PERFORMANCE BASED EVALUATION AND RISK ANALYSIS

E. MistakidisDept. of Civil Engineering, University of Thessaly, 38334 Volos, Greece

R. Vacareanu

Dept. of Reinforced Concrete, Technical University of Civil Engineering,

020396, Bucharest, Romania

A. KapposLaboratory of Reinforced Concrete Technology and Structures

Dept of Civil Engineering, Aristotle University of Thessaloniki, Greece

COST C26: Urban Habitat Constructions under

Catastrophic Events

WG2: Earthquake resistance

Naples, September 16-18 2010

This chapter of the general report of the activities of the action COST-

C26 concerns the topics of :

performance based evaluation of structures

risk analysis

seismic vulnerability assessment.

It is part of the activity developed within the Working Group 2 (WG2)

of the Action, with the title "Earthquake resistance". This activity is

generally documented by the proceedings of the main events of the

Action, i.e.

the workshop that took place in Prague in 2007,

the seminar organized in Malta in 2008, and

the final conference that was organized in Naples in 2010

interesting contributions that were given in the working group

meetings of the Action are presented.

All the presentations of the WG2 members are available on the web

(http://www.civ.uth.gr/cost-c26/index.files/WG2.htm).

Introduction

PERFORMANCE BASED STRUCTURAL

EVALUATION AND DESIGN

Every seismic occasion reminds the need to improve the seismic performance of the built

environment through the development of advanced procedures and guidelines. Such

procedures have been termed Performance Based Seismic Engineering (PBSE) in the

literature and can be applied :

for the design of new structures

for the evaluation of the seismic adequacy of the existing buildings stock.

Early contributions:

capacity spectrum method (Freeman 1975,1987, Deierlein and Hsieh 1990)

acceleration-displacement response spectrum format (Mahaney et al 1993)

These methods have application to low or midrise structures, in which the response is

characterized by the fundamental mode of vibration. The reliability of these methods for

structures in which higher modes of vibration are significant may not be adequate.

Recent contributions:

the adaptive pushover method (Bracci et al. 1997, Elnashai 2000)

the “N2”method (Fajfar and Fischinger, 1988, Fajfar and Gašperšič, 1996)

the incremental response spectrum analysis (Aydinoglu 2003)

modal and multimodal methods (Chopra and Goel 2002, Chopra et al 2004, Sasaki et

al 1998)

upper bound pushover analysis (Jan et al 2004)

A very detailed state of the art is contained in FEMA 440 (FEMA, 2005).

Short state of the art

COST-C26 contribution

Mistakidis E., Apostolska-Petrusevska R., Dubina D., Graf W., Necevska-Cvetanovska G.,

Nogueiro P., Pannier S., Sickert J.-U., Simões da Silva L., Stratan A. & Terzic U. 2007.

Typology of seismic motion and seismic engineering design, Proceedings of Workshop in

Prague, March 2007.

Mandara A., Avossa A.M., Ferraioli M., Ramundo F. & Spina G. Performance-based seismic

retrofit of masonry and R.C. buildings, Proceedings of Workshop in Prague, March 2007.

Pascu R. The performance based approach in seismic rehabilitation of Buildings,

Proceedings of the International Symposium in Malta, October 2008 (Keynote lecture).

Lungu D., Arion C. & Calarasu E. Bucharest soil conditions and input ground motion for the

structural performance analysisProceedings of the International Symposium in Malta, 23-

25 October 2008.

Apostolska, R., Necevska-Cvetanovska, G. & Cvetanovska, J. 2010. Seismic performance

of RC building structures with masonry infill, Proceedings of the Final Conference in Naples,

September 2010.

Ayala, A.G., Mendoza, M. & Apostolska, R. (2010). Development and validation of a

procedure of seismic performance evaluation of structures, Proceedings of the Final

Conference in Naples, September 2010.

