7. seismic design of underground structures -...

7. Seismic Design ofUnderground Structures

G. BouckovalasProfessor N.T.U.A.

October 2010

G. KouretzisCivil Engineer, Ph.D. N.T.U.A.

GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.1

PrefaceThis lecture deals with the seismic design of “infinitely long” cylindrical underground structures i.e. tunnels, pipelines etc. The presented methodology can be easily adapted for the design of structures that feature a non-circular cross-section. However, this (and other relevant) methodologies are not valid for other types of underground structures such as metro stations, storage facilities or shafts.

A common characteristic of the “infinitely long” structures under consideration is their high flexibility and small mass, compared to the surrounding soil. Thus, unlike most common above ground structures, underground structures’ response to the imposed displacements from the surrounding soil is not dominated by inertia effects. As a result, a static analysis (not a pseudo-static) is sufficient for their design, given that the surrounding soil displacements are determined a-priori.

The following presentation focuses initially on the failure patterns attributed to transient and permanent seismic ground displacements. Next, a methodology for the stress analysis of flexible underground structures due to transient displacements is presented in detail, a problem that can be effectively treated by analytical means.

The methodology for the stress analysis of underground structures due to permanent ground displacements is more cumbersome, as it requires the implementation of non-linear numerical tools, at least for real-world design purposes. However, the basic principles of this numerical methodology are outlined, with the aid of a case study: the stress analysis of the Thessaloniki to Skopje crude oil steel pipeline at two active fault crossings: a normal fault crossing and a strike-slip fault crossing.


Α. Earthquakes and Underground Structures

Β. Seismic design against “transient”displacements

C. Seismic design against “permanent”displacements

earthquake-induced transient ground displacements...... are attributed to seismic wave propagation

Rayleigh wave (R)

Love wave (R)

shear wave (S)compression wave (P)


Rayleigh Pα

peripheral cracks

Rayleigh

Pα

concrete spalling(compression)


longitudinal cracks

Rayleigh

S

Rayleigh

S

shear cracks


Locations of underground structures (concrete tunnels) that failed during theCΗΙ-CΗΙ (1999) earthquake, plotted against recorded maximum ground acceleration contours at ground surface.

Note that all tunnels that were damaged lie within the 0.25g contour

failure potential due to seismic wave

propagation effects...

0 30 km

24

120

30E

121E

121

30E

7

4

6

3

59

11

108

2

23 30Nepicenterrupture

1failure sites

1

0.50g

0.25g

Locations of underground structures (concrete tunnels) that failed during theCΗΙ-CΗΙ (1999) earthquake, plotted against recorded maximum ground velocity contours at ground surface.

Note that all tunnels that were damaged lie within the 60cm/sec contour

0 30 km

24

120

30E

121E

121

30E

7

4

6

3

59

11

108

2


1failure sites

1

120cm/sec

60cm/sec


Ch

i-C

hi 1

999

Ch

i-C

hi 1

999

Correlation of strong motion levels with underground structure failures

earthquake-induced permanent ground displacements......are due to ground failure attributed to seismic effects. Typical examples include fault rupture propagation to the ground surface, landslides, steep slope failures, and mild slope failures due to liquefaction (lateral spreading).

fault

rupture


Tunnel collapse due to fault rupture propagation(Shih-Gang dam tunnel, Chi-Chi, 1999)

Empirical relations for the determination of the MEAN anticipated ground displacement due to fault rupture (Wells & Coppersmith, 1994).

The MAXIMUM anticipated displacement is about twice the mean value


Permanent displacements

due to

SLOPEFAILURE

and due to liquefaction-inducedlateral spreading


sub-sealandslides at

Eratini-Tolofonas beach

Aigio (1995) earthquake

(a)

(b)

Eratini port(α)GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.10

river mouth(b)

L=50-200m

W=

50-3

0 0m

Many thousands cubic meters of soil are mobilized during slope failures, and move for distances ranging from a few centimeters to several meters... (...when soil strength deteriorates during shaking, as for example in the case of liquefaction). We will dwell more into the estimation of slope failure-induced displacements in one of the following lectures.However, displacement estimates due to slope failure are not as straightforward (?) as fault-induced displacements... several seismological-geotechnical-topographical factors must be taken into account.

Many thousands cubic meters of soil are mobilized during slope failures, and move for distances ranging from a few centimeters to several meters... (...when soil strength deteriorates during shaking, as for example in the case of liquefaction). We will dwell more into the estimation of slope failure-induced displacements in one of the following lectures.However, displacement estimates due to slope failure are not as straightforward (?) as fault-induced displacements... several seismological-geotechnical-topographical factors must be taken into account.


transverse permanent displacement

high bending and tensile strains

longitudinal permanent displacement

tensile straincompressive strain

Ching-Shue tunnel before and after Chi-Chi earthquake


Failures at the portals of Ling-Leng tunnel (left) and Maa-Ling tunnel (right)

Slope failure above the western portal of the Malakassi C Tunnel. (E. Hoek & P. Marinos, 4th Report on Egnatia Highway Project, March 1999).


