Liu 2009 Journal of Loss Prevention in the Process Industries

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Strain-based design criteria of pipelines

Bing Liu a,*, X.J. Liu b, Hong Zhang b

a PetroChina Pipeline R&D Center, 51 Road Jinguang, Langfang, Hebei Province 065000, PR Chinab China University of Petroleum (Beijing), 18 Fuxue Road, Changping, Beijing 102249, PR China

a r t i c l e i n f o

Article history:

Received 9 August 2007

Received in revised form

21 July 2009

Accepted 22 July 2009

Keywords:

Pipeline

Strain-based

Limit states

Design criteria

Strain limit

a b s t r a c t

Traditional pipeline design analysis methods presented in various codes are usually based on limit stress

criteria. However, these methods may be inapposite to modern steels, especially for displacementcontrolled loads such as ground displacement load. Strain limits, including ovalization limit, tensile strain

limit and compression strain limit, are compared in this paper based upon various codes and recom-

mendations. In addition, most factors of strain limits are also reviewed respectively.

2009 Elsevier Ltd. All rights reserved.

1. Introduction

With the rapid development of oil and gas pipeline industry,

much more new trend is showing, including long-distance, large-

diameter and high-operating-pressure. This requires correspond-

ing pipeline design guidelines and criteria should continue to adapt

to the new situation. From the design step, not only the safety and

reliable of pipeline but also its economic and efficient operation

should be ensured. Most of the existing pipeline design codes are

based on limiting stress criteria, which is considered acceptable for

steel with a well defined yield point and a well defined yield

ductility and strength. But the stress in pipelines may exceed the

limit under some loads, such as earthquakes, landslides, and the

laying of submarine pipelines and other displacement control

loads, and the strength design criteria based on stress is no longer

valid (Pan, 2005).

2. Background

Stress-based design criteria are based on the minimum yield

stress for the pipeline, while strain-based design criteria are based

on limit state design and displacement control load. If the safe

operation can be ensured under displacement load, the pipeline

strain is allowed to be more than the specified yield strain.

Although some plastic deformation occurred in the pipeline here,

the pipeline has been able to meet the operation requirements, and

can play more capacity. Stress-based design method supplemented

with strain-based design method, can utilize this deformation

capability, and make the pipeline fully play its role under security

and economic design.

2.1. Limit state design

Limit state is a state beyond which the structure no longer

satisfies the requirements. Both DNV (Det Norske Veritas, 2000)

and CSA (Canadian Standards Association, 2003) use limit state

method for pipeline design. But there are slightly different in state

limit classification between codes, and in DNV-OS-F101, four kinds

state limits are recognized, including serviceability limit state,

ultimate limit state, fatigue limit state, accidental limit state. Limit

state method is applied to the pipeline design, and appropriate

design criteria are presented in order to make the conservative lesswith more flexibility to the designers.

2.2. Load control and displacement control

There are many different classifications to loads upon the

pipeline. Displacement control loading can be defined more

specifically as a loading that can be reduced to nothing by a change

in the shape of the part of interest. By contrast a load control

loading cannot be reduced to zero by a simple change in shape.

Bigger strain may be allowed to displace control loading. The

loading on a pipeline may generally be a combination of load and* Corresponding author. Tel: þ86 316 2170702; fax: þ86 316 2170240.

E-mail address: [email protected] (B. Liu).

Contents lists available at ScienceDirect

Journal of Loss Prevention in the Process Industries

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / j l p

0950-4230/$ – see front matter 2009 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jlp.2009.07.010

Journal of Loss Prevention in the Process Industries 22 (2009) 884–888

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displacement controlled. The pressure loading will be load

controlled, but the soil motion around a pipeline will usually cause

displacement control moment loading.

3. The strain-based design methodology and the state of art

The main principles of limit states design included in the strain-

based design are the following (Zhou & Glover, 2005):

Identification of all applicable limit states;

Classification of limit states into ultimate limit states and

serviceability limit states dependent on the consequence if the

limit states are violated;

Development of limit state functions; and

Establishment of design criteria to ensure safe and effective

design.

Specifically, limit state functions (or design criteria), in terms of

tensile and compressive strains, can be expressed as follows:

Maximum tensile strain demand Factored tensile strain

capacity.

Maximum compressive strain demand Factored compressivestrain capacity.

Therefore, the key components of applying strain-based design

to a project are the processes and models used to determine both

the strain demands and strain capacities.

