Analytical Estimation of Economic Lossfor Buildings in the Area Struck bythe 1999 Athens Earthquake andComparison with Statistical Repair Costs

A. Kappos,a) V. Lekidis,b) G. Panagopoulos,a) I. Sous,b) N. Theodulidis,b)

Ch. Karakostas,b) T. Anastasiadis,b) T. Salonikios,b) and B. Margarisb)

Reliable loss assessment (in monetary terms) for buildings struck by anearthquake is an essential factor in the development of seismic risk scenariosfor a given urban area. The evaluation of loss due to building damage in acertain region depends both on seismic hazard and the vulnerability of thebuilding stock in the area. The study presented herein consists of predicting theloss to selected groups of buildings struck by the 1999 Athens earthquakeusing an analytical methodology and comparison with statistical repair costscollected after the earthquake. Since no near-field strong ground motionrecordings from the main shock were available, a pilot methodology was usedfor its analytical evaluation for different soil conditions. Different suites ofmotions were derived, based on various theoretical and semi-empiricalapproaches, and were then used in analytical investigations of the seismicbehavior of the buildings in the examined area, aiming at the prediction ofeconomic losses. An in-situ survey of about 10% of the total building stockwas performed, and data regarding the structural type, actual earthquakedamage, and corresponding repair costs were collected. The statisticallyderived repair cost for the area was compared with the economic lossestimation obtained using the analytical procedure and various estimates of theseismic action in the area considered, and was found to agree with itreasonably for some of the seismic hazard scenarios.�DOI: 10.1193/1.2720366�

INTRODUCTION

The aim of the work presented herein is to present analytical techniques for devel-oping earthquake damage scenarios for building stocks typical of those found in South-ern Europe, and to check their validity by applying them to buildings located in the areamost heavily affected by the 7 September 1999 Athens earthquake, and comparing ana-lytically predicted losses with statistical data on repair costs collected after the earth-quake.

a) Aristotle University of Thessaloniki, Laboratory of Reinforced Concrete & Masonry Structures, 54124,Greece; E-mail: ajkap@civil.auth.gr

b)

Institute of Engineering Seismology and Earthquake Engineering, P.O.B. 53, GR-55102 Thessaloniki, Greece

333Earthquake Spectra, Volume 23, No. 2, pages 333–355, May 2007; © 2007, Earthquake Engineering Research Institute

334 A. KAPPOS ET AL.

Seismic damage and loss assessment can be carried out using damage probabilitymatrices derived on the basis of damage statistics from past earthquakes (Braga et al.1986, Spence et al. 1992, Anagnos et al. 1995) or expert judgment (Applied TechnologyCouncil [ATC] 1985), or fragility curves derived from analysis of appropriate mechani-cal models (Singhal et al. 1996, Dymiotis et al. 2001). In the United States, the currenttrend is the use of HAZUS (FEMA-NIBS 2003), a Geographic Information System(GIS)–based software package for the estimation of regional losses due to earthquakehazard. Contrary to previous approaches adopted in the United States that were basedmainly on expert judgment (ATC 1985), vulnerability assessment in HAZUS is done bymeans of a purely analytical procedure combining the so-called capacity spectrum ap-proach with fragility curves expressed as functions of spectral quantities (displacementsin the case of structural damage assessment) rather than of macroseismic intensity oreven peak ground acceleration (PGA). The most common problem when applying apurely empirical approach is the unavailability of (sufficient and reliable) statistical datafor several intensities. This unavailability leads to a relative abundance of statistical datain the intensity range from 6 to 8 and a lack of data for the other intensities, makingdifficult the selection of an appropriate cumulative distribution (since the curve fit erroris significant). On the other hand, purely analytical or expert judgment–based ap-proaches should be avoided, since they might seriously diverge from reality, typically(but not consistently) overestimating the cost of damage; for instance, the ATC (1985)fragility curves based on expert judgment were found to grossly overpredict structuraldamage, at least for some classes of structures for which damage statistics were com-piled (Anagnos et al. 1995).

