Derivation of vulnerability functions for European-type RC ... · T. Rossetto, A. Elnashai /...

Engineering Structures 25 (2003) 1241–1263www.elsevier.com/locate/engstruct

Derivation of vulnerability functions for European-type RCstructures based on observational data

T. Rossettoa, A. Elnashaib

a Civil and Environmental Engineering Department, Imperial College, London, UKb Civil and Environmental Engineering Department, University of Illinois at Urbana-Champaign, Urbana, IL, USA

Received 11 April 2002; received in revised form 21 February 2003; accepted 24 February 2003

Abstract

In this paper existing vulnerability relationships for reinforced concrete structures are reviewed with a view to their applicationto a European (and similar) seismic risk assessment scenario. New empirical fragility curves for reinforced concrete buildingpopulations are derived based on a data bank of 99 post-earthquake damage distributions observed in 19 earthquakes and concerninga total of 340 000 RC structures. The heterogeneous observational data are reinterpreted in terms of a new damage scale: homogen-ised reinforced concrete (HRC-scale), which is calibrated experimentally and allows a distinction to be made between the seismicresistances of different structural systems. The feasibility of using observation-based data for the generation of vulnerability curvesfor different strong ground motion parameters is investigated. The notion of developing a set of ‘homogeneous’ vulnerabilityrelationships, applicable to different lateral-load resisting systems is explored and a series of relationships for different buildingheight and age-classes are proposed. Large uncertainties are associated with the empirical relationships due to the nature and scarcityof observational data. The role of combined observation-testing-analysis as the basis for deriving reliable vulnerability formulationsis thus emphasised. Notwithstanding, the statistics of the new vulnerability functions are a significant improvement over existingobservation-based curves for European RC structures. 2003 Elsevier Science Ltd. All rights reserved.

Keywords: Vulnerability curves; Limit states; Observational damage data; RC buildings

1. Introduction

Seismic risk assessments were carried out on popu-lations of buildings to identify the urban areas mostlikely to undergo large life and economic losses duringan earthquake. The results of such studies are importantin the mitigation of losses under future seismic eventsas they allow strengthening intervention and disastermanagement plans to be drawn up. In Europe, themajority of existing reinforced concrete buildings are notdesigned to meet modern seismic codes. Nevertheless,most have an inherent lateral resistance, born of over-strength factors in design codes, which may be sufficientto resist the moderate earthquakes that typify Europeanseismicity with an acceptable degree of damage. Thedefinition of ‘acceptable’ damage varies according to theimportance of the buildings, their use and the severityof the ground motion. Typically multiple performancecriteria need to be satisfied. Therefore prediction toolssuch as vulnerability curves are required that will allow

0141-0296/03/$ - see front matter 2003 Elsevier Science Ltd. All rights reserved.doi:10.1016/S0141-0296(03)00060-9

the seismic risk assessment of populations of buildingsto be carried out within a performance or consequence-based framework.

Vulnerability curves relate the probability of exceed-ence of multiple damage states to a parameter of groundmotion severity and can therefore be regarded as agraphical representation of seismic risk. In the case ofbuilding populations, their use yields a prediction of theproportion of the exposed stock in each damage stateafter an earthquake that causes a certain spatial distri-bution of ground motion severity. In the first part of thispaper existing vulnerability curves for different classesof reinforced concrete structure are reviewed with a viewto their application as European seismic risk assessmenttools. Consequently the use, application and reliabilityof observational damage data alone as a source for thedevelopment of new vulnerability relationships for popu-lations of RC buildings of typical European, and similar,construction is explored. A concerted effort has beendedicated to the collection of as wide an observational

1242 T. Rossetto, A. Elnashai / Engineering Structures 25 (2003) 1241–1263

data bank as internationally possible. A methodology forthe observational data processing and vulnerability curvegeneration is explained and a new damage scale(homogenised reinforced concrete scale, HRC scale) isdefined and calibrated with respect to experimentalmeasurements for the purpose of damage data harmonis-ation. Various parameters for strong ground motioncharacterisation are considered and conclusions made asto their suitability. Using the newly defined damagescale, the concept of a single set of ‘homogeneous’ vul-nerability relationships, applicable to different lateral-load resisting systems is set forth and series of regressionand sensitivity analyses are carried out to assess its feasi-bility.

2. A critique of existing vulnerability functions

Few vulnerability relationships have been specificallyderived for European countries; however severalrelationships for different classes of RC structures havebeen proposed by government agencies and researchinstitutes worldwide. Herein, the most importantexamples of such curves are investigated (described inTable 1). The influence on the loss prediction reliabilityof the choices made for damage data source, structuralunit, damage measure and ground motion parameter arediscussed both generally and with a view to their appli-cation in a European earthquake risk assessment scen-ario. Conclusions are made regarding the latterimplementation through their comparison with Europeanpost-earthquake damage data.

2.1. Damage data source

Existing vulnerability curves can be classified into thefour generic groups of empirical, judgmental, analyticaland hybrid according to whether the damage data usedin their generation derives mainly from observed post-earthquake surveys, expert opinion, analytical simula-tions, or combinations of these, respectively. Each datasource has associated advantages and disadvantages.Empirical curves use the building damage distributionsreported in post-earthquake surveys as their statisticalbasis. The observational source is the most realistic asall practical details of the exposed stock are taken intoconsideration alongside soil–structure interaction effects,topography, site, path and source characteristics. How-ever, the same aspects that render observational data themost realistic are responsible for the severe limitation intheir application potential. The empirical groundmotion–damage relationships developed for Europeancountries are typically based on very few damage sur-veys carried out for single locations or earthquakeevents, (e.g. Orsini [3]). No distinction between build-ings of different materials, heights or seismic design pro-

visions is commonly made. Consequently the curves arehighly specific to a particular seismo-tectonic, geotechn-ical and built-environment. A wider scope of applicationis possible if the performance of different structural sys-tems is considered and if a large quantity of reliableempirical data, covering a wide range of ground motionsis used for the curve derivation. In practice, this is onlyachievable through the combination of data from differ-ent earthquakes and locations. However, due to theinfrequency of large magnitude earthquake events neardensely populated areas, the observational data used forthe curve generation tend to be scarce and highly clus-tered in the low-damage, low ground-motion severityrange. This leads to large uncertainties being associatedwith their use in large magnitude events. To allow anaccurate determination of the ground motion and for thereported damage distribution to be representative of thevariation in seismic resistance of the buildings, empiricalvulnerability curves should use post-earthquake surveyscarried out for large populations of buildings of similarconstruction, over areas of uniform soil conditions inclose proximity to ground motion recording stations.Errors in building damage classification (especially forthe lighter damage states) are introduced in the statisticsat source due to the typically rapid execution of post-earthquake surveys by engineers of varied experienceand the use of poorly defined damage scales. Moreover,damage due to multiple earthquakes may be aggregatedand attributed to a single event or buildings damaged asa consequence of phenomena other than ground shaking(e.g. ground subsidence, landslides, flooding and fire)included in the data. These errors cannot be removed viamanipulation of the damage statistics and lead to a largedata scatter even in cases where a single event and lim-ited survey area are considered (e.g. Orsini [3]). The lowlevel of refinement in terms of both structure and damageclassification that typifies post-earthquake survey stat-istics therefore poses a real hindrance to the combinationof damage data for building populations of differentcomposition.