Dogariu and Dubina Performance based evaluation of seismic retrofitting techniques,

presentation during the meeting in Aveiro (http://www.civ.uth.gr/cost-

c26/index.files/WG2.htm).

F. Mazzolani, A. Mandara, B. Faggiano, A. Formisano, A. Marzo, A robustness based

method for the validation of seismic retrofit, presentation during the meeting in Aveiro (see

http://www.civ.uth.gr/cost-c26/index.files/WG2.htm)

The report contains two contributions related to performance based design. The first concerns a study on the magnification of seismic action on short

period structures. The study was performed using a nonlinear SDOF oscillatorsubjected to various ground motions recorded in Greece. In order to covervarious structural typologies, different force-displacement models were used.The study compared the results of the various nonlinear analyses performedwith the formulas given in FEMA356 for the estimation of the targetdisplacement using the Displacement Coefficient Method (DCM).

Mistakidis E., Apostolska-Petrusevska R., Dubina D., Graf W., Necevska-CvetanovskaG., Nogueiro P., Pannier S., Sickert J.-U., Simões da Silva L., Stratan A. & Terzic U.2007. Typology of seismic motion and seismic engineering design, Proceedings ofWorkshop in Prague, March 2007.

R=4

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7 8 9 10

Frequency ν

dn/d

e

DCM, T2=0.4

MODEL-A

PROPOSITION

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In the second contribution, an extension of the performance based designprocedure was presented that considered uncertainties through the notion of fuzzyanalysis. Informal and lexical uncertainties are described and quantified on the basis of

fuzzy set theory with the aid of assessed intervals. In the field of seismic structuralanalysis, this framework gives the ability to treat deficits of information describinginput variables, human mistakes and mistakes in fabrication, utilization andmaintenance of structures, etc.

A simple application if presented in which the uncertainty in the input parametersaffects the structural response.

A fuzzy capacity curve is obtained, which is afterwards combined with the seismicdemand to obtain a fuzzy target point.

0.10

0

0.05

0

0.400

0.300

0.200

0.100

0.20

0

0.15

0

0.10

0

0.05

0

0.100

0.200

0.300

0.400

0.10

0

0.15

0

0.20

0

0.05

0

0.00

0

0.000

0.400

0.300

0.200

0.100

H/V

Displacement (m)

0.20

0

0.15

0

Elastic Point

"Fuzzy" capacity curve

Mistakidis E., Apostolska-Petrusevska R., Dubina D., Graf W., Necevska-CvetanovskaG., Nogueiro P., Pannier S., Sickert J.-U., Simões da Silva L., Stratan A. & Terzic U.2007. Typology of seismic motion and seismic engineering design, Proceedings ofWorkshop in Prague, March 2007.

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Applications of performance based seismic retrofit for reinforced concrete andmasonry buildings were presented. The R.C. frames were reinforced by eccentricsteel braces and the masonry walls were strengthened by additional ties. All theanalyses were carried out complying with the basic assumptions of the PerformanceBased Design. A damage-controlled nonlinear static procedure was defined toestimate maximum lateral displacement and plastic dissipated energy of RC frames,in order to keep damage indices in structural elements within tolerable limits at eachperformance level.

Mandara A., Avossa A.M., Ferraioli M., Ramundo F. & Spina G. Performance-basedseismic retrofit of masonry and R.C. buildings, Proceedings of Workshop in Prague,

March 2007.

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The paper presented a brief review and state of the art of Performance BasedSeismic Design (PBSD) methods, focusing on the developments in the U.S. Moreover,the recent European Code EN 1998-3 and the Romanian Code P100-3 werepresented and discussed. Some particular features of the PBSD were also discussed,as the demand assessment through incremental dynamic analysis, nonlinearresponse history analysis and nonlinear static procedures. Finally, an example ofthe rehabilitation design of a residential building in Bucharest was given.

