session 3a overheads

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Reliability-based Models

Other Time Dependent Failure Causes



advantage

technologycreates

C-FERTechnologies

Time-dependent Failure Causes

Mechanisms addressed

●

Metal loss corrosion● external

● internal

● Cracks● manufacturing induced cracking● stress corrosion cracking

● Dent/gouge defects

●

Ground movement● transverse

● longitudinal



advantage

technologycreates

C-FERTechnologies

Recall Failure Rate Calculation

f d f pn ×=

Failure Rate(per km yr)

Probability of Failure(per defect)

Frequency of Defects

(per km yr)

For ground movement: defect = damage site



advantage

technologycreates

C-FERTechnologies

Defect Attributes

● Existing damage●

Initiated in the past and is currently present● Density: Number of defects per km

● Severity: Defect size distributions

● Growth: Size growth distributions

● Subsequent damage*● Initiates in the future

● Initiation rate: Number of new defects per km yr

● Severity: Defect size distributions at initiation

● Growth: Size growth distributions

* Not applicable to manufacturing cracks or ground movement



advantage

technologycreates

C-FERTechnologies

Effect of Maintenance

● Rehabilitation philosophy● Find and eliminate defects before they become critical

● Maintenance options● Above ground surveys

● In-line inspection● Hydrotest

● Other ground movement only

● Maintenance impact● Reduce number of defects per unit line length

● Shift size and growth rate distributions toward smaller values



advantage

technologycreates

C-FERTechnologies

Cracks - defect characterization

● Axially oriented planar surface flaws only

● Defined by● maximum depth, h

● length, l

●

and shape (assume semi-elliptical)

A

A

td

h

hl

Section A-AManufacturing Cracks

hl

Section A-AStress Corrosion Cracking



advantage

technologycreates

C-FERTechnologies

Cracks - defect growth model

● Manufacturing induced cracks● fatigue mechanism (depth growth only)● Paris law growth rate parameters: a, m

● Stress Corrosion Cracking● metal dissolution (depth and length growth)

● depth and length growth rates: gh, gl

( )

( )

∫∆

=→∆=

f

i

h

h

m

m

K a

dh N K a

dN

dh

( )l ht d n p f K ,,,,,,∆=∆

( ) ( ) l h g hl g hh τ τ +=+=



advantage

technologycreates

C-FERTechnologies

Cracks - performance model

● Failure strength● Battelle surface flaw model (Kiefner et al. 1973)

● Failure mode (leak vs. rupture)

● Battelle through-wall flaw model

r ( )

( )

+−

+=

−

l s

E C

md

st V

p

c95.68

5.12expcos

95.684 1

π

td

h( )l t d f mt h

t mhm p ,,1

1 =−

−=

( )

( )

+−

+=

−

l s

E C

md

st r V

c95.68

125.3expcos

95.684 1 π

π



advantage

technologycreates

C-FERTechnologies

Cracks - inspection methods

● Manufacturing induced cracks● Hi-resolution in-line crack detection tool

● locate and size crack

● measure maximum depth and length

● Hydrotest

● Stress corrosion cracking● Targeted excavation programs

● locate and size ‘significant SCC’ on exposed sections

● measure maximum depth* and length**assume sizing action leaves a blunt defect

● Hi-resolution in-line crack detection tool

● Hydrotest



advantage

technologycreates

C-FERTechnologies

Dent/gouge - defect characterization

● Metal loss (gouge) within dent

● Assume gouge work hardened and cracked

● Defined by● dent depth, b

● maximum gouge depth, h● gouge length, l

dt

A

A

b

h

hl

Section A-A



advantage

technologycreates

C-FERTechnologies

Dent/gouge - defect growth model

● Fatigue mechanism (depth growth only)

● Paris law growth rate parameters: a, m

( )( )∫∆

=→∆=

f

i

h

h

m

m

K a

dh N K a

dN

dh

( )bht d n p f K ,,,,,, τ ∆=∆



advantage

technologycreates

C-FERTechnologies

Dent/gouge - performance model

● Failure strength● British Gas model (Hopkins et al. 1988)

● Failure mode (leak vs. rupture)

● Battelle through-wall flaw model

( )

( )

+−

+=

−

l s

E C

md

st r V

c95.68

125.3expcos

95.684 1 π

π

=

−=

t h f Y and Y

t h s s 21115.1

dt

b

h

( )

−

+

−−=

−

−

57.0

9.1lnexp29.757.21

914.0expcos

4 2

212

1 V c

C

t

bY

d

bY

h s

E

d

st r

π

π



advantage

technologycreates

C-FERTechnologies

Dent/gouge - inspection methods

● In-line geometry tool● locate and size dent● measure dent amplitude, no gouge information

● Hi-resolution in-line crack detection tool●

locate and size gouge● measure max. gouge depth & length, no dent information

● Combined geometry & crack detection tool(s)● locate and size combined dent/gouge feature

● measure dent amplitude

● measure maximum gouge depth and length

T G d M t



advantage

technologycreatesC-FER

Technologies

Transverse Ground Movement

- defect characterization

Defined by● free field ground movement, w

● maximum pipe curvature, φ

} Correlated attribute pair

w = w/2

w

d

1

φ

1

φ

w



advantage


Technologies

Transverse Ground Movement - defect correlation and pipe soil interaction

Pipe-soil spring model

w

Et I

E I

Iterative solution

w

1/φ

M-φ model (Gresnigt 1986)