In order to overcome these problems, the first author and his coworkers (Kapposet al. 1998b, 2002, 2004) have developed the so-called hybrid approach, a method thatstarts from available damage statistics (appropriate for the area and structural typologyunder consideration) and estimates damage at the intensities for which no data is avail-able using nonlinear analysis of typical structures. Fragility curves in terms of PGA orspectral displacement were derived (Kappos et al. 2004) combining nonlinear time-history analysis of models representative of common reinforced concrete (R/C) buildingtypes with damage statistics (in terms of cost of interventions) from the 1978 Thessal-oniki (Greece) earthquake. It should be noted that the cost of the intervention is gener-ally much better defined (in the files of the intervention studies) than the degree of struc-tural damage; in fact, the latter is taken into account, generally in a satisfactory way(especially for R/C structures), by the engineers who decide the repair/strengtheningscheme to be applied in each building damaged by the earthquake. A slightly differentapproach, still based on the hybrid technique but involving nonlinear static (rather thandynamic) analysis, again combined with statistical data on cost of interventions, wasused for deriving fragility curves for unreinforced masonry (URM) buildings (Penelis etal. 2003).

Despite the sound concept on which the hybrid method is based, the statistical dataused so far in its context were very limited; in the case of R/C buildings only data fromthe 1978 Thessaloniki was used (two more earthquakes were used in the case of URMbuildings; see Penelis et al. 2003). The 1999 Athens earthquake presented a unique op-

ESTIMATION OF ECONOMIC LOSS FOR BUILDINGS STRUCK BY THE 1999 ATHENS EARTHQUAKE 335

portunity for the authors to check the validity of their basic analytical models (describedlater in this paper) against new statistical data collected in the meisoseismal area of thatearthquake. Comparison of damage and loss assessments based on a purely analyticalapproach with corresponding statistical data from the Athens earthquake is the focus ofthis paper.

OVERVIEW OF THE STUDY

In the first part of the study, given that no recordings from the main shock wereavailable for the meisoseismal area (i.e., no records in the near-field strong ground mo-tion), a pilot methodology is used for its analytical evaluation for different soil condi-tions. Using both deterministic and stochastic approaches, as well as actual records, re-ferring at outcropping bedrock soil conditions, and taking into account the properties ofthe 7 September 1999 main shock (fault geometry, source properties, etc.), the simula-tion of near-field strong ground motion is achieved using geotechnical and geophysicaldata. Seven suites of motion are derived for near-field strong ground motion using dif-ferent methodologies, namely: empirical Green’s function (EGF), point-source model(PSM), finite-source model (FSM), finite-source model based on slip distribution (FSM-SDM), two actual records (SGMA, SPLA), and another record (KEDE) deconvolutedthrough geotechnical data. Based on seismological and geophysical information repre-sentative of the meisoseismal area, strong motion at the bedrock of the sites under con-sideration is evaluated. Then, in combination with the dynamic properties of the soil pro-files at the borehole sites, reliable 1-D soil models are developed. Analyticalinvestigations are also carried out in an attempt to evaluate the variation of the seismicresponse of the soil deposits in the broader area under consideration.

The derived suites of ground motion are then used to evaluate the response of bothR/C and URM buildings in the area. Utilizing a more refined version of a methodologyoriginally proposed by Kappos et al. (1998b, 2004), which correlates the structural dam-age index with the repair cost, several inelastic time-history analyses of typical buildingsare carried out and their results are used for the prediction of economic loss due to earth-quake damage in the study area.

The statistical repair cost was derived through data collected in the municipality ofAno Liosia within the meisoseismal area of the September 1999 earthquake. A thoroughin-situ survey of structures in a representative sample of 150 building blocks (corre-sponding to approximately 10% of the total building stock) was performed. The totalstatistical cost as well as the statistical cost for each damage category was estimated. Asuitable grouping of the statistical data was performed for them to be directly compa-rable to the results of the predicted economic loss. Predicted and statistical costs werecompared for the entire area, as well as separately for each geological and geophysicalzone. The analytical economic loss assessment was found to agree to a satisfactory de-gree with the statistical repair costs for some of the derived seismic hazard scenarios.

The proposed methodology can be relatively easily adapted for application in otherurban areas (a proper calibration of the damage- and loss-assessment models would be

336 A. KAPPOS ET AL.

necessary in this case), and can assist in earthquake risk–mitigation efforts, as well as inprioritization policies for strengthening of buildings in seismic regions.

