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Advanced Topics in Buried Analysis

Michael Dowhopoluk, M.Eng., P.Eng.

PVP Engineering Ltd.


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Advanced Topics in Buried Analysis

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Overview Todays Topics

Overview of Buried Pipeline Codes and Design

Pipeline Stress Analysis

Different modeling techniques

Nonlinear Stress Analysis / Limit States Design

Nonlinear analysis with linear tools

Total strain theory of plasticity

Validation and Verification

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OVERVIEW OF BURIED PIPELINECODES AND DESIGN


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Overview

Applicable Codes

B31.4 Liquid Petroluem First appeared in 1959

B31.8 Gas Transmission First appeared in 1958

CSA Z183 Oil Transmission 1967

CSA Z184 Gas Transmission 1968

CSA Z662 Replaced Z183 / Z184 in 1994

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Buried Pipeline Design

Code Requirements

Hoop Stress

Expansion Stress

Combined Stress

Additional Loadings

Contrast to B31.3

No combined limit why not?

Limit on gross deformation due to yielding

Only a concern when there are large axial compressive forces

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B31.4 Liquid Petroleum Pipelines

Basic Allowable Stress

= 0.72 ; , 1.0

Hoop Stress

=

Longitudinal Stress

=

+ 0.75 = 0.525

Thermal Expansion Stress Range

Restrained =

= Max , 0.9

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B31.4 Liquid Petroleum Pipelines


Unrestrained

= + 4 0.7

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B31.8 Gas Transmission Pipelines


= ; , 0.72 0.8

Hoop Stress

=


= + 4 0.72

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CSA Z662 Oil and Gas Pipelines


= ; ,0.8

Hoop Stress

=

Longitudinal Stress

=

+

Combined Hoop and Longitudinal

Restrained =

0.9

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CSA Z662 Oil and Gas Pipelines

Combined Stress for Restrained Spans

+


= + 4 0.72

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PIPELINE STRESS ANALYSIS


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Analysis

Buried pipeline can be classified into fully restrained, partially restrained, and

unrestrained sections

Fully restrained => plane strain problem, no bending

Longitudinal stresses, but no strains

Can be analysed by hand calculations

Partially restrained/Unrestrained => 3D stress state, often approximated as

plane stress

FEA required to capture nonlinear soil response ie. CAESAR

Axial elongation due to pressure and thermal loads

Lets try a sample model

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Sample Problem

Single 15 Bend, Virtual Anchor on each side

CSA Z662 design

NPS 12, 7.9mm (.311 in), Gr. 414 (X60)

Design Pressure 9.93 MPa (1440 psi)

Design Temperature - 60C (140F)

Install Temperature - -25C (-13F)

Depth of Burial 1500mm (5 ft)

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Basic Code Calculations

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CAESAR Model

Five elements

15D Induction Bend

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Soil Model

ALA method preferred

Detailed soils information usually not available

Best Practice

Parametric Study

Minimum of four soil models

Cohesive and non-cohesive

High/low compaction

Extra caution required for:

Frozen Backfill

High Water Table / Muskeg

Slopes

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Results

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Discussion

All Done!

Lets call ourselves pipeline experts and all go home.

But,.perhaps a little Validation and Verification before we go.

Hoop Stress

= /2 = 323.9 * 9.93 / (2*7.9) = 203.6 MPa vs. 193.6 MPa

Restrained Longitudinal Stress

= 1 = 1 .3 203.6 + 2.075 1.2 5 60 25 = 353.7 MPa vs. 327.5 MPa

Allowable Stress

Fully restrained should be 0.9*Sy = 372.6 MPa vs 414 MPa

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Hoop Stress

What is being reported in the Sustained case?

Not hoop stress, but the longitudinal stress due to pressure

ie.1

= 0.5 * 193.6

= 96.8 MPa 97.3 MPa

Revise model inputs

Hoop Stress Calc based on OD

Mill tolerance not required for CSA

Change Poissons ratio to 0.3

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Hoop Stress

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One Down!


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Longitudinal Stress

Revise some more inputs

Replace temperature with thermal strain

Revise elastic modulus

Re-run the analysis

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Longitudinal Stress

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Two Down!


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One more thing.Pressure Thrust

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+20% !

Why did the restrained

stress go up?


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Pressure Loading

By definition, pressure acts in all directions

For a closed cylinder, there are stresses and strains in all 3 directions

When the end cap forces are present, the general treatment is,

=

/4

= /2

= ,, generally neglected

=1

+

1/

(

)

= 1 + 1/

(

)

=1

+

3

(

)

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Pressure Loading

What happens when end cap forces are not present?

Eg. Expansion joint

= 0 = /2

= 0 =

1

+

(

)

=1

+

1

(

)

=1

+

(

)

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Pressure and Thermal Loads

Thermal expansion causes a stress free strain, unless it is restricted.

= ; = 0

= ; = 0

Thus, we can solve for the restrained stress,

+ = 0 =1

+ +

=

For the unrestrained case

= 0

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Pressure Loading

How are the end cap loads treated in CAESAR?