Judgement-based curves are not associated with thesame problems regarding the quantity and quality ofbuilding damage statistics that typify empirical relation-ships. Expert panels of civil engineers with experiencein the field of earthquake engineering are asked to makeestimates of the probable damage distribution withinbuilding populations when subjected to earthquakes ofdifferent intensities. Probability distribution functionsare fit to the expert predictions to represent the range ofdamage estimates at each intensity level. The probabilityof a specified damage state is derived from the resultingdistributions and plotted against the correspondingground-motion level to obtain a set of vulnerabilitycurves, and associated uncertainty bounds. Since theexperts can be asked to provide damage estimates forany number of structural types, the curves can be easily

1243T. Rossetto, A. Elnashai / Engineering Structures 25 (2003) 1241–1263

Tab

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made to include all the factors affecting the seismicresponse of different structures. Consequently expertopinion is the predominant source used by most currentrehabilitation codes in the United States of America forthe generation of damage probability matrices and vul-nerability curves (e.g. ATC-13 [7] and ATC-40 [13]).The reliability of judgement-based curves is question-able, however, due to their dependence on the individualexperience of the experts consulted. It is practicallyimpossible to evaluate of the degree of conservatismassociated with the judgement-based source, andinherent in the expert vulnerability predictions is a con-sideration of local structural types, typical configur-ations, detailing and materials. Hence if the country ofthe fragility curve derivation is characterised by con-struction practices that differ significantly from thoseused in Europe, their application to the latter may be pre-cluded.

Analytical vulnerability curves adopt damage distri-butions simulated from the analyses of structural modelsunder increasing earthquake loads as their statisticalbasis. Analyses can result in a reduced bias andincreased reliability of the vulnerability estimate for dif-ferent structures compared to expert opinion. Despitethis, few analytical vulnerability curves for reinforcedconcrete buildings have been generated in the past dueto the substantial computational effort involved and limi-tations in modelling capabilities. Architectural finishescan not be accounted for, detailed modelling of infillwalls remains a challenge, elaborate soil models cannotbe accommodated alongside elaborate structural modelsand rocking and uplifting of structures poses seriousnumerical modelling difficulties. Many existing analysisenvironments also have difficulties converging whenstructures are subjected to large demands, and numericalcollapse may precede structural failure. However, recentdevelopments have lead to the inclusion of a number ofresponse features, such as shear-flexure–axial interac-tion, soil–structure interaction, interactive confinementon concrete members and reinforcing bar buckling, intoanalytical methods. Furthermore, new analysis tech-niques and solution procedures have been establishedthat enable the generation of damage data for large andcomplex structures at very high speeds. Hence analyticalapproaches to vulnerability curve generation are becom-ing ever more attractive in terms of the ease andefficiency by which data can be generated, but have notyet been fully exploited to the limits of their potential.

Most existing analytical vulnerability relationshipshave been derived for structures in America. A varietyof analysis procedures have been followed, ranging fromthe elastic analysis of equivalent single degree of free-dom systems (Mosalam et al. [11]), to non-linear timehistory analyses of 3D models of RC structures (Singhaland Kiremidjian [9]). The choices made for the analysismethod, structural idealisation, seismic hazard and dam-

age models strongly influence the derived curves andhave been seen to cause significant discrepancies in seis-mic risk assessments made by different authorities forthe same location, structure type and seismicity(Priestley [14]). Their application to European sites maytherefore not be justified unless an appropriate degree ofuncertainty in the structural models and ground motionsare considered.

Hybrid vulnerability curves attempt to compensate forthe scarcity of observational data, subjectivity of judge-mental data and modelling deficiencies of analytical pro-cedures by combining data from the different sources.Existing examples of hybrid curves typically involve themodification of analytical or judgement-based relation-ships with observational data. In most cases the dataderiving from the additional sources are, however, verylimited in quantity and scope. The curves proposed inATC-13 [7] and ATC-40 [13], though based heavily onexpert opinion, also incorporate limited observationaldata from the San Fernando earthquake (USA, 1971) andNorthridge earthquake (USA, 1994), respectively. Insome cases, these data are further supplemented withexperimental test results. The latter source has gainedimportance in recent years as the testing of large andreasonably realistic structures has become more fre-quent. However, due to the cost and time required forfull-scale testing and since small-scale testing is non-definitive on similitude grounds, a very limited numberof parameters can be investigated and parametric vari-ations are not possible. Experimental data are thereforecurrently only used for verification purposes, rather thanas an additional source of building damage statistics.Singhal and Kiremidjian [9] also adopt a Bayesian tech-nique to update analytical curves for low-rise frameswith observational damage data from a tagging survey ofonly 84 buildings affected by the Northridge earthquake(USA, 1994). Observations taken from a single earth-quake event will cover only a small range of groundmotions. Nevertheless their inclusion may have a sig-nificant influence on the vulnerability plot and from Fig.1c can be seen to result in a greater uncertainty. Henceit is concluded that the consideration of multiple datasources is necessary for the correct determination of vul-nerability curve reliability.

2.2. Structural unit and damage measure

The occurrence and consequences of structural dam-age can be considered the greatest cause of life and mon-etary loss in the majority of seismic events. The use invulnerability curves of performance states defined byeconomic criteria (e.g. Algermissen and Steinbrugge[15], Miyakoshi et al. [6]), can preclude their applicationto locations other than those considered and may intro-duce a time dependency if the limit-state values arelinked to the financial situation in place at the time of


Fig. 1. Existing vulnerability curves (a) Spence et al. [1] curves for RC frames using the MSK [2] damage scale; (b) Orsini [3] curves for RCframes using the MSK [2] damage scale; (c) Singhal and Kiremidjian [9] curves for low-rise RC MRF (points updated with observational data areshown as the larger symbols in the shaded area) using the Park and Ang [10] damage index; (d) Mosalam et al. [11] curves for low-rise RC MRFusing inter-storey drift values to define damage.

the earthquake. No simple relationship exists betweenstructural damage and monetary risk, and the curvesbased on property loss of Miyakoshi et al. [6] were seento under-predict the damage observed in RC buildingsafter the Kobe earthquake (Japan, 1995). The use ofapartments as the structural unit by Orsini [3] is not justi-fied physically if soft-storey failure mechanisms are con-sidered and, given the approximate nature of existinginventory data, results in limited practical application.RC buildings and global structural damage must there-fore be used as the structural unit and loss evaluationparameter, respectively. Further, for the purpose of thispaper the buildings must be of similar design to thoseconstituting the European stock.

In order for vulnerability curves to be used in a per-formance-based framework, it is desirable that the selec-ted damage scale is defined in terms of at least threedamage limit states, corresponding to serviceability,damage control and collapse prevention. Miyakoshi etal. [6] and Yamazaki and Murao [4], both fall short ofthis requirement. The damage scale limit states must alsobe clearly defined in terms of the damage expected inthe structural and non-structural elements of buildingswith different lateral load resisting systems. For analyti-cal curve derivation, the damage scale should further becalibrated to a measurable structural response parameter.

The choice of response parameter for the calibration andits values are important in determining the reliability ofthe vulnerability relationships. The use of structural duc-tility for this parameter, as in Onose [8], is deemedunsuitable due to its inability to detect failures arisingfrom damage concentrated at the storey level. Maximuminter-storey drift is able to detect such failure modes andis used by Mosalam et al. [11]. However, the latter useengineering judgement to assign parameter values to thelimit states that are observed to be very low and resultin curves, which despite being labelled ‘heavy’ and‘major’ , are unsuitable for high damage state assess-ments.

2.3. Ground motion characterisation

In a vulnerability relationship, the horizontal axis rep-resents the seismic demand. The measure chosen shouldbe capable of representing the influence of source, pathand site on the strong ground motion and should beevaluated independently of the seismic vulnerability ofthe building stock on which it is imposed. Neverthelessmany existing vulnerability curves adopt intensities tocharacterise the ground motion, which are evaluatedfrom observations of earthquake effects and hence incor-porate elements of structural vulnerability (e.g. ATC-13


[7], Spence et al. [1], Orsini [3]). Intensity has the furtherdisadvantage of being a subjective and discrete scale, notassociated with reliable attenuation relationships. Yama-zaki and Murao [4] adopt peak ground velocity (PGV)to characterise the seismic demand. However the authorsadopt an iterative derivation methodology, wherein thePGV values are re-estimated and the associated damageexceedence probabilities are modified such that the axesof the generated vulnerability curves are effectivelyinter-dependent and the ground motion axis is no longerrepresentative of that observed. The use of a groundmotion parameter that is related to structural damageresults in a reduced data scatter and misleading sense ofconfidence in the risk assessment results.

