24 Reliability-based assessment of polyethylene pipe creep lifetime.pdf

ARTICLE IN PRESS

International Journal of Pressure Vessels and Piping 84 (2007) 697–707

www.elsevier.com/locate/ijpvp

Reliability-based assessment of polyethylene pipe creep lifetime

Rabia Khelif a,b , Alaa Chateauneuf c, , Kamel Chaoui b

a LaMI-UBP & IFMA, Campus de Clermont-Fd, Les C ´ zeaux, BP 265, 63175 Aubi ` re Cedex, France

b LR3MI, D ´partement de G ´nie M ´canique, Universite´ Badji Mokhtar, BP 12, Annaba 23000, Alg ´rie

c LGC—University Blaise Pascal, Campus des C ´zeaux, BP 206, 63174 Aubi `re Cedex, France

Received 2 March 2007; received in revised form 9 July 2007; accepted 1 August 2007

Abstract

Lifetime management of underground pipelines is mandatory for safe hydrocarbon transmission and distribution systems. The use of

high-density polyethylene tubes subjected to internal pressure, external loading and environmental variations requires a reliability study

in order to deﬁne the service limits and the optimal operating conditions. In service, the time-dependent phenomena, especially creep,

take place during the pipe lifetime, leading to signiﬁcant strength reduction. In this work, the reliability-based assessment of pipe lifetime

models is carried out, in order to propose a probabilistic methodology for lifetime model selection and to determine the pipe safety levels

as well as the most important parameters for pipeline reliability. This study is enhanced by parametric analysis on pipe conﬁguration, gas

pressure and operating temperature.

Keywords: Reliability analysis; Polyethylene pipelines; Lifetime models; Creep

1. Introduction

equation linking the time-to-failure, the hoop stress and the

operating temperature [7–9] .

Property deterioration of PE pipes under aging effects,

related to mechanical, environmental and chemical me-

chanisms, leads to the reduction of the useful pipe lifetime.

Under continuous loading and relatively high temperature,

the lifetime is governed by the creep strain. Various models

dealing with creep failure are available in the literature

[10,11] . The creep fracture by slow crack growth has been

studied in a medium-density PE at 60 and 80 1C [12] . Tests

were conducted for noteched tensile specimens and for

cracked gas pipes under constant creep strain rate [13] . The

experimental data indicate two regimes of creep deforma-

tion related to back stress effect and material cracking. The

stress versus time-to-failure curve may be applied for an

incubation time approach, which is for creep initiation.

After this stage, the process zone of the structure is no

longer subjected to uniaxial loading. The defect within the

material induces stress concentration and stress triaxiality

ratio. The predictive model in [13] clearly shows its

superiority and effectiveness over models that take into

account only one inelastic viscoplastic deformation under

uniaxial conditions. From another point of view,

The distribution networks for natural gas and water

supplies in cities are basically made of plastic pipes with

diameters reaching 250mm and more depending on the

pressure rate. Newly installed piping gas systems in the

world are exclusively made of polyethylene (PE) because of

its ease of installation, relatively low cost and long-term

resistance to environmental aggressive agents. These

polymers are still the subject of many studies that highlight

various behavioral aspects in terms of service lifetime [1] ,

mechanical characterization and structure relationship [2] ,

loading modes [3] , residual stresses [4] , failure mechanisms

[5] and environmental effects [6] . The design of thermo-

plastic pipes is achieved through the ‘‘Rate Process Method

for Projecting Performance of Polyethylene Piping Com-

ponents’’, which is standardized in ASTM D-2837 and

D-2513. The calculation is based on a three-parameter

Corresponding author. Tel.: +33 473407526; fax:+33 473407494.

E-mail addresses: rabia.khelif@ifma.fr (R. Khelif) ,

alaa.chateauneuf@polytech.univ-bpclermont.fr (A. Chateauneuf) ,

chaoui@univ-annaba.org (K. Chaoui) .

the

doi: 10.1016/j.ijpvp.2007.08.006

ARTICLE IN PRESS

698

R. Khelif et al. / International Journal of Pressure Vessels and Piping 84 (2007) 697–707

extrapolation method requires at least to check the

mechanisms that would operate at the extrapolated time

to rupture (low stress level for engineering components).