BUILDING STOCK, CLASSIFICATION, AND STATISTICAL COSTESTIMATION

The statistical repair cost was derived through data collected in the field in the mu-nicipality of Ano Liosia, the area most heavily affected by the September 1999 earth-quake. The database that was compiled on the basis of the survey of 150 building blocks(including a total of 1,028 buildings, approximately 10% of the total building stock) in-cluded a full set of data regarding the building block number, the number of each build-ing in the block, the building address, year of construction, whether a building permitwas issued or not, use of the building, total floor area, number of stories, total height,and total volume. Also included were data regarding structural characteristics of thebuilding, such as presence or absence of basement(s), soft ground story (a typical case inGreece is the pilotis building wherein brick masonry infills are discontinued at theground story), and type of construction (reinforced concrete, masonry, etc.). Finally, in-formation regarding damage classification after the second-level inspection was in-cluded. Damage classification was based on the simple and widely used (in Greece andother countries) green/yellow/red tag system, wherein the meaning of each tag is as fol-lows:

• Green: Original seismic capacity has not been decreased, the building is imme-diately usable and entry is unlimited.

• Yellow: Building with decreased seismic capacity that should be repaired. Usageis restricted.

• Red: Buildings in this category are unsafe and entry is prohibited. Decision fordemolition is to be made on the basis of more thorough inspection.

Using the mean repair cost per square meter for each damage category, provided bythe Departments for Seismic Restoration (TAS) in the municipalities of Ano Liosia andMenidi, an estimation of the total statistical cost was performed. The accuracy of thesemean repair costs was tested against corresponding values provided by other Depart-ments for Seismic Restoration in the broader region of Athens. The statistical costs foreach damage category, as well as the total statistical cost, are shown in Table 1. The geo-logical and geophysical zones in Ano Liosia are presented in Figure 1, together with thebuilding blocks, building damage classification (green/yellow/red tag), and statisticalcost distribution.

For the analytical estimation of the retrofit cost, suitable grouping of the buildingdatabase was performed for it to be comparable with the results of analytical modelsdescribed later. First, buildings were grouped depending on construction year into twocategories: (1) buildings designed and built before 1996, according to older seismiccodes (issued in 1959 and 1984); and (2) buildings designed and built according to re-cent seismic codes (issued in 1995 and 2000). All R/C buildings of the first group wereassumed to have space-frame structural systems without shear walls, while buildings ofthe second group were assumed to have space-frame structural systems with shear walls

ESTIMATION OF ECONOMIC LOSS FOR BUILDINGS STRUCK BY THE 1999 ATHENS EARTHQUAKE 337

(dual system); this assumption was verified to a great extent by in-situ inspections. Clas-sification was then further refined, finally leading to the following groups:

Designed and built before 1996

• One- and two-story R/C frame buildings with brick masonry infills, without“soft” ground story (pilotis). Total area of buildings in this group: 83,904 m2.

• One- and two-story R/C frame buildings with brick infills, with “soft” groundstory (pilotis). Total area of buildings in this group: 6,933 m2.

• Three- and four-story R/C frame buildings with brick infills, without “soft”ground floor (pilotis). Total area of buildings in this group: 16,861 m2.

• One- and two-story buildings with load-bearing walls in brick masonry (URM).Total area of buildings in this group: 27,121 m2.

• One-story buildings with load-bearing walls in stone masonry. Total area ofbuildings in this group: 345 m2.

Designed and built in or after 1996

• One- and two-story R/C buildings with dual structural system and brick infillswithout “soft” ground story (pilotis). Total area of buildings in this group:4,733 m2.

• One- and two-story R/C buildings with dual structural system, brick infills with“soft” ground floor (pilotis). Total area of buildings in this group: 2,541 m2.

• Three- and four-story R/C buildings with dual structural system, and brick infillswithout “soft” ground story (pilotis). Total area of buildings in this group:4,381 m2.

• Three- and four-story R/C buildings with dual structural system, brick infillswith “soft” ground floor (pilotis). Total area of buildings in this group: 573 m2.

Classification of the building stock in the examined area into the two main R/C cat-egories (old/modern codes) and the URM category is presented in Figure 2, togetherwith the area per building category. It is shown that the distribution of building typesvaries among different neighborhoods of the municipality.

Table 1. Estimation of “statistical cost”

Damage category Building number Area (m2) Repair cost Total cost �€�

Green 403 59 547 €35.5/m2 2 113 919Yellow 350 61 871 €92.4/m2 5 716 880Red 230 25 974 €361.1/m2 9 379 211TOTAL 983 147 392 — 17 210 010

Note: €1� $1.3 US (2006 rate)

338 A. KAPPOS ET AL.

Figure 1. Geological zones in municipality of Ano Liosia with building damage classification

(top) and statistical cost distribution (bottom).