2.4. Verification with observational damage data

The validity of vulnerability relationships should bedetermined through comparison with actual observationsof post-earthquake damage. Surprisingly, existing vul-nerability curves are rarely verified for field observationsother than those used in their derivation. The limited nat-ure of the empirical data incorporated in hybrid curveshas been discussed above. The lack of empirical cali-bration of the vulnerability relationships in America isfurther highlighted in Reitherman [16]. Of the reviewedcurves, only Singhal and Kiremidjian [9] and Onose [8]make specific attempts at verification with limited quan-tities of observational post-earthquake damage data fromthe Northridge (USA, 1994) and Miyagi-ken Oki (Japan,1978) earthquakes, respectively, and both report a lim-ited success in the damage prediction.

It has previously been stated that vulnerabilityrelationships developed for non-European countries maybe site-specific, due to inherent assumptions as to thebuilding population composition. However, it is possiblethat if the vulnerability relationships distinguish betweenthe seismic resistance of structures with distinct lateral-load resisting systems, heights and seismic design codes,they may be used in the assessment of European build-ings with similar structural characteristics. This state-ment assumes that a sufficient degree of structural uncer-tainty is included in the derivation of the curves toovercome any differences in construction practice anddetailing that may distinguish the different locations. Toassess the validity of this assumption a comparison ismade between existing vulnerability curve damage pre-dictions and observational damage data collected fromthe literature for European structures. The vulnerabilityrelationships used for the comparison are chosen fromeach generic category as those most pertinent to Euro-pean buildings. The observational damage data used forthe comparison derives from the empirical databasedescribed in this paper and is converted to the damagescale associated with the analysed curves using Table 6,and Tables A 1 to A4. Two sets of observational damage

data are used for the comparison and the results are sum-marised in Table 2.

In the first instance, data relating to populations ofEuropean structures with the same lateral load resistingsystem as assumed by the existing curves are used. Inthe second case, the comparison is carried out usingobservations made only for the structures, countries andearthquakes specified by the existing vulnerabilitycurves as being within their limit of application. Largediscrepancies between observed and predicted damageestimates result in both cases, with the mean errors inthe second case always being significantly greater thanin the first case. Though based on very few cases, thissuggests that the uncertainty in prediction associatedwith the application of the curves to building types spe-cific to the country of their origin is comparable to thatobtained from their application to European buildings ofsimilar structural system. This observation thereforeimplies that the use of non-European vulnerabilitycurves in a European risk assessment is indeed possiblegiven appropriate consideration of structural similitude.Furthermore it would seem to justify the combinationof observational damage data for similar constructionsderiving from different countries and earthquakes in thederivation of new empirical relationships.

Despite these positive conclusions, the use of thereviewed curves is not recommended for application tothe seismic assessment of reinforced concrete buildingpopulations in Europe. The small quantity and groundmotion range of the data used for the verification resultsin misleadingly high correlation coefficient values (e.g.Fig. 2), but large errors in prediction are evident in allcases (Table 2). These arise from a combination of errorsinherent in the empirical data used for the comparisonand from the assumptions made regarding damage datasource, structural unit, damage and ground motioncharacterisation in their derivation. From the above dis-cussion it is concluded that there are no vulnerabilitycurves at present that meet all the criteria necessary fora reliable European seismic risk assessment tool.

3. Description of the damage data bank

In this paper, new empirical relationships are derivedfrom a database of observed post-earthquake damagedistributions collected from 29 survey reports publishedby research groups and governmental authorities. The 99datasets forming the statistical basis for the curve deri-vation each consist of the damage distribution observedin a population of reinforced concrete buildings surveyedat a specific location after the occurrence of an earth-quake. For all datasets, site recordings of the groundmotion and information regarding the earthquake andsite geology are included to allow the determination ofits associated ground motion parameter. The database


Table 2Comparison of existing vulnerability curves with observational damage statistics

Source Structure type Comparison with observations for European Comparison with observations for structuresstructures of the same lateral-load resisting of the same type, country and earthquakesystem

No. of No. of m(�)a R2 b No. of No. of m(�) R2

Datasets Bldgs Datasets Bldgs

Spence et al. [1] Non-seismic Bare MRF 28 3306 0.39 0.55 – – – –Orsini [3] Bare MRF 26 293636 0.64 0.50 16 2208 0.77 0.50ATC-13 [7] Non-ductile low-rise MRF 30 3682 0.44 0.52 4 1476 1.82 0.49ATC-13 [7] Non-ductile mid-rise MRF 8 290832 0.31 0.42 – – – –Singhal et al. [9] Low-rise bare MRF 12 1842 0.10 0.38 4 1476 0.15 0.44Singhal et al. [9] Mid-rise bare MRF 8 290832 0.26 0.52 – – – –Mosalam et al. [11] Low-rise bare MRF 14 291847 0.41 0.44 4 1476 1.54 0.49Mosalam et al. [11] Infilled Frame 8 1544 0.78 0.39 – – – –

a m(�) = mean error in prediction.b R2 = coefficient of correlation of the data to the fitted curves.

Fig. 2. Comparison of existing curves with European, (same structure), observational damage statistics (a) Spence et al. [1], using the MSK [2]damage scale; (b) Singhal and Kiremidjian [9] low-rise RC MRF, using the Park and Ang [10] damage scale.

concerns a total of 340 000 reinforced concrete buildingsand includes observations made in 19 earthquakes. Inorder to obtain sufficient data for the vulnerability curveregression and to cover a large range of ground motions,damage statistics for non-European earthquakes areincluded in the database. However, it is not the numberof datasets in absolute terms that determines the shape ofthe curve but rather their distribution with ground motionseverity. Table 3 shows that across most of the groundmotion range, the proportion European data predomi-nates both in terms of dataset and building number. Thenon-uniform distribution of the latter between differentcountries, earthquake events and structural systems(Tables 3 and 4) are considered in the selection of dam-age scale and the empirical curve derivation method-ology. Only observational statistics concerning structuresof similar lateral-load resisting system to those constitut-ing the existing European stock are considered. Predic-tion errors introduced from differences in construction

practice for such structures were shown to be of compa-rable size on a national/single event andinternational/multiple event scale. Thus, given that theground motion parameter chosen realistically representsthe imposed seismic demand, the combination of obser-vational data for similar structures, deriving from differ-ent locations and earthquakes is justified. The databasecontains data from both tagging surveys and morerefined second-stage surveying processes, with eachobservational dataset being characterised by the use ofdifferent damage scales, and it is this heterogeneity thatposes the largest obstacle to the combination of empiri-cal data.

4. A new damage scale for RC buildings

In order to carry out risk assessments for buildingpopulations of varied composition, it is either necessary


Table 3The composition of the observational damage database and the distribution of the relative proportion of European and non-European (a) datasetsand (b) buildings, with Sd5%

Country Earthquake Ms No. of data-sets No. of bldgs

Algeria Chenoua, 1989 5.7 1 1073Chile Valparaiso, 1985 7.8 1 322Greece Korinthos, 1981 6.7 1 97

Alkyonides Gulf, 1981 6.4 2 286Kalamata, 1986 5.9 2 625Aegion, 1995 6.5 1 1157Konitsa, 1996 5.4 3 264

Italy Campania, 1980 6.9 28 3306Umbria-Marche, 1997 5.9 2 753

Japan Miyagi-ken-oki, 1978 7.7 3 349Kobe, 1995 6.8 37 33 857

Mexico Mexico City, 1985 8.1 3 4896Philippines Luzon, 1990 7.8 1 181Turkey Erzincan, 1992 6.8 2 447

Adana-Ceyhan, 1998 6.2 1 65Kocaeli, 1999 7.8 7 290 718

USA Santa Barbara, 1925 6.3 1 24Long Beach, 1933 6.2 1 22Northridge, 1994 6.8 2 1430

Total 99 3 391 872

Table 4The structural composition of the empirical database

Structural type Bare MRF Infilled MRF Shear walls Undefined system Total

Total no. of datasets 43 8 1 47 99Total no. of buildings 296 513 2720 322 40 317 339 872Datasets discretised by height Low-rise (� 3 floor) 36 8 0 10 54

Med-rise (4–7 floor) 13 2 1 43 59High-rise (�8 floor) 6 2 0 8 16

Datasets deiscretised by seismic code Pre-code 33 4 0 28 65Old-code 10 3 1 21 35New-code 0 1 0 2 3

to develop a series of vulnerability curve sets for differ-ent building types where the performance criteria aredefined according to the specified structural character-istics, or use observational damage statistics that providea compositional match to the assessed building stock. Inpractice, it is impossible to find the quantity and rangeof damage distribution data required for either of theseapproaches to be implemented with any confidence inthe result.