3.1. The code provisions development

The general framework for the application of strain-based

design has been the subject of considerable research during the

past twenty years (AME, 1997; Det Norske Veritas, 1982). This work

has been achieved through the publication of limit state design

Rules for submarine pipelines. Det Norske Veritas (DNV) in 1982

proposed the use of combined stress-based design criteria andstrain-based design criteria together. And in 1996 Det Norske

Veritas published a subsea pipelines limit state design criteria ( Det

Norske Veritas, 1996) in which there are many analytical methods

based on a variety of load conditions. In the same year, the Canadian

Standards Association (CSA) published CSA Z662-96 (Canadian

Standards Association, 1996) which comprises strain-based design

criteria for submarine pipeline design and the limit state design. In

2007, the Canadian Standards Association (CSA) published CSA

Z662-2007.

Several codes have provisions that apply to strain-based design

of pipelines, including DNV-OS-F101, CSA-Z662, API RP 1111-1999,

ASCE, ASME B31.8., API 1104 and ABS 2006. These codes can be

placed in three general categories: those that provide a compre-

hensive overall pipeline standard that includes requirements bothfor stress-and strain-based design (DNV, 2000; CSA-Z662), those

that specifically allow strain-based design but do not provide

extensive provisions related to strain-based design (B31.8, API

1104), and those that provide information on strain-based design

related to a specific subgroup of pipelines (ABS, 2006; API RP 1111,

1999).

3.2. The recent years research projects

Several organizations have current research projects that will be

released to the public domain after their completion in areas that

directly or indirectly impact strain-based design of pipelines. The

Minerals Management Service (MMS) and the Office of Pipeline

Safety (OPS) of USA co-funded EWI to provide a general guidance

on strain-based design for pipelines both for the on-and off-shore

environment. DNV and other organizations also have some

researchprojects about it (American Petroleum Institute Publishing

Services, 1999; Chiou, 1996; Ellinas, 1999; Graville & Dinovitzer,

1993; Wang, Denys, Rudland, & Horseley, 2002; Wang, Cheng, &

Horsley, 2004).

3.3. The theoretical and finite-element analysis development

Extensive research has been conducted on the subject of local

buckling, wrinkling and post-buckling behavior of pipe in the last

ten years (Das, Cheng, Murray, & Zhou, 2000; Dorey, Murray, Cheng,

Grondin, & Zhou, 1999; Fatemi et al., 2008; Liu, Liu, & Zhang,

2008a). The experimental and finite-element Analysis have led to

in-depth understanding on the initiation and development of local

buckling and wrinkling. In general for common modern steel pipes,

the initiation of local buckling wasfound to be primarily dependent

on the D/t (pipe diameter to thickness) ratio, the internal pressure,

pipe material properties and initial geometric imperfection. The

initiation of local buckling is also dependent, to a lesser degree, on

other factors including applied load combination, soil restraints,

and residual stresses.The tensile strain limit is determined by the behavior of girth

weld flaws in response to applied strain. The approach to tensile

strain capacity of pipelines has been the hot spot (Dinovitzer, Brian,

& Graville, 1996; Graville & Dinovitzer, 1993; Liu, Liu, & Zhang,

2008b; Wang et al., 2002; Wang et al., 2004). The basic approach is

based on the inter-relationship between the longitudinal pipe

stress-strain properties, the toughness and stress-strain properties

of the weld and HAZ, flaw size and location, and the applied loads.

3.4. The experiment development

Wide plate test is widely viewed as one of the closest repre-

sentations of pipeline girth weld stress state under construction

and service loading conditions. Much of the early tests focused on

achieving plastic collapse of the girth welds, defined as achieving

a measured failure strain of 0.5% or above. In recent years, wide

plate test is being increasingly used to determine tensile failure

strains beyond yield, i.e., greater than 0.5% (Wang, Liu, Chen, &

Horsley, 2006). Such tests are also being used as a tool for welding

procedure qualification for high strain applications (Denys, De

Waele, Lefevre, & De Baets, 2004). In such applications, the wide

plate test is more than a tool to assure plastic collapse on a pass/fail

basis. The test becomes much more influential as the measured

failure strains affect the selection of materials, welding processes,

defect acceptance criteria, and ultimately influence the economics

of pipeline projects in environmentally sensitive areas.

4. Comparison of strain-based design criteria

In this paper Strain limits, including ovalization limit, tensile

strain limit and compression strain limit, are compared based upon

various codes and recommendations (Dinovitzer & Smith, 1998).

