Необходимость Учета Плато Людерса в Расчетах...

1 Copyright © 2010 by ASME

Proceedings of the ASME 2010 29th International Conference on Ocean, Offshore and Arctic Engineering OMAE 2010

June 6-11, 2010, Shanghai, China

OMAE 2010-20715

SIGNIFICANCE OF LÜDER'S PLATEAU ON PIPELINE FAULT CROSSING

ASSESSMENT

Lanre Odina

Xodus Group Pty Ltd

Perth, WA Australia

Robert J Conder

Xodus Group Ltd

Aberdeen, Scotland, UK

ABSTRACT

When subjected to permanent ground deformations,

buried pipelines may fail by local buckling (wrinkling

under compression) or by tensile rupture. The initial

assessment of the effects of predicted seismic fault

movements on the buried pipeline is performed using

analytical approaches by Newmark-Hall and Kennedy et

al, which is restricted to cases when the pipeline is put

into tension. Further analysis is then undertaken using

finite element methods to assess the elasto-plastic

response of the pipeline response to the fault movements,

particularly the compressive strain limits.

The finite element model is set up to account for

the geometric and material non-linear parameters. The

pipe material behaviour is generally assumed to have a

smooth strain hardening (roundhouse) post-yield

behaviour and defined using the Ramberg-Osgood stress-

strain curve definition with the plasticity modelled using

incremental theory with a von Mises yield surface,

associated flow rule and isotropic hardening. However,

material tests on seamless pipes (X-grade) show that the

stress-strain curve typically displays a Lüder’s plateau

behaviour (yield point elongation) in the post-yield state.

The Lüder’s plateau curve is considered conservative for

pipeline design and could have a significant impact on

strain-based integrity assessment.

This paper compares the pipeline response from a

roundhouse stress-strain curve with that obtained from a

pipe material exhibiting Lüder’s plateau behaviour and

also examines the implications of a Lüder’s plateau for

pipeline structural integrity assessments.

BACKGROUND

As part of a structural integrity assessment and

rehabilitation program for a displaced subsea pipeline,

arising from mass gravity flow events related to

typhoons, recommendations were made in order to

improve future pipeline integrity by mitigating and

controlling identified risks to the pipeline. Rock dump

was suggested as a possible solution for stabilisation of

the displaced pipeline. The pipeline, located in

deepwater, was installed exposed on the seabed.

Furthermore, the pipeline is in a seismically active

region and lies on an active seismic fault line.

Pipeline integrity assessment was undertaken to

determine the potential for the buried pipeline to

withstand the large strain bending associated with the

worst-case seismic fault movement. The study

considered a 24-inch pipeline, wall thickness of 17.1mm,

6mm FBE anti-corrosion coat and 40mm concrete coat,

API Grade X-65 material and rock dumped with 0.75m

cover of high density rock (3100kg/m3). This paper

evaluates the effects on pipeline material properties of

the large strain bending. The potential for strain

localisation at the location of the high curvature was also

considered.

INTRODUCTION

Pipeline designs in difficult terrains, such as seismically

active and arctic regions, pose huge challenges and

difficult engineering problems that need to be addressed

to deliver a cost-effective solution. O’Rourke and Liu

[1] noted that buried pipelines generally cover large

areas and are subject to a variety of geotectonic hazards.

Proceedings of the ASME 2010 29th International Conference on Ocean, Offshore and Arctic Engineering OMAE2010

June 6-11, 2010, Shanghai, China

OMAE2010-20715

Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 04/07/2015 Terms of Use: http://asme.org/terms

OMAE2010-20715


They can be damaged either by permanent movements of

ground or by transient seismic wave propagation.

Permanent ground movements include surface faulting,

lateral spreading due to liquefaction, and landsliding.

The hazard is usually limited to small regions within the

pipeline network; however the potential for damage is

very high.

Where fault movements are predicted to occur,

analysis is possible to predict the effect on a buried

pipeline when the direction and magnitude of the fault

movement are known as well as the ground conditions

[2]. Pipelines crossing active faults are typically routed

and designed to be in tension rather than in compression.

When strained in tension, the pipeline is very ductile and

is capable of undergoing large strains before rupture.

Due to the high straining conditions that the pipeline is

subjected to, the structural integrity of these pipelines is

dependent on the pipe steel material and should have

high deformability in addition to high strength [3, 4].