AfterwordCompared to permanent displacements, transient displacements effects are less detrimental regarding underground structure response, since transient displacements are not only... transient, but also related to significantly smaller magnitudes.For example, a very strong earthquake with predominant period 0.70sec and maximum ground acceleration amax = 0.80g, will result in transient displacements with a magnitude in the order of few centimeters only.Smax= amax T2/(2π)2 = 10 cm onlyIn comparison, the permanent displacement due to the fault rupture will well exceed 1.00m

On the other hand ... Transient displacements due to wave propagation affect the whole length of the underground structure (possibly several km), and not only the part of the structure located at the vicinity of the fault trace (+ 50m). Moreover, transient displacements due to wave propagation have a considerably smaller “return period” (100-500 years),compared to the return period of fault activation (10,000-100,000 years). Both these factors highlight the importance of transient displacement effects for the seismic design of underground structures.





PrefaceCompared to permanent displacements, transient displacements effects are less detrimental regarding underground structure response, since transient displacements are not only... transient, but are also related to significantly smaller magnitudes.For example, a very strong earthquake with predominant period 0.70sec and maximum ground acceleration amax = 0.80g, will result in transient displacements with a magnitude in the order of few centimeters only.Smax= amax T2/(2π)2 = 10 cm onlyIn comparison, the permanent displacement due to the fault rupture will well exceed 1.00m

On the other hand ... Transient displacements due to wave propagation affect the whole length of the underground structure (possibly several km), and not only the part of the structure located at the vicinity of the fault trace (+ 50m). Moreover, transient displacements due to wave propagation have a considerably smaller “return period” (100-500 years),compared to the return period of fault activation (10,000-100,000 years). Both these factors highlight the importance of transient displacement effects for the seismic design of underground structures.


Basic Assumptions• Harmonic seismic waves

•No sliding at the soil-structure interface

•kinematic soil-structure interaction effects can be ignored (flexibility factor F)

As a result of the last two assumptions,underground structure displacements are equal and in phase

with the surrounding soil displacements

( )3

32

)1(2)1(2

tvE

DvEF

ml

lm

+

−=

Εm=ground’s Young’s modulusΕl=structure’s Young’s modulusνm=ground’s Poisson ratioνl= structure’s Poisson ratioD=cross-section diametert=cross-section thickness

the 3rd assumption is valid when…

> 20

Example: steel pipeline (e.g. natural gas pipeline)

Εm=1GPa (Cs=400m/sec)Εl=210GPaνm=0.33νl= 0.2D=1mt=0.01m

F≅850>>20


Example: concrete tunnel (e.g. Metro tunnel)

Εm=1GPa (Cs=400m/sec)Εl=30GPaνm=0.33νl= 0.2D=10mt=0.25m

F≅385>>20

( )3

32

)1(2)1(2

tvE

DvEF

ml

lm

+

−=



> 20

Example: concrete sewage pipeline

Εm=1GPa (Cs=400m/sec)Εl=30GPaνm=0.33νl= 0.2D=2.5mt=0.1m

F≅95>>20

( )3

32

)1(2)1(2

tvE

DvEF

ml

lm

+

−=



> 20


All analytical expressions hereinafter refer to strains rather than stresses. That is due to the fact that wave propagation imposes transient deformations on underground structures, and not inertial forces, as in common aboveground structures. Design of underground structures aims at ensuring that the structure can sustain those deformations without failure.

All analytical expressions hereinafter refer to strains rather than stresses. That is due to the fact that wave propagation imposes transient deformations on underground structures, and not inertial forces, as in common aboveground structures. Design of underground structures aims at ensuring that the structure can sustain those deformations without failure.

Basic Assumptions• Harmonic seismic waves

•No sliding at the soil-structure interface

•kinematic soil-structure interaction effects can be ignored (flexibility factor F)

εαγ

εh

γ

Strain state of thin-walled underground structures

x

zy

A 3-D shell modeling the underground structure, when subjected to imposed displacements from the surrounding soil, will develop...

•axial strains εα•in-plane shear strains γ•hoop strains εh

The out-of-plane normal strains, and the shear strains at the inside and the outside face of the shell can be customarily ignored... (why??)

