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Design of Buried Pipelines
against Permanent Ground Displacements
Dr Dimitris KaramitrosLecturer in Civil Engineering
Dr Dimitris Karamitros - Lecturer in Civil Engineering
E-mail: [email protected]
Society for
Earthquake and
Civil Engineering
Dynamics
National
Technical
University of
Athens
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Δf
Δy
Δz
Δx
α
y
z
xβ
Problem DescriptionSeismic Fault Crossings
Kocaeli, Turkey (1999) Chi-Chi, Taiwan (1999)
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Problem DescriptionTypes of Permanent Ground Displacements
Underground works (e.g. tunneling)
Wang et al (2011)
Slope failures
O’Rourke et al (1989)
Lateral-spreading (liquefaction)
O’Rourke et al (1989)
…and others…
Differential settlement / heave
ALA-ASCE (2005)
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Presentation Outline
Dr Dimitris Karamitros - Lecturer in Civil Engineering
E-mail: [email protected] bristol.ac.uk
Problem Description
Current Design Practice
Simplified Analytical Methodologies
Strike-Slip Fault Crossings
Normal Fault Crossings
Oblique Fault Crossings
Pipelines with Bends
Practical Design Considerations
Limitations & Future Research
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Current Design Practice3-D Finite Element Analyses
American Lifelines Alliance
ASCE (2005)
pipeline
transverse horizontal soil springs
axial soil springs
vertical soil springs
applied fault displacement
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Shell elements
Rigid element
Beam elements
Axial soil springs
Horizontal soil springs
Vertical soil springs
Current Design Practice3-D Finite Element Analyses
American Lifelines Alliance
ASCE (2005)
Non-linear behavior of pipeline steel
Elasto-plastic soil springs
Second-order effects
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Current Design PracticeNon-linear Winkler-type Springs
pipeline
transverse horizontal soil springs
axial soil springs
vertical soil springs
applied fault displacement
Tu
ΔΤ
T
Δx
Pu
ΔP
P
Δy
Qu
ΔQu
Q
Δz
Qd
ΔQd
…after Trautman & O’Rourke (1983)
AXIALTRANSVERSE
HORIZONTALVERTICAL
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Current Design PracticeNon-linear Winkler-type Springs
pipeline
transverse horizontal soil springs
axial soil springs
vertical soil springs
applied fault displacement
Tu
ΔΤ
T
Δx
Pu
ΔP
P
Δy
Qu
ΔQu
Q
Δz
Qd
ΔQd
…after Trautman & O’Rourke (1983)
AXIALTRANSVERSE
HORIZONTALVERTICAL
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Current Design PracticeNon-linear Winkler-type Springs
pipeline
transverse horizontal soil springs
axial soil springs
vertical soil springs
applied fault displacement
Tu
ΔΤ
T
Δx
Pu
ΔP
P
Δy
Qu
ΔQu
Q
Δz
Qd
ΔQd
…after Trautman & O’Rourke (1983)
AXIALTRANSVERSE
HORIZONTALVERTICAL
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Current Design PracticeNon-linear Winkler-type Springs
pipeline
transverse horizontal soil springs
axial soil springs
vertical soil springs
applied fault displacement
Tu
ΔΤ
T
Δx
Pu
ΔP
P
Δy
Qu
ΔQu
Q
Δz
Qd
ΔQd
…after Trautman & O’Rourke (1983)
AXIALTRANSVERSE
HORIZONTALVERTICAL
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Current Design PracticeTypical Example
PLAN VIEW
Natural Gas Supply Pipeline for the Alexandroupolis Hospital, Greece
Η=
1.1
0m
Ø10
΄΄
t=6.35mm
ANSI/API5L Grade B
Normal Fault
ψ = 70° (dip angle)
Δf = 0.45m