Mitigation measures for buried pipeline crossing

active faults include optimisation of the angle of crossing

with respect to the fault configuration; together with

various design measures such as pipe wall thickness,

special fault crossing trench design and selected loose

granular backfill material, inclusion of a geotextile

membrane to enhance the mobility of the pipe/trench

material. For the case of the existing pipeline considered

in this paper, some of these measures are not applicable.

Strain-Based Approach

The traditional practice for the design of subsea

pipelines, including those crossing active fault lines is

based upon satisfying several criteria for the strength of

the pipeline. The stress analysis is generally performed

to define the operating conditions where the stresses in

the pipeline remain elastic and the design falls within a

“stress-based” design regime. These stress-based criteria

use a linear elastic material property and acceptance is

based on demonstrating that the resulting stresses are less

than a given fraction of the material specified minimum

yield stress.

The current trend of increasing reservoir

operating conditions, coupled with pipeline traversing

difficult terrains impose limits on the use of a stress-

based design approach and it has been recognised that

there are situations where limited yielding of the pipeline

can occur safely. This has led to the recent

developments geared towards the use of limit state

approach based on strain based methods for efficient

design of offshore pipelines [5-7].

These strain based (displacement-controlled)

design methods are also applicable for developing

economic and practical engineering solutions for buried

pipeline design in seismically active regions. Design

acceptance criteria to assess pipeline mechanical

integrity are established through the application of limit

states concepts with respect to defined target safety

levels. This is also now covered in the DNV Offshore

Pipeline Standard, DNV-OS-F101 [8].

For a buried pipeline subject to seismic faulting

loads, there is the likelihood of bending related

deformation limit states including wrinkling in the pipe

sectors experiencing longitudinal compressive stresses,

ovalisation and bending failure. Other limit states to

consider include local buckling, fracture/plastic collapse

at girth welds and corrosion due to damage to pipe

coatings at high strains.

Strain Localisation

In the strain-based regime and particularly for the buried

pipeline subject to high curvature at the fault crossing,

there is the likelihood that the pipeline will experience

problems associated with localised strains. The

localisation results from variations in wall thickness and

material properties. For example, the thickness

variations can be due to manufacturing tolerances or to

differential corrosion along the pipe. This is generally

addressed in the assessment by including models with a

“weak section”.

Material Properties

In using the strain based approach, the analysis and

assessment of the pipeline requires a detailed

understanding of the pipeline material properties, soils

properties and weld performance. The pipeline material

property, which is the focus of this paper, should be

established for the conditions to be encountered during

the installation and operation phases. It is common for

testing programmes to be initiated for bending and

material tests at the start of the project. The key material

properties established in the tests include: non-linear

stress strain curve, elastic modulus, yield stress, strain

hardening modulus, Charpy V-notch impact toughness

and strain ageing in some instances [6].

It is also noted that studies of pipeline behaviour

show that the critical moment and critical curvature are

primarily governed by D/t ratio, material anisotropy and

shape of the stress-strain curve and strain hardening [6].

Stress-Strain Relationship

Where material plasticity occurs and strain based design

is used, the shape of the stress-strain curve is important.

It is necessary that the pipe steel exhibits a strain

hardening behaviour and does not have a yield plateau

since axial compression failure depends on the Tangent

Modulus of the material. The shape of the stress-strain

curve will influence the predicted pipeline behaviour and

is very important in determining when wrinkling failure

will occur, for instance. It is also acknowledged the

temperature has significant effect both on the shape of

the stress-strain curve and the magnitude of the yield

stress. Thus, it is very important that a representative

curve is used at the required temperature condition.

The pipeline stress-strain constitutive relationship

can be defined by isotropic, elasto-plastic behaviour with

a von Mises yield surface and isotropic hardening rule

with appropriate material parameters. The Ramberg-

Osgood representation [9] is the most widely used


OMAE2010-20715


approach for defining the relationship between “true”

non-linear stress and strain of a material under an

experimental, uniaxial tension test. The Ramberg-

Osgood stress-strain relationship is expressed as: N

o

or

EE

+=

σ

σσασε

where:

ε = total strain

σ = stress

E = Young's Modulus

αr = Ramberg-Osgood coefficient

σo = nominal yield stress

N = Ramberg-Osgood exponent

αr = E εo

σο

- 1

N =

log

E εu

σu - 1 - log

E εo

σo - 1

log

σu

σo

where:

σo = minimum specified yield strength;

εo = strain at σo = 0.5%;

σu = minimum specified ultimate tensile strength;

εu = strain at ultimate strength = 21%.