ESTIMATION OF ECONOMIC LOSS FOR BUILDINGS STRUCK BY THE 1999 ATHENS EARTHQUAKE 339

PREDICTION OF GROUND MOTION IN THE STUDIED AREA

Given that no recordings from the main shock were available for the meisoseismalarea (i.e., no records in the near-field strong ground motion), an analytical prediction ofthe ground motion in different zones of the studied area (required for the analyticalevaluation of building damage in each zone) was carried out using different state-of-the-art techniques, as described below.

In addition, three actual recordings properly scaled for site soil conditions have beenused, namely, the accelerograms of the main shock recorded at the stations SGMA,SPLA, and A399, after proper deconvolution to eliminate effects of surface layers weremodified to records on “seismic bedrock” to be used as input motion in the meisoseismalarea. Then, taking into account geotechnical and geophysical data in selected sites of

Figure 2. Area �m2� /building type.

340 A. KAPPOS ET AL.

Ano Liosia and corresponding transfer functions, acceleration time histories representa-tive of near-field recordings were obtained and normalized to site soil conditions.

SIMULATION OF NEAR-FIELD STRONG GROUND MOTION

Empirical Green’s Function (EGF) Technique

The EGF methodology (Irikura 1983, 1986) was applied to simulate the strongground motion due to the Athens main shock �Mw=5.9�, using one record as empiricalGreen’s function. The methodology is based on a combination of the EGF technique(Hartzell 1978) with the similarity law of earthquakes, and has been described in a num-ber of previous works (e.g., Irikura 1983, 1986; Irikura and Kamae 1994). According toIrikura and Kamae (1994), when two events occur within the same seismic source, thesimilarity law of earthquakes can be described by the equations

L

Le=

W

We=

D

CDe=

�

�e= � M0

CM0e�1/3

= N �1�

Parameters without subscript are for the larger event and those with subscript e arefor the smaller event. L and W are the length and width of the fault, respectively, D is thefinal offset of the dislocation, � is the rise time, and Mo is the scalar seismic moment.Further, C stands for the ratio of stress drop, �, between the two events, and N is a scal-ing parameter used to discretize the fault, defined as the closest integer to the value cal-culated from the equation. Parameters C and N are of great importance for the simula-tions since the first controls the level of the simulated spectrum and the second definesthe number of elements �N�N� into which the target fault is subdivided. The simulatedstrong motion in the meisoseismal area (municipality of Ano Liosia) by use of the EGFtechnique is shown in Figure 3b.

Stochastic Point-Source Model (PSM) Technique

The point-source model is based on the principle that an �2-spectral scheme with adistance R from the event’s hypocenter can be defined as a function of seismic momentM0, of distance R, of corner frequency f0, as well as of the stress parameter ��. Thisanalysis aims mainly towards the definition of parameters that will serve in the predic-tion of ground motion with frequency content of 0.5 Hz to 10 Hz. As shown by Marga-ris and Boore (1998), strong motion data can be predicted with sufficient accuracy byusing this simple theoretical model taking into account the magnitude of the event(Joyner and Boore 1988, Atkinson and Boore 1995). For the estimation, a suitably modi-fied version of the program SmSim (Boore 1996, Margaris 2000) was used.

Stochastic Finite-Source Model (FSM) Technique

The finite-source model was first presented by Beresnev and Atkinson (1998, 1999).In this model a fault surface is discretized into small elements, each one of which is usedas a point source. The radiation model of all point sources is supplemented with a suit-able time delay. This model is adopted for the simulation of seismic events of magnitudeM�5.4. For the finite-source model, the parameters of seismic fault as determined by

ESTIMATION OF ECONOMIC LOSS FOR BUILDINGS STRUCK BY THE 1999 ATHENS EARTHQUAKE 341

Figure 3. Simulated strong motion in the area of Ano Liosia using: (a) FSM and PSM stochas-tic techniques, (b) Empirical Green Function (EGF) and Stochastic Slip Distribution FSM tech-niques, (c) actual records (KEDE, SPLA, and SGMA); all correlated and calculated in PSVvalues.