Pascu R. The performance based approach in seismic rehabilitation of Buildings,Proceedings of the International Symposium in Malta, October 2008 (Keynotelecture).

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The study concerned the Bucharest soil conditions and was based on

the available data obtained from more than 400 boreholes.

The geological results, permit seismic microzonation of Bucharest to be

used as a tool for urban planning and earthquake risk reduction. The

results were correlated with shear wave velocity measurements in

several locations having depth between 30 m and 200 m and with

analysis of recorded strong earthquakes.

Lungu D., Arion C. & Calarasu E. Bucharest soil conditions and input ground motionfor the structural performance analysis. Proceedings of the International Symposiumin Malta, 23-25 October 2008.

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The authors addressed the issue of generalizing the capacity spectrum method sothat it incorporates the behaviour of the foundation, especially for the case of flexibleones.The influence of foundation flexibility on the capacity curve and on the capacityspectrum method as a whole was studied for 2D RC frames and 3D wall systems.

Apostolska, R., Bonev, Z. P., Blagoev, D., Vasseva, E. & Necevska-Cvetanovska G.Design seismic response evaluation for 2D and 3D frames with flexible foundationusing capacity spectrum method, Proceedings of the International Symposium,Malta, October 2008.

The results from the investigations showed that the largest values for the behaviour factor could be achieved if the fixed base is considered. The smallest target displacements are observed in the same case.

If the foundations are flexible, the target displacement is increased but the behaviour factor decreases.

When the soil is soft and the structure reaches the target displacement, the global behaviour of the structure may remain completely elastic.

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The paper deals with the role of wall infills in structural response. Actually, theframes with infill are composite structures consist of bare frames (RC or steel) andinfill which very often are not homogenous and have significant impact on theseismic performance of the structure.

Apostolska, R., Necevska-Cvetanovska, G. & Cvetanovska, J. 2010. Seismicperformance of RC building structures with masonry infill, Proceedings of the FinalConference in Naples, September 2010.

Experience from past earthquakes and results from experimental-analytical investigations have shown that the interaction between unreinforced infill and frame can cause either positive or negative effects.

In this study, 5 and 7 story RC buildings werestudied, with and without infill.The results showed that the effect of infill on the

seismic performance of the structures issignificant.

In the elastic range and in the beginning of thenonlinear range, masonry infill increases theseismic resistance of RC systems and has asignificant influence on the nonlinear dynamicresponse.

Further research is needed for the definition ofappropriate mathematical models for thenonlinear behaviour of infill.

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The paper deals with the approximate methods for the construction of thecapacity curve that is being used for the evaluation of seismic performance ofstructures. A number of methods are reviewed: the capacity spectrum method, the displacement coefficient method the N2 method.

Methods for the construction of the capacity curve are evaluated such as : the incremental dynamic analysis, the static pushover analysis the evolutive modal spectral analysis.

Ayala, A.G., Mendoza, M. & Apostolska, R. (2010). Development and validation of aprocedure of seismic performance evaluation of structures, Proceedings of the FinalConference in Naples, September 2010.

@ 3.30

4.00

@ 8.00

@ 8.00 @3.20

M8N M17N

The application of these methods isdemonstrated through two numericalexamples treating an 8-storey and a 17-storey regular buildings.

The results verify that the evolutive modalspectral method gives results thatcompare well with those of theincremental dynamic analysis. Moreover,it indirectly considers the dissipation ofenergy due to hysteresis.

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PERFORMANCE-RELATED ASPECTS IN SEISMIC

VULNERABILITY ASSESSMENT

The basic idea is that a damage index for a damaged structure

(ratio of repair cost to replacement cost) is estimated both from

actual damage statistics (‘empirical’ data) and from series of

inelastic analyses of representative structural systems.

The ‘primary’ vulnerability curves (plots of degree of damage as a

function of the earthquake intensity) are then obtained by

appropriately weighting the empirical and the analytical data

(Kappos and Panagopoulos 2010).