A typical API Grade X-65 stress-strain material curve

(Ambient conditions) is illustrated in Figure 1.

Figure 1: Stress-strain curve for smooth strain hardening

LÜDER’S RELATIONSHIP

Test results have shown that not all pipe steel exhibit a

smooth Ramberg-Osgood stress-strain curve, with some

materials showing a Lüder’s plateau. The Lüder

phenomenon typically occurs in hot-finished low carbon

steels containing interstitial solid solution elements such

as carbon, oxygen and nitrogen atoms, which migrate to

dislocations where they form solute atmospheres during

or after plastic deformation. The solute atmosphere

locks mobile dislocations, leading to the “upper yield

stress”. When the dislocations break away from their

solute atmospheres, the flow strain is reduced (lower

yield stress). The separation from the solute

atmospheres is localised leading to Lüder’s lines [10].

Figure 2 depicts a typical stress-strain curve, for a

material displaying Lüder’s strain. The stress-strain

curve exhibits a purely elastic deformation with an initial

maximum yield point followed by a drop as strain

increases. The yield stress decreases from the “upper

yield stress” to the “lower yield stress”, and the strain

continues to increase while the stress stays roughly

constant as inhomogeneous yielding propagates through

the material at the lower yield point. At some point, the

stress increases as the material continues to strain. The

relatively flat portion of that stress-strain curve is the

Lüder's strain, and the extent of the Lüder’s strain is

depicted as εL.

Figure 2: Stress-strain curve showing Lüder’s Plateau

In the experimental studies and analytical work

performed by Aguirre et al [11] on bending of steel tubes

with Lüder’s bands, it was noted that as the applied

elongation increases the region of strained material

grows by propagating of a state transition front along the

test specimen. It is also noted that Lüder’s bands are

usually observed in seamless pipe made from X-grade

steel. Lüder bands are often one of the mechanical

effects of static strain aging.

Strain Aging

Hukle et al [3] examined the effects of aging on pipeline

material properties and lists a number of post-forming

thermal activities that may result in strain aging. These

include FBE coating, re-coating, welding pre-heat,

welding interpass, repair welding, field joint coating,

pipe storage and long-term operation. The paper also

noted that the aging effect may either be localised (i.e.

adjacent to a girth weld) or global (i.e. along the entire

0

100

200

300

400

500

600

0.000 0.025 0.050 0.075 0.100

Total Strain

Str

ess

(Nm

m-2

)

Nominal Pipe

Elastic 0

100

200

300

400

500

0.0000 0.0025 0.0050 0.0075 0.0100

Ramberg Osgood

coefficient, Ar=1.31

Upper yield stress

Lower yield stress

Actual σ-ε

Idealised σ-εε

L

εL

= extent of Lüders strain

Engineering Strain

En

gin

eeri

ng S

tres

s

Upper yield stress

Lower yield stress

Actual σ-ε

Idealised σ-εε

L

εL


Engineering Strain

En

gin

eeri

ng S

tres

s

Upper yield stress

Lower yield stress

Actual σ-ε

Idealised σ-εε

L

εL


Engineering Strain

En

gin

eeri

ng S

tres

s


OMAE2010-20715


length of a pipe section) depending on the nature of the

thermal activity.

The heat applied as part of the FBE anti-corrosion

coating process, typically applied in the range of 180 to

250°C (360 to 480°F), has a significant influence on the

pipe steel material. The pipeline discussed in this paper

is FBE-coated and material tests suggest there is

potential for the pipe steel stress-strain curve to display

Luder’s plateau.

FAULT MOVEMENT

The fault movement refers to the relative displacement of

soil or rock across the fracture. Fault movement may be

described as normal, reverse, strike-slip or oblique and

can occur continuously (creep) or episodically. An

episodal occurrence involves a displacement event that

can generate an earthquake. Vertical separation of a

displaced horizon is termed “throw” and horizontal

separation is termed “heave”. Refer to Figure 3 for

illustrations of the various types of faults [12].

Figure 3: Fault Types

PIPE FAILURE CRITERIA

During the deflection of a pipeline arising from soil

movements, a bending moment/bending strain is

developed. The limit states adopted for the integrity

assessment of the pipeline discussed in this paper are as

follows:

• Compressive strain limit

� Critical buckling strain as a function of D/t ratio,

internal pressure and stress–strain curve shape.