1


harmonic excitation: ( )⎟⎠⎞

⎜⎝⎛ −= CtxAuλπ2

sinmax

λ=wavelength C=propagation velocity t=time

disp

lace

men

t (u

)

period (T)

Amax

time (t)

diameter (D)

x

y

( )⎟⎠⎞

⎜⎝⎛ −

Α=

∂∂

== tCxx

up

xxa λ

πλ

πεε 2

cos2 max

( )⎟⎠⎞

⎜⎝⎛ −= tCxAu px λπ2

sinmax

P-wave propagating along the axis(xy plane)

ground strain=structure strain:

thus…p

a C

Vmaxmaxmax,

2=

Α=

λπ

εmaximumseismicvelocity

strain amplitude

plane view

2


No-slip assumption at the soil-structure interface →“shear beam” modelNo slip suggests zero relative displacements between “cross-sections”, thus zero bending strains.

y

x

A full-slip assumption at the soil-structure interface would suggest thatonly bending strains develop, and that shear strains are zero (“bending beam” model)

In the real world, some slippage will always occur, especially during strong excitationsThe conservative no-slip assumption is adopted for design purposes

S-wave propagating along the axis(xy plane)

y

x

( )⎟⎠⎞

⎜⎝⎛ −= tCxAu sy λπ2

sinmax

x

y

( )⎟⎠⎞

⎜⎝⎛ −=

∂

∂= tCx

C

V

x

us

s

y

λπγ 2

cosmax

plane view

adopting the “shear beam model”…

S

maxmax C

Vγ =



strain distribution along the cross-section

strains on a 3-D shell (except axial strain)

do not retain a constant value alongthe cross-section.

Strain distribution is a function of the polar angle α and, of course, time

strong motion axis

z

y

α

±γmax

±γmax

±γ=±γmaxcosαdirection of motion

0 45 90 135 180 225 270 315 360polar angle α (degrees)

-1.5

-1

-0.5

0

0.5

1

1.5

γ/|γ

max

|

t=to

t=to+T/2

±cosαα

angle α is measured clockwise, starting from z-axis

⊗propagation axis

ΔL/2

εmax=ΔL/L

L

direction ofpropagation

y

z

Transverse P-wave (yz plane)

ε12

ε11

εh,max=±εmax

( )⎟⎠⎞

⎜⎝⎛ −= tCyAu py λπ2

sinmax

ground strain:

y

u yy ∂

∂=ε

structure strain atpoints α & α’:

section viewα

α’

( )⎟⎠⎞

⎜⎝⎛ −== tCy

2cos

C

Vp

p

maxyh λ

πεε

3


α


axis of propagation& axis of strong motion

z

y


-1.5

-1

-0.5

0

0.5

1

1.5

ε h/|ε

h,m

ax|

t=to

t=to+T/2

±|cosα|

MX

α

εh,max

direction of motion

εh,max

εh=0

2

angle α is measured clockwise, starting from z-axis

Transverse S-wave (yz-plane)

γmax/2εh,max=γmax/2ε12

ε11

( )⎟⎠⎞

⎜⎝⎛ −= tCyAu sz λπ2

sinmax

ground strain:

y

uzyz ∂

∂=γ

structure strain:

γmax


y

z

section viewα

α’β

β’

( )⎟⎠⎞

⎜⎝⎛ −== tCy

2cos

C2

V2/ s

s

maxyz'&,h λ

πγε αα

( )⎟⎠⎞

⎜⎝⎛ −=−= tCy

2cos

C2

V2/ s

s

maxyz'&,h λ

πγε ββ


propagation axisz

y

α

strong motion axis


-1.5

-1

-0.5

0

0.5

1

1.5

ε h/|ε

h,m

ax|

t=to

t=to+T/2

±sin2α


Principal strains (tensile and compressive)are located at a plane inclined by ±45ο

γmax/2εh,max=γmax/2ε12

ε11

(why??)

compressionγmax/2

extensionγmax/2


x

z

Transverse S-wave (χz-plane)

( )⎟⎠⎞

⎜⎝⎛ −=

∂∂

= tCzC

V

z

us

s

x

λπγ 2

cosmax

( )⎟⎠⎞

⎜⎝⎛ −= tCzAu sx λπ2

sinmax

side view




-1.5

-1

-0.5

0

0.5

1

1.5

γ/|γ

max

|

t=to

t=to+T/2

±sin2α α

propagation axis

strong motion axis.

z

y

Transverse S-wave propagation results in shear structure strains(as in the case of S-wave propagation along the axis, at xy-plane)but with different strain distribution along the cross-section


Case εα,max γmax εh,max

P-wave along the axis(xy)

S-wave along the axis(xy)

Transverse P-wave (yz)

Transverse S-wave (yz)

Transverse S-wave (xz)

pCVmax

sCVmax

pCVmax

sCV

2max

sCVmax

Summarizing…


However, in the real world…a seismic wave will cross the axis of the structure under a random angle φ, measured at the plane defined by the structure axis and the wave propagation axis.