4.1. Ovalization limit

Ovalization limit criteria on strain-based are compared shown

in Table 1. Ovalization limit criteria generally used to limit the

maximum ovality to a fixed percent or meet a general requirement

that ovality should not promote structural failure or affect pipeline

operation including maintenance and inspection.

B. Liu et al. / Journal of Loss Prevention in the Process Industries 22 (2009) 884–888 885



4.2. Tensile strain limit

Tensile criteria on strain-based are compared, see Table 2.

Tensile limit is often given by not only elastic but also plastic

method. DNV-OS-F101 (2000) rules that Engineering Critical

Assessment (ECA) is needed if the accumulated plastic strain is

more than 0.3%. Tothe accumulated plastic strain is more than 2.0%,

both ECA and other additional requirements of materials are

needed. In CSA, DNV and ASCE, the application of these tensile

limits are based on the assumption of a defect-free homogeneous

pipe material.

4.3. Compression strain limit

The compression strain limit may be estimated using the

following empirical formula in CSA Z662:

3critc ¼ 0:5

t

D 0:0025 þ 3000

ðP i P eÞD

2tE s

2

(1)

where 3c crit is the ultimate compressive strain capacity of the pipe

wall, and t is the pipe wall thickness, and D is the outside pipe

diameter, and pi is the maximum internal design pressure, and pe is

the minimum external hydrostatic pressure, and E s ¼ 207 000 MPa.

The compression strain limit for pipe members subjected tolongitudinal compressive strain (bending moment and axial force)

and internal over pressure may be estimated using the following

empirical formula in DNV-OS-F101:

3c ¼ 0:78

t 2D 0:01

1 þ 5

sh

f y

!a1:5h agw

D

t 45; pi pe

(2)

where 3c is the compression strain limit, andsh is the hoop stress, t 2¼ t t corr, and f y is the yield stress to be used in design, ah is the

maximum allowed yield to tensile ratio, and agw is the girth weld

factor.

5. Factors of strain limit

Strain-based design criteria are depended on the strain limits

which are influenced by a large number of factors.

5.1. Factors of ovalization strain limit

The key factors of ovalization limit are as follows: D/t ratio,

bending strain, etc. Ovalization limit may decrease with the change

of D/t ratio, on the other hand, generallyspeaking there is a trend of

increase with bending strain.

BS 8010 (1993) includes a means of estimating ovality, but does

not indicate the maximum allowable limit. The ovalization limit can

be calculated by Equation (3):

f ¼ 0:06

1 þ

D0

120t

D03b

t

2

(3)

where f is the ovalization, and D0 is the outside diameter, and t is

the pipe wall thickness, and 3b is the bending strain.

This formulation may be used to relate the minimum bending

strain and pipe D/t ratio to the resulting ovality as shown in Fig. 1.

This figure describes the relationship between pipe geometry,

bending strain and the degree of ovality which is produced.

5.2. Factors of tensile strain limit

The tensile limit can be determined to some extent by the girthweld defects under applied strain. Usually pipelines can take

greater strain if the defects in welds are smaller and the weld metal

with a high strength match and appropriate fracture toughness.

The key factors of tensile strain limit are as follows:

Girth Weld

a) Crack: Crack size, crack location, etc.

b) Geometry Size: Weld cap height, Bevel angle, etc.

c) Weld strength mismatch: High strength match is needed

generally.

d) CTOD toughness: With the increase of CTOD the tensile

strain limit also increases generally.

Y /T

For the base material whose accumulated plastic strain may be

more than 2%, DNV (2000) recommends that Y /T (Yield strength to

Tensile Strength) is a lower level: 0.85. For the base materials

whose minimum yield stress are 415 MPa or more, DNV (2000)

recommends that Y /T in transverse is 0.92; while for less than

415 MPa, DNV (2000) recommends 0.90. The tensile strain limit

may decrease with the increase of Y /T , just as shown in Fig. 2.

Elongation-to-Failure Limits for Pipe Material

The minimumelongation (e) for pipeto API 5L (2000) are given by

an equationbasedon thespecified minimum ultimate tensile strength

(U ) and the cross-sectional area ( A) of the tensile test specimen. The

minimum elongation in 2 in.is given in percent tothe nearest 0.5%. InSI unit, the equations is e ¼ 1944( A)0.2/(U )0.9. DNV (2000) provides

a recommendation that pipe for service at accumulated plastic strain

of 2% or more have elongation of 25%. The minimum requirement is

18% for steels with SMYS (Specified Minimum Yield Strength)

415 MPa and 20 to 22% for steels of lower strength.

5.3. Factors of compression strain limit

The key factors of compression strain limit are as follows:

D/t

Geometry, especially including D/t , has a big effect upon

compressive strain limit. Generally speaking, with the increase of

Table 1

Pipeline ovalization limit comparison.