• Tensile strain limit

� Pipeline strain capacity limited by girth weld

defects.

� Established by fracture mechanics and defect

assessment.

The pipeline basis of design utilised a limiting strain of

2% for a conservative design of the pipeline and this has

also been utilised for the integrity assessment. A

maximum fault displacement of 1.9m has also been

assumed for the assessment.

DESCRIPTION OF FE MODELS

The assessment of the effects of predicted fault

movements on buried pipeline is generally performed

using the analytical approaches proposed by Newmark-

Hall [13] and the Kennedy et al [14]. The two analytical

procedures, provide respective lower bound and upper

bound estimate of the stress and strain, and are restricted

to cases when the pipeline is in tension. For cases where

the soil movement puts the pipeline in compression, the

finite element (FE) method is used. The FE method is

also used in this study to assess the impact of the

material stress-strain curves on the pipeline structural

integrity under operational and faulting conditions.

Assessment of pipelines subject to fault

displacement is generally undertaken using global FE

models [2]. However, for instances where local

deformations such as pipe ovalisation and pipe wall

buckling are required, local FE models using Shell

elements are more suitable. The general-purpose finite

element Program Abaqus [15] is employed for the

seismic fault assessment.

It is essential to predict the non-linear behaviour of

the pipeline under the applied loading and determine

when an unacceptable condition will occur. The FE

analysis of the buried pipeline subject to fault crossing is

performed using the approach detailed in ASCE Design

Guideline [2]. The modelling accounts for the:

• non-linear behaviour of the surrounding soil mass;

• large deflection including stress-stiffening effects

(geometric non-linearity); and

• elasto-plastic pipeline behaviour.

The static analysis takes into account the

sequence of application of the loads, i.e. the pipeline

equilibrium configuration is determined considering the

application of the loads on the updated deformed

structure. Therefore a load step approach is adopted for

the analysis model. The Newton-Raphson algorithm is

used for the analysis convergence.

Figure 4 shows a sketch of a buried pipeline

subject to oblique (normal and strike-slip) fault crossing

due to an earthquake [16].

Figure 4: Buried Pipeline subject to Oblique

Fault Crossing


OMAE2010-20715


Pipeline Model

A straight pipe section (coated with Fusion Bonded

Epoxy and Concrete) laying on the seabed is modelled

using a three dimensional model. The FE model

comprises of nodes and the Abaqus 3D elastic-plastic

beam elements (type PIPE31H). The beam elements

model a one-dimensional approximation of a 3D

continuum. PIPE31H is a 2-node linear pipe element

(including hybrid formulation) with a hollow, thin-

walled circular cross section and has 6 degrees of

freedom at each node. The element accounts for the

hoop strain caused by internal and external pressure

loading in the pipe. The pipe axis is aligned with the

global X-direction as shown in Figure 5. The horizontal

(lateral) direction has been chosen as the global Y-

direction and the vertical direction as the global Z-

direction.

For the assessment, the strains and stresses have

been extracted at 32 integration points around the

circumference of the pipe wall.

Figure 5: FE Pipe Model Coordinate System

The pipeline length (1.4km long) modelled is based on

the effective unanchored length in the fault zone. This

length is a function of the yield force and the

longitudinal frictional restraint per unit length. The

mesh is refined in the critical region of high curvature

within the vicinity of the fault (100m either side of fault)

with element lengths of 0.5m specified. The remainder

of the pipeline was modelled with 1m long elements in

the relatively undisturbed area. Appropriate boundary

conditions were also applied to the model.

Sensitivity analyses were undertaken to verify the

mesh applicability. This was accomplished by

comparing the results from the analytical approach to the

response from the FE analysis.

Soil-Pipe Interaction

The FE model assumes the pipeline lies on a perfectly

flat and rigid seabed. The pipe-soil interaction was

modelled following the methodology detailed in ASCE

Seismic Design Guideline. The seabed is described as

sand/silty sand with coral and rock outcrops.

The actual three-dimensional soil-pipe

interactions can be ideally modelled as pipe resting on

continuous multi-linear soil springs as shown in Figure

6, with the soil surrounding the pipeline modelled as

discrete elasto-plastic springs in the axial, lateral and

vertical (up/down) directions.