This approach has not been considered in the present

paper.

Some comparative studies have been carried out on the

basis of a deterministic framework. However, the un-

certainties represent an intrinsic part of the material

behavior, and hence should be appropriately taken into

account.

Reliability analysis is recognized as a powerful decision-

making tool for risk-based design and maintenance. It

allows us to understand how the uncertainties are

propagated within the system, and hence it gives comple-

mentary information for deterministic analysis. For this

reason, several reliability studies have been performed

for steel pipelines [14–16] . To the authors’ knowledge,

there is yet no reliability study on PE pipes in the literature,

especially for lifetime model comparison and qualiﬁcation.

The aim of this study is the probabilistic characterization

of the lifetime of high-density polyethylene (HDPE) pipes,

in order to assess their reliability levels under operating

conditions. The study is carried out through three steps: the

ﬁrst one compares the probabilistic distributions of two

lifetime models, in order to show the insufﬁciency of

deterministic approaches; the second step considers the

time-based model uncertainties to show the high sensitivity

to experimental data, as well as to gas pressure and

temperature; and the third step concerns the pipe reliability

assessment under various operating conditions.

stress due to overlaying soil can be expressed by [17]

s s ¼ 6k m C d gB 2 Ehr

Eh 3 þ 24k d pr 3 ,

(3)

where B is the ditch width at the pipe top level, C d is the

coefﬁcient of earth pressure, E is the modulus of elasticity, k m

is the bending coefﬁcient depending on load and soil reaction,

k d is the deﬂection coefﬁcient and g is the soil density.

2.2. Lifetime model

In 1962, the Plastic Pipe Institute (PPI) selected stress

rupture testing as the most suitable test method for rating

plastic piping materials. The design of the pipes is achieved

through the ‘‘Rate Process Method for Projecting Perfor-

mance of Polyethylene Piping Components’’, which is also

described in ISO 9080. It is well established that the PE

creep rupture curve may be divided into three regions and

the same testing procedure allows us to distinguish between

various PE resins and manufacturing processes. Fig. 1

shows the typical test results for lifetime for different PE

lots under various hoop stress levels [18,19] .

The long-term hydrostatic strength (LTHS) is deﬁned as

the hoop stress that, when applied continuously, will cause

the failure of the pipe at 10 5 h (11.4 years). This strength

determines the design lifetime for thermoplastic pipes. For

design purposes, the standard extrapolation method (SEM)

can be applied according to the ISO/TR 9080 model:

log t f ¼ A þ B

þ C

log s c ,

T þ D

(4)

where t f is the time to failure (h), T is the temperature (K),

s c is the hoop stress (MPa) and A, B, C and D are

parameters to be determined from experimental results.

Experience shows that the rate process method (RPM)

provides the best correlation between long-term perfor-

mance projections and known ﬁeld data for several PE

piping materials [20] . Testing of pipes has to be carried out

according to ASTM D 1598: ‘‘Standard test method for

time-to-failure of plastic pipe under constant pressure’’.

2. Long-term behavior

2.1. Mechanical stress

In general, thin-wall underground pipelines are mainly

subjected to radial, longitudinal and circumferential

stresses. The radial and longitudinal stresses are not

considered in this study because they have no signiﬁcant

inﬂuence on the creep of buried plastic pipes. The lifetime

models are deﬁned in terms of hoop stress s c , which can

be determined by the superposition of three principal

stresses:

100

PE2306-IA, lot: ANL0283

PE2306-IA, lot: ANL482

PE2306-IA, lot: BCL374

PE2306-IIC, lot: ANL031683

PE2306-IIC, lot: BCL1075

s c ¼ s p þ s s þ s t ,

(1)

where s p is the stress due to internal pressure, s s is due

to soil loading and s t is the trafﬁc bending stress. For

creep analysis, only permanent load is considered and so

trafﬁc stress is not considered for long-term design (it is

noted that this stress is neglected compared with pressure

stress). For thin-wall tubes, the pressure stress is given

by [17]

s p ¼ pr

h ,

(2)

0.1

100

1000

10000

100000 1000000

Time to Failure, hr

where p is the internal pressure, r is the internal pipe radius

and h is the pipe wall thickness. The circumferential bending

Fig. 1. Stress versus time-to-failure for 50mm OD pipes [18,19] .

