Seismic Design and Risk
Assessment of Underground Long
Structures
Kyriazis Pitilakis
Sotiris Argyroudis and Grigoris Tsinidis
MONICO Workshop – 18 March 2011, Athens
Aristotle University
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE2
Underground structures - tunnels
• Mountain tunnels in rock conditions
• Subways
• Highway, railway, water and sewage tunnels in alluvial soils
• Metro stations
• Underground parking stations, commercial centers etc
• Their seismic design and risk assessment in seismically prone
areas is of major importance
• Public Safety - Economy
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
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Introduction
• Conceptual, geometrical, and operational features of
underground long structures, make their seismic behavior very
distinct from aboveground structures
• Imposed seismic ground deformations rather than inertial forces
dominate the structure’s seismic response
• Relative lack of well-documented case histories, lack of well
validated methodologies and lack of specific guidelines and
seismic code regulations for seismic design
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
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Introduction
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
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Summary
• To provide a short but comprehensive review of the analysis and
design methods of long underground structures
• To highlight and discuss some open issues mentioned before
• To provide a short review and ongoing research activities of
underground structures vulnerability and risk assessment under
seismic loading
• Example:
• an immersed tunnel that is planned to be constructed also in
Thessaloniki, is utilized as a typical example
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
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Contents
• Typology – construction methods – case studies
• Observed damages and behavior in past earthquakes
• Design principles in practice
• Determination of input motion
• Transversal seismic analysis
• Longitudinal seismic analysis
• Ground failure
• Importance of seismic design compared to static
• Real time risk assessment and Early Warning Systems
• Vulnerability of underground structures under seismic loading
• Conclusions
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
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Typology
Construction methods
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
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Typology
cut and cover (rectangular) bored tunnel (circular)
Power et al.,1996
cut and cover (vertical tubes)
cut and cover
(center columns or wall)
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
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Immersed tunnel Aktio-Preveza, Greece
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
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Bosporous-Marmara railway crossing, Turkey
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
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Athens Metro, Sepolia Station, Greece
Station Entrance
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
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Construction methods
• Bored linear underground structures (e.g. tunnels) – Usually
circular cross sections
• Cut and cover type structures (e.g. tunnels or subway stations,
parking and metro stations) - Rectangular cross sections
• Immersed structures (e.g. immersed tunnels) – Segmented
constructions connected through special joints
Before Initial Contact
roof
IPEGina gasket steel strip
gasket supporting plate
boltsroof
boltsgrout fill
steel stripOmega seal
bolts
After installation of Omega
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
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Example : Immersed highway tunnel
• 2.9 km cut and cover segmented tunnels
• 1.2 km immersed tunnel (8 segments, 155m each)
• 1.2 km conjunction ramps to the local road system
Section A-A :
immersed tunnel (2x3 lanes)
Section C-C :
cut and cover tunnel (1 lane)Section B-B :
cut and cover tunnel (2x3 lanes)
Section E-E :
cut and cover tunnel
(2x2 lanes)
Section D-D :
cut and cover tunnel
(3 lanes)
open entry rampfrom Kountouriotou Str.
entry tunnel branch
from Kountouriotou Str. open exit ramp
from Politechniou Str.
exit tunnel branchtowards Politechniou Str.
legends
immersed tunnel
cut and cover tunnels
open entry / exit ramps
service buildings
number of traffic lanes3
C
CE
E
Thermaikos Gulf
A
A
33
B
B
2
1
2
2
33
1
2
3
open exit ramp
towards M. Alexandrou Ave.
eastern cut and cover tunnel
immersed tunnel
service building C
open entry ramp
from Kaftantzoglou Str.
entry tunnel branch
from Kaftantzoglou Str.
open entry ramp
from M. Alexandrou Ave.
service building B
western
cut and cover
tunnel
open entry/exit ramp
at the new western
entrance of Thessaloniki
service building A
ΔΙΑΤΗ
ΡΗΤΕ
Ο
ΚΤΙΣΜ
Α ΟΣΕ
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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Cross section 35.1
8.8
1.11.30.6 1.45
1.3
1.1
17
7.5
P1 P2
Τ1Τ2
P3
Τ4Τ3
P4 P5 P6
17
SM-SC
Loose silty clayey sand
CL
Stiff sandy silty clay
SM-SC
Dense silty clayey sand
CL
Very stiff sandy clay
Section A-A
A-A
A-A
CL
Stiff sandy silty clay
CL
Very stiff sandy clay
Section B-B
B-B
B-B
GM
Well graded gravels -
sand mixtures
water - Thermaikos bay
0.00 m
-10.50 m
-14.50 m
-22.50 m
-30.50 m
-66.50 m
-110.50 m
Vs =130m/s, γ=18.6kN/m³
Vs =270m/s, γ=21.0kN/m³
Vs =380m/s, γ=21.5kN/m³
Vs =500m/s, γ=22.0kN/m³
Vs =700m/s, γ=22.0kN/m³
Compacted gravel material
Vs =380m/s, γ=21.5kN/m³tunnel cross section
Example : Immersed highway tunnel
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
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Observed damages and
behavior in past earthquakes
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
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Heavy
to moderate damages
when:
• Depth < 50m
• Soft soils
• PGA surf > 0.15g
• M > 6
• R < 50 km
Sarma et al, 1991
Seismic performance of tunnels
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
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Seismic performance of tunnels: Overview 1/2
• Underground structures seem less vulnerable than above ground
structures
• Deep or underground structures in rock seem to be safer
• Lined and grouted tunnels are safer than unlined tunnels in rock
• Damage from shaking can be reduced by stabilizing the ground
around a tunnel
• Structure vulnerability is better correlated with ground velocity
than peak ground acceleration
• Spatial variability of ground motion, together with the magnitude
Mw and epicentre distance R, are the main controlling parameters
for the seismic design and vulnerability assessment
Hashash et al., 2001
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
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Seismic performance of tunnels : Overview 2/2
• Duration of earthquake is of utmost importance because it may
cause fatigue failure and therefore, large deformations
• High frequency motions, expected mainly at small distances from
the causative fault, may explain the local spalling of rock or
concrete along planes of weakness
• Ground motion may be amplified if wavelengths are between one
and four times the tunnel diameter
• Damages manifested with slope instability near tunnel portals may
be significant
• Typical case of good performance: BART tunnel in San Francisco CA
design and constructed in ’60. (Loma Prieta earthquake, 1989,
Mw=6.9)
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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Observed damages in past earthquakes
• Collapse of the station
• Designed with poor seismic design considerations
Dakai subway, Kobe, 1995, Mw=6.9
Large space underground structures present certain particularities
compared to classical circular lined or unlined bored tunnels
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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• The main cause of collapse is due to the shear and buckling failure
of the centre columns, which were designed and constructed with
insufficient transverse shear reinforcement
Iida et al., 1996, Kawashima, 1999, Hashash et al., 2001
Dakai subway, Kobe, 1995, Mw=6.9
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
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Dakai subway, Kobe, 1995, Mw=6.9
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
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Dakai subway, Kobe, 1995, Mw=6.9
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
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Seismic behavior
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
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Seismic behavior
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
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• In general the inertial forces (accelerations) are lower for
underground structures
Mmax=683kNm
0.20g
0.37g
0.20g
0.62gMmax=444kNm
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
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• PGA is not the best parameter to evaluate the seismic performance of an
underground structure. The response and the seismic vulnerability of an
underground structure is controlled by the imposed seismic ground
deformations and not by the inertial forces
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE27
Deformation modes of
tunnels due to ground
shaking (travelling
seismic waves)
Seismic response – ground shaking
Owen & Scholl, 1981
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE28
Seismic behavior
• Shaking
• The imposed seismic ground deformations and the relative stiffness
or the stiffness contrast between the structure and surrounding soil,
control the overall seismic behaviour of an underground structure
• Ground failure
• The response is also controlled by the imposed permanent ground
deformations and displacements
• Large permanent deformations due to:
• Liquefaction : Settlements, lateral spreading
• Slope failure
• Fault movements
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE29
Design principles
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
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Design principles
Static analysis
Seismic analysis
1. Seismicity –
Earthquake design
criteria
MDE
Final analysis output and Design
Seismic hazard
(PSHA or DSHA)
2. Ground response
characteristics
Ground
shaking
3. Structure
seismic response analysis
and design
Transversal seismic
analysis
Longitudinal seismic
analysis
Ground
failure
ODE
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
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Design principles
• Design loading criteria
• Operational Design Earthquake (ODE) (10% in 50 years): The
structure remain in elastic range
• Maximum Design Earthquake (MDE) (5% in 50 years):
Prevention collapse, inelastic deformation acceptable, plastic
hinges occur, design to provide sufficient ductility to crucial
components of the structure (e.g. joints)
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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AUTH SDGEE32
• Total seismic and static loads
MDE U = D + L + E1 + E2 + EQ
ODE U =1.05D + 1.3L + (1.05-1.30)E1 + E2 + 1.3EQ
D : Dead loads
L : Live loads
E1 : Vertical loads (soils, water)
E2 : Horizontal loads (soils, water)
EQ : Seismic loads
max U for (max E2, min E1)• If the flexural strength of the structure lining, using elastic
analysis, is found not to be exceeded, no more check needed
• If it is exceeded, sufficient ductility (if it is possible) must be
provided
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
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Input motion
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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Design input motion
Seismic code regulations
• Practically inexistent
• Seismic regulations normally refer to aboveground structures
and usually to different return periods
Site specific seismic hazard analysis
• Mandatory
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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Required design input motion parameters
• Determination of seismic input for outcrop (Seismic Hazard)
• Site effects in free-field conditions (1D,2D,3D)
• PHGA, PVGA, PGV, PGD, PSA, PSV, Sd, strains (γ), and stresses (σ) at
the ground surface and at different depths
• Asynchronous motion characteristics (apparent velocity...),
differential displacements
• Induced phenomena and ground failure (liquefaction and liquefaction
induced phenomena, uplift, settlements, lateral spreading...), fault
displacement, landslide displacements
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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SW
Lateral
propagation
SH
1D
Design input motion considering complex 2D effects
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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Bedrock motion > Deconvolution design principles
Usually ground motion deconvolution method is applied to estimate,
from a known surface ground motion, the bedrock motion and finally the
FREE FIELD ground response at the level of each tunnel segment
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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22.7 22.75 22.8 22.85 22.9 22.95 23 23.05 23.1 23.15 23.2
40.4
40.45
40.5
40.55
40.6
40.65
40.7
40.75
40.8
100
120
140
160
180
200
220
240
260
280
300
320
340
360
380
400
0.15g
0.20g
0.24g
0.28g
Τm=475
Site specific seismic
hazard assessment
Thessaloniki T= 475
years
0.1
0.15
0.2
0.25
0.3
0.35
PHGA (g)
Design input motion
Metro
Immersed
roadway
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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0 5 10 15 20 25 30
Settlements (cm) due to liquefaction
0
0.05
0.1
0.15
0.2
0.25
Thessaloniki, Tm = 500 years
500 years PGV
Design input motion (PGV m/s) and liquefaction settlements
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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Design input motion in the longitudinal analysis
• Spatial variability of ground motion
• Time lag (Phase difference)
• Incoherency of the ground motion
Wavefront
1 2 3 1 2 3
epicenter
heterogeneity
1 2 3
epicenter
A
faultB
1 2 3
1 2 3: Underground structure
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Transversal seismic analysis
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Methods
• Equivalent static analysis
• Analytical close-form solutions
• Statically imposed seismic ground deformations
• Full dynamic time-history analysis
“Open” issues
• Estimation of seismic earth pressures
• Estimation of seismic shear stresses along the perimeter
• Impedance functions
• Modeling features
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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AUTH SDGEE43
• Seismic forces are acting as equivalent static inertial forces:
• Equivalent static forces: Calculated for an average acceleration
estimated along the structure’s depth. Applied either directly on the
structure or through springs
• Dynamic earth pressures: Limit - state Mononobe - Okabe approach
and seismic code regulations for non-deformable walls
• Hydrodynamic pressures: Westergaard theory
• Seismic shear stresses: Applied through the shear springs
Equivalent static analysis
H
λογH 0.5 aγH
1.5 aγH
H
i
β
δ
h
EAE
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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AUTH SDGEE44
• Equivalent static forces (case A)
Equivalent static analysis
(a)
(d)
(c) (b) (e)
(b)
(a)(c)(b) (e)(f)g2+q
structure's
weight +
inertia forces
soils weight + inertia forces
(a) geostatic pressures, (b) hydro-dynamic pressures, (c) hydrostatic pressures, (d) seismic shear stresses,
(e) seismic earth pressures, (f) dead (g2) and live loads (q)
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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AUTH SDGEE45
• Equivalent static forces (only dynamic part) (case B)
Equivalent static analysis
δx
structure's
weight +
inertia forces
soils weight + inertia forces
seismic shearstresses
springs-impedance
functionsKx,Ky
seismic shearstresses
bedrock
dynamic pressures
ground differential displacement
between surface and bedrock
hydro-dynamic pressures
hydro-dynamic pressures
dynamic pressures
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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AUTH SDGEE46
Equivalent static analysis
Open issues
• Impedance functions for underground structures ?
• Modeling of kinematic and inertial aspects of Soil-Structure
Interaction
• Seismic earth pressures considering structure’s flexibility
• Ground acceleration ?
• Seismic shear stresses in the perimeter ?
• Importance and effect of relative soil-structure flexibility ?
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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Example : Immersed roadway tunnel
• Model- loads (dynamic part)
a: Equivalent static inertial forces, b: Seismic earth pressure, c: Hydrodynamic pressures
Kwx
Kwz
Ksx
x
z F1=32.95kN/m
F2=5.90kN/m
1.5 aγΗ=76.44 kN/m
0.5aγΗ=
32.34 kN/m
(b)
(a)
(a)
Kzx
Kwz
Ksx
x
z
15.20 kN/m
26.95 kN/m
15.20 kN/m
26.95 kN/mKzx
(c) (c)
2B=34m
h=
7.5
m
D=
11
m
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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AUTH SDGEE48
Impedance functions – Kw,x Few are specifically for tunnels
Kwx
Kwz
Ksx Ksz
x
z
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE49
Impedance functions – Ks,x – Kb,z Few are specifically for tunnels
Kwx
Kwz
Ksx Ksz
x
z
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE50
Impedance functions – Ks,z – Kw,z Few are specifically for tunnels
Kwx
Kwz
Ksx Ksz
x
z
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE51
Analytical close-form solutions
Two categories:
• Solutions ignoring SSI effects
• Solutions taking into account SSI effects
Main assumptions:
• The soil behaves as elastic infinite homogeneous isotropic medium
• Elastic behavior for the structure
• Structure is modeled an elastic beam on elastic foundation in the
longitudinal direction
• Structure considered under plane strain conditions in the
transversal direction
• Full slip or no slip conditions may be considered for the soil-
structure interface
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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AUTH SDGEE52
Analytical close-form solutions with no SSI
• Νο SSI effects
• Circular cross section
Wang, 1993, Hashash et al., 2001
maxγΔd
d 2
max m
Δdγ v
d2 1
structure free fieldγ γ
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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AUTH SDGEE53
Analytical close-form solutions with no SSI
• SSI effects are not taken into account
• Rectangular cross section
Hashash et al., 2001
structure free fieldγ γ
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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AUTH SDGEE54
• SSI effects are taken into account in a simplified way
• Circular cross section
• Solutions for full slip
Analytical close-form solutions considering SSI
1 max
Δd 1K Fγ
d 3
mmax 1 max
m
E1T K Rγ
6 1 ν
2mmax 1 max
m
E1M K R γ
6 1 ν
m1
m
12 1-νK =
2F+5-6ν
όπου:
Wang, 1993
Moment:
Axial force:
2m l
l m m
E 1-ν RC
E t 1 ν 1- 2ν
2 3m l
l m
E 1-ν RF
6E I 1 ν
Compressibility
ratio
Flexibility
ratio
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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AUTH SDGEE55
• SSI effects are taken into account in a simplified way
• Circular cross section
• Solutions for no slip
Analytical close-form solutions considering SSI
όπου:
mmax 2 max 2 max
m
ET =±K τ r=±K Rγ
2(1+ν )
2
m m m
22
m m m m m
1F 1- 2ν - 1- 2ν C - 1- 2ν 2
2K 15
F 3 - 2ν 1- 2ν C C - 8ν 6ν 6 - 8ν2
Hoeg, 1968
Axial force:
2m l
l m m
E 1-ν RC
E t 1 ν 1- 2ν
2 3m l
l m
E 1-ν RF
6E I 1 ν
Compressibility
ratio
Flexibility
ratio
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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AUTH SDGEE56
• Rectangular cross section
Racking coefficient 1
structure
structure structure
free-fieldfree-field free-field
ΔΔ γHR= = = β( vs)
ΔΔ γ
HPenzien (2000)
“Racking” Approach (Penzien)
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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AUTH SDGEE57
• Rectangular cross section
• Estimation of free field deformations (through 1D analysis)
• Estimation of “flexibility ratio” F = soils stiffness/ structure stiffness
ΙR
ΙS
ΙW
Δstructure=R x Δfree field
W
H
E
2 2
m
w R
G H W HWF= +
24 EI EI
“Racking” Approach (Wang, Penzien)
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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AUTH SDGEE58
F 0 Rigid structureNo racking deformation will be
displayed
F<1.0Structure is stiffer than the
surrounding soil
Structural deformation smaller
than free-field deformation
level
F=1.0Structure and soil have
the same stiffness
Structure will follow the free-
field deformation
F>1.0 Soil stiffer than the structure
Structure racking deformations
amplified compared to the free-
field deformations
“Racking” Approach (Wang, Penzien)
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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AUTH SDGEE59
• Estimation of Δstructure through the racking evaluation
• “Static” analysis of the structure with the imposed Δstructure
F flexibility ratio
R=Δ
stru
ctu
re/Δ
free f
ield
Wang,1993
Circular Tunnels
Rectangular
Tunnels
“Racking” Approach (Wang)
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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AUTH SDGEE60
• Pseudo-Static numerical analysis
• Free-field ground deformations applied at the mesh soil boundaries
• Soil-structure interaction is explicitly taking into account
• 2D FE models utilizing 2D plain strain elements or springs for the
soil and beam elements for the structure
Imposed seismic ground deformations
Open issues
• Appropriate side-boundaries distances to the structure’s cross
section?
• Spring values in case of using this model
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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AUTH SDGEE61
• Case A : SSI modeling using soil springs
seismic shear
stresses
seismic shear
stresses
δ'x
Free Field
ux (m)
t (sec)
Free Field
ux (m)
t (sec)
t1
δx(t1)=
ux surface (t1)-
ux bedrock(t1) =max
δ'x
δx (t1)
springs-impedance
functions
Kx,Ky
bedrock
Max free-field ground
differential displacement
δ'x
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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AUTH SDGEE62
• Case B : Soil and SSI modeling through 2D plain strain elements -
the ground seismic displacements are imposed at the soil
boundaries
free field ground differential displacement
between surface and bedrock
Plain Strain
Finite Elements
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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AUTH SDGEESeismic design of large, long underground structures: Metro and parking stations, highway tunnels 63
Example : Immersed roadway tunnel
Model boundary
Initial
soil
layers
Δu=0.012m
d = 5.0m
z = -20.0m
Inclined bed
• Seismic ground deformations for the initial soil layers
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
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AUTH SDGEE64
Example : Immersed roadway tunnel
2D model
(ADINA FE code)
Full dynamic analysis
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AUTH SDGEE65
Example : Immersed roadway tunnel
water - Thermaikos bay
-10.50 m
-14.50 m
-22.50 m
-30.50 m
-66.50 m
-110.50 m
Vs =130m/s, γ=18.6kN/m³
Vs =270m/s, γ=21.0kN/m³
Vs =380m/s, γ=21.5kN/m³
Vs =500m/s, γ=22.0kN/m³
Vs =700m/s, γ=22.0kN/m³
Compacted gravel materialVs =380m/s, γ=21.5kN/m³tunnel cross section
Thessaloniki 1978
Surface
-6
-4
-2
0
2
4
6
A (
m/s
ec2)
Free Field (0.50g)Near the structure (0.39g)
z=-14.50m
-6
-4
-2
0
2
4
A (
m/s
ec2)
Free Field (0.39g)Near the structure (0.44g)
z=-22.50m
-4
-3
-2
-1
0
1
2
3
A (
m/s
ec2)
Free Field (0.28g)
Near the structure (0.27g)
z=-30.50m
-3
-2
-1
0
1
2
3
A (
m/s
ec2)
Free Field (0.27g)Near the structure (0.24g)
Input motion - Bedrock (0.24g)
-2
-1
0
1
2
A (
m/s
ec2
)Full dynamic analysis
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE66
Discussion
• Differential slab displacements (drift)
• Seismic earth pressures
• Seismic shear stress developed around the structure
• Bending moments, axial and shear forces on critical cross sections
• Accuracy of the impedance factors
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE67
a) Differential slab displacements (drift)
F-R analytical
solution
and
full dynamic analysis
are well compared
Example : Immersed roadway tunnel
Differential slab displacements (Thessaloniki 78)
-0.008
-0.004
0
0.004
0.008
d (
m)
Differential slab displacements (Kozani95)
-0.008
-0.004
0
0.004
0.008
d (
m)
Closed-form solution (Wang)
Full dynamic time-history analysis
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE68
• Due to the tunnel’s complex behaviour during ground shaking, the earth
pressures developed along the side-walls, vary between passive and active
limit state, reaching values between the two limit state earth pressures
Example : Immersed roadway tunnel
b) Seismic earth pressures
σyy Earth Pressure on tunnel wall
-7.5
-6.5
-5.5
-4.5
-3.5
-2.5
-1.5
-0.5
0 50 100 150 200 250 300 350
σyy(kPa)
z(m
)
Seismic pressure THESS
Seismic pressure KOZ
Rigid Wall E.A.K. 2003
Average (time history)
M.O.- uniformly distributed
M.O. triangularly distributed
M.O. passive
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE69
c) Seismic shear stresses
Example : Metro tunnel in Thessaloniki
1D site response analysis
MethodShear stress YZ (KN/m²)
Max Effective
1D FF Analysis (mean value) 95.0 66.5
1D FF Analysis (Kozani 95) 68.0 47.6
Dynamic Analysis (Kozani 95) 65.0-70.0 48.0
• 1D ground response analysis provides reasonable estimation of the
horizontal shear stresses
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE70
Example : Immersed roadway tunnel
• Comparison with soil shear strength (Mohr Coulomb)
• Solid connection between structure and soil, usually adopted in dynamic
analysis, does not always occur. Interface behavior maybe quite complex
• Side walls:
Effective shear stress at side walls
-7.5
-5
-2.5
0
-50 -25 0 25 50 75 100 125 150 175 200
σyz(kPa)
z(m
)
Thessaloniki time-history
Kozani time-history
Mohr-Coulomb limit stress
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE71
Example : Immersed roadway tunnel
• Roof slab:
Effective shear stress σyz at roof slab
-150
-100
-50
0
50
100
0 8.5 17 25.5 34
L (m)σyz (
kPa)
Thessaloniki time-history- Roof slab
Kozani time-history- Roof slab
Mohr Coulomb limit stress-Roof slab
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE72
Example : Immersed roadway tunnel
• Inverted slab:
Effective shear stress σyz at inverted slab
-50
0
50
100
150
200
250
0 8.5 17 25.5 34
L (m)
σyz (
kPa)
Thessaloniki time-history- Inverted slab
Kozani time-history- Inverted slab
Mohr Coulomb limit stress- Inverted slab
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE73
Example : Immersed roadway tunnel
• Side walls: Effective shear stresses applying different methods
Effective seismic shear stress σyz at the side walls (Kozani95)
-7.5
-5
-2.5
0
-60 -40 -20 0 20 40 60 80 100 120
σyz(kPa)
z(m
)
Dynamic analysis
Imposed seismic
ground deformations
Wang (mean value)
Wang (Initial soil
properties)
Wang (Gravel material
properties)
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE74
Example : Immersed roadway tunnel
• Roof slab: Effective shear stresses applying different methods
Effective seismic shear stress σyz at the roof slab (Kozani95)
-140
-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
0 8.5 17 25.5 34
L (m)
σyz (
kPa)
Dynamic analysis
Imposed seismic ground deformations
Wang (mean value)
Wang (Initial soil properties)
Wang (Gravel material properties)
..
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE75
Example : Immersed roadway tunnel
• Inverted Slab: Effective shear stresses applying different methods
Effective seismic shear stress σyz at the inverted slab
(Kozani95)
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
0 8.5 17 25.5 34
L (m)
σyz (
kPa)
Dynamic analysis
Imposed seismic ground deformations
Wang (mean value)
Wang (Initial soil properties)
Wang (Gravel material properties)
.
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE76
d) Section internal forces
• “Effective” values
Bending moment time - history (Thessaloniki78)
-2000
-1600
-1200
-800
-400
0
400
800
1200
1600
Bendin
g m
om
ent
(kN
m)
P4 left bending moment time history
Effective value (1123.8kNm)
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE77
Example : Immersed roadway tunnel
P1 P2
Τ1 Τ2
P3
Τ4Τ3
P4 P5 P6
Axial force results
-1250
-1000
-750
-500
-250
0
250
500
750
1000
P1 l
eft
P1 c
ente
r
P1 r
ight
P2 l
eft
P2 c
ente
r
P2 r
ight
P3 l
eft
P3 c
ente
r
P3 r
ight
P4 l
eft
P4 c
ente
r
P4 r
ight
P5 l
eft
P5 c
ente
r
P5 r
ight
P6 l
eft
P6 c
ente
r
P6 r
ight
T1 u
p
T1 d
ow
n
T2 u
p
T2 d
ow
n
T3 u
p
T3 d
ow
n
T4 u
p
T4 d
ow
n
Axia
l fo
rce (
kN
)
Imposed seismic ground deformationsDynamic analysis Equivalent static analysis
• Equivalent static - Imposed seismic ground displacements – Full
dynamic analysis
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE78
Example : Immersed roadway tunnel
• Equivalent static - Imposed seismic ground displacements – Full
dynamic analysisP1 P2
Τ1 Τ2
P3
Τ4Τ3
P4 P5 P6
Shear force results
-1000
-800
-600
-400
-200
0
200
400
600
800
P1 l
eft
P1 c
ente
r
P1 r
ight
P2 l
eft
P2 c
ente
r
P2 r
ight
P3 l
eft
P3 c
ente
r
P3 r
ight
P4 l
eft
P4 c
ente
r
P4 r
ight
P5 l
eft
P5 c
ente
r
P5 r
ight
P6 l
eft
P6 c
ente
r
P6 r
ight
T1 u
p
T1 d
ow
n
T2 u
p
T2 d
ow
n
T3 u
p
T3 d
ow
n
T4 u
p
T4 d
ow
n
Shear
forc
e (
kN
)
Imposed seismic ground deformationsDynamic analysis Equivalent static analysis
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE79
Example : Immersed roadway tunnel
P1 P2
Τ1 Τ2
P3
Τ4Τ3
P4 P5 P6
• Equivalent static - Imposed seismic ground displacements – Full
dynamic analysis
Bending moment results
-1750
-1500
-1250
-1000
-750
-500
-250
0
250
500
750
1000
1250
1500
P1 l
eft
P1 c
ente
r
P1 r
ight
P2 l
eft
P2 c
ente
r
P2 r
ight
P3 l
eft
P3 c
ente
r
P3 r
ight
P4 l
eft
P4 c
ente
r
P4 r
ight
P5 l
eft
P5 c
ente
r
P5 r
ight
P6 l
eft
P6 c
ente
r
P6 r
ight
T1 u
p
T1 d
ow
n
T2 u
p
T2 d
ow
n
T3 u
p
T3 d
ow
n
T4 u
p
T4 d
ow
n
Bendin
g m
om
ent
(kN
m)
Imposed seismic ground deformationsDynamic analysis Equivalent static analysis
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE80
Longitudinal seismic analysis
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE81
Longitudinal seismic analysis
• Full dynamic time history analysis utilizing continuum FE models
• Dynamic Beam on Winkler foundation type models
• Analytical closed form solutions
Open issues
• Asynchronous seismic ground motion
• Joints seismic performance and modeling, in case of segmented
underground structures (e.g. immersed tunnels)
• Impedance functions (springs and dashpots frequency depended)
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE82
• Seismic shaking varies in space in terms of wave amplitude, frequency
characteristics, time of arrival and duration
• Simplest modeling is with a phase difference approach
• Apparent velocity : Vapp (Cs) = 700 -1500 m/sec
• For tunnels min L = 100 m - 150 m (Kawashima et al.,1996)
• Time lag due to apparent velocity:
Asynchronous motion – Apparent velocity
θ tunnel
propagation direction
shear wave
iapp i+1 i
app
V LV t -t =
Vsinψ
ad
t
ad
t
ad
t
ad
t
t i t i+1 t i+2
Li LiLi
S1 S2 S3 S4
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE83
• Joints of segmented tunnels, consist of special joints (e.g. Gina) and
shear keys
• Joints (Gina-Omega Seal)
Joints seismic design and modeling
0 20 40 60 80 100 120
Compression (mm)
2500
0
250
500
750
1000
1250
1500
1750
2000
2250
Forc
e(kN
/m)
10
0
1
2
3
4
5
6
7
8
9
Conta
ct p
ress
ure
(N
/mm
²)
Force of endless seal Local contact pressure
Daewoo,2004
Material law for GINA gasket
Treleborg
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE84
Fy, Fz
δy, δz
< 5cm
• Shear keys
shear key
shear key
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE85
• Joints final design
roof
inverted slab
Shear Key
Detail A
Omega seal
Gina Gasket
TendonDetail A
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE86
Analytical close-form solutions with no SSI
• Analytical solution based on Newmark’s 1965 work
• SSI effects are not taken into account
St. John & Zahrah, 1987
Tunnel under simple
harmonic wave excitation
structure free fieldγ γ
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE87
Analytical close-form solutions with no SSI
• Tunnel under simple harmonic wave excitation
2
3c cc c
E I 2π 2πxM cos φE I Asin
ρ L L / cosφ
3
4c c
M 2π 2πxV cos φE I Acos
x L L / cosφ
c c
2π 2πxQ sinφcosφE A Acos
L L / cosφ
St. John & Zahrah, 1987
Moment:
Shear force:
Axial force:
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE88
• SSI effects are taken into account in a simplified way
• Elastic beam theory
Analytical close-form solutions considering SSI
όπου:
St. John & Zahrah, 1987
2
3
c c4
4c c
h
2πcos φ
2πxLM E I Asin
L / cosφE I 2π1 cos φ
K L
3
4
c c4
4c c
h
2πcos φ
2πxLV E I Acos
L / cosφE I 2π1 cos φ
K L
c c2
2c c
a
2πsinφcosφ
2πxLQ E A Acos
L / cosφE A 2π1 cos φ
K L
Moment:
Shear force:
Axial force:
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE89
• How can we calculate the soil stiffness ?
• Still, an open issue
• St. John & Zahrah, proposed:
Analytical close-form solutions considering SSI
όπου:
St. John & Zahrah, 1987
h a
ym
16πG 1 vP dK K
u 3 4v L
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE90
• Closed form solution
• Free field ground deformations (γstructure = γfree-field )
Longitudinal seismic analysis – Analytical solutions
3s s
axial u axial e2
s s
v αε = ×sinφ×cosφ+r× ×cos φ Δ ε l
C CPower et al.,1996
Example : Immersed roadway tunnel
Max joint deformation as function of Cs
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
500 750 1000 1250 1500 1750 2000 2250 2500Cs (m/sec)
Δu (
m)
Thessaloniki 78
Kozani 95
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE91
3s s
axial 2
s s
u axial e
v αε = ×sinφ×cosφ+r× ×cos φ
C C
ε l Power et al.,1996
Example : Immersed roadway tunnel
Max joint deformation as function of φ
0.000
0.005
0.010
0.015
0.020
0.025
0 10 20 30 40 50 60 70 80 90φ (deg)
Δu (
m)
Thessaloniki 78
Kozani 95
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE92
• Tunnel is modelled as a linear equivalent elastic beam on dynamic Winkler
foundation modelled with springs and dashpots
Beam on Dynamic Winkler Foundation Model
• Crucial issues for modelling:
• The joints’ behaviour (between segments) is
difficult to be modelled, as their stiffness is
varying with seismic excitation
• Asynchronous motion
• Soil springs and dashpots (frequency depended)
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE93
• Sensibility analysis: effect of phase difference, joints stiffness and
variability of soil properties along the tunnel axis
Example : Immersed roadway tunnel
time lagjoint
material law soil properties
Model A no linear Uniform soil - no damping
Model B yes linear Uniform soil - no damping
Model C yes linear Uniform soil - damping
Model D yes linear Variable soil - damping
Model E yes bi-linear Uniform soil - damping
Model F yes bi-linear Variable soil - damping
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE94
Example : Immersed roadway tunnel
• Joint axial deformations
Joint 5 axial deformation (Winkler models)
-0.225
-0.2
-0.175
-0.15
-0.125
-0.1
-0.075
-0.05
-0.025
0
0.025
δx(m
)
Model BModel CModel DModel EModel F
Hydrostatic pressure Seismic excitation
t = 0
sec
+ (tension)
- (compresion)
Joint Failure
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE95
Example : Immersed roadway tunnel
• Joint axial deformations
Thessaloniki 78
m
o
d
e
l
Joint 1 Joint 5 Joint 9
maxΔx
(m)
minΔx
(m)
maxΔx
(m)
minΔx
(m)
maxΔx
(m)
minΔx
(m)
A 0.058 -0.056 0.011 -0.01 0.059 -0.062
B 0.07 -0.061 0.045 -0.048 0.06 -0.058
C 0.07 -0.061 0.044 -0.046 0.06 -0.058
D 0.07 -0.057 0.099 -0.088 0.088 -0.049
E 0.07 -0.052 0.043 -0.039 0.059 -0.06
F 0.07 -0.052 0.099 -0.071 0.078 -0.05
analytical solution
(φ=0o, Cs=1000 m/sec)
0.0095 m
Joint 1
Joint 9
Joint 5
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE96
Ground failure
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE97
• Ground failure Large permanent deformations due to:
• Liquefaction
• Slope instability
• Fault displacements
• Liquefaction: pore water pressure build-up due to seismic excitation
reduction of effective stresses in saturated loose cohesionless silty sandy
soils deformations due to lateral spreading or settlements - uplift
• Liquefaction uplift mechanism: Study of retrofitting the BART system
Ground failure – Liquefaction
Kutter et al.,2008
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE98
• Centrifuge experiments and numerical analyses (FLAC, UBCSAND and
OpenSees (Elgamal et al.))
• Uplift mechanism related primarily to movement of soil under the tunnel
during an earthquake
Kutter et al.,2008
FLAC (Version 5.00)
LEGEND
17-Oct-07 5:59 step 879504
Flow Time 4.0000E+01Dynamic Time 4.0000E+01
-6.500E+01 <x< 6.500E+01 -1.300E+02 <y< -2.000E+01
User-defined Groups
MPSA_ClayOFill
SurmudFCourseSFill
Grid plot
0 2E 1
Displacement vectors
scaled to max = 3.000E+00
max vector = 2.885E+00
0 1E 1
-1.200
-1.000
-0.800
-0.600
-0.400
(*10 2̂)
-5.000 -3.000 -1.000 1.000 3.000 5.000(*10 1̂)
JOB TITLE :
fugro fugro
0
10
20
30
0 20 40 60 80 100 120 Ανύ
ψω
ση
Σή
ρα
γγα
ς (
cm
)
Πείραμα
FLAC
OpenSees
Tunnel
uplift
(cm
)
Travasarou & Chacko, 2008
Experiment
FLAC
OpenSees
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE99
• Differential shear displacements at joints (e.g. due to liquefaction lateral
spreading) are anticipated with the use of shear keys
• Liquefied soil soil-spring stiffness is usually reduced to 10% of their
initial values
• Two shear-slip scenarios are examined:
• (a) Uniform displacement (horizontal and vertical) imposed upon the tunnel
segment, while the segments next to it remain in their place
• (b) Differential displacement imposed upon the tunnel segment, due to
possible movement of the opposite segment
Example : Immersed roadway tunnel
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE100
• Horizontal shear key - b x d x l=1900x600x700 (mm)
• Vertical shear key - b x d x l=600x1650x700 (mm)
• Model adopted:
tunnel segment
shear key
restrains ux=uy=uz=0
displacement time history
Example : Immersed roadway tunnel
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE101
Concrete shear strength
1500 kN (without
considering the shear key
reinforcement and the
participation of the
tendons at the joint)
Horizontal lateral spreading displacement
Case (a) Case (b)
d (m) Vsd (kN) d (m) Vsd (kN)
0.10 3630 0.10 19200 15600
0.05 1815 0.05 9600 7800
0.01 363 0.01 1920 1560
Vertical displacement (settlements)
Case (a) Case (b)
d (m) Vsd (kN) d (m) Vsd (kN)
0.10 38150 0.10 51330 13160
0.05 19075 0.05 25665 6580
0.01 3815 0.01 5133 1316
Example : Immersed roadway tunnel
Concrete shear
strength 2600 kN
Extreme scenario
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE102
Importance of the seismic loads
compared to the static ones
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE103
• Static loads:
• Dead loads of the structure (g1+g2)
• Live loads of the structure (q)
• Hydrostatic pressures and uplift force at the structure (E1)
• Geostatic pressures at the structure (E2)
g1
Kwx
Kwz
KsxKsz
g1+g2
g1+g2+E1
g1
E1 E1
E1
E2 E2
g1+g2+q
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE104
Real Time
Early Warning
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE105
Different components and time scales in seismic risk
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE106
Basic concepts and measurements of earthquake early
warning systems
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE107
Time depended risk assessment
Hazard
Exposure/value
Vulnerability
Risk
Non-Poissonian recurrence
* * *
Population & economic growth
=
?
Foreshock
Aftershock
Retrofitting
Time
Evacuation
Time
Time
Time
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE108
Vulnerability assessment
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE109
Vulnerability assessment
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE110
Fragility Curves
• Empirical / statistical
• Analytical / numerical
• Expert judgment
• Hybrid
• Provide the probability for the element at risk to be in or exceed a certain
damage state under a seismic event of given intensity
• Illustration of the relationship between seismic excitation and damage
1.0
0.0
0.0
Damage
Probability
Seismic
Motion
Complete Damages
NOT FUNCTIONAL
Minor damage
FUNCTIONALITY
ai
Pf
Pc
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE111
Empirical fragility curves for tunnels (ALA, 2001)
• Fragility curves for tunnels with poor to average construction quality in soil
or cut and cover conditions, subject to ground shaking
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE112
General flowchart of the procedure for deriving
numerical fragility curves for tunnels in alluvial deposits
Tunnel typology
Basic models
Soil type
Typical soil profiles (P)
Seismic input motion
Accelerograms (A), intensity levels (S)
1D equivalent linear analysis of the soil profiles - input motions
models (PxAxS)
Quasi static response of the soil-tunnel
models
Soil deformations and soil stiffness parameters
Damage index (DI), damage states (ds),
thresholds values of DI for each ds
Evolution of damage with earthquake parameter (EP), median threshold
value of EP for each ds
Fragility curves for each tunnel and soil type
Uncertainties
(seismic demand, tunnel capacity, definition of DI and ds)
Argyroudis & Pitilakis 2011 (submitted)
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE113
Deformed Mesh
Extreme total displacement 43.07*10-3
m
(displacements scaled up 100.00 times)
Bending momentExtreme bending moment -84.28 kNm/m
Mmax=-84.3 kNm/m
Axial forcesExtreme axial force -692.68 kN/m
Nmax=-692.7 kN/m
b)
Tunnel response analysis
• A plane strain ground model and the tunnel cross sections are simulated
using the Plaxis finite element code (Plaxis, 2002)
• Shear deformations that are calculated by 1D linear equivalent soil
response analysis, for the different levels of peak ground acceleration are
imposed on the boundaries of the plain strain model
• Stresses and deformations of tunnel lining can be assessed due to the shear
distortion of the surrounding ground
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE114
Comparison Analytical vs Empirical (minor damage)
Circular (bored) tunnel - Minor damage
0.0
0.3
0.5
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
PGA (g)
Pro
ba
bilit
y o
f d
am
ag
e 0
soil D
soil C
soil B
Empirial - ALA 2001
(good quality construction)
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE115
Comparison Analytical vs Empirical (moderate damage)
Circular (bored) tunnel - Moderate damage
0.00
0.25
0.50
0.75
1.00
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
PGA (g)
Pro
ba
bilit
y o
f d
am
ag
e
soil D
soil Csoil B
Empirial - ALA 2001
(good quality construction)
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE116
Conclusions
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE117
• Input motions and seismic design loads must be estimated
through a detailed seismic hazard analysis, considering the
specific site effects due to local soil and site conditions
• There is no doubt that the most accurate method for seismic
design of extended underground structures is the full dynamic
time-history analysis, utilizing 2D or 3D FE, FD, BE models, and
adequate soil and structural models with appropriate
constitutive relationships. This approach can successfully model
the complex soil-structure interaction effects
• Underground structures should be designed for imposed seismic
ground deformations rather than inertial forces
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE118
• Analytical methods utilizing the racking coefficient method (i.e.
Wang, 1993), seems to give rather acceptable results, in case of
shallow underground structures (tunnels). Further improvement
and extension is deemed necessary
• Quasi-static imposed seismic ground deformation methods
combined with numerical modelling, provide an interesting
approach. Soil-structure interaction can be directly taken into
account.
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE119
• Equivalent static analysis is proved to be conservative for
shallow tunnels, while for subway stations and deep large
underground structures is clearly un-conservative
• In general it is unable to describe correctly all seismic
phenomena and the actual seismic response of the deep and
large spaced structures
• Issues, such as the estimation of appropriate impedance
functions for underground structures to model soils behaviour
and SSI effects, the modelling of equivalent static seismic
inertial forces, the estimation of seismic earth pressures, the
seismic shear stress developed during the shaking along the
perimeter of the structure, are still open, and more research is
deemed necessary
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE120
• Longitudinal seismic analysis of long segmented structures is
equally important with the transversal analysis. Asynchronous
ground motion must be absolutely considered in the analysis
procedure. Simple phase difference introducing a simple time
lag may not be always accurate enough. The apparent velocity
should be accurately estimated based on accurate geological and
geotechnical data. A conservative value of Capp = 800m/s could
be used. Special seismic design provisions must be taken for
joints and shear keys, as these elements are the most vulnerable
parts of an underground structure
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE121
• Ground permanent displacements due to liquefaction, slope
instability or fault rupture must be seriously taken into
consideration, as they can affect seriously the overall design and
safety of the structure
• Static loads and especially uplifting from buoyancy, are
controlling in general the overall design of an underground
structure
• Seismic loads are becoming very important when uplift buoyancy
loads are minimized, for PGA >0.2g (outcrop conditions) and
medium stiffness soils which amplifies considerably the ground
motion
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE122
• A research program is undergo in Aristotle University aiming to
provide specific answers to several of the subjects discussed,
namely:
- Seismic earth pressures for rigid and flexible structures
- Shear stresses development and distribution
- Impedance functions (frequency depended springs and
dashpots)
- Importance and quantification of structure’s flexibility
and to propose a solid methodology for the seismic analysis and
design of tunnels and large space underground structures
• Centrifuge test experiments in LCPC-Nantes and the University of
Cambridge will provide the necessary experimental validation and
breakthrough to better understand the physical problems and
validate the numerical modelling (SERIES project)
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE123
Moreover Aristotle University is participating in ongoing major EU
research projects aiming to contribute significantly to:
• the development of improved methods for the risk assessment
at system’s level considering intra and inter-dependencies in
the system’s vulnerability and risk assessment considering
buildings, facilities, lifelines and infrastructures, including
tunnels as parts of a global system
(SYNER-G http://www.syner-g.eu) Coordinator
• the real time seismic risk assessment of structures (buildings,
tunnels etc) with emphasis to the development of time
depended fragility (vulnerability) of elements at risk and
advanced, more efficient, early warning technology
(REAKT)
MONICO Workshop - Structural Monitoring and Assessment of Underground Transportation Facilities
March 18, 2011 - Athens, Greece
AUTH SDGEE124
Thank you