342 A. KAPPOS ET AL.

Harvard and by Papazachos et al. (2001) were used. The input parameters of both sto-chastic (point and finite) source models, which have been derived by Margaris andBoore (1998) and Margaris (2000), are adopted. Moreover, for both source models andfor each examined site, amplification was achieved by use of normalized amplificationfactors according to available geotechnical information (Klimis et al. 1999).

The simulated strong motion in the meisoseismal area (municipality of Ano Liosia),by use of both the finite-source (FSM) and point-source models (PSM), is shown in Fig-ure 3a.

Stochastic Slip Distribution Model (SD-FSM) Technique

In this approach the FSM technique is also applied, but using non-homogeneous slipdistribution on the fault. Such slip distribution during the Athens earthquake has beenobtained by inversion of source time functions using a rupture velocity of 2.7 km/secand a rise time of 0.4 sec (Roumelioti et al. 2003). This model is used to draw maps withsynthetic acceleration values, extending simulation of strong motion to sites where noreal accelerograph recordings are available, especially in the meisoseismal area.

In total, 1,200 synthetic accelerograms were evaluated at selected grid sites. The re-sulting maximum accelerations of the 1,200 synthetic accelerograms are displayed in themap of Figure 4. Fault projection, as well as its extension to surface, is also illustrated onthe same map. The meisoseismal area (Ano Liosia, Thrakomakedones, and Menidi) is

Figure 4. Maximum accelerations of 1,200 synthetic accelerograms at the underlain bedrock(after Roumelioti et al. 2003).

ESTIMATION OF ECONOMIC LOSS FOR BUILDINGS STRUCK BY THE 1999 ATHENS EARTHQUAKE 343

located near the fault, pointing out the role of seismic source in damage distribution.These accelerations refer to underlying bedrock conditions; effects of local dynamicproperties of soil profiles are not taken into account herein.

The simulated strong motion in the municipality of Ano Liosia, using the SD-FSMtechnique, is shown in Figure 3b.

FORMULATION OF RELIABLE 1-D SOIL MODELS AND SITE RESPONSEANALYSIS

All available data and information related to geology, geotechnical conditions, andgeophysical characteristics were gathered and transferred to a global GIS. Representa-tive maps of the meisoseismal area are presented with geological/geotechnical zones(Figure 5), sites of accelerographs, and available geotechnical/geophysical data (Figure6). In certain sites of the meisoseismal area where aftershock events were recorded byITSAK accelerographs, the technique of horizontal-to-vertical component spectral ratio(HVSR) was employed. This technique provides useful information for the predominantfrequency of the examined sites (receiver function) (Nakamura 1989, Lermo andChavez-Garcia 1993, Theodulidis and Bard 1995). Mean values of HVSR, as well aspredominant periods, can be additionally evaluated in the soil response site character-ization. In combination with the dynamic properties of the soil profiles at the recording

Figure 5. Geological/geotechnical zones of meisoseismal area (after Koukis and Sabatakakis2000).

344 A. KAPPOS ET AL.

stations, theoretical transfer functions are evaluated. Comparison between analytical andempirical transfer functions leads to the formulation of reliable 1-D soil models.

The methodology adopted for seismic wave propagation through soil is based on 1-Dseismic response analysis performed using the computer code CYBERQUAKE Version1.1 (developed by BRGM, France, 1998). The code is based on multiple reflectiontheory, and nonlinearity of soil is considered by the equivalent linear (EQL) method(Schnabel et al. 1972). Hysteretic damping is taken into account by employing the com-plex modulus. Even if equivalent linear analysis overestimates the calculated shearstresses and underestimates amplifications in the high-frequency range, it is acceptableat medium strain levels. For the needs of seismic response analyses, seven accelerogramshave been considered. The first group includes the records of the 7 June 1999 earthquakeat the sites (see Figure 6) Syntagma-SGMA �0.24 g�, Sepolia-SPLA �0.27 g�, andKEDE-A399 �0.19 g� after a deconvolution procedure, and the second includes theaforementioned stochastic simulated strong motions at the sites of Ano Liosia (ALS-FSM: 0.52 g, ALS-PSM: 0.48 g) and Menidi (MND-FSM: 0.49 g, MND-PSM: 0.39 g),considered as rock (Site Class B) according to UBC 1997. To examine the fluctuation ofresponse characteristics (shear strain amplitude, amplification, acceleration level, etc.)