Figure 6: 3D Pipe-Soil Interaction FE Model

The Abaqus SPRING2 element was used to model the

non-linear springs. The SPRING2 element is between 2

nodes, acting in a fixed direction. The soil stiffness

used in the modeling has been determined using the

relations in the ASCE guideline. The elastic-plastic

multi-linear spring is fully defined by two parameters:

the maximum force per unit length at the soil pipe

interface and the relative displacement at which slippage

between pipe and soil occurs in the axial, transverse and

vertical directions.

Analysis Cases

Three cases have been analysed; two examples are

presented to show the effect of material stress-strain

curves on the pipeline integrity and another to assess the

effect of strain localisation:

• Case 1 assumes a Ramberg-Osgood smooth stress-

strain curve.

• Case 2 assumes a stress-strain curve displaying the

Lüder’s plateau.

• Case 3 assesses the effect of strain localisation

using the Ramberg-Osgood representation.

0

100

200

300

400

500

600

0.000 0.020 0.040 0.060 0.080 0.100

Engineering Strain

No

min

al S

tres

s (N

mm

-2)

ElasticNominal PipeLuder's PlateauWeak Joint

Figure 7: Stress-Strain Curves for the Case Study

The stress-strain curves utilised for the analyses are

presented in Figure 7. The stress-strain curve exhibiting

Lüder’s plateau was acquired from sample tests


OMAE2010-20715


performed for the production pipeline, i.e. API Grade X-

65 material, with FBE anti-corrosion coating. It is noted

the curve is based on the upper yield stress point, as

shown in Figure 7.

For the pipeline outside diameter of 24-inch

(610mm) and wall thickness of 17.1mm, the diameter to

thickness (D/t) ratio is 35.67. Corrosion allowance is

specified as zero.

Strain Localisation

As the properties of a pipeline generally varies along the

length, as a result of geometric tolerances and stress-

strain variations across and within individual joints, there

will be potential for strain localisation to develop at any

position on a pipeline at which there is discontinuity in

the stiffness of the pipeline, either bending or axial.

This is addressed by incorporating in the FE

model a “weak” joint of linepipe at the worst (highest

strains/moments) location of global response and

represented by a different element set at this location.

It is recommended for strain-based design [17] that the

designer should perform an assessment to identify the

suitable level of strength mismatch. However, in the

absence of such a study, a weakened joint, with a plastic

moment capacity 10% below the nominal value, may be

inserted in the region of highest longitudinal strains.

The length of the weak section is taken as a full

joint of 12 m and is based on the minimum material

properties. The stress-strain curves (based on Ramberg-

Osgood) for the nominal and weak joints are shown in

Figure 7.

FINITE ELEMENT ANALYSIS LOAD STEPS

In the Abaqus model, loads are applied to the pipeline

after all nodal positions have been defined, elements set

up and boundary conditions applied.

The pipe is initially modelled stress free on the

seabed and residual loads applied to simulate the current

state of stress. The rock cover was then installed,

followed by the operating loads (design pressure of 200

bar and ambient temperature). Fault displacement (fault

angle of 22o) is then input to the model as displacements

of the soil springs.

Plasticity is modelled using incremental theory

with a von Mises yield surface, associated flow rule, and

isotropic hardening. The material property is defined in

terms of the true stress versus logarithmic strain as

required by the Abaqus program.

Post-processing of the FE analyses outputs was

carried out to assess the consequences to pipeline

integrity.

RESULTS

Model Validation

The FE model, using Ramberg-Osgood approximation,

was validated by comparison with the predictions from

the analytical procedures of Newmark-Hall [13] and

Kennedy et al [14]. The axial stress plots presented in

Figure 8 show that the FE analysis is broadly in good

agreement with the analytical work, predicting response

between a lower-bound and upper-bound maximum axial

stress along the total length of the pipeline.

0.0

50.0

100.0

150.0

200.0

250.0

300.0

350.0

400.0

450.0

500.0

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Distance (m)

Axi

al S

tres

s (N

/mm

2)

FEA

New ton-Hall

Kennedy et al

Figure 8: Comparison of maximum Axial Stress

from analytical and FE approaches

Ramberg-Osgood Stress-Strain Curve

The longitudinal strains profile along the pipeline length

is presented in Figures 9 and 10 for a fault displacement

of 1.2m and 2.5m respectively. The respective

maximum longitudinal strains are calculated as 0.012

and 0.027.

