PERFORMANCE BASED EVALUATION AND RISK ANALYSIS E. Mistakidis Dept. - - PowerPoint PPT Presentation

PERFORMANCE BASED EVALUATION AND RISK ANALYSIS

• E. Mistakidis
• Dept. of Civil Engineering, University of Thessaly, 38334 Volos, Greece
• R. Vacareanu
• Dept. of Reinforced Concrete, Technical University of Civil Engineering,

020396, Bucharest, Romania

• A. Kappos

Laboratory 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)

• f 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
• f 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
• f 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 oscillator subjected to various ground motions recorded in Greece. In order to cover various structural typologies, different force-displacement models were used. The study compared the results of the various nonlinear analyses performed with the formulas given in FEMA356 for the estimation

• f

the target displacement using the Displacement Coefficient Method (DCM). 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.

R=4

1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 10 Frequency ν dn/de

DCM, T2=0.4 MODEL-A PROPOSITION

COST-C26 contribution

In the second contribution, an extension of the performance based design procedure was presented that considered uncertainties through the notion of fuzzy analysis.

• 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 structural analysis, this framework gives the ability to treat deficits of information describing input variables, human mistakes and mistakes in fabrication, utilization and maintenance of structures, etc.

• A simple application if presented in which the uncertainty in the input parameters

affects the structural response.

• A fuzzy capacity curve is obtained, which is afterwards combined with the seismic

demand to obtain a fuzzy target point.

0.100 0.050 0.400 0.300 0.200 0.100 0.200 0.150 0.100 0.050 0.100 0.200 0.300 0.400 0.100 0.150 0.200 0.050 0.000 0.000 0.400 0.300 0.200 0.100

H/V

Displacement (m) 0.200 0.150

Elastic Point "Fuzzy" capacity curve

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.

COST-C26 contribution

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

COST-C26 contribution

The paper presented a brief review and state of the art of Performance Based Seismic 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 were presented and discussed. Some particular features of the PBSD were also discussed, as the demand assessment through incremental dynamic analysis, nonlinear response history analysis and nonlinear static procedures. Finally, an example of the 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 (Keynote lecture).

COST-C26 contribution

• 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 motion for the structural performance analysis. Proceedings of the International Symposium in Malta, 23-25 October 2008.

COST-C26 contribution

The authors addressed the issue of generalizing the capacity spectrum method so that it incorporates the behaviour of the foundation, especially for the case of flexible

• nes.

The influence of foundation flexibility on the capacity curve and on the capacity spectrum 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 foundation using 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.

COST-C26 contribution

The paper deals with the role of wall infills in structural response. Actually, the frames with infill are composite structures consist of bare frames (RC or steel) and infill which very often are not homogenous and have significant impact on the seismic performance of the structure. 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. 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 were studied, with and without infill.

• The results showed that the effect of infill on the

seismic performance

• f

the structures is significant.

• In the elastic range and in the beginning of the

nonlinear range, masonry infill increases the seismic resistance of RC systems and has a significant influence on the nonlinear dynamic response.

• Further research is needed for the definition of

appropriate mathematical models for the nonlinear behaviour of infill.

COST-C26 contribution

The paper deals with the approximate methods for the construction of the capacity curve that is being used for the evaluation of seismic performance of

• structures. 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 a procedure of seismic performance evaluation of structures, Proceedings of the Final Conference in Naples, September 2010.

@ 3.30 4.00 @ 8.00 @ 8.00 @3.20

M8N M17N

• The

application

• f

these methods is demonstrated through two numerical examples treating an 8-storey and a 17- storey regular buildings.

• The results verify that the evolutive modal

spectral method gives results that compare well with those

• f

the incremental dynamic analysis. Moreover, it indirectly considers the dissipation of energy due to hysteresis.

COST-C26 contribution

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

• f

the earthquake intensity) are then

• btained

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.

COST-C26 contribution

Kappos, A. J., Panagopoulos, G., Panagiotopoulos, Ch. & Penelis, Gr. 2006. A hybrid method for the vulnerability assessment of R/C and URM buildings.

• Bull. of

Earthquake 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 each

category 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 member

damage indices proposed by Kappos et al. (1998). The total loss (L) for the entire building is derived from empirical equations (calibrated against cost of damage data from 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 of the building, respectively.

COST-C26 contribution

Situations leading to the need for replacement (rather than repair/strengthening) of the building 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 either

50% or more of the columns in a storey exceed their plastic rotation capacity or if the interstorey 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 either

50% or more of the columns in a storey ‘fail’, or the walls fail, or the interstorey drift exceeds a value of 2% at any storey. This set of failure criteria (proposed by Kappos et al. 2006) resulted after evaluating a large number of inelastic time-history analyses.