A new approach is therefore proposed in this paperwherein data for different structural systems can be com-bined to produce a single set of ‘homogenised’ or ‘gen-eral’ curves applicable to all, through the use of a dam-age scale that accounts for the differences in the damagerate of disparate systems. Such a damage scale isrequired to adopt limit states that are defined in terms

of both the damage expected in different structural sys-tems and of a structural response parameter indicativeof the global building damage state. Existing codifieddamage scales were reviewed (Rossetto [23]) but werenot found to be appropriate for use in the homogeneouscurve generation. Many use unclear or ambiguous word-ing to define the damage limit states, do not explicitlyconsider differences in building lateral-load resistingsystem or damage to non-structural members. The defi-nition of limit states in terms of structural response para-meter values is infrequent and is carried out using eitherover-conservative values based on engineering judge-ment, or experimental calibrations based on small quan-tities of data that do not concern the full range of struc-tures covered by the scales. For example, the differencesshown in Table 7 between empirically defined limit state


inter-storey drift values for non-ductile frames and shearwalls and those proposed by FEMA-273 [19] is mainlyattributed to the fact that experimental data used in thecalibration of FEMA-273 [19] is limited to tests on low-rise concrete shear walls, new RC structures and non-structural elements published in Kircher et al. [24], Fer-ritto [25], and Division of the State Architect Report[26], respectively. In the case of rehabilitation codes thatadopt force-based methods of structural assessment theparameter values proposed may be unreliable even whenempirically calibrated as they may be representative ofspecified reductions in building strength rather than dif-ferent observed damage states.

A new damage scale named the homogenisedreinforced concrete damage scale (HRC scale) is there-fore proposed and used herein to generate vulnerabilitycurves. The scale is subdivided into seven damage states,each of which is clearly defined in Table 5 in terms of

Table 5The HRC-Scale: Typical damage expected in ductile, non-ductile and infilled RC moment resisting frames andin RC shear-wall structures

the typical structural and non-structural damageexpected in the four main types of reinforced concretestructure found in Europe. The limit states are furtherdefined in terms of a damage index, the HRC-damageindex (DIHRC), which provides a numerical referencescale for experimental calibration with the structuralresponse parameter of maximum inter-storey drift ratio(ISDmax%). The calibration was carried out using pub-lished experimental reports on 25 dynamic tests for RCbare, infilled and shear-wall structural models, whereinthe progression of structural damage and inter-storeydrift response were recorded. Through interpretation ofthe reported global damage, HRC-damage index valueswere assigned to the test specimens at different timesduring the experiments, resulting in a total of 105 pairsof ISDmax%–DIHRC values. Non-linear regressions werecarried out on these points and relationships derived foreach of the building categories of Table 5 separately, as


well as for general structures of unknown lateral load-resisting system. These relationships were further vali-dated and updated using the results of pseudo-dynamictests carried out on two full-scale frames (one bare andone infilled) and two shear-wall structure within the‘ Innovative Seismic Design Concepts for New andExisting Structures’ (ICONS) European Union fundednetwork. The final equations and the correlation coef-ficients resulting from their fit to the experimental dataare presented in Eqs. (1–4), where ISDmax% is expressedin terms of percentage.

DIHRC � 34.89Ln(ISDmax%) � 39.39, R2 � 0.991 for non-ductile MRF (1)

DIHRC � 22.49Ln(ISDmax%) � 66.88, R2 � 0.822 for infilled frames (2)

DIHRC � 39.31Ln(ISDmax%) � 52.98, R2 � 0.985 for shear-wall systems (3)

DIHRC � 27.89Ln(ISDmax%) � 56.36, R2 � 0.760 for general structures (4)

These equations are used to define the limit state bound-ary values of ISDmax% for the HRC-scale shown in Table7, which are used to determine the damage state exceed-ence probabilities in the vulnerability curve generation.

5. Derivation of new empirical vulnerabilityfunctions for Europe

Empirical vulnerability functions for reinforced con-crete buildings in Europe were derived using the 99observed post-earthquake damage distributionsdescribed in Table 3. Each dataset can be visualised asa bar chart (Fig. 3a), wherein the proportion of the sur-veyed buildings lying within each damage state are plot-ted side-by-side in order of increasing damage severity.As the datasets are each defined in terms of differentdamage scales, the bar charts thus obtained cannot bedirectly compared to each other. Furthermore theassumption of a uniform distribution of the damagestates along the horizontal axis of the plots is physicallyunrealistic due to the non-linear nature of damage pro-gression in structures. To allow the different damage lev-els described in disparate datasets to be compared andallow a uniform criterion for the damage evaluation, all99 datasets were re-interpreted in terms of the HRC-scale. Poland [27] attempted to correlate three damagescales in America, however there is no such publishedrelationship of equivalence on an international level.Therefore four approximate correlation tables,(corresponding to the different structural systems ofTable 5), were drawn between the HRC and other exist-ing damage scales from the authors’ personal interpret-ation of the relative limit state damage descriptions. Thecorrelation tables are presented in the Appendix and

were used to assign DIHRC values to the damage statesof every dataset according to the predominant lateral-load resisting system of the surveyed buildings. Afurther correlation table for general RC structures isshown in Table 6 for use when the latter is not inferablefrom post-earthquake survey reports. Eqs. (1–4) werethen used to convert the thus assigned damage indicesinto equivalent ISDmax% values. The 99 datasets were re-plotted using maximum inter-storey drift ratio(normalised to 6%) as the horizontal axis (Fig. 3b) andcontinuous probability distribution functions fit to each

(Fig. 3c). Many functional forms were considered forthe damage frequency representation and Kolmogorov-Smirnov one-sample tests at significance levels of 1, 5and 10% were carried out to assess the goodness of fitof the functions with the data. A bias of the frequencyplots towards the low or high damage states wasobserved in the case of small and severe ground motionsrespectively, which was seen to be best represented bybeta-probability distribution functions. Cumulative betadistributions were therefore fitted to each of the 99 re-interpreted damage datasets using the non-linearregression module of the program STATISTICA(Version 5.0, StatSoft [28]), which evaluates the modelfunction shape parameters through minimisation of thesquare of the residuals. The HRC damage state exceed-ence probabilities were next determined from the fittedcumulative distributions using the ISDmax% valuesdefined in Table 7 for the appropriate structural system.This results in 99 values of exceedence probability foreach of the HRC damage limit states, which when plot-ted against the corresponding ground motion parameterforms a vulnerability plot.