ARTICLE IN PRESS

R. Khelif et al. / International Journal of Pressure Vessels and Piping 84 (2007) 697–707

699

Using the slit failure data, the three-coefﬁcient RPM

equation is given by putting D ¼ 0 in Eq. (4), leading to

25.37, 11.97 and 18.59MPa; note that for the strain-based

criterion, the failure strain is deﬁned as 0.9%, which is a

pessimistic value, compared with a short-term failure strain

of 1.5%.

log t f ¼ A þ B

T þ C log s c

(5)

2.3. Long-term creep model

For the available test data at 60 and 80 1C( Fig. 2 ), the

constants are ﬁtted to give A ¼16.241, B ¼ 9342.2 and

C ¼1120.4. As it can be seen in Fig. 2 , the data show a

large scatter in lifetime results leading to large uncertainties

on the model parameters. For design purposes, these

uncertainties are traditionally covered by the applied safety

factor. However, a more realistic approach can be

developed by the use of the probabilistic design theory, in

order to better balance the cost/safety requirements.

It is to be noted that the model parameters are very

sensitive to the type of HDPE; for example, Tra¨ nkner

et al. [9] have found A ¼12.931, B ¼ 5904.042 and

C ¼996.957, for HDPE with a density of 953 kg/m 3 and

a nominal yield point of 23.7MPa; the comparison

between experimental results and ﬁtted equation also

showed a signiﬁcant test data scatter.

Beside these uncertainties, the choice of the failure

criterion is still a key point and the consequences on

lifetime predictions are far from being negligible. Farshad

[21] has performed an interesting study on lifetime

predictive models at 20 1C, using the parameters: a ¼

A þ B=T and b ¼ C=T. He compared two new criteria for

predicting the long-term (creep rupture) behavior of plastic

pipes under hydrostatic pressure. One of these is the

ultimate strain extrapolation method (USEM) and the

other is called the distortion energy extrapolation method

(DEEM). The three models employed were the stress-

based, the strain-based and the energy-based regression

analyses. These models have been compared: linear

regression (equivalent to SEM) leading to a ¼40.75

and b ¼25, ultimate strain extrapolation leading to

a ¼45.5 and b ¼25, and distortion energy extrapola-

tion leading to a ¼7.714 and b ¼14.286. For these

three methods, the 50-year failure stress is, respectively,

An alternative formulation of pipe lifetime can be given

in terms of long-term deformations. On the basis of

experimental observations, Lai

et al.

[22] proposed

an expression to predict

long-term creep deformation,

given by

ðtÞ¼sgD 0 þ X

t e

ð1 mÞt i a s

D i 1 exp

i¼1

#!!#

1 þ t

t e

ð6Þ

where s is the applied stress, a s and g correspond,

respectively, to horizontal and vertical shift factors,

estimated by a s ¼ 10 0:4ðs2Þ and g ¼ 10 0:04375ðs2Þ for

s o 10MPa, m is a factor estimated by 0.69 for s o 6MPa, t i

are the characteristic retardation times chosen as t i ¼ 10 i ,

t e is the elapsed time for creep compliance measurement

(taken as 4 h), and D 0 and D i are tabulated coefﬁcients

obtained by ﬁtting the experimental data [22] .

The equivalence between the time-based and the

deformation-based criteria are given by specifying an

appropriate failure creep strain. As shown by Farshad

[21] , setting a low failure creep strain leads to strongly

under-estimate the long-term failure stress, by a factor

close to 2. The consistency condition implies that coherent

limits have to be deﬁned for strain, stress and material

modulus, in order to prevent arbitrary choice of lifetime

predictive models. This adjustment implies some difﬁculties

that are related not only to average values but also to data

and model scatter; this will be discussed in the following

sections.