Definition of damage - R/C buildings COST-C26 contribution Definition of damage - URM buildings

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

• Median values for each damage state in the fragility curves are estimated for

each 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 for

each PGA in the fragility analysis depends on whether an empirical value is available for that PGA or not.

Derivation of fragility curves COST-C26 contribution

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

• f

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

• f

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 , given that 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 earthquake can 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 lowerbound value D e medianvalue D e upperbound value

Major earthquakes in 20 th century

USA, Northridge, 1994 USA, Loma Prieta, 1989 Japan, Kobe, 1995 Italy, 1980 Turkey, Kocaeli, 1999 Nicaragua, 1972 Guatemala, 1976 Taiwan, 1999 Romania, 1977 Colombia, 1999 El Salvador, 1986 Mexico, 1985 Iran, 1990 Armenia, 1988 Philippines, 1990 Skopje, 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 Deaths, D

D=0.06e1.5M

• D is the number of deaths, and
• M is the magnitude of the earthquake.

COST-C26 contribution

Vacareanu, R., Lungu, D., Aldea, A. & Arion, C. 2004. Seismic Risk Scenarios Handbook, WP7 Report – RISK UE Project

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

lg 0.6 0.2lg lg 0.06 0.2lg lg 0.9 0.2lg L D lowerbound value L D medianvalue L D upperbound value

• L are the economic losses expressed

in billion US$,

• D is the number of deaths.

Major earthquakes in 20 th century

Skopje, 1963 Armenia, 1988 Iran, 1990 Mexico, 1985 El Salvador, 1986 Colombia, 1999 Philippines, 1990 Taiwan, 1999 Guatemala, 1976 Nicaragua, 1972 Turkey, Kocaeli, 1999 Italy, 1980 Japan, Kobe, 1995 USA, Loma Prieta, 1989 USA, Northridge, 1994 Montenegro, 1979 1 10 100 1000 10 100 1,000 10,000 100,000 Deaths Economic losses, US$ bn. Romania, 1977

COST-C26 contribution

Vacareanu, R., Lungu, D., Aldea, A. & Arion, C. 2004. Seismic Risk Scenarios Handbook, WP7 Report – RISK UE Project

Case studies by COST-C26 members (1)

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

• M. Fischinger, M. Kramar, T. Isaković, Seismic collapse risk of precast industrial

buildings with strong connections, Earthquake Engng Struct. Dyn. (2009).

COST-C26 contribution

These buildings were designed according to the requirements of Eurocode 8. The numerical models and procedures were modified in order to address the particular characteristics of the analyzed system. They were also verified by pseudo-dynamic and cyclic tests of full-scale large buildings. The intensity measure (IM)-based solution strategy described in the PEER methodology was used to estimate the seismic collapse risk in terms of peak ground acceleration capacity and the probability

• f

exceeding the global collapse limit

• state. The effect of the uncertainty in

the model parameters

• n

the dispersion of collapse capacity was investigated in depth.

• Reasonable seismic safety was demonstrated for all the regular single-storey precast

industrial buildings addressed in this study.

• If the flexural strength required by EC8 was exactly matched, and the additional

strength, which results from minimum longitudinal reinforcement, was disregarded as well as large dispersion in records was considered, the seismic risk might in some cases exceed the acceptable limits.

• M. Fischinger, M. Kramar, T. Isaković, Seismic collapse risk of precast industrial

buildings with strong connections, Earthquake Engng Struct. Dyn. (2009).

COST-C26 contribution

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

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 RC Moment-Resisting Frames. Estimation of Drift Hazard, Proc. First European Conference

• n Earthquake Engineering and Seismology, paper no. 1000, Geneva, Switzerland

COST-C26 contribution

DRmax median values

y = 20.929x

1.7458

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 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

PGA , 'g DRrmax, %

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 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

T, s

• Abs. accel., '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 peak horizontal ground acceleration, PGA. The seismic motions used in the Inelastic Dynamic Analysis consist

• f

nine suites (classes) of random processes comprising ten samples each. Target elastic acceleration spectra are used to generate acceleration time-history

• samples. For parametric analysis purpose,

the accelerograms are artificially generated at predefined values of PGA. Vacareanu, R., Olteanu, P. & Chesca, A. B. 2006. Seismic Fragility of High-Rise RC Moment-Resisting Frames. Estimation of Drift Hazard, Proc. First European Conference

• n Earthquake Engineering and Seismology, paper no. 1000, Geneva, Switzerland

COST-C26 contribution

Thank you very much for your attention!

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