Figure 6. Accelerograph sites and sites with geotechnical/geophysical data.

ESTIMATION OF ECONOMIC LOSS FOR BUILDINGS STRUCK BY THE 1999 ATHENS EARTHQUAKE 345

and to encompass margins and threshold of highly nonlinear soil behavior, site responseanalyses were performed using total stress at ten locations in the area under examinationfor which the soil profiles were known (Figure 7), and for all seismic excitations. In thispaper, site response analyses are restricted only to the central area of the Ano Liosia,which was identified as being the most representative and appropriate for earthquakeloss assessment. For this reason, shear modulus reduction curves �G/Gmax� and dampingratio (DS), both dependent on shear strain, were selected from the international literature(Vucetic and Dobry 1991, Ishibashi et al. 1993, Anastasiadis 1994, Hatanaka andUchida 1995, Pitilakis et al. 1999). The results of 1-D-EQL, together with geological,geophysical, and geotechnical information, were used as the basis for the definition offive different zones (A, B, C, D1, and D2; see Figure 7) representing the relative shakinghazard in relation to the entire investigated area.

Theoretical site response analysis results at representative sites of Ano Liosia areaare presented in Table 2, with PGA (in g) values at ground surface (columns 3, 5, 7, 9,11, and 13) from six seismic motions (PSM, FSM, SD-FSM, KEDEd, SPLAd, andSGMAd); in the same table values of bedrock acceleration from six seismic scenariosare presented (columns 2, 4, 6, 8, 10, and 12). It is seen that, depending on the modelused, estimated bedrock accelerations vary from as low as 0.2 g to as high as 0.5 g,while accelerations at the surface reach up to about 0.7 g at some sites.

Specific site response analysis results calculated at a representative site (site P4) ofAno Liosia using different recorded seismic motions (KEDEd, SPLAd, and SGMAd) areshown in Figure 3c; pseudo-velocity spectra calculated at site P4 for the three actualrecords (KEDEd, SPLAd, and SGMAd) as well as the three stochastic seismic motions(PSM, FSM, and SD-FSM) are also illustrated.

Figure 7. Definition of zones and building blocks studied.

a: PGA (in g) values at ground surfaceLAd, and SGMAd)

SGMAd SD-FSM

(PGA)r (PGA)s (PGA)r (PGA)s

(10) (11) (12) (13)

0.24 0.27 0.19 0.22

0.31 0.24

0.36 0.24

0.26 0.20

346A

.KA

PP

OS

ET

AL

.

Table 2. Theoretical site response analysis results at representative sites of Ano Liosia are(columns 3, 5, 7, 9, 11, and 13) from six seismic motions (PSM, FSM, SD-FSM, KEDEd, SP

ExcitationSite

PSM FSM KEDEd SPLAd

(PGA)r (PGA)s (PGA)r (PGA)s (PGA)r (PGA)s (PGA)r (PGA)s

(1) (2) (3) (4) (5) (6) (7) (8) (9)

P-3 0.47 0.56 0.51 0.55 0.19 0.21 0.27 0.28

P-4 0.60 0.61 0.25 0.30

P-7 0.66 0.69 0.32 0.36

P-9 0.40 0.45 0.25 0.29

ESTIMATION OF ECONOMIC LOSS FOR BUILDINGS STRUCK BY THE 1999 ATHENS EARTHQUAKE 347

VULNERABILITY ANALYSIS AND DIRECT LOSS ASSESSMENT

R/C BUILDINGS

The aforementioned seven suites of accelerograms were used to evaluate the re-sponse of typical R/C buildings. Based on the hybrid (combined analytical and statisti-cal) procedure originally proposed by Kappos et al. (1998b, 2004), which correlates thestructural damage index with the repair cost, and using a more refined set of collapsecriteria, a number of inelastic time-history analyses of typical R/C buildings allowed theprediction of (direct) economic loss in the study area.

Referring to the height of the buildings, two-story, four-story, and nine-story R/Cbuildings were analyzed, corresponding to low-rise (one- to three-story), medium-rise(four- to seven-story), and high-rise (eight-story plus) buildings, respectively. With re-gard to the structural system, both frames and dual (frame + shear wall) systems wereaddressed. Each of the above buildings was assumed to have three different configura-tions, namely, bare, infilled, and pilotis (soft ground story) type. Two seismic code levelswere considered: low (early seismic codes) and high (modern seismic codes); the spe-cific codes applied for designing the structures were the 1959 and the 2000 Greek codes(the latter is similar to the 1995 code). This classification resulted in a total of 36 R/Ctypes, not all of which were present in the study area (the actual building stock was notclearly known at the time the analyses were performed). To keep the cost of analysiswithin reasonable limits, all buildings were analyzed as 2-D structures.

Using the DRAIN2000 code, an in-house–developed extended version of the well-known DRAIN-2D program (Kappos and Dymiotis 2000), R/C members were modeledusing lumped plasticity beam-column elements, while infill walls were modeled usingshear panel isoparametric elements (Kappos et al. 1998a, Dymiotis et al. 2001). Fromeach analysis, the cost of repair (which is less than or equal to the replacement cost) isestimated for the building type analyzed, using the models for member damage indicesproposed by Kappos et al. (1998b). These are simple models correlating rotational duc-tility ratio µ� (in the case of R/C members) and interstory drift (in the case of brick ma-sonry infills) to the normalized cost of repair; for instance, in the case of R/C members,the normalized cost is assumed to increase linearly from 0 at µ�=0.75, to 1 at µ�=4.0,wherein a cost of 1 means that the most expensive type of intervention is used (in thiscase, R/C jacketing of the entire member).

The total loss for the entire building is derived from empirical equations (calibratedagainst damage cost data from Greece):

G = Gc + Gp = 0.25Dc + 0.08Dp ��5 stories� , �2�

and

G = Gc + Gp = 0.30Dc + 0.08Dp �6 − 10 stories� �3�

where Dc and Dp are the global damage indices ��1� for the R/C members and the ma-sonry infills of the building, respectively, calculated as the weighted average of theaforementioned normalized costs estimated for each member type. Due to the fact that

348 A. KAPPOS ET AL.

the cost of the R/C structural system and the infills totals less than 40% of the cost of a(new) building, Equations 2 and 3 give values up to 38% for the loss index G, which isthe ratio of the total cost of interventions to the replacement cost of the entire building(Gc and Gp are the values of the loss index for R/C members and masonry infills, re-spectively). In the absence of a more exact model, situations leading to the need for re-placement (rather than repair/strengthening) of the building are identified using failurecriteria for members and/or stories, as follows:

• In R/C frame structures, failure is assumed to occur (hence G=1) whenever ei-ther 50% or more of the columns in a story “fail” (i.e., their plastic rotation ca-pacity is less than the corresponding demand calculated from the inelastic analy-sis), or the interstory drift exceeds a value of 4% at any story.

• In R/C dual structures, failure is assumed to occur whenever either 50% or moreof the columns in a story “fail,” or the walls (which carry most of the lateralload) in a story fail, or the interstory drift exceeds a value of 2% at any story(drifts at failure are much lower in systems with R/C walls).

This is a new, more refined set of failure criteria (compared to those used in previousstudies by the authors; Kappos et al. 1998b, 2002) that resulted after carrying out a largenumber of (time-history) analyses; a more detailed discussion of these criteria and theirlimitations can be found in Kappos et al. (2004).

Given the classification of buildings in the area, described in an earlier section,single-story and two-story buildings were assumed to correspond to low-rise (two-story)analytical models, while three- and four-story buildings were assumed to correspond tomid-rise (four-story) analytical models. No high-rise buildings existed in the area underconsideration.

Typical analysis results are presented in Figures 8 and 9; note that red bars indicate“collapse” in the charts. It is clear that the set of stochastic motions results in signifi-cantly higher values of calculated loss compared to the set of recorded motions, forwhich no collapse was predicted for all building types (note the different scale in the

Figure 8. Two-story dual infilled R/C building/new code—PSM series (left), SPLA series(right).

ESTIMATION OF ECONOMIC LOSS FOR BUILDINGS STRUCK BY THE 1999 ATHENS EARTHQUAKE 349

figures). The effect of seismic design is found to be very significant especially for themore severe motion sets (all “collapses” were predicted for low-code building types).

URM BUILDINGS

It is well known that the nonlinear response of URM buildings is not easy to model,mainly because the frame element (beam/column) commonly used in the case of R/Cbuildings is generally not amenable to modeling URM buildings. The difficulties aremultiplied in the case of dynamic analysis where the inertia forces cannot be concen-trated at the diaphragm levels, which is the rule for R/C buildings. Therefore, for thecurrent study an alternative procedure was adopted for the evaluation of the economicloss of the URM buildings based on the use of capacity curves (estimated using push-over analysis) and fragility curves in terms of displacement, wherein the possibility ofexceeding a certain damage state is expressed in terms of spectral displacement (and notintensity or PGA).