Closed-form interaction (Rajani and Morgenstern 1993)

Correlation functions relate w toφ

w = f(E, p, d, t, φ, Sy, σ

z, κ

z)

φ

= f(E, p, d, t,

w,

Sy, σz, κz)

line

attributes

defect

attributes

Inelastic pipe behavior in bending

M

Me

φ

Bi-linear soil springs

σz

kz




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Technologies


- growth model

● Single parameter ●

Free field ground movement rate: g w

( ) w g ww +=




advantage


Technologies


- performance model

Failure condition

z z ycr cr cr k S t d p E f www ,,,,,,, σ φ =≥

or

cr φ φ ≥

t d or

t d of lesser cr cr ct

cr −−

=ε ε

φ 22

( )( )

defined user

n st

t d pt d

d

t

cr

cr

t

c

=

−

+

−−+

=

ε

ε 018.053.10021.02

2

5000

/1205.8

22

where

and

Compressive wrinkling model(C-FER 1994)




advantage


Technologies


- inspection methods

● Ground movement survey●

locate movement sites● measure free field ground displacement

● Enhanced ground movement survey● locate movement sites

● for detected sites conduct pipe-soil interaction analysis

● estimate maximum pipe curvature(consistent with measured free field ground movement)

● In-line spatial geometry tool● locate movement sites

● measure maximum pipe curvature




advantage


Technologies


- other maintenance options

● Slope stabilization●

Reduce ground movement growth rate

● Strain relief ● reduce existing damage pipe curvature

● Isolation● modify backfill to reduce soil strength/stiffness

Longitudinal Ground Movement



advantage


Technologies


- defect characterization

Defined by● free field ground movement, u

u

dεt

Tensilestrain

εc

Compressivestrain

u




advantage


Technologies


- pipe soil interaction

u

Etkx

σx

Bi-linear soil springs

Closed-form interaction(Yoosef-Ghodsi and Murray 1999)

εt

Tensilestrain

ε

c

Compressivestrain

Pipe-soil spring model

u u u

u u u

Bi-linear pipe behaviour under axial load

Sy

E




advantage


Technologies


- growth model

● Single parameter

●

Free field ground movement rate: g u

( ) u g uu +=




advantage


Technologies


- performance model

Failure condition

x xcr yt cr cr k S T t d p E E f uuu ,,,,,,,,,, σ ε ∆=≥

where

Compressive wrinkling model(C-FER 1994)cr cr ct cr or of lesser ε ε ε =

( )( )

defined user

n st

t d pt d

d

t

cr

cr

t

c

=

−

+

−−

+

=

ε

ε 018.053.10021.02

2

5000

/1205.8

22

and




advantage


Technologies


- inspection methods

● Ground movement survey

●

locate movement sites● measure free field ground displacement




advantage


Technologies


- other maintenance options

● Slope stabilization

●

Reduce ground movement growth rate

● Strain relief ● reduce effective damage axial ground displacement

● Isolation● modify backfill to reduce soil strength/stiffness



advantage


Technologies

Ground Movement Considerations

Damage site characteristics

● Case 1● Where pipe damage attributes are strongly correlated

● Contained ground movement zone

● Consistent soil strength and stiffness properties

●

Consistent pipe geometry and mechanical properties● One movement zone a single dominant defect

● Case 2

● Where pipe damage attributes are not strongly correlated● Extended ground movement zone● Variable soil strength and stiffness properties

● Variable pipe geometry and mechanical properties

● One movement zone multiple defects



advantage


Technologies

Damage Site Characteristics – Case 1

E.g. Pipeline crossing a single transverse ground movement site

w

Local curvaturemaxima

Radius of curvature

Far fielddisplacement

Where conditions throughout zone are similar, theperformance will be controlled by a single location

one movement zone has one dominant defect



advantage


Technologies


E.g. Single site – conditions consistent throughout

No movement Zone 1 No movement

(200 m)

Zone 1 defect density = 1 dominant feature in 0.2 km = 5 per km



advantage


Technologies


E.g. Single site – conditions vary

No movement No movementNo movement

( 500 m)

Zone 1 Zone 2

(50 m) (50 m)

Zone 1 and 2 defect densities = 1 dominant feature in each 0.05 km transition = 20 per km



advantage

technologycreatesC-FERTechnologies


E.g. Multiple sites – conditions vary

No movement Zone 1 No movement

( 10 km)

Zone 1 defect density = 6 transitions in 10 km = 0.6 per km



advantage


Demo 1

Longitudinal ground movement problem

2) Characterize movement zone- ground movement rate- current displacement

0 . 5 k m

914 mm diameter gas pipeline @ 7000 kPain remote land use

3) Consider mitigation scenariosa – slope drains to slow movementb – slope drains to slow movement (alt)c – strain relief

1) Specify interruption costs



advantage


Demo 1

● Metric (SI) example

Gas pipeline –X:\Program Files\C-FER\PIRAMID\2002 Training Seminar\Level 3\Demo 1

Demo 1 – Decision Analysis Results for All



advantage


Maintenance Scenarios on Segment

Demo 1 – Site Analysis Results for



advantage


All Maintenance Scenarios on Segment

session 3a overheads

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