Equal weighting of the exceedence probability pointsis commonly assumed in the generation of existingempirical curves due to the small quantities of obser-vational data considered. In the present case a weightingprocedure is required to deal with the substantial amountof raw data available and large associated scatter (Fig.4a). In the presence of similar ground motion severitiesthe damage state exceedence probabilities derived fromeach dataset were therefore combined according to rela-tive numbers of surveyed buildings. The weighted stat-istics were plotted against the median value of the corre-sponding ground motion interval and non-linearregressions carried out to derive the vulnerability


Fig. 3. Conversion of the RC building damage statistics observed inPlateas after the Korinthos earthquake (Greece, 1981) to the HRC-scale.

relationships (Fig. 4b). Apart from facilitating the identi-fication of trends in the data, the weighting procedurereduces the influence on the curve shape of single earth-quake events and of non-European earthquakes (in viewof the relative proportions of European and non-Euro-pean data in Table 3). The high frequency of small mag-nitude earthquake observations at low ground motionslessens the influence of any single such event, as wellas any large magnitude event observation, for thisregion. As probabilities of exceedence of damage statesrather than damaged building numbers are combined forthe curve determination, the influence of datasets withlarge sample sizes is attenuated and are not seen tounduly influence the curve shape at low ground motion

levels. This is seen to be true even in the specific caseof the Kocaeli earthquake (Turkey, 1999), which has dat-asets of large sample size. The latter earthquake providesa vast source of damage data for a variety of structuralclasses and a unique source for European damage obser-vations in the large ground motion range. Its influenceon the vulnerability curve shape in this range is seen tobe significant but is justified by the high reliability ofthe data and its relevance to a European risk assessmentscenario. The scarcity of observations for the highground motion range does however result in wide confi-dence bounds that more-than compensate for the uncer-tainty in the vulnerability curve shape. Various cumulat-ive distribution functions were again assessed to modelthe vulnerability curve shapes. A comparison of themodels was carried out considering both accelerationand displacement-based peak and spectral groundmotion parameters. The functions most commonly usedin existing relationships are cumulative normal and log-normal distributions, however following many trials arelationship of the form of Eq. (5) was found to yield theoptimum fit for all considered ground motion parameters(GM). This functional form is therefore used to derivethe empirical vulnerability curves in this paper, with theparameters a and b being found from non-linearregression on the plotted observational data.

P(d�DIHRC|GM) � 1�exp(�a.GMb) (5)

Vulnerability curves were derived using peak groundacceleration (PGA), spectral acceleration and displace-ment for 5% of critical damping (Sa5%(Telastic) andSd5%(Telastic)) and inelastic spectral displacement for aductility based damping value (Sdm%(Tinelastic)), see Fig.5. Where ground motion records were available for thesurvey location these were used to evaluate the con-sidered parameters, otherwise attenuation relationshipswere selected based on the survey site location and rel-evant fault mechanism. In the case of PGA andSa5%(Telastic), the relationships of Ambraseys et al. [29]were used for datasets regarding European and MiddleEastern countries, Joyner and Boore [30] for the UnitedStates of America and Youngs and Chiou [31] for Japan,Chile, Mexico and other subduction zones. For the spec-tral displacements the attenuation relationships of Borziet al. [32] were used for all site locations. Unless a spe-cific estimate of the typical structural period wasreported, this was estimated from the predominant sur-veyed building heights using the expressions in Euroc-ode 8. Sdm%(Tinelastic)) was introduced in an attempt toaccount for the effects of damage, consequent periodelongation and increased energy dissipation on the seis-mic demand. The ductility values associated with the dif-ferent damage state curves were calculated assuming topdrifts of equal value to the inter-storey drifts in Table 7(i.e. linear variation in structural displacement withheight) and that the ‘moderate’ damage state corre-


Table 6The equivalence between existing damage scales and HRC-Scale for general RC structures

Table 7Threshold values of ISDmax% defining the HRC-scale damage limit states for general RC structures (All), non-ductile MRF, infilled MRF and shear-wall structures

ISDmax%(%) limits for HRC-scale HRC and FEMA- 273 [19] ISDmax%(%) limits

HRC damage state All N-D MRF Infilled MRF Shear-walls FEMA-273 damage state N-D MRF Shear-walls

HRC F273 HRC F273

None 0.00 0.00 0.00 0.00Slight 0.13 0.32 0.05 0.26 Immediate occupancy 0.00 0.00 0.00 0.00Light 0.19 0.43 0.08 0.34Moderate 0.56 1.02 0.30 0.72 Life safety 1.36 1.00 0.93 0.50Extensive 1.63 2.41 1.15 1.54Part. Coll. 3.34 4.27 2.80 2.56 Collapse prevention 3.20 4.00 1.99 2.00Collapse �4.78 �5.68 �4.36 �3.31

Comparison of the ISDmax% limit state threshold values in FEMA-273 [19] with those given by Eqs. 1 and 3 using the scale correlation TablesA1 and A4.

sponded to structural yield, (e.g. for general structures:m = 2, 4.15 and 6 for ‘extensive’ , ‘partial collapse’ and‘collapse’ , respectively). The resulting ductilities werethen used to calculate the damping, inelastic period andcorresponding inelastic spectral displacement(Sdm%(Tinelastic)), for all limit states exceeding ‘Moderate’using Borzi et al. [32]. The empirical vulnerabilityrelationships for the different ground motion parametersare summarised in Table 8. An increase in the damageprobability of buildings is expected to coincide with anincrease in seismic demand. Therefore, as the samesources are used for the attenuation relationships in eachcase, the correlation of the curves with the observational

data gives a direct indication of the relative worth of theparameters as measures of earthquake damage potential.

The correlation is fairly poor and the mean predictionerror is substantial in all cases. PGA yields a worse fitthan the spectral parameters as it is unable to accountfor the contribution of earthquake duration, record cycle,peak and frequency content on the ground motion dam-age potential, nor the effects of structural dynamicproperties and site geology on the seismic demand (Fig.6). This factor contributed to the large under-predictionof damage observed by Rossetto [33] when the derivedPGA curves were applied to a case study of the Bhujearthquake (India, 2001). The vulnerability curves


Fig. 4. The final homogenised empirical vulnerability curves for RCstructures compared to (a) the unweighted observational damage stat-istics and (b) the weighted observational damage statistics.

derived using spectral displacement show a better corre-lation to the empirical data than those using spectralacceleration, and demonstrate the superiority of displace-ments in the representation of earthquake damage poten-tial. In the case of Sdm%(Tinelastic), the correlation for thehigher damage states is improved compared toSd5%(Telastic) and the width of the confidence bounds isconsiderably reduced. This parameter shows promise butdue to the limited data available for higher damage statesfurther investigation is required. The final proposed vul-nerability curves therefore adopt Sd5%(Telastic), and arehence amenable for use in a displacement-based assess-ment framework.

The vulnerability curves described in Table 8 are‘homogeneous’ as they combine all the available obser-vational data regardless of structural type. This assumesthat the use of the HRC damage scale, which distingu-ishes between buildings with different dynamic proper-ties, is sufficient to eliminate the curve shape depen-dency on structural type. In order to test this assumption,the vulnerability curves were re-derived considering sub-sets of the observational data appertaining to the differ-ent lateral-load resisting system, seismic design code andheight classes of Table 4. The resulting ‘class-specific’curves are summarised in Table A5. Where insufficientempirical data are available for the class-specific curvederivation the observations are compared directly to thegeneral curves to assess the building class influence.

In the case of infilled frames, the vulnerability is veryslightly under-predicted by the general curves in the lowdamage range whilst no difference is observed at highlevels of damage and only slight differences between thegeneral and bare MRF vulnerability curve shapes areseen for the ‘moderate’ damage state. Furthermore, simi-lar correlation values and prediction errors are obtainedwhen the structure-specific and homogenised curves areapplied in the damage prediction of infilled and bareframes. This indicates that the influence of the non-struc-tural wall presence on the building response is mostlyremoved from the curve shape and therefore that thehomogeneous curves can be used with a good degree ofconfidence in the assessment of these systems. Insuf-ficient data are available for any conclusion to be maderegarding shear-wall structures, and it is recommendedthat the homogenised vulnerability curves not be usedor the lower bound 90% confidence curve be adopted inthis case. Due to a lack of experimental data for cali-bration, the different levels of structural seismic designor construction quality are neglected by the HRC-scaleand hence the influence of these factors is not success-fully removed from the general curves. This is illustratedby the significant influence of height- and seismic-codeclass on the ‘slight’ to ‘extensive’ damage state curves.The general curves tend to over-predict the damageobserved in low-rise bare moment resisting frames forthe low damage states and under-predict that for higherlimit states (Fig. 7a), whilst the reverse is true in thecase of mid-rise frames. The discrepancies between thehomogeneous and ‘height-specific’ curves are attributedto the typically different building regulations used in thedesign of buildings of disparate height-classes. This isfurther illustrated by the damage observations availablefor high-rise bare MRF, which are over-predicted by thehomogeneous curves at high ground motions due to thegreater redundancy and lateral resistance shown com-pared to structures of smaller height. When the re-derived code-specific curves are compared to the generalcurves, the latter are seen to significantly under- andover-predict the vulnerability of pre- and old-seismic