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Current Design PracticeTypical Example
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Current Design PracticeTypical Example
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Current Design PracticeTypical Example
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Current Design PracticeTypical Example
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Current Design PracticeTypical Example
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Current Design PracticeTypical Example
Typical mitigation measures:
Increased pipeline thickness
Higher grade pipeline steel
Use of different backfill material
Protective casing
Flexible joints
Alteration of pipeline route
…
Allowable longitudinal strains:
Tensile strain: e.g. 4% (0.5% for welded pipelines)
Compressive strain: e.g. 1.76 t/D (to avoid buckling)
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Current Design PracticeTypical Example
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Current Design PracticeTypical Example
need for Simplified Design Methodologies
Preliminary design
Determine critical areas
Quick checking of numerical results
Evaluation of mitigation measures
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Presentation Outline
Dr Dimitris Karamitros - Lecturer in Civil Engineering
E-mail: [email protected] bristol.ac.uk
Problem Description
Current Design Practice
Simplified Analytical Methodologies
Strike-Slip Fault Crossings
Normal Fault Crossings
Oblique Fault Crossings
Pipelines with Bends
Practical Design Considerations
Limitations & Future Research
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Existing Analytical MethodologiesStrike-slip fault crossings
x
yz
β
initial route
deformed pipeline
x
y
β
Δx
ΔyPLAN
VIEW
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Existing Analytical MethodologiesStrike-slip fault crossings
Newmark & Hall (1975)
Kennedy et al. (1977) adopted by the ASCE (1984) Guidelines
✔ Non-linear behavior of pipeline steel
✔ Soil-pipeline interaction in both longitudinal & transverse directions
✖ Large fault movement ➭ pipeline section under yield ➭ ignore bending stiffness
➭ overestimate curvature ➭ (over) conservative
Wang & Yeh (1985)
✔ Bending stiffness taken into account
✖ Ignore the effect of axial tension on bending stiffness
➭ underestimate curvature ➭ under conservative
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0 0.5 1 1.5 2
Fault movement (Δf) /Pipeline diameter (D)
0 0.5 1 1.5 2
Fault movement (Δf) /Pipeline diameter (D)
0 0.5 1 1.5 2
Fault movement (Δf) /Pipeline diameter (D)
0
1
2
3
Maxim
um
Str
ain
εm
ax (
%)
0
1
2
3
Ben
din
g S
train
εb (
%)
Kennedy et al.
Wang & Yeh
Num. Analyses
0
1
2
3
Axia
l S
train
εa (
%)
Crossing angle: β=30° β=45° β=60°β=30° β=45° β=65°
Existing Analytical MethodologiesStrike-slip fault crossings
Typical HPTS
Natural Gas Pipe
Diameter D=0.9144 m
Thickenss t=0.0119 m
API5L-X65 steel
(σy=490MPa)
Medium dense sand
(γ=18KN/m3 , φ=36°)
Embedment H=1.30m
Δfβ
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B
C
Ax
w
q(x) = - k w(x)
A'
x
w
q(x) = - k w(x)
C'Lc
quδ=
Δy/2
δ=
Δy/2
qu
Lc
Δy
A
B
C
fault
pipeline
A'
C'
Δx
New Analytical MethodologyKaramitros et al (2007) – Strike-Slip Fault Crossings
Basic Principle: Partitioning of the pipeline into 4 segments
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B
C
Ax
w
q(x) = - k w(x)
A'
x
w