Orientation of this plane at the 3-D space is random (there is no practical way to predict it or define it)

φ

direction of wave propagation

structure axis

plane of wave motion

wave-structureplane

β

φ


Amax

-Amaxsinφ

Amaxcosφ

φ

direction of wave propagation

λ/cosφ

λ/sinφ

x

y

x'

structure axis

Amax

Amax

A SV-wave (the direction of motion coincides with the plane of propagation xy) can be analyzed into 4 “apparent” waves:

transverse P (xy plane)& transverse S (xy plane)-wavelength λ/sinφ-propagation velocity Cs/sinφ

P, S along the axis(xy plane)

-wavelength λ/cosφ-propagation velocity Cs/cosφ(the wave period is constant)

4

In order to estimate maximum design strains for this generic case, we must consider:

a) superposition of strains (distribution along the cross-section) that result from each “apparent” wave propagation.

b) maximization of the resulting expressions for strains, toeliminate the unknown angles φ & β

(angle β is the angle formed by the plane of strong motion and the plane of propagation, and is defined for S-waves only)


maximum strainsS-wave

(normalized over theVmax/Cs ratio)

P-wave

(normalized over theVmax/Cp ratio)

axial εα 0.50 1.00

shear γ 1.00 1.00

hoop εh 0.50 1.00

von Misses εvM 0.87/(1+ νl) 1.00/(1+ νl)

major principal ε1 0.71 1.00

minor principal ε3 -0.71 -1.00

Implementing this procedure for S- and P-waves propagating at a randomangle relatively to the structure axis, results in the following maximum design strains...

ATTENTION: Strain components do not attain these maximum values at the same position along the cross-section. Thus, simply adding them to derive von Misses and principal strains is an over-conservative approach.

5

Underground structures are located relatively close to the ground surface, and are subjected to surface Rayleigh wave effects too (e.g. at valleys, near slopes, at large distances from rupture)

A Rayleigh waves is equivalent to a P-wave and a SV-wave, propagating simultaneously and featuring a phase lag equal to π/2

ATTENTION: We should not just... add strains for a P-wave and a SV-wave propagating at the same angle φ in order to find the maximum strains, as maxima do not occur at the same time.

structure axisφx

x'y

z

P-componentRayleigh wave

S-component

However, in the real world…

6


Note:Rayleigh wave propagation velocity CR≅0.94 Cs is estimated at a depth z=1.0λR

maximum strainR-wave

(normalized over theVmax,V/CR ratio)

axial εα 0.68

shear γ 1

hoop εh 0.68

von Misses εvM 0.86/(1+ νl)

major principal ε1 0.68

minor principal ε3 -0.68

Maximum (after proper superposition) design strains for a Rayleigh wave propagating at a random angle relatively to the structure axis:

7

It is worth trying to verify the above expressions for Rayleigh waves at home!


Homework…

homogeneous soilCs=200m/sec και ν=1/3

steel pipeline

- D=1.5m, t=0.015m- εall

compression=40t/d (%)<5% (EC8)

- εallextension =2% for the main body

=0.5% for peripheralbutt welds

concrete tunnel

- D=10m, t=0.20m- εall

compression=0.35%- εall

extension=2%

Verify the structural integrity of the following structures:

Leukada 16/8/03 earthquake

0 5 10 15 20Time (s)

-0.4

-0.2

0

0.2

0.4

V (

m/s

)

Vmax=0.317m/sec

Justify the expressions that you apply for the estimation of seismic strains!


αrock

αsoil

Seismic waves propagate to the soil-bedrock interface at a random angle αrock, refract, and continue tothe soft soil layer

rock

soilrocksoil C

Ccosacosa =

the predominant period of the refracted wave

is not altered, thus...

rock

soilrocksoil C

Cλλ =

However, in the real world…Consider the case of an underground structure located in a soft soil layer, overlying the bedrock

soilCsoil

rockCrock

according to Snell’s law:

The refracted wave, propagating at an angle αsoil relatively to the structure, can be analyzed (as before) into apparent waves...

The horizontal apparent wave is equivalent to the apparent wave propagating along the soil-bedrock interface.

= rockhoriz

rock

λλ cosaand wavelength:

structure axis

αrock

αsoil

λtrans=λsoil/sinαsoil

λaxial=λsoil/cosαsoil

αsoil

λrock/cosαrock

= = ⇒

soilrock

soil rockhoriz

soil soilrock

rock

Cλλ Cλ cosa Ccosa

C

(projection)

A. a horizontal apparent wave with a propagation velocity Csoil/cosasoil …


1CCαcos1αcos1sinα

2

rock

soilrock

2soil

2soil ≈⎟⎟

⎠

⎞⎜⎜⎝

⎛−=−=

0 10 20 30 40 50 60 70 80 90αrock

0.84

0.88

0.92

0.96

1

sinα

soil

Csoil/Crock=0.5

0.333

0.25

0.125

on the other hand:

So, the “apparent” propagation velocity of the vertical apparent wave is practically equal to the wave propagation velocity in soft soil Csoil

(and λtrans=λsoil=Csoil T)

B. a vertical apparent wave with a propagation velocity Csoil/sinasoil …

Design strains are estimated via the superposition of strains along the cross-section, and the subsequent maximization of the resulting expressions for the unknown angles φ, β και αrock …

An extra, unknown parameter must be considered here, compared to the homogeneous rockmass case- the angle αrock

The above expressions are valid for Csoil/Crock ratio values less than 0.35. For Csoil/Crock>0.35 , results will be over-conservative, and the use of the corresponding expressions for homogeneous rockmass conditions is proposed.

normalized

strains S-wave

(C=CS)

P-wave

(C=CP)

axial εα 0.50Csoil/Crock 0.3Csoil/Crock

shear γ 0.43Csoil/Crock+0.98 2.0Csoil/Crock

hoop εh 0.36Csoil/Crock+0.50 0.5Csoil/Crock+1.0

von Misses εvM (0.38Csoil/Crock+0.85)/(1+νl) (0.58Csoil/Crock+1.0)/(1+νl)

major principal ε1 0.5Csoil/Crock+0. 5 0.63Csoil/Crock+1.0

minor principal ε3 -0.5Csoil/Crock-0. 5 -0.63Csoil/Crock-1.0

max

soil

VC

ε 8


ALA-ASCE 2001 aCVε max

a =

Vmax= peak ground velocity generated by ground shaking

C = apparent propagation velocity for seismic waves, conservatively (?) assumed to be equal to 2000 m/s.

a = 1 for P and R waves, 2 for S waves

StrainsS-wave

(C=CS)

P-wave

(C=CP)

axial εα 0.50·Vmax/Crock 0.3·Vmax/Crock

shear γ (0.98+0.43·Csoil/Crock) ·Vmax/Csoil 2.00·Vmax/Crock

hoop εh (0.50+0.36·Csoil/Crock) ·Vmax/Csoil (1.00+0.50·Csoil/Crock) ·Vmax/Csoil

Comparison to ALA-ASCE (2001) recommendations

input data:

Strains

Homogeneous rock Soft soil

Rayleigh wave

S-wave P-wave S-wave P-wave

axial εα 0.019% 0.019% 0.019% 0.005% 0.255%

shear γ 0.037% 0.019% 0.383% 0.037% 0.375%

hoop εh 0.019% 0.019% 0.201% 0.196% 0.255%

ALA-ASCE 2001

=0.037% (conservatively a=1)

Csoil=200m/secCrock=2000m/sec (bedrock)Cp=2CsVmax=75cm/sec

major discrepancy...!

aCVε max

a =

Comparison to ALA-ASCE (2001) recommendations


Homework…

Repeat the previous homework assignment for the case where the the structure is constructed near the surface of a homogeneous softsoil layer (CS,SOIL=200m/s), overlying the marl bedrock (CS,ROCK=700m/s).

Case studies of underground structures failures duringKobe & Chi-Chi earthquakes

0 30 km

24

120

30E

121E

121

30E

7

4

6

3

59

11

108

2


1failure sites

1

120cm/sec

60cm/sec


Case studies of underground structures failures duringKobe & Chi-Chi earthquakes

0 30 km

24

120

30E

121E

121

30E

1

7

4

6

3

59

8

108

2

Holocene alluvium

Pleistocene deposits

Miocene deposits

Oligocene deposits

Neocene deposits

Metamorphic rocks

bedrockepicenterrupture

23 30N

failure sites1

Soil classificationNEHRP (1997) CS (m/sec) This study CS (m/sec)

AHard rock CS>1500

AGranite bedrock 2000

BRocks 760<CS<1500

B1Cretaceous rocks (igneous and

metamorphic rocks, limestone, solid volcanic deposits)

1200

B2Stiff soils and soft rocks (Pleio-

Pleistocence sandstones, conglomerates, schists, marls)

850

CVery stiff soils/soft

rocks360< CS <760

CPleistocene clayey deposits, sands and

gravels550

DStiff soils 180< CS <360

DHolocence alluvium (sand, gravels,

clay) and man-made deposits250

ESoft soils CS<180

«soft soil»


spall

ing

longit

udina

l crac

ks

other

crack

s

shea

r crac

ks

circu

mferen

tial c

racks

steel

reinf

orce

ment b

uckli

ng

floor

uplif

t0

10

20

30

40nu

mbe

r of

rec

orde

d fa

ilur

es

34

18 18

15

8

2 2

Frequency of failure types

development of cracks wider than w>0.2mm

30.076 s cd Aw fβ= ⋅ ⋅ ⋅

crack width is related to the stress applied on the steel reinforcement bars(Gergely and Lutz, 1968, ACI Committee 224, 1995)

for a typical tunnel... fs,lim=140MPa

failure when: ε1*Εsteel >fs,lim

stresses higher than fs,lim suggest larger crack widths, or concrete spalling

«Failure criterion»