As a uniform tensile (+ve) strain applied over the entire system

=1

+

1/

(

)

For restrained sections, = 0, this results in a compressive stress

In actuality, it should be a tensile force and a ve strain

This method is computationally attractive, but has some drawbacks

Point of application of the force is lost; this leads to an incorrect distribution of

forces, stresses, and strains in the pipeline model

Compressive stresses in the restrained portions of the pipeline are over-reported.

Lets look at this in more detail

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Pressure Loading

Returning to the sample problem,

=

=

..3

. 9.93

33.8

.9= .02% ; = 40.7 ;

+ = 353.7 + 40.7 = 394.4 . 391.3

Now we know what CAESAR is calculating

How can we go about improving this model?

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Pressure Loading PVP Method

Step #1 Add thrust forces at the correct locations

Thrust force = ()

Use the near and far points on the bend

Bend mid-point is not advisable

Step #2 Convert to an equivalent strain; subtract from thermal strain

Set Poissons ratio to a very small value (0.001)

Step #3 Post-process the bend manually

Introduction of thrust forces generates compressive forces in the bend that are notreal

Pressure thrust acts on the projected area of the pipe tangents, on the backside of

the bend; there is no net section compression

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Step #1 Add Thrust Forces

Thrust Force = = 9.93 (

33.9

7.9)= 740 !

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Step 2 Poisson Effect

Calculate the compressive strain/ = -.3*203.5/2.07e5 = .000295

Subtract from thermal strain (.00102 - .000295 = .000725)

Note that the Poisson strain can be converted to an

equivalent temperature by dividing by the co-efficient of

thermal expansion (ie. .000295/1.2e-5 = 24.5C)

Now, run the analysis!

Note the load cases Ive

set up.

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Step 3 Post-process

Take the local axial forces for the bend in the OPE (W+T1+P1+F) case

Subtract the local axial force over the bend from the OPE (F) case

Manually calculate the axial and bending stresses

Excel time!

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Post Processing - Excel

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Results Discussion

What do you end up with?

Maximum OPE stress of 571 MPa vs 704 MPa (23% reduction)

Displacements 36mm vs 44mm (23% reduction)

Restrained Axial Force 1176 kN vs 1951 kN

Restrained Stress 353 MPa vs 391 MPa

Is it worth the effort?

For the right problem, yes.

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Results Discussion

Axial force in the line

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A little V&V

Those numbers look good, but.

weve always used the CAESAR defaults with/without Bourdon

the CAESAR method is the industry standard

weve never had any issues

We thought the same, so..

PVP developed an ANSYS APDL Pipeline design suite.

Linear/nonlinear steel plasticity models

Large deformation theory

New generation pipe elements including shell deformation modes

We benchmarked the same problem using ANSYS

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ANSYS Results

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Results Agreement -

2% on Stress

10% on Displacement


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NONLINEAR STRESS ANALYSIS


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Nonlinear Pipeline Design

What is Nonlinear Analysis?

Metal Plasticity

Geometric (ie. bend ovalization)

Path dependent loading

Why bother for a Pipeline?

Reduction in capital cost

Better defined safety margin

Failure assessment

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Cost Reduction

Comparison of Required Wall Thickness

NPS 12, Gr. 483, 9.93 MPa

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Cost Reduction

Substitution of Lower Grade

NPS 12, 7.9mm, 9.93 MPa

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Safety Margin

Higher stress = increased safety margin ?

Pipelines fail for many reasons.

(corrosion, external damage, denting, cracking)

Does a single allowable stress appropriately address these failure modes?

Limit states design

Reliability based design method based on factored loads and factored resistances

Based on identification of failure modes

Assignment of appropriate safety factors for Ultimate, Serviceability

Conclusion

Better defined safety margin

Remove waste in the design from by using a consistent safety margins

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Plasticity

Theory of strain past yield

Two main theories Incremental and Total

Incremental

Increments of plastic strain related to plastic

stress by the tangent modulus

Overall response is the integral over the

load path

Total (Secant)

Total strain related to total stress by thesecant modulus

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Incremental Theory

More widely known and implemented (ANSYS, ABAQUS, etc)

Capable as a general theory

More computationally intensive

= (, )

Much more complex than we have

time for.

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Total strain theory

Total strains related to total stresses by secant modulus

For a certain class of problems its much easier to apply

Restrictions

Stress history effects cannot be accounted for

Proportional loading only

Isotropic hardening only

Lets investigate this further

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Nonlinear Material Models

Many well known models to choose from

Bilinear

= ;

= 1 + 1 ; >

Ramberg-Osgood

=

+ (

) ;

= 10. . 30

ASME VIII

Multi-parameter

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Yield Criteria

Two main theories

Maximum Shear Stress

( ) =

Equivalent Stress

1

1 + 3

+ 3 1 =

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Yield Surfaces

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Hardening Laws

What happens when you load a material past yield?