Figure 9: Ramberg-Osgood Curve - Longitudinal Strain (At Fault Displacement of 1.2m)

Figure 10: Ramberg-Osgood Curve - Longitudinal Strain (At Fault Displacement of 2.5m)


OMAE2010-20715


The maximum longitudinal strain profiles for the mid-

element (Element 800), extracted at the integration

points, are plotted against the fault displacement as

shown in Figure 11.

For the crossing angle and rock properties

assessed, the limiting tensile strains of 2% occur for a

maximum fault displacement of 1.8m.

Pipeline Response at Fault Crossing (Element 800)(Rock Cover=0.75m, Rock Density=3100kg/m3)

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20

Fault Displacement (m)

Max

imu

m L

on

git

ud

inal

S

trai

ns

(%)

Int -1

Int-9

Int-17

Int-25

2% Strain

1.8m @2% strain

M ax F ault D isp,1.9m

Figure 11: Longitudinal Strain profile at Crossing Location

Stress-Strain Curve with Lüder’s Plateau

The longitudinal strains along the pipeline length at a

fault displacement of 1.2m are presented in Figure 12.

Indeed, it is noted that the maximum strain is already

0.020 at this displacement.

Figure 12: Lüder’s - Longitudinal Strain (At Fault

Displacement of 1.2m)

Figure 13 shows the comparison between the peak

longitudinal strains in the plateau curve and the smooth

roundhouse strain-hardening response.

Figure 13: Longitudinal Strain profiles at Crossing Location

In the Lüder’s stress-strain plateau model, the plateau

persists until a strain of 1.6% is reached (see Figure 13),

at which point it starts to exhibit properties of strain

hardening. This response from the Lüder’s plateau

model shows that the plasticity is most severe and

confirms that the shape of the stress-strain curve is

extremely important for analysis of the effect of fault

displacements.

The response reflects some of the observations

from the studies by Aguirre et al [11], assessing the

effect of Lüder’s banding on the moment-curvature

relationship of steel tubes (for D/t=27.23). It was noted

from the studies that the maximum moment occurs

essentially as soon as the pipe starts to yield, with

relatively sharp transition from the elastic to the plastic

regime followed by extended moment plateaus.

Strain Localisation

The impact of the weak joint is presented in Figure 14

for the pipeline at the fault crossing location. It is

observed that the 10% mismatch in material properties

for the weak joint has a significant effect on the peak

longitudinal strains in the pipeline, when compared with

results for the nominal pipe properties. It is also noted

that the effects of material plasticity on strain localisation

is increased with reducing yield stress.

Location 2 - Fault Crossing at KP469.6

(Material Strength Mismatch Sensitvity, Rock Cover=1.5m, Rock Density=3100kg/m3)

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50


Ma

xim

um

Lon

gitu

din

al S

tra

ins

(%

)

Nominal

Weak Joint

Max. Fault Disp, 1.9m

2% Strain

Average Fault Disp, 1.2m

Figure 14: Longitudinal Strain profile at

Crossing Location

Pipeline Response at Fault Crossing (Element 800)(Rock Cover=0.75m, Rock Density=3100kg/m3)

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0.00 0.20 0.40 0.60 0.80 1.00 1.20


Max

imu

m L

on

git

ud

inal

S

trai

ns

(%)

Smo o th R amberg-Osgo o d M o del

Luder's P la teau M o de l

2% Strain


OMAE2010-20715


DISCUSSION AND CONCLUSIONS

The comparison of results shows that the shape of the

stress-strain curve has a significant effect in the

magnitude of the longitudinal strains developed. The

plot in Figure 13 shows that at a fault displacement of

0.75m, the peak longitudinal strains developed in the

plateau model is almost three times that developed when

the smooth strain-hardening model is employed (Figure

11). It is also observed that for the material with a

plateau in the stress-strain curve, the localised strains are

arrested at the onset of strain hardening (i.e. at the end of

the plateau). The fault displacement at the allowable

strain of 2% is 1.22m, compared with a displacement of

1.8m for the smooth curve.

For pipelines with Fusion Bonded Epoxy (FBE)

anti-corrosion coating, a Lüder’s plateau behaviour is

likely for the pipeline during its design life. It is also

worth remarking that materials which have not been

work-hardened (seamless pipe) will exhibit plateau

behaviour and materials which have been formed (e.g.

UOE pipe) will tend to show a smooth strain hardening

response. For pipelines manufactured using the UOE

method, the use of the smooth strain-hardening model

for the seismic fault analysis is reasonable.