Number of failures

0

50

100

150

200

250

300

350

400

450

500

550

600

σ s (Μ

Pa)

this studyASCE-ALA/EC8fs,lim for crack width=0.2mm

14 19 29 38 47

soil type:A B1 B2 C D

proposed: 64%ASCE&EC8: 8%

a-posteriori failure prediction

Number of failures

0

50

100

150

200

250

300

350

400

450

500

550

600

σ s (Μ

Pa)

structures that failedstructures that survivedfs,lim for crack width 0.2mm

34 52 78 92 101

soil type:A B1 B2 C D

Prediction of actual structure response

proposed: 74%ASCE&EC8: 57%+ all non-successful predictions of ASCE & ΕC8

are non-conservative estimates


Afterword…

The presented analytical expressions are valid for flexible (F>20), and “infinitely long”underground structures. The stress state becomes more complicated in areas of bends andΤ-ees. However, analytical methodologies have been proposed for such cases too, and provide relatively accurate results. When the underground structure is constructed by discrete, jointed pieces, the flexibility of the joints must also be taken into account in the assessment of its response.

Generally speaking, when the in-situ conditions diverge significantly from the discussed assumptions, more elaborate numerical analysis tools must be applied for the seismic design of the underground structure. The structure is modeled as a beam or a shell, soil-structure interaction is simulated via elasto-plastic springs, and the seismic excitation is applied at the base of the springs that are used to model soil response.

An extensive presentation of such numerical methodologies is beyond the scope of this lecture. Their basic principles are however presented in the following case study,regarding the numerical stress analysis of a crude oil steel pipeline, due to the possible activation of a normal and a strike slip fault crossing its route (permanent ground displacements)


ANALYSISOF BURIED PIPELINESAT FAULT CROSSINGS

ANALYSISANALYSISOF BURIED PIPELINESOF BURIED PIPELINESAT FAULT CROSSINGSAT FAULT CROSSINGS

C.J. Gantes, G.D. BoukovalasDepartment of Civil Engineering

National Technical University of Athens

2Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS

NationalTechnicalUniversityof Athens

Contents of presentationContents of presentationContents of presentation

•• Pipeline Geometry, Material Properties & Construction TechniquesPipeline Geometry, Material Properties & Construction Techniques

•• Failure CriteriaFailure Criteria

•• Downthrows at Seismic FaultsDownthrows at Seismic Faults

•• Pipeline Modeling Pipeline Modeling -- Fault Movement ModelingFault Movement Modeling

•• Beam & Mixed Model Results Beam & Mixed Model Results -- Influence of Internal PressureInfluence of Internal Pressure

•• ConclusionsConclusions




Geometry, material properties and construction techniques

Geometry, material properties and Geometry, material properties and construction techniquesconstruction techniques

At the specific locations of active faults crossings, heavy wall NPS 16 line pipes with a wall thickness of 8.74mm will be installed, made of API-5LX60 steel.

The pipeline steel is modeled with a typical API-5LX60 tri-linear stress-strain curve based on the provisions of ASCE.

The nominal backfill cover varies from 0.60m in rocky areas to 0.90m in cross-country areas and 1.20m under major roads.


NationalTechnicalUniversityof Athens Pipeline material propertiesPipeline material propertiesPipeline material properties

0 2 4 6STRAIN (%)

0

200

400

600

ST

RE

SS

(M

Pa)

Tri-linear Idealization

Ramberg-Osgood

(σ1,ε1)

(minimum)Ultimate Tensile Strength

(σ2,ε2)

E=210.000 KPa

(minimum)Yield Strength

1

-600

-500

-400

-300

-200

-100

0

100

200

300

400

500

600

-0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06strain

stre

ss (

MP

a)




Failure criteriaFailureFailure criteriacriteria

Pipelines resist the imposed displacements mainly through axial (tensile or compressive) strains, thus it is more meaningful to talk in terms of strains

than stresses.

Considered Failure Criteria

1. Limiting compressive strain to avoid elastic or plastic buckle, associated with local wrinkling.

t

D0035.084.0e c* −=

For an NPS 16 in. x 8.74mm pipe the former expression yields 0.677%.



Failure criteriaFailure criteriaFailure criteria

2. Limiting the tensile strain for girth welds due to metallurgical alterations induced to the heat-affected zone during the welding process.

The allowable tensile strain for butt (peripheral) welding is conservatively taken as 5‰. The latter criterion is used throughout the analysis.

