Design of Buried Pipelines against Permanent Ground ...

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

Δf

Δy

Δz

Δx

α

y

z

xβ

Problem DescriptionSeismic Fault Crossings

Kocaeli, Turkey (1999) Chi-Chi, Taiwan (1999)

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)

Presentation Outline


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

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

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

Current Design PracticeNon-linear Winkler-type Springs

pipeline


axial soil springs



Tu

ΔΤ

T

Δx

Pu

ΔP

P

Δy

Qu

ΔQu

Q

Δz

Qd

ΔQd

…after Trautman & O’Rourke (1983)

AXIALTRANSVERSE

HORIZONTALVERTICAL

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


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)


need for Simplified Design Methodologies

Preliminary design

Determine critical areas

Quick checking of numerical results

Evaluation of mitigation measures




Problem Description









Existing Analytical MethodologiesStrike-slip fault crossings

x

yz

β

initial route

deformed pipeline

x

y

β

Δx

ΔyPLAN

VIEW


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

0 0.5 1 1.5 2

Fault movement (Δf) /Pipeline diameter (D)

0 0.5 1 1.5 2


0 0.5 1 1.5 2


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°


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

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

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



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

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



Lc

Cr

qu

δ=

Δy/2

φA

A

BVA

MA

[ M ]

Segments ΑB (and BC)

Maximum Bending Moment

→ Maximum Bending Strain

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)


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


0 0.5 1 1.5 2


0 0.5 1 1.5 2


0 0.5 1 1.5 2


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


API5L-X65 steel

(σy=490MPa)

Medium dense sand

(γ=18KN/m3 , φ=36°)

Embedment H=1.30m

Δfβ


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

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:


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


API5L-X65 steel

(σy=490MPa)

Medium dense sand

(γ=18KN/m3 , φ=36°)

Embedment H=1.30m

Δfψ


= max { , }


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


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

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

Typical Pipeline Layout in Practice




Problem Description








Limitations & Ongoing Research

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

uA

Step 1: Analysis of the Bend

Analysis using the Direct Stiffness Method:

𝑷 − 𝑷𝑳 = 𝑲 + 𝑲𝒔𝒑𝒓 𝒖

uA




Lateral and Rotational Springs

Elastic beam on elastic foundation

➭ Obtain relations between Μ(0), Q(0) and w΄(0), w(0)

uA




Axial Spring at end Β

Axial force (and strain) distribution along the pipeline

➭ Obtain relation between FB and uB

Step 2: Fault-Bend Interaction

Axial component of

Fault movement

Axial displacement

at bend uΑ

Integral of strains

along the pipeline= +

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)

New Analytical MethodologyKaramitros et al (2016) – Pipelines with Bends




Problem Description









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.

Limitations & Ongoing Research

Both numerical & analytical solutions are affected by the p-y curves

considered for the (Winkler-type) soil springs.

pipeline


axial soil springs



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!

H

D

Limitations & Ongoing ResearchCoupling-effects

Winkler-type

representation:

?

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

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