This economic damage index is used to define a number of damage

states (performance levels) for which fragility curves are derived

using assumptions regarding the form of the type of probability

distribution and the variability in the response.

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nKappos, A. J., Panagopoulos, G., Panagiotopoulos, Ch. & Penelis, Gr. 2006. A hybridmethod for the vulnerability assessment of R/C and URM buildings. Bull. ofEarthquake Engineering 4 (4): 391-413.

Performance-based estimation of economic loss

It is based on a series of inelastic dynamic analyses of ‘generic’ buildings in eachcategory of the classification scheme used for vulnerability purposes (Kappos et al.2006).

From each analysis, the cost of repair is estimated using the models for memberdamage indices proposed by Kappos et al. (1998). The total loss (L) for the entirebuilding is derived from empirical equations (calibrated against cost of damage datafrom Greece)L = 0.25Dc + 0.08Dp ( 5 storeys) (1)L = 0.30 Dc + 0.08Dp (6 - 10 storeys) (2)

Dc and Dp : global damage indices ( 1) for the R/C members and the masonry infills ofthe building, respectively.

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Situations leading to the need for replacement (rather than repair/strengthening) of thebuilding are identified using failure criteria for members and/or storeys, as follows: In R/C frame structures, failure is assumed to occur (and then L=1) whenever either50% or more of the columns in a storey exceed their plastic rotation capacity or if theinterstorey drift exceeds a value of 4% at any storey (Dymiotis et al. 1999).

In R/C dual (wall+frame) structures, failure is assumed to occur (L=1) whenever either50% or more of the columns in a storey ‘fail’, or the walls fail, or the interstorey driftexceeds a value of 2% at any storey.

This set of failure criteria (proposed by Kappos et al. 2006) resulted after evaluating alarge number of inelastic time-history analyses.

Definition of damage - R/C buildingsC

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Definition of damage - URM buildings

Instead of using semi-empirical interstorey drift values (the HAZUS approach), theThessaloniki group (Kappos 2001, Kappos et al. 2006) has suggested expressing thedamage state thresholds in terms of the basic parameters of the capacity curve(yield displacement and ultimate displacement, both referring to a bilinearisedcapacity curve).

Median values for each damage state in the fragility curves are estimated foreach of the building systems analysed.

The starting point for estimating these values is the plot of the damage index(calculated from inelastic time history analysis as described in Kappos et al.2006) as a function of the earthquake intensity (PGA).

Having established analytically the loss index, the final value to be used foreach PGA in the fragility analysis depends on whether an empirical value isavailable for that PGA or not.

Derivation of fragility curves C

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PROBABILISTIC SEISMIC RISK ASSESSMENT

The probabilistic seismic risk assessment explicitly takes into account the

uncertainties in the basic variables involved in the analysis. Both aleatory

and random uncertainties can be considered in the probabilistic risk

analysis. The probabilistic seismic risk analysis integrates the results of the

probabilistic seismic hazard analysis and of the seismic

fragility/vulnerability analysis.

Definitions

The seismic hazard is a characteristic of the earthquake that might

produce structural damage or losses. The outcome of a probabilistic

seismic hazard analysis is the mean annual frequency with which a

seismic hazard will occur.

The seismic fragility describes the probability of reaching or exceeding

a considered level of seismic damage for a structural system given the

level of the seismic hazard.

The seismic vulnerability describes the probability of reaching a

considered level of seismic losses given the level of the seismic hazard.

Risk is the expectancy of damage and/or losses derived on the basis of

present knowledge. The outcome of a probabilistic seismic risk analysis

is the mean annual frequency with which a certain level of damage

and/or loss will occur for a given structural system (or for an extended

built system). Based on this result, rational decisions on seismic risk

reduction can be made.

Introduction

The risk analysis recognizes the impossibility of deterministic prediction of

events of interest:

future earthquakes,

exposure of elements at risk,

chain effects occurring as a consequence of the earthquake-induced

damage.