Relative ground movements caused by fault rupture are displacement-controlled The limiting strain is taken equal to 5‰

Section Conclusions




Downthrowsat seismic faults

DownthrowsDownthrowsat seismic faultsat seismic faults

Two fault types are considered:

•Normal fault

•Strike slip fault

The critical crossings are identified with reference to:

•Anticipated ground movements

•Geology at the area of crossing

•Angle of intersection between fault trace and pipeline axis



Εμπειρικές σχέσεις υπολογισμού της ΜΕΣΗΣ αναμενόμενηςμετατόπισης λόγω τεκτονικών διαρρήξεων Wells & Coppersmith, 1994). Οι ΜΕΓΙΣΤΕΣ αναμενόμενες μετατοπίσεις είναι περίπουδιπλάσιες.




Normal faultNormal Normal ffaultault

Fault geometry

XY

Pipeline axis

Fault trace

β

Anticipated downthrow DZ = 30 cm

( ) ( ) ( ) ( )βψβψ sincotcoscot ⋅⋅=⋅⋅= DZDYDZDX

For β=45° and ψ = 63° DX=DY=0.36DZ

XΖ

Pipeline axis

Fault trace

ψ



Strike slip faultStrike slip faultStrike slip fault

Fault geometry

Anticipated left lateral Slip S = 30 cm, β=80°

( ) ( ) SSDYSSDX 98.0sin17.0cos =⋅==⋅= ββ

XY

Pipeline axis

Fault trace

β




Pipeline modelingPipelinePipeline modelingmodeling

• Non linear FE Analysis for material behavior and large deformations are considered using NASTRAN.

• Two models, a beam (BM) and a mixed beam-shell model (MM) are used for the analysis.

• A straight pipeline segment of length 1200m is considered for both models and the fault rupture is applied in the middle.

•The Beam Model (BM) implements 3D beam elements, having the mechanical properties of a tube with 16” diameter and 8.74mm thickness made of API-5LX60 steel.

•The Mixed Model (MM) combines shell elements near the expected fault to capture stress concentrations, and 3D beam elements further away from the fault, where low stresses are expected. Coupling of shell and the beam part of the model is done with the use of rigid elements.




Coupling of shell and beam elements

X

Y

Z

V1L1C1G14




Modeling of soilaround buried pipelines

Modeling of soilModeling of soilaround buried pipelinesaround buried pipelines

The soil is modeled with four sets of inelastic springs, two in the local X-Y plane and two in the global vertical Z direction

where different upward and downward reactions occur

The soil springs are computed assuming cohesionless materials (sands) such as the backfill soil used along the pipeline route

Properties of the springs are calculated according toALA-ASCE (2005) guidelines for the seismic design of buried pipelines

(for sand trench backfill)




Transverse soil springs in the beam part of the modelGEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.45




Transverse soil springs in the shell part of the model




Transverse soil springs in the shell part of the modelGEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.46



Axial soil springsAxial soil springsAxial soil springs

Maximum axial soil force per unit length ofthe pipeline

0 1tan

2uT DHπ γ δΚ +⎛ ⎞= ⎜ ⎟⎝ ⎠

Δt= 3mm (dense sand)5mm (loose sand)

[sum of interface shear (friction) forces along the perimeter of the pipeline]

2 for a steel pipeline3δ φ≈



Transverse horizontal soil springs

Transverse horizontal Transverse horizontal soil springssoil springs

These springs simulate the resistance from the surrounding soils to any horizontal translation of the pipeline. Thus, the mechanisms of soil-pipeline interaction are similar to those of vertical anchor plates or

footings moving horizontally relative to the surrounding soils and thus mobilizing a passive type of earth pressure.

A = 0.15 yu/pu

B = 0.85/pu

pu = γ H Nqh DNqh=horizontal bearing capacity factor yu = 0.07 to 0.10 (H+D/2) for loose sand

0.02 to 0.03 (H+D/2) for dense sand

Relationship between force p per unit length and horizontal displacement y p

y

A B y=

+ ⋅




u qhP N HDγ=

bearing capacity factor for sand (Hanshen, 1961)

maximum lateral soil force per unit length

[passive earth pressure on a horizontally moving shallow footing]

Transverse horizontal soil springs

Transverse horizontal Transverse horizontal soil springssoil springs



Transverse vertical soil springs

Transverse vertical Transverse vertical soil springssoil springs

Nq, Nγ = bearing capacity factors for horizontal strip footings, vertically loaded in the downward direction

γ = effective unit weight of soil

γγγ ND5.0DNHq 2qu ⋅⋅⋅+⋅⋅⋅=

Downward Motions: the pipeline is assumed to act as a cylindrically-shaped strip footing and the ultimate soil resistance qu is given by conventional bearing capacity theory. For cohesionless soils the force per unit length is:






Nq, Nγ = bearing capacity factors for horizontal strip footings, vertically loaded in the downward direction