Fig. 5. Empirical vulnerability curves generated for different ground motion parameters.

code structures, respectively. Due to the lack of obser-vational data, no observations can be made regardingstructures designed to modern seismic codes. The differ-ence in the curve shapes is mainly due to the absenceof capacity design in pre-seismic code structures, whichcauses their failure in earthquakes via predominantly softstorey modes. This mode of failure is associated with arapid transition between low levels of damage and thecollapse limit state, which is reflected in the pre-codevulnerability relationships by a closer proximity of thecurves and a more rapid ascension with increasingground motion. The contribution of poor constructionquality and irregularity in precipitating localised struc-ture failure modes was observed to be the main causeof the large under prediction of damage to RC structuresin Ahmedabad after the Ms 7.9 Bhuj earthquake (India,2001) by the homogenised curves (Rossetto [33]).

The structure type, height and code-specific vulner-ability relationships are associated with higher corre-lation coefficients and lower prediction errors than thehomogenised curves, however, the size of the scatterremains large. Both homogenous and class-specificcurves assume that damage data deriving from differentcountries and earthquakes for similar lateral loadresisting systems can be combined. In Table 1 it isobserved that the proposed relationships give a better fitto the damage data used for their derivation than isreported by the authors of other existing empirical

curves, despite the substantially larger number of obser-vations and structural types considered. This indicatesthat the procedure used to define the damage states,exceedence probabilities and choice of ground motionparameter have indeed succeeded to significantly hom-ogenise the damage database. This statement is furtherproven by the comparable size of the scatter seen in thegeneral relationships and re-derived ‘single-event’curves obtained using data deriving from the Kobe(Japan, 1995) and Campania (Italy, 1980) earthquakesonly (Table A6). Indeed the difference in shape betweenthe fragility curve sets can almost solely be attributed tothe influence of the predominant structure classes, (mid-rise, old-seismic code and low-rise, pre-seismic codeframes for Kobe and Campania, respectively). The simi-lar scatter for single and multiple events tends to confirmthe stipulation that much of the uncertainty arises fromdamage classification errors inherent in the obser-vational data.

To allow conservative risk assessments to be madeconfidence bounds were defined for the homogeneouscurves. It is not sufficient to assume a constant standarddeviation from the mean prediction for all damage statecurves and ground motions (e.g. Spence et al. [1]) as therelationships are non-linear, the distribution of scatteraround the curves is not constant and that there is a biasin the quantity of data for low damage states and groundmotions. Therefore in this paper, the confidence associa-


Table 8Summary of the empirical vulnerability relationships developed for different ground motion parameters and their fit to the observational data

HRC damage Curve parameters Bldgs Non-weighted data Weighted datastate

Mean U90% L90% Data sets m(�) cov (�) R2 Data sets m(�) cov (�) R2

a b a b a b

PGASlight 1.556 1.60 3.950 1.60 0.830 1.60 339872 99 0.27 0.80 0.37 9 0.37 0.77 0.33Light 1.055 1.80 2.732 1.80 0.620 1.80 339187 90 0.24 1.04 0.29 8 0.37 0.76 0.35Moderate 0.250 3.00 0.903 3.00 0.102 3.00 331702 69 0.21 0.96 0.34 8 0.26 0.74 0.36Extensive 0.093 4.00 0.538 4.00 0.010 4.00 329152 49 0.08 1.32 0.27 7 0.08 0.92 0.36P.Collapse 0.009 5.80 0.162 5.80 0.001 5.80 292839 35 0.03 1.41 0.26 7 0.01 0.78 0.39Collapse 0.001 8.00 0.005 8.00 0.001 8.00 77876 24 0.01 1.42 0.26 4 0.00 1.51 0.28

Sa5%(Telastic)Slight 0.633 1.80 1.865 1.80 0.192 1.80 339872 99 0.25 0.84 0.39 15 0.30 1.04 0.39Light 0.396 1.80 1.356 1.80 0.116 1.80 339187 90 0.22 1.05 0.30 15 0.29 1.05 0.37Moderate 0.153 1.80 0.524 1.80 0.041 1.80 331702 69 0.17 1.07 0.28 14 0.19 0.99 0.39Extensive 0.090 2.00 0.447 2.00 0.036 2.00 329152 49 0.08 1.13 0.26 14 0.08 1.00 0.52P.Collapse 0.050 2.20 0.265 2.20 0.031 2.20 292839 35 0.04 1.40 0.40 13 0.05 1.68 0.49Collapse 0.010 3.00 0.056 3.00 0.006 3.00 77876 24 0.01 2.29 0.44 8 0.03 2.27 0.49

Sd5%(Telastic)Slight 25.82 1.10 76.45 1.10 13.72 1.10 339872 99 0.23 0.83 0.37 15 0.23 1.25 0.58Light 21.08 1.20 73.88 1.20 8.350 1.20 339187 90 0.23 0.93 0.30 15 0.22 1.27 0.59Moderate 6.500 1.15 29.57 1.15 2.342 1.15 331702 69 0.17 1.02 0.30 14 0.14 1.37 0.50Extensive 3.000 1.30 17.52 1.30 1.323 1.30 329152 49 0.07 1.32 0.28 13 0.06 0.97 0.49P.Collapse 2.500 2.00 13.45 2.00 1.200 2.00 292839 35 0.03 1.37 0.28 12 0.02 0.72 0.47Collapse 2.000 2.40 9.37 2.40 1.119 2.40 77876 24 0.01 1.62 0.36 6 0.02 1.07 0.29

Sdm%(Tinelastic)Extensive 2.500 1.30 10.18 1.30 0.926 1.30 329152 49 0.08 1.27 0.28 19 0.07 1.56 0.57P.Collapse 1.600 2.00 7.497 2.00 0.740 2.00 292839 35 0.03 1.40 0.27 16 0.06 1.60 0.48Collapse 0.600 2.40 1.076 2.40 0.125 2.40 77876 24 0.01 1.42 0.27 5 0.003 0.76 0.45

a and b, the parameters defining the curves according to Eq. (5) for the mean curves, upper and lower 90% confidence bounds (U90% and L90%,respectively). Datasets, no. of datasets used for the derivation and comparison (weighted and non-weighted respectively). m(�), mean error inprediction; cov(�), the coefficient of variation of the error in prediction; R2, coefficient of correlation of the data to the fitted curves.

Fig. 6. Example of the difference in the vulnerability point distribution for different ground motion parameters using observations of low andmid-rise building damage (small and large symbols, respectively) in Aegion after the Aegion (Greece, 1995) earthquake.


Fig. 7. Comparison of homogeneous curves (full grey lines) with vulnerability curves derived for specific structural categories (dashed blacklines): (a) Low-rise frames; (b) Pre-seismic code frames.

ted with each damage state curve was assessed acrossthe vulnerability plot by dividing the ground motion axisinto intervals. Each interval was taken in turn, and thestandard deviation of the plotted data about each damagestate curve was calculated. Student-T distribution func-tions were hence defined for each ground motion intervaland damage limit state, and were used to locate the pos-ition of the 95% and 5% confidence levels. Non-linearregressions were carried out on these points to definerelationships of the form of Eq. (5) for the upper andlower 90% confidence bounds of each damage state.Wide confidence bounds are observed for all limit states(Fig. 8), which are similar in size to those derived bySinghal and Kiremidjian [9] for their analytical curves.At low damage states wide confidence bounds arise fromscatter associated with errors inherent in the survey stat-istics (discussed previously), whilst scarcity of dataresults in wide confidence bounds when Student T-distri-butions are applied to high damage states.