q(x) = - k w(x)
C'Lc
quδ=
Δy/2
δ=
Δy/2
qu
Lc
Δy
A
B
C
fault
pipeline
A'
C'
Δx
New Analytical MethodologyKaramitros et al (2007) – Strike-Slip Fault Crossings
Basic Principle: Partitioning of the pipeline into 4 segments
q(x) = - k w(x)
xφA
A
w
VA
MAA'
Segment Α´Α (and CC´):
Elastic Beam on Elastic Foundation
Boundary conditions for segments ΑΒ and BC
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B
C
Ax
w
q(x) = - k w(x)
A'
x
w
q(x) = - k w(x)
C'Lc
quδ=
Δy/2
δ=
Δy/2
qu
Lc
Δy
A
B
C
fault
pipeline
A'
C'
Δx
New Analytical MethodologyKaramitros et al (2007) – Strike-Slip Fault Crossings
Basic Principle: Partitioning of the pipeline into 4 segments
Lc
Cr
qu
δ=
Δy/2
φA
A
BVA
MA
[ M ]
Segments ΑB (and BC)
Maximum Bending Moment
→ Maximum Bending Strain
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Compatibility of displacements:
(pipeline elongation = fault displacement)
Obtain axial force Fa
anchL
0
ΔL 2 ε L dL Δx
Simplified computation of axial strains (similar to existing methodologies)
New Analytical MethodologyKaramitros et al (2007) – Strike-Slip Fault Crossings
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Compatibility of displacements:
(pipeline elongation = fault displacement)
Obtain axial force Fa
anchL
0
ΔL 2 ε L dL Δx
Simplified computation of axial strains (similar to existing methodologies)
New Analytical MethodologyKaramitros et al (2007) – Strike-Slip Fault Crossings
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Equivalent linear solution (iterative), using secant modulus:
φ1
θ
π-φ2
ε1
εmax=εa+εb
σ1
εa
-ε1
εmin=εa-εb
σa
-σ1
σmin
σmax
Τμήματα της διατομής σε διαρροή
ΑνηγμένεςΠαραμορφώσεις
Τάσεις
Steel Under Yield
stressesstrains
Obtain maximum bending strain εb and maximum axial force Fa
from elastic solution
➭ Calculate axial strains εa, so that 𝜎 ∙ 𝑑𝐴 = 𝐹𝑎
➭ Readjust secant Young’s modulus 𝐄′ =Mmax∙𝐷
2∙I∙𝜀𝑏
New Analytical MethodologyKaramitros et al (2007) – Strike-Slip Fault Crossings
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0 0.5 1 1.5 2
Fault movement (Δf) /Pipeline diameter (D)
0 0.5 1 1.5 2
Fault movement (Δf) /Pipeline diameter (D)
0 0.5 1 1.5 2
Fault movement (Δf) /Pipeline diameter (D)
0
1
2
3
Maxim
um
Str
ain
εm
ax (
%)
0
1
2
3
Ben
din
g S
train
εb (
%)
Kennedy et al.
Wang & Yeh
Prop. Methodology
Num. Analyses
0
1
2
3
Axia
l S
train
εa (
%)
Crossing angle: β=30° β=45° β=60°β=30° β=45° β=65°
Typical HPTS
Natural Gas Pipe
Diameter D=0.9144 m
Thickenss t=0.0119 m
API5L-X65 steel
(σy=490MPa)
Medium dense sand
(γ=18KN/m3 , φ=36°)
Embedment H=1.30m
Δfβ
New Analytical MethodologyKaramitros et al (2007) – Strike-Slip Fault Crossings
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New Analytical MethodologyKaramitros et al (2011) – Normal Fault Crossings
α
z
x
ΔfΔz
Δx
ψ
initial route
deformed pipeline
x
z
Δf
Δx
Δz
SIDE
VIEW
ψ
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A
C
qBC
qAB
LAB LBC
B Δz
x
w
q(x) = - k w(x)
A'
x
w
q(x) = - k w(x)
C'
AB
C C'
A'
ρήγμ
α
Δx
Δz
αγωγός
Δf
pipeline
Pipeline discretized in 3 segments:
New Analytical MethodologyKaramitros et al (2011) – Normal Fault Crossings
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0
1
2
3
4
εa (
%)
0
1
2
3
4
εb (
%)
Numerical
Analytical
0 0.5 1 1.5 2
Δf / D
0
1
2
3
4
εm
ax (
%)
0 0.5 1 1.5 2
Δf / D0 0.5 1 1.5 2
Δf / D
ψ=55° ψ=70° ψ=85°
Typical HPTS
Natural Gas Pipe
Diameter D=0.9144 m
Thickenss t=0.0119 m
API5L-X65 steel
(σy=490MPa)