The findings from this work imply that the use of

smooth strain-hardening model for the fault displacement

analysis would significantly underestimate the response

of the pipeline. The literature also infers that the flat

region makes the pipeline steel susceptible to strain

localisation and limit states such as wrinkling. Whilst

the Lüder’s plateau might lead to predictions that the

pipeline could wrinkle as a result of fault displacements,

it is not anticipated that such a wrinkle would lead to loss

of pressure containment of the pipeline.

Hence, it is critical that the stress-strain behaviour

of the steel material is well understood prior to

undertaking strain-based design. For integrity

assessment of existing pipelines, it is also prudent to use

suitable material tests data for random samples chosen

from the production pipe. In conclusion, if the pipeline

material is prone to stress-strain plateaus then the

behaviour must be accounted for in the seismic fault

displacement assessment.

ACKNOWLEDGEMENTS

The authors wish to thank the management of Xodus

Group for permission to publish this paper.

REFERENCES

[1] O’Rourke, M. J. and Liu X., “Response of Buried

Pipelines Subject to Earthquake Effects”,

Multidisciplinary Center for Earthquake

Engineering Research, 1999, preface.

[2] ASCE (1984), Guidelines for the Seismic Design of

Oil and Gas Pipeline Systems, Committee on Gas

and Liquid Fuel Lifeline, ASCE, 1984.

[3] Hukle, M., Newbury, B., Lillig, D., Regina, J. and

Horn, A. M. “Effects of Aging on the Mechanical

Properties of Pipeline Steels”, Estoril, OMAE 2008.

[4] Liessem, A., Knauf, G. and Zimmermann, S.,

“Strain based Design – What the Contribution of a

Pipe manufacturer Can be”, ISOPE 2007.

[5] Ellinas, C. P., Raven, P. W. J., Walker, A.C. and

Davies, P., “Limit State Philosophy in Pipeline

Design”, 3rd

OMAE, New Orleans, 1984.

[6] Walker, A. C., Williams, K. A. J., “The Safe use of

strain based criteria for the design and assessment

of offshore pipelines, OPT 1996.

[7] Vitali, L., Torselletti, E., Marchesani, F. and

Bruschi, R., “Strain based design for land high

grade pipelines in harsh environments”, Proc.

Super-High Strength Steels, 2-4 November 2005,

Rome, Italy, Associazione Italiana di Metallurgia.

[8] Det Norske Veritas, Offshore Standard DNV-OS-

F101, Submarine Pipeline Systems, 2007.

[9] Ramberg, W. and Osgood, W. R., “Description of

Stress-Strain Curves by Three Parameters”, NACA

Technical Note, TN902, July 1943.

[10] Li J. C. M. (Editor), “Microstructure and Properties

of Materials”, Volume 2, World Scientific, Oct

2000.

[11] Aguirre, F., Kyriakides, S. and Yun, H.D. “Bending

of Steel Tubes with Lüders Bands”, International

Journal of Plasticity Volume 20, Issue 7, 1199-

1225, 2004.

[12] Odina, L. and Tan, R., “Seismic Fault

Displacement of Buried Pipelines using Continuum

Finite Element Methods”, 28th

OMAE, Honolulu,

Hawaii, 2009.

[13] Newmark, N.M. and Hall, W.J., “Pipeline Design

to Resist Large Fault Displacement’, Proc. Of US

National Conference on Earthquake Engineering,

Ann Arbor, Michigan, 1975.

[14] Kennedy, R. P., Chow, A. W. and Williamson, R.

A., “Fault Movement Effects on Buried Oil

Pipeline”, Transportation Engineering Journal,

Amsterdam, September 1977.

[15] ABAQUS Version 6.8, Simulia Inc., October 2007.

[16] Bai, Q., Zeng, W., and Tao, L., “Seismic Design of

offshore Pipeline Systems”, Offshore, Vol. 64, No.

10, 2004, PP. 100-104.

[17] Bruton, D., Carr, M., Crawford, M. & Poiate, E.,

“The Safe Design of Hot On-Bottom Pipelines with

Lateral Buckling using Design Guideline

Developed by the Safebuck Joint Industry Project”,

Deep Offshore Technology Conference, Vitoria,

Brazil, 2005.


Необходимость Учета Плато Людерса в Расчетах...

Documents

Transcript of Необходимость Учета Плато Людерса в Расчетах...