6. Concluding remarks on application and futuredevelopment

Empirical vulnerability curves have been presentedfor use in the seismic risk assessment of populations ofreinforced concrete buildings. A new damage scalenamed the HRC-scale is introduced, which is experimen-tally calibrated to the parameter of maximum inter-storeydrift ratio, for structures of different lateral load resistingsystem. This scale is related to existing damage scalesand adopted in the empirical curve generation with theaim of producing a single set of ‘homogeneous’ or ‘gen-eral’ vulnerability relationships that are applicable to alllateral-load resisting systems. These empirical vulner-ability curves relate the probability of exceeding thedeformation-based HRC damage limit states to the seis-mic demand parameter of spectral displacement evalu-ated at the elastic period of vibration for 5% criticaldamping, and are adequate for use in a displacement-

based assessment framework. The proposed homo-geneous relationships show a better correlation withobserved damage than existing empirical relationshipsdespite their inclusion of a greater number of structuralclasses. In the case of the structure specific curves, thecorrelation is further improved and hence a substantialimprovement has been achieved, within the limitsimposed by the quality and quantity of data available,through use of the proposed vulnerability curve gener-ation process, selection of damage scale and groundmotion parameter. The sensitivity of the homogeneouscurves to different building characteristics was investi-gated and a considerable success was observed in theremoval of the influence of lateral load resisting systemon the vulnerability curve shape through the use of theHRC damage scale. However, other building character-istics that affect the lateral load resistance are seen topreclude the curve use in the vulnerability assessment ofhigh-rise buildings and buildings pre-dating seismiccode implementation. It is therefore concluded thatunless a greater quantity and variety of large-scaleexperiments are carried out for the calibration of theHRC-damage scale, the effects of construction qualityand seismic design may only be accounted for throughthe use of separate vulnerability curve sets, generated forstructures of predominantly different heights and seismicdesign codes. Curves for pre- and old seismic code, low-and medium-rise frame categories are presented in theAppendix, however a greater quantity of empirical datais needed in order to generate curves for shear-wall,high-rise and new seismic code structures. As it isimpossible to remove from the curves the scatter orig-inating from the inherent heterogeneity of the buildingsurvey sample and erroneous assessments of buildingdamage in the original reported statistics, it is rec-ommended that the curves be applied with due consider-ation of the associated uncertainties.

From the results of this investigation, it is evident thatthe derivation of vulnerability curves from empiricaldata alone is not sufficient for the realisation of a risk


Fig. 8. The proposed empirical vulnerability curves (dark lines) and 90% confidence bounds (light lines): (a) Mean curves; (b) Slight and extensivedamage states; (c) Light and partial collapse damage states; (d) Moderate and collapse damage states.

assessment tool that can be applied with a high degreeof confidence to populations of reinforced concretebuildings in Europe. It is concluded that for such a toolto be developed it is essential that empirical observationsare supplemented by analytically-simulated damage stat-istics. Further research is currently underway for thispurpose.

Acknowledgements

The research work represented in this paper wasfunded by the European Community under the auspices

of the ‘Safety Assessment For Earthquake RiskReduction’ (SAFERR) Research Training Network.Thanks are also due to Dr. Antonios Pomonis (RMS,Greece) and Ms. Maria Panoutsopoulou (OA�,Greece) for their contribution to the collection of earth-quake damage data. Funding for the primary author’svisit to Gujarat (India) was provided by the EngineeringSeismology and Earthquake Engineering Section atImperial College and logistical arrangements wereundertaken by the Mid-America Earthquake (MAE)Center (NSF-funded, Grant EEC-9701785), who alsoprovided financial support for the primary author’s workat the University of Illinois at Urbana-Champaign duringNovember 2001.


Appendix

Table A1Damage scale correlation table for ductile RC MRF

Table A2Damage scale correlation table for non-ductile RC MRF


Table A3Damage scale correlation table for infilled RC frames

Table A4Damage scale correlation table for RC shear-wall structures


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0.53

10.

561

0.44

2M

oder

ate

7.50

01.

1529

.570

1.15

2.34

21.

1527

204

0.22

01.

136

0.39

10.

226

1.09

90.

391

2720

80.

238

0.86

80.

379

0.24

40.

847

0.38

2E

xten

sive

3.20

01.

3017

.518

1.30

1.32

31.

3024

604

0.00

41.

982

0.98

70.

003

2.53

30.

987

2460

70.

006

0.86

40.

444

0.00

60.

889

0.42

7

Low

-ris

eba

reM

RF

(�3

floor

s)Sl

ight

25.8

171.

1012

5.27

1.10

2.39

01.

1053

729

0.10

42.

598

0.72

00.

104

2.59

80.

720

5372

350.

140

0.70

40.

552

0.14

00.

704

0.55

2L

ight

18.5

601.

2080

.480

1.20

4.10

01.

2051

598

0.09

01.

205

0.90

90.

112

0.91

00.

909

5159

290.

099

0.94

20.

395

0.10

30.

932

0.43

0M

oder

ate

5.50

01.

3030

.560

1.30

2.00

01.

3024

385

0.05

00.

875

0.94

30.

076

0.66

00.

943

2438

100.

087

1.41

90.

179

0.09

11.

200

0.19

7E

xten

sive

4.67

11.

3016

.380

1.30

0.60

01.

3016

673

0.08

01.

832

0.21

20.

091

1.58

70.

212

1667

50.

061

1.41

80.

284

0.06

61.

475

0.26

6P.

Col

laps

e5.

100

1.60

17.1

151.

600.

500

1.60

1455

30.

033

1.88

80.

020

0.04

31.

413

0.02

014

553

0.03

31.

338

0.34

90.

043

1.35

50.

311

Col

laps

e3.

160

2.00

10.3

202.

000.

300

2.00

1455

30.

005

2.31

60.

004

0.00

71.

746

0.00

414

553

0.00

51.

648

0.30

40.

007

1.65

80.

262

Mid

-ris

eba

reM

RF

(4–7

floor

s)Sl

ight

48.4

101.

0515

0.00

1.05

3.00

01.

0529

0912

70.

167

2.99

90.

418

0.23

41.

858

0.41

829

0912

100.

151

0.77

80.

651

0.26

10.

469

0.58

5L

ight

39.0

001.

1014

0.00

1.10

5.40

01.

1029

0912

70.

199

2.17

60.

405

0.25

11.

539

0.40

529

0912

100.

180

0.72

40.

643

0.27

60.

575

0.57

2M

oder

ate

5.30

01.

1510

5.00

1.15

0.80

01.

1529

0912

70.

178

1.39

90.

342

0.18

51.

316

0.34

229

0912

100.

172

0.79

30.

561

0.17

50.

752

0.58

4E

xten

sive

4.00

01.

3021

.600

1.30

0.80

01.

3029

0832

60.

127

0.29

10.

314

0.10

10.

396

0.31

429

0832

80.

108

1.06

50.

567

0.08

70.

961

0.57

9P.

Col

laps

e3.

000

2.40

14.7

002.

400.

500

2.40

2571

726

0.02

80.

656

0.36

50.

038

0.77

10.

365

2571

726

0.02

81.

217

0.52

60.

0383

1.41

10.

516

Col

laps

e2.

500

3.00

9.60

03.

000.

300

3.00

6626

12

0.02

21.

405

0.96

90.

039

1.40

90.

969

6626

12

0.02

21.

350

0.50

00.

0395

1.27

00.