Probabilistic seismic risk is the outcome of the convolution of seismic

hazard, exposure of elements at risk and vulnerability of the elements at

risk, using the total probability theorem. In the most general format, the

general relation for the determination of the total risk can be expressed

as (Whitman & Cornell, 1976):

[ ] [ / ] [ ]i i j j

j

P R P R S P S

Probability that the state of the system is i

probability that the state of the system will be Ri , giventhat the seismic input Sj takes place

Probability that the seismic input experienced is level j

Introduction

Based on data of the previous Table, the number of deaths from an earthquakecan be related to the magnitude of the earthquake by the following relations:

1.5

1.5

1.5

0.002

0.06

0.4

M

M

M

D e lower bound value

D e medianvalue

D e upper bound value

Major earthquakes in 20th

century

USA, Northridge, 1994USA, Loma Prieta, 1989

Japan, Kobe, 1995

Italy, 1980

Turkey, Kocaeli, 1999

Nicaragua, 1972

Guatemala, 1976

Taiwan, 1999

Romania, 1977Colombia, 1999El Salvador, 1986

Mexico, 1985

Iran, 1990

Armenia, 1988

Philippines, 1990Skopje, 1963

Montenegro, 1979

1

10

100

1,000

10,000

100,000

5.5 6 6.5 7 7.5 8 8.5

Magnitude, M

Dea

ths,

DD =0.06e

1.5M

D is the number of deaths, andM is the magnitude of the earthquake.

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nVacareanu, R., Lungu, D., Aldea, A. & Arion, C. 2004. Seismic Risk ScenariosHandbook, WP7 Report – RISK UE Project

The economic losses can be related to the number of deaths from anearthquake by the following relations:

lg 0.6 0.2lg

lg 0.06 0.2lg

lg 0.9 0.2lg

L D lower bound value

L D medianvalue

L D upper bound value

L are the economic losses expressedin billion US$,

D is the number of deaths.

Major earthquakes in 20th

century

Skopje, 1963

Armenia, 1988

Iran, 1990Mexico, 1985

El Salvador, 1986

Colombia, 1999

Philippines, 1990Taiwan, 1999 Guatemala, 1976

Nicaragua, 1972

Turkey, Kocaeli, 1999Italy, 1980

Japan, Kobe, 1995

USA, Loma Prieta, 1989

USA, Northridge, 1994

Montenegro, 1979

0

1

10

100

1000

10 100 1,000 10,000 100,000

Deaths

Eco

nom

ic loss

es, U

S$ b

n.

Romania, 1977

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nVacareanu, R., Lungu, D., Aldea, A. & Arion, C. 2004. Seismic Risk ScenariosHandbook, WP7 Report – RISK UE Project

Case studies by COST-C26 members (1)

The paper presents a systematic seismic risk study that has been performed onsome typical precast industrial buildings that consists of assemblages of cantilevercolumns with high shear-span ratios connected to an essentially rigid roof systemwith strong pinned connections.

M. Fischinger, M. Kramar, T. Isaković, Seismic collapse risk of precast industrialbuildings with strong connections, Earthquake Engng Struct. Dyn. (2009).

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These buildings were designed according to the requirements of Eurocode 8. Thenumerical models and procedures were modified in order to address theparticular characteristics of the analyzed system. They were also verified bypseudo-dynamic and cyclic tests of full-scale large buildings.

The intensity measure (IM)-basedsolution strategy described in thePEER methodology was used toestimate the seismic collapse risk interms of peak ground accelerationcapacity and the probability ofexceeding the global collapse limitstate. The effect of the uncertainty inthe model parameters on thedispersion of collapse capacity wasinvestigated in depth.

Reasonable seismic safety was demonstrated for all the regular single-storey precastindustrial buildings addressed in this study.

