Concepts of Seismic Vulnerability and Risk

Definitions

Hazard Vulnerability Exposure

Seismic Risk

Hazard Vulnerability Exposure

Seismic RiskTarget of the lecture

Vulnerability

• It is fundamental to understand the vulnerability concept

• The seismic risk, that quantifies the losses, is the convolution of vulnerability, hazard and exposure. It is impossible to act on hazard, nearly impossible to act on exposure, it is feasible to act on vulnerability. Hence, the feasible way to mitigate the seismic risk is to mitigate the seismic vulnerabilityseismic vulnerability

• Vulnerability measures how prone a structure is to be damaged when an earthquake occurs

• To deal with vulnerability, a mathematical definition is needed

Pik = P[D≥di | S=sk]

Damage Shaking

Mathematical Definition of Vulnerability

Methods to quantify the vulnerability

� Empirical methods based on post earthquake observations

� Mechanic methods

� Hybrid methods

Methods to quantify the vulnerability

� Damage Probability Matrix (DPM)

� Fragility curves

Intensity ScaleVI VII VIII IX X XI XII

Dam

age

leve

l012345

DPM

Fragility Curves

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ag [g]

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Fragility Curves

Seismic Risk

• Unconditional damage/failure probability

If the probability of having a certain ground shaking severity is also taken into account, the unconditional damage/failure probability is computed. The probability of having a certain ground shaking severity is taken into account through the hazard curve:

R² = 0.9941

0.0001

0.001

0.01

0.1

1

0.01 0.1 1

AF

E

Sd(cm)PGA

AF

E

AFE: Annual frequency of exceedance

AFE=1/Tr with Tr the return period of the ground shaking

Unconditional damage/failure probability

In order to compute the seismic risk, the hazard curve must be transformed in terms of probability. The assumption usually undertaken is that the events follow the Poisson’s distribution, that is the probability distribution of rare events without memory (what happens one year is independent from what happened in the years before). The occurrence probability “q” of a ground happened in the years before). The occurrence probability “q” of a ground shaking with a certain AFE in an observation time window td is:

q = 1- exp (td AFE)

Hence, the seismic risk is computed by solving the integral of structural reliability

dE )]E(F-[1 )E(f dE )E(F )E(fP dccdf ∫∫+∞

∞−

+∞

∞−

==

integral of structural reliability

Exceedace Fragility curve

Where:

•f and F are the probability density function and the cumulative probability, respectively•E is the parameter that represents the ground motion severity;•d and c are the random variables that represent the demand and the capacity respectively

Exceedace probability of ground shaking severity “q”

Fragility curve

Mechanics Based Vulnerability Assessment:

SP-BELA (Simplified P ushover - B ased Earthquake L oss A ssessment)

1st step : choice of prototype building

Trave di spina

Trave di bordo

Trave di bordo

P1 P2 P3 P3 P2 P1

P4 P5 P6 P6 P5 P4

P1 P2 P3 P3 P2 P1

lx

lx

lx

lx

ly

lx

ly

x

y

SP-BELA – Building Capacity

2nd step : definition of random variables that describe the bldg.(i.e.: loads, material properties, geometry, etc.)

4th step : simulated building design with reference to the regulation adopted in the year of real building design

3rd step : montecarlo generation of buildings’ population

5th step : simplified pushover analysis

Check of relative resistance of beams and columns

Collapse mechanism Deformed shape:� Assumption of linear deformed

shape into the elastic range� Deformed shape consisent with the

failure mechanism into the inelastic range

Resistance

λ

∆ ∆y=∆light damage ∆severe damage ∆coll apse

Once the deformed shape, the limit conditions and the resistance are known ….

λ

∝ (TLSi)-2∝ (TLSy)-2

Contribution of infill walls

∆

∆y=∆ light damage ∆severe damage ∆collapse

Bare frame

Frame withinfill walls

1st step : choice of spectral shape

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Periodo

Sd

SP-BELA – Seismic Demand

2nd step : definition of random variables that describe the spectral shape (i.e. corner periods, dynamic amplification, …)

3rd step : montecarlo generation of a population of spectral shapes

Random sample of pushover curves (j=1,n) Random sample of spectral shapes (j=1,n)

∇ agk (k=1,m)

∇ SLi (i=1,3)

From pushover: ∆SLi, TSLi, µSLi From spectral shape: Sdi (agk, TSLi,

µSLi)

j=1

µSLi)

Sdi > ∆SLi

SI NO

hj=1 hj=0

j=n? j=j+1NO

SI

Pf (agk, SLi)= Σ hj/n

i=3?

SI

k=m ?

SI

END

i=i+1NO

k=k+1NO

CASE 1Bare framey

x CASE 2Regular distributed infill walls

SP-BELA – Validation Exercise

x Regular distributed infill walls

yx

CASE 3 Non regular distributed infill walls

yx

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collapse

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yx

CASE 1Bare frame

Non seismically designed buildings

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roof displacement, ∆∆∆∆ [m]

collapse

multip

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Direction x

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collapse

multip

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λ λ λ λ

.