3. Reliability model

7.00

In this section, the probabilistic model, to be used in

pipeline reliability analyses, is presented. The strength and

loading variables are represented by a set of random

variables, described by the distribution type and para-

meters (generally, the mean and the standard deviation).

Speciﬁc algorithms are then applied for searching the most

probable failure conﬁguration.

6.00

Tests at 80 ° C

Tests at 60 ° C

RPM for 80 ° C

RPM for 60 ° C

5.00

4.00

3.00

2.00

3.1. Design limit states

1.00

In this work, reliability analysis is applied to an

underground pipeline made of HDPE tubes, which is used

to convey gas under a working pressure of 0.4MPa. The

failure function G(x) corresponds to the lifetime safety

margin deﬁned by the difference between the failure age

0.00

1000

2000

3000

4000

Time-to-failure (hours)

Fig. 2. Experimental results and ﬁtted RPM curves.

ARTICLE IN PRESS

700

R. Khelif et al. / International Journal of Pressure Vessels and Piping 84 (2007) 697–707

and the required service lifetime t service , that is

3.2. Pipe and loading uncertainties

Gðx i Þ¼tðx i Þt service ,

(7)

The pipe uncertainties are related to geometry, loading,

manufacturing and service conditions. On the basis of data

from the literature [16] , Table 1 indicates the statistical

parameters for the selected random variables. Due to lack

of information, correlation between variables is assumed to

be neglected. While the uncertainty associated with the

coefﬁcient C d is rather large, the coefﬁcients k d and k m

have moderate uncertainties since they need to be selected

for a given situation on the basis of imperfect information.

The geometrical parameters such as ditch width B, pipe

radius r and wall thickness h contain uncertainties highly

dependent on workmanship and quality control after the

ditch construction and pipe production process. The

pressure parameters are deﬁned by operating conditions.

For the considered HDPE pipe with diameter 200mm,

the gas pressure of 0.4MPa produces a hoop stress,

s p ¼ 2.93MPa, which is much higher than the stress

s s ¼ 0.01MPa due to soil loading (for information, the

bending stress due to trafﬁc wheels is s t ¼ 0.06MPa); that

is why soil and trafﬁc stresses can be neglected.

where x i are the random variables in the system. The

condition G(x i )40 indicates safety and G(x j ) p 0 corre-

sponds to conventional failure. In this expression, the

failure age depends on the hoop stress and the model

parameters reﬂecting the material properties (i.e. aging

resistance). To evaluate the failure probability, one can

apply Monte Carlo techniques to produce a random

sample of pipe lifetime distribution. This procedure is

convenient for the evaluation of the distribution para-

meters, but it requires a very large number of simulations

for the evaluation of low failure probabilities, which is

generally the case in engineering design. In order to reduce

the computation time, iterative algorithms [23] are con-

veniently applied to deal with nonlinear

limit

state

functions.

For the failure scenario (7), the reliability index b is

deﬁned as the minimum distance between the median point

and the failure domain in the equivalent Gaussian space.

This

index is

evaluated by solving the

constrained

optimization problem:

3.3. Model uncertainties

½T i ðx j Þ 2

b ¼ minimize

subjected to Gðx j Þ p 0,

(8)

As described in Section 2.2, the RPM has been calibrated

to give the best ﬁtting with experimental data. It is thus

necessary to take account for model uncertainties in

predicting the real lifetime of the pipeline. In the present

work, two uncertain parameters d 1 and d 2 are introduced in

order to reﬂect the scatter observed during pipe testing.

log 10 t f ¼ d 1 A þ B

where T i (x j ) is any suitable probabilistic transformation.

The solution of this optimization problem can be obtained

by standard optimization algorithms. In our case, speciﬁc

reliability algorithms have been used and combined with a

line search procedure. The solution of problem (8) is

usually referred to as the design point, noted P * . In ﬁrst-

order reliability methods (FORM)

þ d 2 C

log 10 s c .

