Post on 27-Mar-2016
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7/21/2019 Session 3A Overheads
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Reliability-based Models
Other Time Dependent Failure Causes
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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
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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
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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
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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
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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
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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 +=+=
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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
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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
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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
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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 ∆=∆
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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
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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
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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
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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
Transverse Ground Movement
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Technologies
Transverse Ground Movement
- growth model
● Single parameter ●
Free field ground movement rate: g w
( ) w g ww +=
Transverse Ground Movement
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Transverse Ground Movement
- 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)
Transverse Ground Movement
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Transverse Ground Movement
- 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
Transverse Ground Movement
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Transverse Ground Movement
- 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
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Longitudinal Ground Movement
- defect characterization
Defined by● free field ground movement, u
u
dεt
Tensilestrain
εc
Compressivestrain
u
Longitudinal Ground Movement
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Technologies
Longitudinal Ground Movement
- 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
Longitudinal Ground Movement
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Longitudinal Ground Movement
- growth model
● Single parameter
●
Free field ground movement rate: g u
( ) u g uu +=
Longitudinal Ground Movement
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Technologies
Longitudinal Ground Movement
- 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
Longitudinal Ground Movement
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Technologies
Longitudinal Ground Movement
- inspection methods
● Ground movement survey
●
locate movement sites● measure free field ground displacement
Longitudinal Ground Movement
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Technologies
Longitudinal Ground Movement
- 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
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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
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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
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Damage Site Characteristics – Case 1
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
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Damage Site Characteristics – Case 2
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
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Damage Site Characteristics – Case 2
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
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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
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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
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Maintenance Scenarios on Segment
Demo 1 – Site Analysis Results for
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All Maintenance Scenarios on Segment