Elastic-Plastic

No change in stress

Strain is undefined

Isotropic

Uniform expansion of yield surface

Same center point

Kinematic

A shift in the yield surface

Same size

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Plastic Incompressibility

Elastic deformation is compressible

Obvious since Poissons ratio is < , usually about 0.3

Plastic deformation is incompressible

Less obvious, had been assumed; proven experimentally by Bridgman

Poisson ratio equal to 0.5

What about the range in the middle?

There is a transition, =

It can be proven that the relation is as follows

=1

[

1

]

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Load Path Dependence

Ex. - Thin Cylinder with Tension and Torsion

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Initial Yield Curve

Yield Curve after

Hardening


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Ex. Thin Cylinderwith Tensile Loading

Load along OABAO

Yield at point A, strain harden to point B, remove load ( = 0)

= ;

=

= ;

= 0

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Initial Yield Curve

Yield Curve after

Hardening


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Ex. Thin Cylinderwith Torsional Loading

Load along OCDCO

Yield at point C, strain harden to point D, remove load ( = 0)

= 0 ;

= ;

=

= 0

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Initial Yield Curve

Yield Curve after

Hardening


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Ex. Arbit rary Loading

Two different load paths - OABAEF and OCDF.

Same final stress state. Different strains.

What are they?

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Initial Yield Curve

Yield Curve after

Hardening


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Ex. Arbit rary Loading

OABAEF -

= ;

=

=

OCDF -

=

They are unchanged. All unloading/reloading is elastic!

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Initial Yield Curve

Yield Curve after

Hardening


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Ex. Deformation Plasticity

Recall that it only can handle proportional loading.

Path OF is proportional

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Initial Yield Curve

Yield Curve after

Hardening


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CAESAR Nonlinear Analysis

Step #1 Linear solution

Step #2 Extract Element Stress

Step #3 Calculate effective modulus (E) and effective Poisson ratio (v)

Step #4 Repeat Steps #2 and #3 by element

Step #5 Solve

Step #6 Compare change in stress to convergence criteria. If converged,

then stop, else Step #2.

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Step #1 Start with Solution from PVP Method

Step #2 Extract Element Stress

Select range of elements with stress above yield

Step #3 Calculate E and v

Use material model to calculate E and v

Step #4 Repeat by Element

Step #5 - Solve

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Compare change in stress to convergence criteria (eg. 5%)

Repeat.repeat.repeat

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Iteration #2Iteration #1 Iterations #3,4,5,6


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Max + , Bend Midpoint

Iteration #1 571 MPa






We have convergence to 2%, and have achieved a 20% stress reduction

Based on the material model, we have 0.2% plastic strain.

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Results Discussion

Is it worth the effort?

Quite laborious and time consuming

Lots of data manipulation, error prone.

But, for the right problem,

You get a much better understanding of the actual stress in the line.

You are not forced to make design changes due to the limitations of

your analysis method.

That all looks very nice, but have you validated the results?

Of course we did.

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ANSYS N li


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ANSYS Nonlinear

Kinematic Hardening, Small Def. Theory, Pipe289 Elements

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Agreement

to 2.5%!

ANSYS N li


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ANSYS - Nonlinear

Kinematic Hardening, Small Def. Theory, Pipe289 Elements

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Agreement

to 5%.

A W d f C ti


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A Word of Caution

There are limits to the capabilities of the beam theory elements

Key problem is the assumption that cross-sections remain plane and

undistorted after deformation

Not capable of capturing ovalization, wrinkling, or collapse

Ovalization has a pronounced effect at higher strain levels

Be wary of problems with high D/t

Initial imperfections play a large role in wrinkle and buckle initiation

We do not consider the method to be sufficiently robust to do a full strain-

based design.

So what is it good for?

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CAESAR N li


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CAESAR Nonlinear

Stress based design!

There is a lot to be gained

between 70% SMYS and

90% SMYS

Codes dont say you cant vary

E and v.

About .1% more strain

allowed

=

1

E

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RISER DESIGN

D i Phil h


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Design Philosophy

Why is there an issue?

Numerous failures

Reasons difficult to model

Backfill conditions

Compaction

Local stresses

Restrained or Unrestrained?

Design Robustness

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Backfill


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Backfill

Can be somewhat different than what you model.

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Piled Risers


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Piled Risers

The outcome of multiple lawsuits.

About the worst stress design you

could come up with.

Lets discuss

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Piled Risers


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Piled Risers

And a common outcome.

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Restrained Risers


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Restrained Risers

Restrained = Anchor Block

Usually concrete due to loadrequirements.

Points to Consider

Familiarity with the design and

installation of an anchor block

Design of the attachment to the pipe Protection of pipe coating

Availability of concrete

Load calculation

Cost

Recommendation

Least preferred option

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Unrestrained Risers


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Unrestrained Risers

Unrestrained is a matter of degree

Shallow angle riser Buried Offset

Points to Consider

Extra space requirements

May required controlled backfill

compaction May require imported backfill

Generally more economical

Easiest to implement early in

design process

Recommendation This is my preferred riser solution

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