Medium dense sand
(γ=18KN/m3 , φ=36°)
Embedment H=1.30m
Δfψ
New Analytical MethodologyKaramitros et al (2011) – Normal Fault Crossings
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= max { , }
Oblique Fault Crossings
Δf
Δy
Δz
Δx
α
y
z
xβ
Oblique
Crossing
Δx, Δy, Δz
fault
Normal Fault
Crossing
Δx, Δz (Δy=0)
Strike-Slip
Fault Crossing
Δx, Δy (Δz=0)
str
ike
-slip
fault
Maximum strains occur at:
• different locations along the pipeline
• different positions on the cross-section
y
z εmax,normal
εmax,strike-slip
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Oblique Fault Crossings
0
1
2
3
4
εa (
%)
0
1
2
3
4
εb (
%)
0 0.5 1 1.5 2
Δf / D
0
1
2
3
4
εm
ax (
%)
Numerical
Analytical(normal)
Analytical(strike-slip)
0 0.5 1 1.5 2
Δf / D0 0.5 1 1.5 2
Δf / D
ψ=30° - β=30° ψ=45° - β=45° ψ=60° - β=60°
obliq
ue
cro
ssin
gstr
ike
-slip
fault
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Application to Practical Cases
Range of Parameters
Pipelines
✔ D = 4÷36 in
✔ t/D = 1.3÷4.2 %
✔ Grade B, X52, X65
Faults
✔ Δf = 0.08÷1.06 m
✔ β = 20÷90˚
✔ ψ = 60÷70˚
0.1 1
εmax (%)
Aναλυτική μεθοδολογία
0.1
1
ε ma
x (
%)
Aρ
ιθμ
ητι
κές
ανα
λύσ
εις
+ 50
%
- 50%
Analytical Methodology
Num
erical A
naly
ses
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Typical Pipeline Layout in Practice
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Presentation Outline
Dr Dimitris Karamitros - Lecturer in Civil Engineering
E-mail: [email protected] bristol.ac.uk
Problem Description
Current Design Practice
Simplified Analytical Methodologies
Strike-Slip Fault Crossings
Normal Fault Crossings
Oblique Fault Crossings
Pipelines with Bends
Practical Design Considerations
Limitations & Ongoing Research
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pipeline
φ
A
B R
LA
PL
AN
VIE
W
fault trace
Δf
Step 1: Analyze the pipeline close to the bend
Step 2: Fault – bend interaction
Step 3: Analyze the pipe at the fault crossing
φ
A
B R
LA fault trace
Δf
New Analytical MethodologyKaramitros et al (2016) – Pipelines with Bends
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uA
Step 1: Analysis of the Bend
Analysis using the Direct Stiffness Method:
𝑷 − 𝑷𝑳 = 𝑲 + 𝑲𝒔𝒑𝒓 𝒖
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uA
Step 1: Analysis of the Bend
Analysis using the Direct Stiffness Method:
𝑷 − 𝑷𝑳 = 𝑲 + 𝑲𝒔𝒑𝒓 𝒖
Lateral and Rotational Springs
Elastic beam on elastic foundation
➭ Obtain relations between Μ(0), Q(0) and w΄(0), w(0)
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uA
Step 1: Analysis of the Bend
Analysis using the Direct Stiffness Method:
𝑷 − 𝑷𝑳 = 𝑲 + 𝑲𝒔𝒑𝒓 𝒖
Axial Spring at end Β
Axial force (and strain) distribution along the pipeline
➭ Obtain relation between FB and uB
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Step 2: Fault-Bend Interaction
Axial component of
Fault movement
Axial displacement
at bend uΑ
Integral of strains
along the pipeline= +
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Step 3: Verification at Fault Crossing
Analytical Methodology
for normal fault crossings
Karamitros et al (2011)
Analytical Methodology for
strike-slip fault crossings
Karamitros et al (2007)
B
C
A
Δy
A
B
C
ρήγμα
αγωγός
A'
C'
Δx
x
w
q(x) = - k w(x)
A'
x
w
q(x) = - k w(x)
C'Lc
qu
δ=
Δy/2
δ=
Δy/2
qu
Lc
A
C
qBC
qAB
LAB LBC
B Δz
x
w
q(x) = - k w(x)
A'
x
w
q(x) = - k w(x)
C'
AB
C C'
A'
ρήγμ
α
Δx
Δz
αγωγός
Δf
Calculate axial force Ffault at the position of the fault
