7. seismic design of underground structures -...
TRANSCRIPT
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.
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.2
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)
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.3
Rayleigh Pα
peripheral cracks
Rayleigh
Pα
concrete spalling(compression)
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.4
longitudinal cracks
Rayleigh
S
Rayleigh
S
shear cracks
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.5
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
23 30Nepicenterrupture
1failure sites
1
120cm/sec
60cm/sec
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.6
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
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.7
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
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.8
Permanent displacements
due to
SLOPEFAILURE
and due to liquefaction-inducedlateral spreading
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.9
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.
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.11
transverse permanent displacement
high bending and tensile strains
longitudinal permanent displacement
tensile straincompressive strain
Ching-Shue tunnel before and after Chi-Chi earthquake
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.12
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).
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.13
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.
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.14
Α. Earthquakes and Underground Structures
Β. Seismic design against “transient”displacements
C. Seismic design against “permanent”displacements
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.
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.15
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
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.16
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
+
−=
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: 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
+
−=
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
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.17
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
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.18
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
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.19
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 =
ground strain=structure strain:
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.20
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
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.21
α
strain distribution along the cross-section
axis of propagation& axis of strong motion
z
y
0 45 90 135 180 225 270 315 360polar angle α (degrees)
-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
direction ofpropagation
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
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.22
propagation axisz
y
α
strong motion axis
0 45 90 135 180 225 270 315 360polar angle α (degrees)
-1.5
-1
-0.5
0
0.5
1
1.5
ε h/|ε
h,m
ax|
t=to
t=to+T/2
±sin2α
strain distribution along the cross-section
Principal strains (tensile and compressive)are located at a plane inclined by ±45ο
γmax/2εh,max=γmax/2ε12
ε11
(why??)
compressionγmax/2
extensionγmax/2
direction ofpropagation
x
z
Transverse S-wave (χz-plane)
( )⎟⎠⎞
⎜⎝⎛ −=
∂∂
= tCzC
V
z
us
s
x
λπγ 2
cosmax
( )⎟⎠⎞
⎜⎝⎛ −= tCzAu sx λπ2
sinmax
side view
ground strain=structure strain:
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.23
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
±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
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…
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.24
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
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.25
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)
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.26
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
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.27
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!
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.28
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!
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.29
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 …
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.30
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
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.31
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
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.32
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
23 30Nepicenterrupture
1failure sites
1
120cm/sec
60cm/sec
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.33
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»
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.34
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»
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.35
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
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.36
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)
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.37
Β. Seismic design against “transient”displacements
Α. Earthquakes and Underground Structures
C. Seismic design against “permanent”displacements
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.38
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
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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
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.39
3Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS
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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.
4Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS
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)
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.40
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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%.
6Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS
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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
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.41
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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
8Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS
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Εμπειρικές σχέσεις υπολογισμού της ΜΕΣΗΣ αναμενόμενηςμετατόπισης λόγω τεκτονικών διαρρήξεων Wells & Coppersmith, 1994). Οι ΜΕΓΙΣΤΕΣ αναμενόμενες μετατοπίσεις είναι περίπουδιπλάσιες.
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.42
9Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS
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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
10Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS
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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
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.43
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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.
12Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS
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Pipeline modelingPipelinePipeline modelingmodeling
Coupling of shell and beam elements
X
Y
Z
V1L1C1G14
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.44
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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)
14Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS
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Pipeline modelingPipelinePipeline modelingmodeling
Transverse soil springs in the beam part of the modelGEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.45
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Pipeline modelingPipelinePipeline modelingmodeling
Transverse soil springs in the shell part of the model
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Pipeline modelingPipelinePipeline modelingmodeling
Transverse soil springs in the shell part of the modelGEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.46
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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≈
18Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS
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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=
+ ⋅
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.47
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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
20Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS
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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:
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.48
21Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS
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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:
Meyerhof, 1965
22Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS
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Transverse vertical soil springs
Transverse vertical Transverse vertical soil springssoil springs
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
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.49
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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
24Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS
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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
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.50
25Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS
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Normal faultresults
NormalNormal ffaultaultrresultsesults
Beam Model – Deflected shape
26Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS
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Normal faultresults
NormalNormal ffaultaultrresultsesults
Beam Model – Axial spring stresses
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.51
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Normal faultresults
Normal Normal ffaultaultrresultsesults
Beam Model – Strains
Beam Model – Stresses
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Normal faultresults
Normal Normal ffaultaultrresultsesults
Mixed Model – Deflected shapeGEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.52
29Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS
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Normal faultresults
Normal Normal ffaultaultrresultsesults
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
30Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS
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Normal faultresults
Normal Normal ffaultaultrresultsesults
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
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.53
31Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS
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Normal faultresults
Normal Normal ffaultaultrresultsesults
Mixed Model – Strains
Mixed Model – Stresses
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
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
32Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS
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Mixed Model – Strains
With pressure
Displacement 0.15m
Mixed Model – Strains
With pressure
Displacement 0.30m
Normal faultresults
Normal Normal ffaultaultrresultsesults
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.54
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Strike slip faultresults
Strike Strike sslip lip ffaultaultrresultsesults
Beam Model – Deflected shape
34Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS
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Strike slip faultresults
Strike Strike sslip lip ffaultaultrresultsesults
Beam Model – Axial spring stresses
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.55
35Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS
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Strike slip faultresults
Strike Strike sslip lip ffaultaultrresultsesults
Beam Model – Strains
Beam Model – Stresses
36Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS
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Mixed Model – Strains
Mixed 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
Major 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
Pressure 10.2 MPa
Strike slip faultresults
Strike Strike sslip lip ffaultaultrresultsesults
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.56
37Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS
NationalTechnicalUniversityof Athens
Mixed Model – Strains
With pressure
Displacement 0.15m
Mixed Model – Strains
With pressure
Displacement 0.30m
Strike slip faultresults
Strike Strike sslip lip ffaultaultrresultsesults
38Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS
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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.
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.57
39Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS
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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
40Gantes & Bouckovalas – ANALYSIS OF BURIED PIPELINES AT FAULT CROSSINGS
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Construction countermeasures
Construction Construction countermeasurescountermeasures
GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 7.58