Criteria Ovalization Limit/%

CSA-Z662-07 App.C 3.0(6.0)a

DNV-OS-F101 (2000) 3.0

API 1111-1999 5.5w6.2

Murray et al. (Murray, & Bilston, 1992) 4.3w6.5b

a Numberin brackets indicates upper bound of behavior if it canbe demonstrated

that the behavior does not affect pipeline operation or maintenance or promotefailure.

b Ovality which produces the yield level hoop stresses in the pipe, assuming

a yield strength of 480 MPa and a wall thickness of 10 mm.

Table 2

Pipeline tensile limit comparison.

Criteria Tensile Limit/%

CSA-Z662-07 App.C 2.5a

DNV-OS-F101 (2000) Accumulated Plastic Strain 2.0b

ASCE (2005) 2.0c

a Applies to installation and or infrequent loads of subsea pipelines.b Installation and materials for different circumstances need to meet additional

requirements.c Longitudinal strain from ground movement due to earthquake, landslide, or

mine subsidence.

B. Liu et al. / Journal of Loss Prevention in the Process Industries 22 (2009) 884–888886



D/t the compressive strain limit decreases generally, from DNV and

CSA,as shown in Fig. 3. Andstrain limit without pressurecorrection

is well in line with the trend. However, to CSA with pressure

correction, maximum compressive strain had rebounded.

Y /T

As shown in Fig. 3, strain limit without pressure correction

decreases with the increase of Y /T .

Internal Pressure

Internal pressure increases resistance to local buckling because

the tensile hoop stress it helps the pipe resist the diametricalchanges that occur locally at the buckle. The quantitative rela-

tionship between pressure and the critical strain of the different

viewers is not unanimous. DNV (2000) uses a factor of (1 þ5sh/ f y),

and it is more applicable to large-diameter pipeline and the pipe-

line whose ratio of hoop stress to yield strength is between 0.2 and

0.5. CSA 2000 uses a factor of Equation (4):

3000

ðP i P eÞD

2tE s

2

(4)

As shown in Fig. 3, strain limit with internal pressure correc-

tion is bigger than the one without internal pressure correction

factor, and strain limit increases with the increase of internal

pressure.

External Pressure

On the contrary with the internal pressure, external pressure can

reduce the resistance of local buckling andmay also spread buckling

along the collapse. For external pressure, DNV (2000) uses another

factor with similar parameters to internal pressure: (1(ape/ pc)1.25

),where a is safety factor of between 1.2 and 1.5, pe is external pres-

sure, pc is the external pressure coefficient. API 1111-1999 uses

the composite parameters: ( g pe/ pc), where g is the correction

factor for the initial ovalization. The factor from API 1111 is

conservative for pipeline with a higher external pressure or lower

internal pressure.

Fig. 1. Ovalization strain limit by BS 8010.

Fig. 2. Comparison of tensile strain limit. Fig. 3. Comparison of compression strain limit from CSA and DNV.

B. Liu et al. / Journal of Loss Prevention in the Process Industries 22 (2009) 884–888 887



Girth Weld

Girth weld may reduce the compressive strain limit of pipelines.

Welding residual stresses, differences in material strength across

the weld, and misalignment of the pipe wall across the weld are all

considered to affect the buckle location and the girth weld. DNV

(2000) provided a girth weld factor to correct the compressive

strain limit, as shown in Fig. 4.

6. Conclusion remark

This paper has presented an overview of the strain-based design

methodology. In recent years, strain-based design of pipeline has

become a hot spot. Although some workable strain-based design

methodology and the supporting engineering processes and

models have been achieved and validated, some improvements and

enhancements are needed, especially as we move to high pressure,

high strength pipe and large-diameter pipelines.

Acknowledgement

Thiswork wassupported by ChinaNationalPetroleumCorporation(CNPC). Wewould likethankall colleaguesfrom mechanics laboratory

of CUPB for their discussions and advice regarding this work.

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Further reading

Joe, Z., & Alan, G. (2005). Strain-based design of pipelines – the path. Rio Pipeline 2005 Conference & Exhibition.

Fig. 4. Girth weld factor from DNV.

B. Liu et al. / Journal of Loss Prevention in the Process Industries 22 (2009) 884–888888

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Liu 2009 Journal of Loss Prevention in the Process Industries