and employ one of the existing analytical methodologies:
…or their newer versions, e.g. Trifonov & Cherniy (2010)
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New Analytical MethodologyKaramitros et al (2016) – Pipelines with Bends
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Presentation Outline
Dr Dimitris Karamitros - Lecturer in Civil Engineering
E-mail: [email protected] bristol.ac.uk
Problem Description
Current Design Practice
Simplified Analytical Methodologies
Strike-Slip Fault Crossings
Normal Fault Crossings
Oblique Fault Crossings
Pipelines with Bends
Practical Design Considerations
Limitations & Future Research
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Practical design considerations
Numerical simulations & analytical methodologies should take into
account material (pipeline steel, soil) & geometric non-linearities.
When the axial force exceeds the yielding limit, pipeline strains
become very sensitive to the applied movement.
The existence of bends along the pipeline route needs to be taken into
account.
The assumption of 90° bending angles is not always conservative.
Pipeline behavior at bends is significantly affected by the radius of
curvature.
Analytical methodologies should only be employed within their defined
range of application.
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Limitations & Ongoing Research
Both numerical & analytical solutions are affected by the p-y curves
considered for the (Winkler-type) soil springs.
pipeline
transverse horizontal soil springs
axial soil springs
vertical soil springs
applied fault displacement
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Limitations & Ongoing ResearchTrench Effects
Bouckovalas, G.D., Chaloulos, Y.K., Karamitros, D.K. (2016): “Trench effects on lateral p-y
relations for embedded pipelines”, Computers & Geotechnics (under review)
H
D
d θ
x+ymax
Ultimate soil resistance may increase up to one order of magnitude!
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H
D
Limitations & Ongoing ResearchCoupling-effects
Winkler-type
representation:
?
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Dr Dimitris Karamitros – Lecturer in Civil Engineering
E-mail: [email protected]
Thank you for your attention!
Karamitros D.K., Bouckovalas G.D., Kouretzis G.P. (2007): “Stress Analysis of Buried Steel Pipelines at
Strike-slip Fault Crossings”, Soil Dynamics and Earthquake Engineering, vol. 27, pp. 200–211.
Karamitros D.K., Bouckovalas G.D., Kouretzis G.P., Gkesouli V. (2011): “An Analytical Method for Strength
Verification of Buried Steel Pipelines at Normal Fault Crossings”, Soil Dynamics and Earthquake
Engineering, vol. 31(11), pp. 1452-1464.
Kouretzis G.P., Karamitros D.K., Sloan S.W. (2015): “Analysis of buried pipelines subjected to ground
surface settlement and heave”, Canadian Geotechnical Journal, vol. 52(8), pp. 1058-1071.
Karamitros D.K., Bouckovalas G.D., Zoupantis C. (2016): “Buried Pipelines with bends: Analytical
verification against permanent ground displacements”, Canadian Geotechnical Journal (under review)
Bouckovalas G.D., Chaloulos Y.K., Karamitros D.K. (2016): “Trench effects on lateral p-y relations for
embedded pipelines”, Computers & Geotechnics (under review)
Calculation spreadsheets available at: www.dimitriskaramitros.com
National
Technical
University of
Athens
Society for
Earthquake and
Civil Engineering
Dynamics