γ = effective unit weight of soil

γγγ ND5.0DNHq 2qu ⋅⋅⋅+⋅⋅⋅=

Downward Motions: the pipeline is assumed to act as a cylindrically-shaped strip footing and the ultimate soil resistance qu is given by conventional bearing capacity theory. For cohesionless soils the force per unit length is:

Meyerhof, 1965





Upward motions: Based on tests performed with pipes buried in dry uniform sand, the relationship between the force q and the vertical upward displacement z, has been shown to vary according to the following hyperbolic relation

A = 0.07 zu /qu

B = 0.93/qu

ultimate uplift resistance

qz

A B z=

+ ⋅

q H N Du qv= ⋅ ⋅ ⋅γ

The vertical uplift factor Nqv is a function of the depth to diameter ratio H/D and the friction angle of the soil φ

Trautmann & O’ Rourke, 1983




Load modelingLoad modelingLoad modeling

Fault activation is modeled as an imposed displacementat the base of the soil springs attached on one side of the fault line

Deformed shape

Fault movement



Load modelingLoad modelingLoad modeling

For the Mixed Model the internal pressure is modeled as a uniform load normal to the internal face of the shell elements. The nominal pressure is 10.2 MPa according to the specification of ASME.

P

The displacement field is imposed in a number of steps to capture eventual non-linearities in the pipe’s response with regard to fault rapture




Normal faultresults

NormalNormal ffaultaultrresultsesults

Beam Model – Deflected shape



Normal faultresults

NormalNormal ffaultaultrresultsesults

Beam Model – Axial spring stresses




Normal faultresults

Normal Normal ffaultaultrresultsesults

Beam Model – Strains

Beam Model – Stresses



Normal faultresults


Mixed Model – Deflected shapeGEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.52



Normal faultresults


Mixed Model – % difference of total translation due to internal pressure

Percentage Difference of Total Translation

-8%

-4%

0%

4%

8%

580 585 590 595 600 605 610 615 620

Pipe Length (m)

Dif

fere

nce

Disp 0.15 m

Disp 0.30 m



Normal faultresults


Mixed Model – Strains

Mixed Model – Stresses

Major Stress at Bottom Plane

0

100

200

300

400

500

580 585 590 595 600 605 610 615 620

Pipeline length (m)

Str

ess

(MP

a)

disp = 0,15 m

disp = 0,30 m

Major Strain at Bottom Plane

0.00%

0.05%

0.10%

0.15%

0.20%

0.25%

0.30%

580 585 590 595 600 605 610 615 620

Pipeline length (m)

Str

ain

disp = 0,15 m

disp = 0,30 m

No pressure




Normal faultresults




Pressure 10.2 MPa

Major Stress at Bottom Plane

0

100

200

300

400

500

580 585 590 595 600 605 610 615 620

Pipeline length (m)

Str

ess

(MP

a)

disp = 0,15 m

disp = 0,30 m


0.00%

0.05%

0.10%

0.15%

0.20%

0.25%

0.30%

580 585 590 595 600 605 610 615 620

Pipeline length (m)

Str

ain

disp = 0,15 m

disp = 0,30 m




With pressure

Displacement 0.15m


With pressure

Displacement 0.30m

Normal faultresults





Strike slip faultresults

Strike Strike sslip lip ffaultaultrresultsesults

Beam Model – Deflected shape





Beam Model – Axial spring stresses






Beam Model – Strains

Beam Model – Stresses





No PressureMajor Strain at Bottom Plane

0.00%

0.10%

0.20%

0.30%

0.40%

580 585 590 595 600 605 610 615 620

Pipeline length (m)

Str

ain

disp = 0.15 m

disp = 0.30 m


0.00%

0.10%

0.20%

0.30%

0.40%

580 585 590 595 600 605 610 615 620

Pipeline length (m)

Str

ain

disp = 0.15 m

disp = 0.30 m

Pressure 10.2 MPa







With pressure

Displacement 0.15m


With pressure

Displacement 0.30m





Analysis conclusionsAnalysis conclusionsAnalysis conclusions

• No failure of the pipeline at zones of active faults is expected.

• For the “strike-slip” fault case yielding of the pipeline at places near the fault is anticipated.

• Good agreement of the results from the two models for both studies is observed.




Construction countermeasures

Construction Construction countermeasurescountermeasures

Heavy wall sections near active faultsThis measure will increase the pipeline stiffness relative to that of the backfill and will lead to smaller curvatures and smaller internal strains

Arrangement of loose backfill around the pipe, extending beyond the anticipated displacement along the critical zone

Wrap the pipeline with a proper, friction reducing geotextile which will provide a lower friction coefficient

Enclose the pipeline within a casing, so that the pipeline can move freely along the intensely distorted length, on both sides of the fault trace



Construction countermeasures

Construction Construction countermeasurescountermeasures


7. seismic design of underground structures -...

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