xc)o0.2d=t 0:22; l=D 0:22

Mean (MPa) 26.41 25.88 24.93

Std. dev. (MPa) 2.60 2.86 3.37

COV 0.098 0.110 0.135

Skewness 0.061 0.265 0.603

Table 8

Statistical moments of the bust pressure Pb (P(X4Xc)o0.1)

Netto et al. [13] B31G

Mean (MPa) 25.88 25.26

Std. dev. (MPa) 2.86 2.74

COV 0.110 0.108

Skewness 0.265 0.005

Table 7

Probabilistic models of the basic variables (pipe with corrosion defect)

Basic variable Distribution Mean Std. dev.

sy Yield stress Lognormal 410.7 MPa 32.86 MPa

D Diameter Normal 406.4 mm 0.41 mm

t Thickness Normal 12.7 mm 0.13 mm

Corrosion

defect

P(d4dc)o0.1,

P(l4lc)o0.1

d=t 0:24; l=D 0:60

d Corrosion

depth

Weibull 3.02 mm 1.51 mm

lCorrosion

length


Corrosion

defect

P(d4dc)o0.2,

P(l4lc)o0.2

d=t 0:28; l=D 0:71

d Corrosion

depth


lCorrosion

length




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By means of an uncertainty analysis carried out using the

Monte Carlo simulation method, it was shown that the

larger importance of the depth of the corrosion defect

contributes to an increase of the uncertainty associated

with the predictions of the equation proposed by Netto et

al. as the corrosion level increases. This fact is responsible

for the lower reliability indices obtained with this model for

pipes with large corrosion defects, although it over-

estimates by approximately 4% the burst pressure of thepipe over the range of variation of the corrosion damage.

This showed the importance of the reliability methods in

comparing different design equations used to predict the

burst capacity of pipelines with corrosion defects.

Acknowledgements

This work has been performed in the scope of the

bilateral cooperation programme on Submarine Systems

for Oil Production, between the Unit of Marine Technol-

ogy and Engineering of Instituto Superior Te cnico and the

Laboratory of Underwater Technology of COPPE, fromthe Federal University of Rio de Janeiro, which was

financed in Portugal by ICCTI (FCT) and in Brazil by

CAPES.

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