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SYNER-G Final Workshop, Milano, 21-22 March 2013 1
Fragility functions of elements at risk
(WP3)
Amir M. Kaynia, NGI (WP3 Leader)
Sotiris Argyroudis, AUTH
Systemic Seismic Vulnerability and Risk Analysis
for Buildings, Lifeline Networks
and Infrastructures Safety Gain
SYNER-G Final Workshop, Milano, 21-22 March 2013 2
3.1 Fragility of buildings:
3.1.1 Fragility of RC buildings (UPAV)
3.1.1 Fragility of masonry buildings (UPAV)
3.2 Fragility of elements within utility networks:
3.2.1 Fragility of elements of electric power systems (UROMA)
3.2.2 Fragility of elements of gas and oil pipeline systems (BRGM)
3.2.3 Fragility of elements of water and waste-water systems (AUTH)
3.3 Fragility of elements within transportation infrastructures:
3.3.1 Fragility of elements of roadway bridges (UPAV)
3.3.2 Fragility of elements of road networks (NGI)
3.3.3 Fragility of elements of railway networks (NGI)
3.3.4 Fragility of elements of harbour systems (AUTH)
3.4 Fragility of elements within critical facilities:
3.4.1 Fragility of elements of health-care facilities (UROMA)
3.4.2 Fragility of elements of fire-fighting system (AUTH)
WP3 tasks
SYNER-G Final Workshop, Milano, 21-22 March 2013 3
Existing fragility curves
USA
(1997- ) (1998- )
Europe
(2001-2004) (2003-2006)
National research projects
• Italy: DPC-Eucentre convention, RELUIS
• Greece: SRM-LIFE (2003-2007), AsProGe (2003-2007)
Numerous research efforts (worldwide)
SYNER-G Final Workshop, Milano, 21-22 March 2013 4
- Review available fragility curves (typology, damage scales,
intensity measures, performance indicators)
- Select fragility curves based on SYNER-G taxonomy, through:
- Adapt/modify of existing ones
- Validation studies
- Develop new fragility curves
- Fragility Function Manager Tool (store, harmonize, compare)
- Link with SYNER-G software/code
SYNER-G contribution
SYNER-G Final Workshop, Milano, 21-22 March 2013 5
WP3 Tasks & Deliverables
Τ3.1 Fragility of
buildings
D3.1
Fragility Function
Manager tool
Τ3.2 Fragility of
elements within
utility networks
Τ3.3 Fragility of elements
within transportation
infrastructures
Τ3.4 Fragility of
elements within
critical facilities
SΤ3.1.1 RC
buildings (UPAV,
UPAT, JRC, METU)
SΤ3.1.2 Masonry
buildings (UPAV,
UPAT, JRC, METU)
D3.2
SΤ3.2.1 Electric
power (UROMA)
SΤ3.2.2 Gas and oil
(BRGM)
SΤ3.2.3 Water and
waste-water
(AUTH)
SΤ3.3.1 Bridges
(UPAT)
SΤ3.3.2 Road
(NGI, AUTH)
SΤ3.3.3 Railway
(NGI, AUTH)
SΤ3.3.4 Harbor
(AUTH)
SΤ3.4.1 Health-care
(UROMA)
SΤ3.4.2 Fire-
fighting (AUTH)
D3.3
D3.4
D3.5 D3.6
D3.7
D3.8
D3.9 D3.10
D3.11
Completed
To be completed (WP7)
D 3.12
(Synthetic, M36) Reference Report #4 www.syner-g.eu > Deliverables
SYNER-G Final Workshop, Milano, 21-22 March 2013 6
Fragility Curves
• Constitute one of the key elements in seismic probabilistic risk assessment.
• Relate the seismic intensity to the probability of reaching or exceeding a level of
damage (e.g. minor, moderate, extensive, collapse) for each element at risk.
• Usually described by a lognormal probability distribution function.
Different approaches:
- Empirical
- Expert Judgment
- Analytical
- Hybrid
1.0
0.0
Damage
Probability
Seismic
Motion
Complete Damages NOT
FUNCTIONAL
Minor damage
FUNCTIONALITY
IMi
Ρf
Ρc
SYNER-G Final Workshop, Milano, 21-22 March 2013 7
FRM/FRMM/P/E/C-CM/D/FS-FSM/RS-RSM/HL-NS/CL
Force Resisting Mechanism (FRM)
FRM Material (FRMM)
Plan (P)
Elevation (E)
Cladding (C)
Cladding Material (CM)
Detailing (D)
Floor System (FS)
Floor System Material (FSM)
Roof System (RS)
Roof System Material (RSM)
Height Level (HL)/Number of Stories (NS)
Code Level (CL)
Taxonomy of Buildings
SYNER-G Final Workshop, Milano, 21-22 March 2013 8
FRM/FRMM/P/E/C-CM/D/FS-FSM/RS-RSM/HL-NS/CL
Force Resisting Mechanism (FRM) Moment Resisting Frame, Bearing Wall..
FRM Material (FRMM) Masonry, Concrete, Fired Brick, Stone..
Plan (P) Regular, Irregular..
Elevation (E) Regular/irregular geometry..
Cladding (C) Regular/irregular vertically..
Cladding Material (CM) Fired brick, glazing, open first floor..
Detailing (D) Ductile, non-ductile, with tie-rods..
Floor System (FS) Rigid, flexible..
Floor System Material (FSM) RC, steel, timber..
Roof System (RS) Peaked, flat..
Roof System Material (RSM) Timber, thatch..
Height Level (HL)/Number of Stories (NS) Low, mid, high-rise, 1, 2, 3..
Code Level (CL) None, low code, mid code, high code..
Taxonomy of Buildings
SYNER-G Final Workshop, Milano, 21-22 March 2013 9
Taxonomy of Bridges MM1-MM2/TD1-TD2-DC/DSS/PDC/TP1-NP/TS1-TS2-HP/SP-SC/TCA/SK/BC/FT/SDL
Material (MM1)
Material (MM2)
Type of deck (TD1)
Type of deck (TD2)
Deck characteristics (DC)
Deck structural system (DSS)
Pier to deck connection (PDC)
Type of pier (TP1)
Number of piers per column (NP)
Type of section of piers (TS1)
Type of section of piers (TS2)
Height of pier (HP)
Spans (SP)
Span characteristics (SC)
Type of connection to abutments (TCA)
Skew (SK)
Bridge configuration (BC)
Foundation type (FT)
Seismic design level (SDL)
SYNER-G Final Workshop, Milano, 21-22 March 2013 10
Taxonomy of Bridges MM1-MM2/TD1-TD2-DC/DSS/PDC/TP1-NP/TS1-TS2-HP/SP-SC/TCA/SK/BC/FT/SDL
Material (MM1) concrete, masonry, steel, iron, wood, mixed
Material (MM2) reinforced concrete, pre-stressed concrete, unreinforced masonry, …
Type of deck (TD1) girder, arch, suspension, cable-stayed, moveable
Type of deck (TD2) solid slab, slab with voids, box girder, modern arch, ancient arch, …
Deck characteristics (DC) width
Deck structural system (DSS) simply supported, continuous
Pier to deck connection (PDC) monolithic, isolated, combination
Type of pier (TP1) single-column pier, multi-column pier
Number of piers per column (NP)
Type of section of piers (TS1) cylindrical, rectangular, oblong, wall-type
Type of section of piers (TS2) solid, hollow
Height of pier (HP)
Spans (SP) single-span, multi-span
Span characteristics (SC ) number of spans, span length
Type of connection to the abutments (TCA) free, monolithic, isolated
Skew (SK) straight, skewed
Bridge configuration (BC) regular or semi-regular, irregular
Foundation type (FT) shallow foundation, deep foundation
Seismic design level (SDL) no seismic design, low-code, medium-code, high-code
SYNER-G Final Workshop, Milano, 21-22 March 2013 11
Past Earthquake Damages
1. ground shaking
2. ground failure (liquefaction, fault displacement, slope instability).
Damage due to landslide Damage due to liquefaction Damage due to fault offset
SYNER-G Final Workshop, Milano, 21-22 March 2013 12
Past Earthquake Damages
3. Interactions
SYNER-G Final Workshop, Milano, 21-22 March 2013 13
Classification of Damage States
Definition of damage states for roadway
elements (embankments, trenches,
abutments, slopes) in SYNER-G
• qualitative/empirical, based on post-
earthquake damage statistics
• quantitative, based on damage indices
that define limit states of the structure
Permanent Ground Deformation (m)
Damage State min max mean
DS1. Minor 0.02 0.08 0.05
DS2. Moderate 0.08 0.22 0.15
DS3. Extensive/Complete 0.22 0.58 0.40
Damage state Description Serviceability
DS1 Minor/ Slight minor cracking and spalling and other minor distress to tunnel
liners
Open to traffic, closed or partially closed during inspection,
cleaning and possible repair works
DS2 Moderate Ranges from major cracking and spalling to rock falls
Closed during repair works for 2 to 3days
DS3 Heavy Collapse of the liner or surrounding soils to the extent that the tunnel is blocked either
immediately or within a few days after the main shock
Closed for a long period of time
Description of damage states for tunnels (ALA 2001)
SYNER-G Final Workshop, Milano, 21-22 March 2013 14
Recommended IMs for
different systems (D2.12)
Appropriate
earthquake intensity
measures (IM)
- best captures the response of
each element
- minimizes the dispersion of
response
- depends on the approach for
derivation of fragility curves
SYNER-G Final Workshop, Milano, 21-22 March 2013 15
Fragility Functions - Buildings
Methodologies
Reinforced Concrete
Masonry
SYNER-G Final Workshop, Milano, 21-22 March 2013 16
Fragility Functions - Buildings
Intensity Measure Types
Reinforced Concrete
Masonry
SYNER-G Final Workshop, Milano, 21-22 March 2013 17
Fragility curves -
Literature Review
Example of
review form
for buildings
SYNER-G Final Workshop, Milano, 21-22 March 2013 18
Fragility curves -
Literature Review
Example of
review form
for buildings
SYNER-G Final Workshop, Milano, 21-22 March 2013 19
Example of
review form
for bridges
Reviewer UPAT
Element at risk Bridge Element Code RDN01
Reference Choi et al, 2004
Method Analytical – nonlinear dynamic
Function Lognormal
Typology Multi-span RC and steel bridges
Damage states No Minor Moderate Major Collapse
Minor cracking, spalling of abutment; cracks in shear keys; minor spalling and cracks at hinges; minor spalling at column; minor cracking at deck
Moderate cracking and spalling of column; cracked shear keys or bent bolts of connection; moderate settlement of approach
Column degrading; connection losing bearing support; major settlement of approach
Column collapsing and connection losing all bearing support
Column μ < 2.0 μ < 4.0 μ < 7.0 μ > 7.0
Steel bearing δ < 6 mm δ < 20 mm δ < 40mm δ > 40 mm
Expansion bearing δ < 50 mm δ < 100 mm δ < 150mm δ > 150 mm
Fixed dowel δ < 100 mm δ < 150 mm δ < 255mm δ > 255 mm
Expansions dowel δ < 30 mm δ < 100 mm δ < 150mm δ > 150 mm
Functionality states
Seismic intensity parameter
Peak ground acceleration
Background 3-span simply supported or continuous highway bridges Schematic bridges, typical for Central and Southeastern United States, designed to modern USA code The numerical model included pile foundations, active and passive behaviour of abutments and pounding between deck sections Different span lengths, 100 artificial accelerograms
Figures
Deck type: (a) continuous (MSC) precast (b) continuous steel (c) simply supported (MSSS) precast (d) simply supported steel
Parameters (median values, β values)
Comments Vulnerability curves were produced for each component and then combined to
provide fragility curves for the complete bridge structure.
Literature Review
SYNER-G Final Workshop, Milano, 21-22 March 2013 20
• ATC (1985)
• Avşar et al. (2011)
• Azevedo et al. (2010)
• Banerjee and Shinozuka (2008)
• Basöz et al. (1999)
• Cardone et al. (2011)
• Ceresa et al. (2012)
• Choe et al. (2009)
• Choi et al. (2004)
• Elnashai et al. (2004)
• FEMA (2010)
• Franchin et al. (2006)
• Gardoni et al. (2003)
• Jeong and Elnashai (2007)
• Karim and Yamazaki (2001, 2003)
• Kibboua et al. (2011)
• Kim and Shinozuka (2004)
• Kurian et al. (2006)
• Lupoi et al. (2004, 2005)
• Mackie and Stojadinovic (2004, 2007)
• Marano et al. (2006)
• Monti and Nisticò (2002)
• Moschonas et al. (2009)
• Nateghi and Shahsavar (2004)
• Nielson and DesRoches (2007)
• Padgett and DesRoches (2009)
• Qi'ang et al. (2012)
• Saxena et al. (2000)
• Shinozuka et al. (2000)
• Shirazian et al. (2011)
• Sullivan (2010)
• Yamazaki et al. (2000)
• Yi et al. (2007)
• Zhang et al. (2008)
Variation of fragility curve parameters for the same typology
Literature Review – RDN01 Road Bridges
SYNER-G Final Workshop, Milano, 21-22 March 2013
66%14%
11% 7% 2%
PGASpectral accelerationPGVSpectrum intensityReturn period
44%
24%
18%
12% 3%
MDOF nonlinear dynamicSDOF nonlinear dynamicCapacity spectrumEmpiricalExpert opinion
21
Methodologies Intensity Measure types
Fragility Functions – Bridges
SYNER-G Final Workshop, Milano, 21-22 March 2013
Fragility Functions – Bridge Damage States
22
Definition of damage states for piers and bearings
Damage measure Reference Slight Moderate Extensive Complete
Drift ratio, δ/h Banerjee and Shinozuka (2008) 1.0% 2.5% 5.0% 7.5%
Yi et al. (2007) 0.7% 1.5% 2.5% 5.0%
Curvature, φ Avşar et al. (2011) φy φu
Cardone et al. (2008) φy 0.5φu φu
Choi et al. (2004) φy 2.0φy 4.0φy 7.0φy
Jeong and Elnashai (2007) φy φu
Nielson and DesRoches (2007) 1.3φy 2.1φy 3.5φy 5.2φy
Zhang et al. (2008) φy 2.0φy 4.0φy 7.0φy
Rotation, θ Qi’ang et al. (2012) θy 2.0θy 6.0θy 11.0θy
Saxena et al. (2000) θy 2.0θy 6.0θy 11.0θy
Shinozuka et al. (2000a) θy 2.0θy
Yi et al. (2007) θy 1.3θy 2.6θy
Displacement Monti and Nisticò (2002) 0.5δu 0.7δu δu
Shear deformation
of bearings, γ
Moschonas et al. (2009) 0.2 1.5 2.0 5.0
Zhang et al. (2008) 1.0 1.5 2.0 2.5
SYNER-G Final Workshop, Milano, 21-22 March 2013
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Pro
babili
ty
Peak ground acceleration (g)
Pier yielding Pier 1 L Pier 2 L Pier 3 L
Pier 1 T Pier 2 T Pier 3 T
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Pro
babili
ty
Peak ground acceleration (g)
Pier ultimate Pier 1 L Pier 2 L Pier 3 L
Pier 1 T Pier 2 T Pier 3 T
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Pro
babili
ty
Peak ground acceleration (g)
Bearings Pier 1 L Pier 2 L Pier 3 L
Pier 1 T Pier 2 T Pier 3 T
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Pro
babili
ty
Peak ground acceleration (g)
Angle V<120km/h Angle, 120<V<200km/hAngle, V>200km/h Curvature, V<120km/hCurvature, 120<V<200km/h Curvature, V>120km/h
Typologies:
Deck-pier connection: monolithic; through elastomeric bearings; combination
Transverse translation at the abutments: free; constrained
Pier cross-section: hollow rectangular;
wall-type; circular
Level of seismic design: EC2; EC8
Number of spans: 2; 3; 4; 6
Pier height: 10 m; 25 m
Damage measures: pier chord
rotation & shear force, bearing & deck
deformation
Damage states: yielding (limited use);
near collapse
Intensity measure: PGA
23
Numerical Analyses: Road and Railway Bridges
six-span bridge with continuous deck supported
on bearings and constrained transverse
translation at the abutments, designed to EC2
SYNER-G Final Workshop, Milano, 21-22 March 2013
Empirical curves: GAS06 Pipeline
Repair rate per km (ALA, 2001):
24
PGV in cm/s PGVKRR 002416.01
80% leaks
20% breaks
Wave
propagation K1: corrective factor based on pipe properties
SYNER-G Final Workshop, Milano, 21-22 March 2013
Repair rate per km (ALA, 2001):
25
PGD in cm 319.0
2 58.2 PGDKRR
20% leaks
80% breaks
Ground
failure
Empirical curves: GAS06 Pipeline
K1: corrective factor based on pipe properties
SYNER-G Final Workshop, Milano, 21-22 March 2013 26
• Katayama et al, 1975
• Eguchi, 1983
• ATC-13, 1985
• Isoyama & Katayama, 1982
• Memphis, Tennessee, 1985
• Wang et al, 1991
• O’ Rourke & Ayala, 1993
• Eidinger et al. 1995, Eidinger, 1998
• Isoyama, 1998
• O’Rourke et al,1998
• O’Rourke & Leon, 1999
• Eidinger & Avila, 1999
• Isoyama et al, 2000
• Toprak, 1998
• Hung, 2001
• O’Rourke & Deyoe, 2004
• Porter et al, 1991
• Honegger & Eguchi, 1992
• Heubach, 1995
• Eidinger et al,1999
• ΑLA, 2001a,b
• Yeh et al. 2006
• Ballantyne & Heubach, 1996
• O’Rourke et al, 2012
Empirical relation:
pipe material;
Peak Ground Velocity (PGV);
Repair rate per km
Empirical relation:
pipe material;
Permanent Ground Deformation (PGD);
Repair rate per km
Fragility curves - Literature Review
WSN05 Water Pipes
SYNER-G Final Workshop, Milano, 21-22 March 2013 27
Lefkas earthquake, 2003 (Mw=6.4)
!!
!
!
!
!
!
!
!
!
!
Legend
waterfsecond
! waterfailures
Waterpipes(PGVPGDEID)
break
leak
full-function
¯
240 0 240120 m
P8 P9
P10
P4
P3
P2
P1
P5
P6
P7
Recorded damages (points)
Estimated damages (lines)
(Eidinger & Avila 1999)
Validation Studies: WSN05 Water Pipes
Break
Leak
No damage
Wave Propagation (PGV) Permanent Deformations (PGD)
SYNER-G Final Workshop, Milano, 21-22 March 2013 28
HAZUS/NIBS (2004) – expert judgment
Roads with two traffic lanes
0.00
0.25
0.50
0.75
1.00
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40
PGD (m)
Pro
bab
ilit
y o
f exceed
an
ce
slight damage moderate damage extensive/complete
Roads with four or more traffic lanes
0.00
0.25
0.50
0.75
1.00
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40
PGD (m)
Pro
bab
ilit
y o
f exceed
an
ce
slight damage moderate damage extensive/complete
validation based on (limited) recorded damages from past earthquakes in Greece
Validation Studies: RDN06 Road pavements
SYNER-G Final Workshop, Milano, 21-22 March 2013
a Earthquake: Lefkas, 14/8/2003, M=6.4
Location: Golemi street-City of Lefkas
b Earthquake: Lefkas, 14/8/2003, M=6.4
Location: Sikelianou street -City of Lefkas
c Earthquake: Lefkas, 14/8/2003, M=6.4
Location: Road in Marina of Lefkas
d Earthquake: Lefkas, 14/8/2003, M=6.4
Location: Road in channel entrance from Aktio to Lefkas
e Earthquake: Lefkas, 14/8/2003, M=6.4
Location: Coastal road in Vasiliki
f Earthquake: Kozani, 13/5/1995, M=6.6
Location: Approach road to Rymnio bridge
g Earthquake: Peloponnisos, 8/7/2008, Μ=6.5
Location: Coastal road in Vrahneika
h Earthquake: Peloponnisos, 8/7/2008, Μ=6.5
Location: Road to Alissos
a Earthquake: Lefkas, 14/8/2003, M=6.4
Location: Golemi street-City of Lefkas
b Earthquake: Lefkas, 14/8/2003, M=6.4
Location: Sikelianou street -City of Lefkas
c Earthquake: Lefkas, 14/8/2003, M=6.4
Location: Road in Marina of Lefkas
d Earthquake: Lefkas, 14/8/2003, M=6.4
Location: Road in channel entrance from Aktio to Lefkas
e Earthquake: Lefkas, 14/8/2003, M=6.4
Location: Coastal road in Vasiliki
f Earthquake: Kozani, 13/5/1995, M=6.6
Location: Approach road to Rymnio bridge
g Earthquake: Peloponnisos, 8/7/2008, Μ=6.5
Location: Coastal road in Vrahneika
h Earthquake: Peloponnisos, 8/7/2008, Μ=6.5
Location: Road to Alissos
a Earthquake: Lefkas, 14/8/2003, M=6.4
Location: Golemi street-City of Lefkas
b Earthquake: Lefkas, 14/8/2003, M=6.4
Location: Sikelianou street -City of Lefkas
c Earthquake: Lefkas, 14/8/2003, M=6.4
Location: Road in Marina of Lefkas
d Earthquake: Lefkas, 14/8/2003, M=6.4
Location: Road in channel entrance from Aktio to Lefkas
e Earthquake: Lefkas, 14/8/2003, M=6.4
Location: Coastal road in Vasiliki
f Earthquake: Kozani, 13/5/1995, M=6.6
Location: Approach road to Rymnio bridge
g Earthquake: Peloponnisos, 8/7/2008, Μ=6.5
Location: Coastal road in Vrahneika
h Earthquake: Peloponnisos, 8/7/2008, Μ=6.5
Location: Road to Alissos
a Earthquake: Lefkas, 14/8/2003, M=6.4
Location: Golemi street-City of Lefkas
b Earthquake: Lefkas, 14/8/2003, M=6.4
Location: Sikelianou street -City of Lefkas
c Earthquake: Lefkas, 14/8/2003, M=6.4
Location: Road in Marina of Lefkas
d Earthquake: Lefkas, 14/8/2003, M=6.4
Location: Road in channel entrance from Aktio to Lefkas
e Earthquake: Lefkas, 14/8/2003, M=6.4
Location: Coastal road in Vasiliki
f Earthquake: Kozani, 13/5/1995, M=6.6
Location: Approach road to Rymnio bridge
g Earthquake: Peloponnisos, 8/7/2008, Μ=6.5
Location: Coastal road in Vrahneika
h Earthquake: Peloponnisos, 8/7/2008, Μ=6.5
Location: Road to Alissos
29
The validation indicates a good agreement between the
estimated and observed damage states.
Validation Studies: RDN06 Road pavements
SYNER-G Final Workshop, Milano, 21-22 March 2013 30
Numerical analyses: RDN01 Roadway bridges Typologies:
continuous deck; with intermediate joints
Deck-pier connection: monolithic; through elastomeric bearings; combination
Intensity Measure: Peak Ground Acceleration
Damage Scale: Yielding - limited (emergency) use; Near collapse
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Pro
babili
ty
Peak ground acceleration (g)
Pier yielding Pier 1 L Pier 2 L Pier 3 L
Pier 1 T Pier 2 T Pier 3 T
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Pro
babili
ty
Peak ground acceleration (g)
Pier ultimate Pier 1 L Pier 2 L Pier 3 L
Pier 1 T Pier 2 T Pier 3 T
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Pro
babili
ty
Peak ground acceleration (g)
Bearings Pier 1 L Pier 2 L Pier 3 L
Pier 1 T Pier 2 T Pier 3 T
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Pro
babili
ty
Peak ground acceleration (g)
Angle V<120km/h Angle, 120<V<200km/hAngle, V>200km/h Curvature, V<120km/hCurvature, 120<V<200km/h Curvature, V>120km/h
six-span bridge with continuous
deck supported on bearings and
constrained transverse translation
at the abutments, designed to EC2
SYNER-G Final Workshop, Milano, 21-22 March 2013 31
Numerical analyses: Geotechnical structures
`
Dam
age In
dex
Intensity Measure ln IMmi
ln D
I (d
si)
βD
βD
Evolution of damage with earthquake intensity measure (IM) and definition of threshold median value (IMmi)
for the damage state i (dsi). Definition of standard deviation (βD) due to variability of input motion (demand).
SYNER-G Final Workshop, Milano, 21-22 March 2013 32
Numerical analyses: RDN07 Abutments
Typologies: Cantilever wall
Height (h): 6; 7.5 m
Ground depth (H): 50 m
Ground types (EC8): C; D
Intensity Measure: PGA free field
Damage Scale:
Minor; Moderate; Extensive/Complete
Damage Measures:
Settlement on the backfill
Analysis:
1D equivalent linear analysis (EERA)
2D dynamic FE models (PLAXIS)
5 records (x 0.1, 0.2, 0.3, 0.4, 0.5g)
t2
t3
L
h
Backfill
Bedrock
SoilH
t1
200kN
EQ
Bridge deck
Argyroudis et al 2013
SYNER-G Final Workshop, Milano, 21-22 March 2013 33
Numerical analyses: RDN07 Abutments
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Pro
ba
bili
ty o
f d
am
ag
e
PGA free field (g)
Minor damage-h=6.0m
Moderatedamage-h=6.0m
Extensivedamage-h=6.0m
Minor damage-h=7.5m
Moderatedamage-h=7.5m
Extensivedamage-h=7.5m
Soil C
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Pro
babili
ty o
f .
dam
ag
e
PGA free field (g)
Minor damage-h=6.0m
Moderatedamage-h=6.0m
Extensivedamage-h=6.0m
Minor damage-h=7.5m
Moderatedamage-h=7.5m
Extensivedamage-h=7.5m
Soil C
Soil D
SYNER-G Final Workshop, Milano, 21-22 March 2013 34
Potable Water System (Sub-Task 3.2.3) Numerical analyses: RDN02 Tunnels (in alluvial)
Typologies:
Circular (Bored); Rectangular (Cut & Cover)
Ground depth: 30; 60; 120 m
Ground types (EC8): B; C; D
Intensity Measure: PGA free field
Damage Scale: Minor; Moderate; Extensive
Damage Measure: exceedance of lining strength capacity
Analysis:
1D equivalent linear analysis (EERA)
> 3 records x 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7g
seismic ground deformations
2D FE models (PLAXIS) – Psevdostatic analysis
Elasto-plastic soil behaviour
Argyroudis & Pitilakis 2012
SYNER-G Final Workshop, Milano, 21-22 March 2013 35
Potable Water System (Sub-Task 3.2.3) Numerical analyses: RDN02 Tunnels (in alluvial)
SYNER-G Final Workshop, Milano, 21-22 March 2013 36
Potable Water System (Sub-Task 3.2.3) Numerical analyses
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Pro
ba
bili
ty o
f d
am
ag
e
PGA free field (g)
Minor damage-h=4m
Moderatedamage-h=4m
Extensivedamage-h=4m
Minor damage-h=2m
Moderatedamage-h=2m
Extensivedamage-h=2m
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Pro
babili
ty o
f d
am
ag
e
PGA free field (g)
Minor damage-h=4.0m
Moderatedamage-h=4.0m
Extensivedamage-h=4.0m
Minor damage-h=6.0m
Moderatedamage-h=6.0m
Extensivedamage-h=6.0m
Soil C
Soil D
RDN04 Trenches
RDN03 Embankments
SYNER-G Final Workshop, Milano, 21-22 March 2013 37
Potable Water System (Sub-Task 3.2.3) Fault tree analysis:
Physical components of Health Care Facilities
Object Demand Distr. Mean cv References
Cylinders Acceleration LN 0.50g 0.25 Expert judgment
Pipes Drift LN 0.90% 0.25 Kuwata and Takada, 2003
Probabilistic characterization of the capacity of the medical gas system
HCS03-5: Medical Gas
SYNER-G Final Workshop, Milano, 21-22 March 2013
38
Fragility Function Manager Tool
Store, Visualize, Manage large number of fragility functions sets
SYNER-G Final Workshop, Milano, 21-22 March 2013 39
THANK YOU
FOR YOUR ATTENTION!
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