Direction y

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ag [g] ag [g]

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8 storey

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Collapse

yx

CASE 1Bare frame

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multip

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yx

CASE 1Bare frame

Seismically designed buildings

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collapse

multip

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λ λ λ λ

.Direction x

Direction y

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ag [g]

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ag [g]

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. Non Prog.

C=5%

C=7,5%

C=10%

C=12,5%y

x

Collapse

CASE 1Bare frame

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x

Non seismically designed buildings

CASE 2Regular distributed infill walls

Direzion

e y0

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collapse

multip

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yx Direction y

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roof displacement, ∆∆∆∆ [m]

CASE 3 Non regular distributed infill walls

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Light damage

Severe damage

Collapse

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PGA [g]ag [g]

CASE 3 Non regular distributed infill walls

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Seismically designed buildings

CASE 2Non regular distributed infill walls

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collapse

multip

lier,

λ λ λ λ

.

Direction yy

x

0 0.05 0.1 0.15 0.2 0.25 0.3

roof displacement, ∆∆∆∆ [m]

CASE 3 Non regular distributed infill walls

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a [g]

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Non regular distributed infill walls

Light damage

Severe damage

Collapse

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PGA [g]

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ag [g]

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PGA [g]ag [g]

CASE 3 Non regular distributed infill walls

Borzi B., Crowley H., Pinho R. (2008b), “Simplified pushover-based earthquake loss assessment (SP-BELA) for masonrybuildings,” International Journal of Architectural Heritage, Vol.2, No. 4, pp. 353-376.

Masonry Buildings

Bolognini D., Borzi B., Pinho R. “Simplified Pushover-BasedVulnerability Analysis of Traditional Italian RC PrecastStructures”, Proceeding of 14th World Conference onEarthquake Engineering, Bejing 2008

Precast RC Buildings

Seismic Risk Assessment of Hospitals in Lombardia Distr ict

Seismic risk assessment of a large industrial estate

Applications

DPC ProjectSeismic risk assessment of Italian building stock

DPC ProjectPriority of intervention on Italian school building s

DPC ProjectSeismic risk assessment of transportation network

Related Publications

Borzi B., Pinho R., Crowley H. [2007], “Simplified Pushover-Based Vulnerability Analysis for Large Scale Assessment of RC Buildings”, EngineeringStructures, Vol. 30, No. 3, pp. 804-820

Borzi B., Crowley H., Pinho R. [2008], “Simplified Pushover-Based Earthquake Loss Assessment (SP-BELA) Method for Masonry Buildings”,International Journal of Architectural Heritage, Vol. 2, No. 4, pp. 353-376

Borzi B., Crowley H., Pinho R. [2008], “The Influence of Infill Panels on Vulnerability Curves for RC Buildings”, Proceeding of 14th World Conference onEarthquake Engineering, Bejing 2008

Bolognini D., Borzi B., Pinho R. [2008], “Simplified Pushover-Based Vulnerability Analysis of Traditional Italian RC Precast Structures”, Proceeding of14th World Conference on Earthquake Engineering, Bejing 2008

Fiorini E., Onida M., Borzi B., Pacor F., Luzi L., Meletti C., D’Amico V., Marzorati S., Ameri G. [2008], “Microzonation study for an industrial site insouthern Italy”, Proceeding of 14th World Conference on Earthquake Engineering, Bejing 2008

Borzi B., Dell’Acqua F., Faravelli M., Gamba P., Lisini G., Onida M., Polli D. [2011], “Vulnerability study on a large industrial area using satellite remotelysensed images”, Bulletin of Earthquake Engineering 2011, No. 9, pp. 675-690.

Borzi B., Ceresa P., Faravelli M., Fiorini E., Onida M. [2011], “Definition of a prioritization procedure for structural retrofitting of Italian school buildings”,Proceedings of COMPDYN 2011, Corfù, Paper N. 302.

Fiorini E., Borzi B., Iaccino R. [2012], “Real Time damage scenario: case study for the L'Aquila Earthquake”, 15WCEE, Paper N. 3707

Borzi B., Ceresa P., Faravelli M., Onida M. [2012], “Vulnerability study of steel storage tanks in a large industrial area of Sicily”, 15WCEE, Paper N. 4137

Ceresa P., Fiorini E., Borzi B. [2012], “Effects of the seismic input variability on the seismic risk assessment of the RC bridges”,15WCEE, Paper N. 5414

Ceresa P., Borzi B., Noto F., Onida M. [2012],, “Application of a probabilistic mechanics-based methodology for the seismic risk assessment of the ItalianRC bridges”,15WCEE, Paper N. 5102