500

(con

tinu

edon

next

page

)


Tab

leA

5(c

onti

nued

)

HR

CC

lass

-spe

cific

curv

epa

ram

eter

sC

orre

latio

nw

ithw

eigh

ted

clas

s-sp

ecifi

cda

taC

orre

latio

nw

ithno

n-w

eigh

ted

clas

s-sp

ecifi

cem

piri

cal

data

dam

age

stat

eM

ean

U90

%L

90%

Bld

gsD

ata

Cla

ss-s

peci

ficcu

rves

Hom

ogen

eous

curv

esB

ldgs

Dat

aC

lass

-spe

cific

curv

esH

omog

eneo

uscu

rves

sets

sets

ab

ab

ab

m(�)

cov(

�)R

2m(

�)co

v(�)

R2

m(�)

cov(

�)R

2m(

�)co

v(�)

R2

Pre

-sei

smic

code

bare

MR

FSl

ight

29.4

301.

1022

2.00

1.10

3.47

01.

1036

558

0.12

22.

043

0.72

40.

110

2.35

90.

724

3655

310.

127

0.75

80.

582

0.13

40.

093

0.56

4L

ight

23.0

001.

2016

3.00

1.20

2.50

01.

2034

427

0.12

30.

813

0.93

80.

109

0.88

60.

938

3442

250.

096

0.93

80.

493

0.09

30.

084

0.47

3M

oder

ate

8.86

01.

1575

.000

1.15

2.00

01.

1572

12

0.06

90.

584

0.96

00.

047

0.68

60.

960

721

60.

085

1.18

30.

319

0.08

50.

113

0.23

5E

xten

sive

5.00

01.

3080

.000

1.30

1.70

01.

3025

62

0.09

92.

000

0.15

60.

113

1.71

40.

156

256

30.

069

1.57

80.

287

0.07

90.

126

0.26

7P.

Col

laps

e5.

500

1.60

60.0

001.

601.

200

1.60

642

0.04

12.

061

0.01

40.

055

1.46

20.

014

642

0.04

11.

350

0.35

80.

055

0.07

70.

335

Col

laps

e6.

000

2.00

36.8

002.

001.

000

2.00

251

0.01

00.

000

0.00

10.

019

0.00

00.

001

251

0.00

90.

000

0.50

00.

019

0.00

00.

500

Old

-sei

smic

code

bare

MR

FSl

ight

42.0

001.

1032

0.00

1.10

10.4

001.

1029

2572

80.

228

1.76

30.

466

0.25

61.

486

0.46

629

2572

100.

229

0.57

30.

557

0.28

10.

446

0.54

3L

ight

45.0

001.

2030

8.00

1.20

2.40

01.

2029

2572

80.

240

1.50

20.

447

0.26

61.

281

0.44

729

2572

100.

242

0.53

70.

574

0.29

80.

511

0.54

5M

oder

ate

6.70

01.

2071

.200

1.20

1.80

01.

2029

2572

80.

187

1.15

60.

378

0.18

81.

152

0.37

829

2572

100.

195

0.67

00.

567

0.19

30.

645

0.57

3E

xten

sive

2.00

01.

3023

.500

1.30

1.10

01.

3029

2572

80.

093

0.56

20.

380

0.08

90.

590

0.38

029

2572

100.

084

0.98

60.

587

0.08

00.

959

0.58

9P.

Col

laps

e2.

000

2.00

10.0

002.

000.

600

2.00

2589

128

0.02

60.

691

0.39

60.

031

0.74

70.

396

2589

128

0.02

61.

438

0.52

60.

031

1.53

40.

520

Col

laps

e1.

100

2.50

4.77

02.

500.

300

2.50

6757

73

0.01

21.

200

0.86

40.

025

1.21

30.

864

6757

73

0.01

21.

691

0.49

90.

025

1.71

30.

499

aan

db,

the

para

met

ers

defin

ing

the

curv

esac

cord

ing

toE

q.(5

)fo

rth

em

ean

curv

es,

uppe

ran

dlo

wer

90%

confi

denc

ebo

unds

(U90

%an

dL

90%

resp

ectiv

ely)

.D

atas

ets,

No.

ofda

tase

tsus

edfo

rth

ede

riva

tion

and

com

pari

son

(wei

ghte

dan

dno

n-w

eigh

ted

resp

ectiv

ely)

.m( �

),m

ean

erro

rin

pred

ictio

n;co

v(�)

,the

coef

ficie

ntof

vari

atio

nof

the

erro

rin

pred

ictio

n;R

2,c

oeffi

cien

tof

corr

elat

ion

ofth

eda

tato

the

fitte

dcu

rves

.


Tab

leA

6T

hepr

opos

edsi

ngle

even

tem

piri

cal

curv

esan

dth

eir

corr

elat

ion

toth

ew

eigh

ted

and

non-

wei

ghte

dob

serv

atio

nal

data

HR

Cda

mag

est

ate

Eve

nt-s

peci

ficcu

rve

Cor

rela

tion

with

wei

ghte

dev

ent-

spec

ific

empi

rica

lda

taC

orre

latio

nw

ithno

n-w

eigh

ted

even

t-sp

ecifi

cem

piri

cal

data

para

met

ers

Mea

nB

ldgs

Dat

aset

sE

vent

-spe

cific

curv

esH

omog

eneo

uscu

rves

Bld

gsD

atas

ets

Eve

nt-s

peci

ficcu

rves

Hom

ogen

eous

curv

es

ab

m(�)

cov

(�)

R2

m(�)

cov

(�)

R2

m(�)

cov

(�)

R2

m(�)

cov

(�)

R2

Kob

e(1

995)

Slig

ht10

.697

1.05

3385

73

0.07

74.

151

0.73

50.

121

2.18

10.

735

3385

737

0.90

10.

807

0.24

80.

298

0.52

30.

097

Lig

ht6.

532

1.05

3385

73

0.05

83.

745

0.82

10.

075

2.62

60.

821

3385

737

0.90

10.

797

0.26

20.

254

0.59

80.

025

Mod

erat

e4.

038

1.05

2969

43

0.05

62.

120

0.80

00.

047

2.67

00.

800

2969

433

0.62

20.

819

0.16

70.

160

1.05

50.

126

Ext

ensi

ve1.

591

1.10

2918

62

0.01

24.

973

0.69

80.

012

5.39

30.

698

2918

626

0.36

60.

826

0.16

70.

096

1.12

50.

168

P.C

olla

pse

1.10

01.

7028

848

20.

005

1.95

40.

431

0.00

61.

785

0.43

128

848

210.

135

0.83

20.

258

0.03

81.

122

0.26

3C

olla

pse

0.89

82.

0055

182

0.00

11.

972

0.15

50.

001

1.78

20.

155

5518

170.

037

0.85

30.

237

0.01

01.

251

0.25

3

Cam

pani

a(1

980)

Slig

ht30

.81

1.10

3306

80.

126

1.92

80.

725

0.11

2.41

0.73

3306

280.

127

0.79

70.

583

0.13

0.73

0.56

Lig

ht22

.00

1.20

2621

70.

118

0.87

50.

939

0.11

0.91

0.94

2621

190.

093

0.99

20.

514

0.09

0.98

0.50

Mod

erat

e3.

161.

1537

22

0.00

514

.291

0.96

40.

040.

980.

9637

23

0.14

01.

483

0.23

00.

141.

060.

19E

xten

sive

2.96

1.30

251

0.22

60.

000

0.08

50.

230.

000.

0825

10.

226

0.00

00.

500

0.22

0.00

0.50

aan

db,

the

para

met

ers

defin

ing

the

curv

esac

cord

ing

toE

q.(5

)fo

rth

em

ean

curv

es,

uppe

ran

dlo

wer

90%

confi

denc

ebo

unds

(U90

%an

dL

90%

resp

ectiv

ely)

.D

atas

ets,

No.

ofda

tase

tsus

edfo

rth

ede

riva

tion

and

com

pari

son

(wei

ghte

dan

dno

n-w

eigh

ted

resp

ectiv

ely)

.m( �

),m

ean

erro

rin

pred

ictio

n;co

v(�)

,the

coef

ficie

ntof

vari

atio

nof

the

erro

rin

pred

ictio

n;R

2,c

oeffi

cien

tof

corr

elat

ion

ofth

eda

tato

the

fitte

dcu

rves

.


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