If the flexural strength required by EC8 was exactly matched, and the additionalstrength, which results from minimum longitudinal reinforcement, was disregarded aswell as large dispersion in records was considered, the seismic risk might in somecases exceed the acceptable limits.

M. Fischinger, M. Kramar, T. Isaković, Seismic collapse risk of precast industrialbuildings with strong connections, Earthquake Engng Struct. Dyn. (2009).

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The paper gives detailed information on the procedure for computing MAF ofexceedance of a limit state, specialized for drift hazard, as well as numericalresults.The case study refers to a high-rise reinforced concrete moment-resisting framestructure designed according to the earthquake resistant design code in forcein Romania, P100-1/2006, that is in line with the provisions of EN 1998-1.

hp =

20 c

m

hp =

20 c

m

hp =

20 c

m

S1A 800x1000 S2A 800x1000 S3A 800x1000 S4A 800x1000 S5A 800x1000 S6A 800x1000

S1C 800x1000 S2C 800x1000 S3C 800x1000 S4C 800x1000 S5C 800x1000 S6C 800x1000

S2B

1000x1000

S1B

800x1000

S3B

1000x1000

S4B

1000x1000

S5B

1000x1000

S6B

800x1000

GL1 500x550

GL1 500x550

GL1 500x550

GT

1 6

00

x6

50

GT

1 6

00

x6

50

GT

1 6

00

x6

50

GT

1 6

00

x6

50

GT

1 6

00

x6

50

GT

1 6

00

x6

50

GT

1 6

00

x6

50

GT

1 6

00

x6

50

GT

1 6

00

x6

50

GT

1 6

00

x6

50

GT

1 6

00

x6

50

GT

1 6

00

x6

50

0.500 6.000 6.000 6.000 6.000 6.000 0.500

31.000

6.0

00

0.4

00

12

.80

0

6.0

00

1 2 3 4 5 6

A

B

C

hp =

20 c

m

hp =

20 c

m

hp =

20 c

m

hp =

20 c

m

hp =

20 c

m

hp =

20 c

m

0.4

00

PLAN COFRAJ SI ARMARE PLANSEU PESTE PARTER

SCARA 1 : 50

Case studies by COST-C26 members (2)

Vacareanu, R., Olteanu, P. & Chesca, A. B. 2006. Seismic Fragility of High-Rise RCMoment-Resisting Frames. Estimation of Drift Hazard, Proc. First European Conferenceon Earthquake Engineering and Seismology, paper no. 1000, Geneva, Switzerland

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DRmax median values

y = 20.929x1.7458

R2 = 0.9809

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

PGA , 'g

DR

rma

x, %

IDA results: Maximum interstory drift (median values) versus peak horizontal ground acceleration

1.E-03

1.E-02

1.E-01

1.E+00

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

DRmax, d %

HD

(d)

Hazard curve derived for maximum interstory drift values

Response spectra of generated accelerograms at 0.24g

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

T , s

Ab

s. a

ccel.

, 'g

Acc1_24

Acc2_24

Acc3_24

Acc4_24

Acc5_24

Mean

Code_el

Target Spectrum and Response Spectra of generated accelerograms at 0.24g

The seismic motion Intensity Measure is peakhorizontal ground acceleration, PGA. Theseismic motions used in the InelasticDynamic Analysis consist of nine suites(classes) of random processes comprisingten samples each.Target elastic acceleration spectra are usedto generate acceleration time-historysamples. For parametric analysis purpose,the accelerograms are artificially generatedat predefined values of PGA.

Vacareanu, R., Olteanu, P. & Chesca, A. B. 2006. Seismic Fragility of High-Rise RCMoment-Resisting Frames. Estimation of Drift Hazard, Proc. First European Conferenceon Earthquake Engineering and Seismology, paper no. 1000, Geneva, Switzerland

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Thank you very much for your attention!

Fortunately COST-C26 has been completed in time (Sept. 2010) !