(10)

[24,25] ,

the failure

In this expression, the parameters d 1 and d 2 are assumed

to follow a normally distributed probability function with

mean values equal to one and with coefﬁcients of variation

identiﬁed by test results. By applying the resampling

technique, it has been found that the coefﬁcients of

variation of 0.004 and 0.015 are appropriate for d 1 and

probability P f is simply calculated by

P f ¼ Pr½G p 0¼FðbÞ,

(9)

where Pr[ ] is the probability operator and FðÞ is the

cumulative Gaussian probability function.

Table 1

Random variables and corresponding parameters

Variable

Description

Mean value

Coefﬁcient of variation

Geometry

Internal radius of the tube

100 or 62.5mm

0.02

Wall thickness

11.4mm

0.05

Width of the ditch

440mm

0.10

Coefﬁcients

C d

Calculation coefﬁcient

1.32

0.20

k d

Deﬂection coefﬁcient

0.108

0.15

k m

Bending moment coefﬁcient

0.235

0.15

1.8910 5

Unit weight of soil

0.10

Internal pressure

0.2 to 0.5MPa

0.10

Operating temperature

20 1C

0.10

ARTICLE IN PRESS

R. Khelif et al. / International Journal of Pressure Vessels and Piping 84 (2007) 697–707

701

1.4

1.2

2.8

1.0

0.8

2.6

0.6

0.4

2.4

0.2

2.2

0.0

0.5

1.5

2.5

Time-to-failure (log-hours)

Log(time) in hours

Fig. 3. Scatter of the RPM ﬁtting for the two tested PE types.

d 2 , respectively. For T ¼ 80 1C, Fig. 3 shows the scatter of

the time-to-failure and some test results.

4. Pipeline reliability assessment

The reliability assessment is ﬁrstly focused on the

comparison of the lifetime prediction models based on

time and on creep strain, in order to identify the model

sensitivity to pipe uncertainties. In the second step, the

sensitivity of the RPM model parameters is analyzed

according to the available data; for instance, this cannot be

performed for creep strain due to lack of sufﬁcient

experimental data. Finally, the reliability assessment of a

pipeline is considered for a practical design situation.

4.1. Probabilistic comparison of lifetime models

In this section, the RPM is compared with the ultimate

deformation model. In this part of the work, the random

variables are related to pipe geometry and applied loading,

as given in Table 1 . To allow for fair comparison, the

model parameters are considered deterministic for both

models.

The choice of the target reliability results from engineer-

ing practice and society acceptability. The admissible safety

level depends on the failure consequences. According to

natural risks in human activities, the admissible failure

probability ranges from 10 2 for low failure consequences

to 10 7 for high failure consequences (e.g. nuclear power

plants). For civil structures, the admissible value of 10 4

seems to be appropriate as described by the Joint

Committee on Structural Safety (JCSS) [26,27] .

Fig. 4. Lifetime distribution under system uncertainties.

is 36 years. The distribution is clearly skewed and the

lognormal law allows us to adequately estimate the lifetime

scatter, as shown in Fig. 4 .At201C, the probability of

failure before reaching 50 years of service is 4.910 3 ,

which is

signiﬁcant, knowing the material

strength

uncertainties.

The sensitivity of system reliability is shown in Fig. 5 for

the three signiﬁcant parameters: pipe wall thickness, gas

pressure and pipe diameter. The other parameters in Table 1

have very low effects on the pipe safety. The difference

between the importance factors for the two pipes with

diameters 125 and 200mm is very low for practical use.

For pipe with diameter 125mm, Fig. 6 shows the

cumulated distribution functions (CDF) of the pipe lifetime

under different internal pressures (while the left-side ﬁgure

gives the overall distributions, the right-side one illustrates

these distributions in the range of interest for design). The

effect of gas pressure on the lifetime distribution is

4.1.1. RPM model

For pipes with diameters of 200mm at a constant

temperature of 20 1C, Fig. 4 shows the lifetime distribution

according to the RPM model, obtained by 10,000 Monte

Carlo simulations. Under the service pressure of 0.3MPa,

the mean lifetime is 115 years while the standard deviation

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika: