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![MDOF
Simplification of 3D or 2D structures into a SDOF
he equivalent SDOF system can be either elastic or inelastic de-
ending on the chosen inelastic analysis method (see Section
.1.3).
he computation of the pushover curve and the subsequent deter-
mination of the properties of the equivalent SDOF system are thor-
ughly discussed in Section 7.2.
Global deformations ∆
Detailed
model
Static force
sing monotonically
m*
h*k*
Equivalent SDOF
system
0
1
2
3
0.0 0.1 0.2 0.3
Global deformation ∆ [m]
HorizontalforceV[MN]
ushover curve“
linear, inelastic
ormation relationship
ndamentals of Seismic Design”
Substitute SDoF structure
Effective displacement
(design displacement)
Effective mass
Effective height ( ) ( )¦¦
==
∆∆=
n
i
ii
n
i
iiie
mHmH
11
/
( ) ( )¦¦
==
∆∆=∆
n
i
ii
n
i
iid
mm
11
2
/
( ) d
n
i
iie
mm ∆∆= ¦
=
/
1
He
me
He
me ∆d
∆i
∆i-1
∆3
∆2
∆1
He
me
He
me ∆d
∆i
∆i-1
∆3
∆2
∆1
Cours
SDOF
Definition of structural models for vulnerability analysis
−0.25 −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25
−0.5
−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
0.5
Sd [m]
Sa[g]
sdof
pinching4
Hysteresis model](https://image.slidesharecdn.com/05-ccaravulnerability-180517141444/75/05-ccara-vulnerability-17-2048.jpg)
![Derivation of Fragility/Vulnerability functions
Ground motion
records
Single degree of
freedom systems
Period of vibration (sec)
10
-1
10
0
Spectralacceleration(g)
10
-4
10
-3
10
-2
10
-1
10
0
101
median spectrum
+1/-1 sigma spectrum
individual spectrum
Spectral displacement (m)
0 0.1 0.2 0.3 0.4 0.5
Spectralacceleration(g)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
median curve
+1/-1 sigma curve
sampled curve
Risk Modelers
Toolkit
Spectral acceleration at 0.3 s [g]
0 0.2 0.4 0.6 0.8 1 1.2
Probabilityofexceedance
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Limit state 1
Limit state 2
Limit state 3
Limit state 4](https://image.slidesharecdn.com/05-ccaravulnerability-180517141444/75/05-ccara-vulnerability-22-2048.jpg)
Uploaded bySergio Navarro Hudiel
05 ccara vulnerability
This document discusses the development of a global vulnerability database. It describes estimating earthquake losses using characteristics of past seismic events. It discusses challenges in developing fragility models for different regions and building classes. It also describes the process of deriving fragility and vulnerability functions, including defining structural models, selecting ground motion records, and using the models to estimate damage and losses. Calibration and validation of the models is emphasized.
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More from Sergio Navarro Hudiel
05 ccara vulnerability
- 1. Development of aGlobal Vulnerability Database Vitor Silva, Seismic Risk Coordinator On behalf of the risk team April 2017 – Pavia, Italy
- 2. Estimation of earthquakelosses Using the characteristics of past seismic events 18° E 18° E 16° E 16° E 14° E 14° E 12° E 12° E 10° E 10° E 8° E 8° E 46° N 46° N 44° N 44° N 42° N 42° N 40° N 40° N 38° N 38° N 36° N 36° N Residential value (EUR) 2.0e+009 - 6.5e+009 6.6e+009 - 8.4e+009 8.5e+009 - 9.3e+009 9.4e+009 - 1.1e+010 1.2e+010 - 1.6e+010 1.7e+010 - 2.6e+010 2.7e+010 - 4.9e+010 5.0e+010 - 1.0e+011 Ground shaking Exposure
- 3. Estimation of earthquakelosses - Masonry No damage Seismic Intensity Extensive damage Slight damage Collapse
- 4. Estimation of earthquakelosses - RC No damage Seismic Intensity Extensive damage Slight damage Collapse
- 5. Estimation of earthquakelosses - Wooden No damage Seismic Intensity Extensive damage Slight damage Collapse
- 6. Estimation of earthquakelosses Seismic Intensity 0.00 0.20 0.40 0.60 0.80 1.00 0 0.2 0.4 0.6 0.8 1 1.2 Probabilityofexceedance Peak ground acceleration (g) Slight Moderate Extensive Collapse
- 7. Estimation of earthquakelosses Using the characteristics of past seismic events 18° E 18° E 16° E 16° E 14° E 14° E 12° E 12° E 10° E 10° E 8° E 8° E 46° N 46° N 44° N 44° N 42° N 42° N 40° N 40° N 38° N 38° N 36° N 36° N Residential value (EUR) 2.0e+009 - 6.5e+009 6.6e+009 - 8.4e+009 8.5e+009 - 9.3e+009 9.4e+009 - 1.1e+010 1.2e+010 - 1.6e+010 1.7e+010 - 2.6e+010 2.7e+010 - 4.9e+010 5.0e+010 - 1.0e+011 0.00 0.20 0.40 0.60 0.80 1.00 0 0.2 0.4 0.6 0.8 1 1.2 Probabilityofexceedance Peak ground acceleration (g) Slight Moderate Extensive Collapse Ground shaking Exposure
- 8. Estimation of earthquakelosses Using the characteristics of past seismic events 18° E 18° E 16° E 16° E 14° E 14° E 12° E 12° E 10° E 10° E 8° E 8° E 46° N 46° N 44° N 44° N 42° N 42° N 40° N 40° N 38° N 38° N 36° N 36° N Residential value (EUR) 2.0e+009 - 6.5e+009 6.6e+009 - 8.4e+009 8.5e+009 - 9.3e+009 9.4e+009 - 1.1e+010 1.2e+010 - 1.6e+010 1.7e+010 - 2.6e+010 2.7e+010 - 4.9e+010 5.0e+010 - 1.0e+011 Ground shaking Exposure 0.00 0.20 0.40 0.60 0.80 1.00 0 0.2 0.4 0.6 0.8 1 1.2 Probabilityofexceedance Peak ground acceleration (g) Slight Moderate Extensive Collapse LossesDamage
- 9. Lack of vulnerabilitymodels globally
- 10. Challenges in regionalfragility assessment 1. Large number of building classes. 2. Variety of failure mechanisms and hysteresis behavior. 3. Select ground motion records compatible with the tectonic environment 4. Need to maintain consistency in the damage criterion. 5. Need to propagate the three main sources of uncertainty: 1. Record-to-record variability 2. Building-to-building variability 3. Damage definition uncertainty
- 11.
- 12. Building classification forGreece 0% 10% 20% 30% 40% 50% RC (4-6 floors) Mod duc?lity RC (4-6 floors) High duc?lity RC (7-12 floors) Mod duc?lity RC (7-12 floors) High duc?lity Masonry (<3 floors) Concrete block Masonry (<3 floors) Field stone RC (<3 floors) Mod duc?lity RC (<3 floors) Mod duc?lity RC (<3 floors) High duc?lity RC (4-6 floors) Non duc?le Urban Rural
- 13. Chile USA Mexico Costa Rica Ecuador Portugal ItalyTurkeyGreece Iran Japan Selection of ground motion records Indonesia Colombia
- 14. Selection of groundmotion records Collection of records for the region according to the tectonic environment Period of vibration (sec) 10 -1 10 0 Spectralacceleration(g) 10 -4 10 -3 10 -2 10 -1 10 0 10 1 median spectrum +1/-1 sigma spectrum individual spectrum
- 15. Derivation methodology Nonlinear dynamicanalyses on 2D/3D MDOF systems Nonlinear static procedures (e.g. N2, CSM) or direct fragility methodologies (e.g. SPO2IDA) Accuracyandreliability Computationaleffort
- 16. Derivation methodology Nonlinear dynamicanalyses on 2D/3D MDOF systems Nonlinear static procedures (e.g. N2, CSM) or direct fragility methodologies (e.g. SPO2IDA) Accuracyandreliability Computationaleffort Nonlinear dynamic analyses on SDOF systems
- 17. MDOF Simplification of 3Dor 2D structures into a SDOF he equivalent SDOF system can be either elastic or inelastic de- ending on the chosen inelastic analysis method (see Section .1.3). he computation of the pushover curve and the subsequent deter- mination of the properties of the equivalent SDOF system are thor- ughly discussed in Section 7.2. Global deformations ∆ Detailed model Static force sing monotonically m* h*k* Equivalent SDOF system 0 1 2 3 0.0 0.1 0.2 0.3 Global deformation ∆ [m] HorizontalforceV[MN] ushover curve“ linear, inelastic ormation relationship ndamentals of Seismic Design” Substitute SDoF structure Effective displacement (design displacement) Effective mass Effective height ( ) ( )¦¦ == ∆∆= n i ii n i iiie mHmH 11 / ( ) ( )¦¦ == ∆∆=∆ n i ii n i iid mm 11 2 / ( ) d n i iie mm ∆∆= ¦ = / 1 He me He me ∆d ∆i ∆i-1 ∆3 ∆2 ∆1 He me He me ∆d ∆i ∆i-1 ∆3 ∆2 ∆1 Cours SDOF Definition of structural models for vulnerability analysis −0.25 −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25 −0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5 Sd [m] Sa[g] sdof pinching4 Hysteresis model
- 18. Definition of structuralmodels for vulnerability analysis • +100 peer-reviewed publications • +20 technical reports • +500 fragility functions and capacity curves Years 1975 1980 1985 1990 1995 2000 2005 2010 2015 Cumulativenumberofstudies 0 25 50 75 100 125 150 Cumulativenumberofmodels 0 200 400 600 800 1000 1200 Number of studies Number of models
- 19. Definition of structuralmodels for vulnerability analysis Numerical modeling
- 20. Definition of structuralmodels for vulnerability analysis Experimental tests
- 21.
- 22. Derivation of Fragility/Vulnerabilityfunctions Ground motion records Single degree of freedom systems Period of vibration (sec) 10 -1 10 0 Spectralacceleration(g) 10 -4 10 -3 10 -2 10 -1 10 0 101 median spectrum +1/-1 sigma spectrum individual spectrum Spectral displacement (m) 0 0.1 0.2 0.3 0.4 0.5 Spectralacceleration(g) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 median curve +1/-1 sigma curve sampled curve Risk Modelers Toolkit Spectral acceleration at 0.3 s [g] 0 0.2 0.4 0.6 0.8 1 1.2 Probabilityofexceedance 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Limit state 1 Limit state 2 Limit state 3 Limit state 4
- 24. Vulnerability Modelling –Costa Rica 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.4 0.8 1.2 1.6 2.0 Probability of excedense MCF/DUC/H:1 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.4 0.8 1.2 1.6 2.0 Probability of excedense MCF/DUC/H:2 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.4 0.8 1.2 1.6 2.0 Probability of excedense CR+PC/DUC/H:1 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.4 0.8 1.2 1.6 2.0 Probability of excedense CR+PC/DLO/H:1 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.4 0.8 1.2 1.6 2.0 Probability of excedense W+WLI/DLO/H:1 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.4 0.8 1.2 1.6 2.0 Probability of excedense MCF/DLO/H:1 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.4 0.8 1.2 1.6 2.0 Probability of excedense UNK 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.50 1.00 1.50 2.00 Probability of Exceedance MCF/DUC/H:3-6 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.50 1.00 1.50 2.00 Probability of Exceedance MUR+ADO/DNO/H:1 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.25 0.50 0.75 1.00 Probability of Exceedance CR+CIP/DUH/H:6-12 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.25 0.50 0.75 1.00 Probability of Exceedance CR+CIP/DUH/H:3-6 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.25 0.50 0.75 1.00 ProbabilityofExceedance CR+CIP/DLO/H:3-6 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.50 1.00 1.50 2.00 ProbabilityofExceedance CR/LINF+DUH/H:2-6 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.50 1.00 1.50 2.00 ProbabilityofExceedance CR+CIP/LFM+DLO/H:1 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.50 1.00 1.50 2.00 Probability of Exceedance CR+CIP/LFM+DLO/H:2-6 Slight Moderate Extensive Collpase
- 25. The need forvulnerability calibration/verification ”Often, all the model ingredients look fine, but their combination makes no sense. Calibration is key” Alex Allmann, Heard of GeoRisk at Munich Re 0 50 100 150 200 250 300 350 400 Model A Model B Model C Model D Model E Number of collapses Thousands Observed Estimated collapses for adobe buildings due to the 2007 M8.7 Pisco event
- 26. Damage assessment inSouth America Assessment of damage considering the 1999 M6.2 Armenia earthquake 0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000 Calculated Observed Numberofcollapses Ground shaking Collapse map Results
- 27. Damage assessment inSouth America Assessment of damage considering the 2016 M7.8 Muisne earthquake Ground shaking Collapse map Results 0 5000 10000 15000 Calculated Observed Numberofcollapses
- 28. The need forvulnerability calibration/verification Probabilistic seismic risk assessment for Costa Rica $43,529 $26,622 $12,293 $5,487 $4,334 $4,181 $3,744 $3,126 $1,621 $464 MCF/DUC/HEX:2 W+WLI/DNO/HEX:1 CR+PC/DLO/HEX:1 MATO/DNO/HEX:1 MCF/DLO/HEX:1 MCF/DUC/HEX:1 W+WLI/DLO/HEX:1 CR+PC/DUC/HEX:1 MR/DLO/HEX:1 MR/DUC/HEX:1 0 50000 Thousands of USD
- 29. The need forvulnerability calibration/verification Average annual losses • This model: 105M USD • GAR model: 103M USD Capital stock • This model: 76B USD • GAR model: 63M USD AAL high-residential: • This model: 60% • GAR model: 68% $43,529 $26,622 $12,293 $5,487 $4,334 $4,181 $3,744 $3,126 $1,621 $464 MCF/DUC/HEX:2 W+WLI/DNO/HEX:1 CR+PC/DLO/HEX:1 MATO/DNO/HEX:1 MCF/DLO/HEX:1 MCF/DUC/HEX:1 W+WLI/DLO/HEX:1 CR+PC/DUC/HEX:1 MR/DLO/HEX:1 MR/DUC/HEX:1 0 50000 Thousands of USD Probabilistic seismic risk assessment for Costa Rica
- 30. What about theregions with no damage data? A probabilistic approach can be explored
- 31. Collection of existingfragility and vulnerability models
- 32. Availability of vulnerabilitymodels in 2016
- 33. Availability of vulnerabilitymodels in 2018
- 34.