Appropriate capacity as well as fragility curves for typical URM buildings in Greecewere proposed by Penelis et al. (2003) using the so-called hybrid approach, which com-bines the results of analytical results (in this case from pushover analyses) with statisti-cal damage data from past earthquakes. The fragility curves (Figure 10) were based ondata from several earthquakes that struck Greece during the last three decades; they aretherefore deemed suitable for the current study. In line with many other studies on fra-gility curves, four damage states were considered: DS1, slight damage; DS2, moderatedamage; DS3, extensive damage; and DS4, very heavy damage and collapse. Each dam-age state is associated with a loss index; for instance, DS2 corresponds to a range be-tween 5% and 20% (of the replacement cost); more details are given in Penelis et al.(2003).

Figure 9. Four-story frame infilled R/C building/old code—FSM series (left), KEDE series(right).

350 A. KAPPOS ET AL.

The procedure used for estimating economic loss was the following:

• Using the pseudo-acceleration spectra of the aforementioned input motions, eachmean pseudo-acceleration spectrum of interest was calculated (e.g., mean spec-trum for zone B of Figure 7, and the FSM set of records).

• Based on each mean pseudo-acceleration spectrum, the corresponding spectraldisplacement was estimated for every URM building typology, using the corre-sponding capacity curve for each typology—as given by Penelis et al. (2003)—and the Capacity Spectrum approach (ATC 1996).

• Using the spectral displacement value and the aforementioned fragility curves,the mean damage factor is estimated for each building typology and the corre-sponding area is multiplied by the replacement cost �€361/m2� to yield the finalcost estimate.

COMPARISON OF PREDICTED AND STATISTICAL LOSSES

The cost of earthquake damage predicted using the analytical methodology describedin the previous section was compared with the statistical cost of damage, estimated asdescribed in the second section of the paper. It has to be emphasized that this statisticalcost is generally far from an objective measure of the cost of the retrofit scheme (repairand/or strengthening in the case of lightly or moderately damaged buildings, replace-ment in the case of heavily damaged and/or collapsed buildings) that was commensuratewith the actual degree of damage in each building. Experience with interventions afterpast earthquakes in Greece has shown that for the same degree of damage, quite differ-ent retrofit schemes have been used; a typical case is that of old URM buildings, whichare usually replaced, even when only moderately damaged (whenever they are not listedbuildings). The fact that 50% to 100% of the cost of retrofit is provided by the state as agrant and/or as an interest-free loan leads to decisions for heavier interventions thanthose that would be used if the owners bore the entire cost themselves. On the otherhand, it is also known from past experience that some lightly damaged buildings arenever repaired and only cosmetic interventions are made. Last and not least, the waypost-earthquake inspections are carried out is far from ideal, from the point of view of

Figure 10. Fragility curves for stone (left) and brick masonry (right) buildings.

ESTIMATION OF ECONOMIC LOSS FOR BUILDINGS STRUCK BY THE 1999 ATHENS EARTHQUAKE 351

giving a complete and reliable picture of damage distribution in the affected area. In-spections are typically carried out on the owners’ request (they file an application at theTAS office mentioned earlier), which means that it is indeed common that several build-ings are never inspected, either because they are not damaged or because the owner(s),for whatever reasons (that usually have nothing to do with the degree of damage), havedecided not to apply for an inspection.

The cost figures shown in Table 3 refer to the building stock (988 buildings, i.e., 96%of the number included in the compiled database) in four out of the five zones of Figure7, since no data were found for the soil profile in zone A. As seen in the table, predictionof total economic loss seems to be quite good when the stochastic motion sets (FSM andPSM) are used. On the other hand, the sets derived from the (far-field) actual recordedmotions underestimate significantly the economic loss. A closer examination reveals thatthe accuracy of the stochastic motion–based predictions (for the entire area) deteriorateswhen each zone is examined separately; nevertheless the results are still quite satisfac-tory (especially for the PSM set), bearing in mind all the uncertainties involved in themethodology used as well as in the estimation of the statistical cost of retrofit.

As expected, the age (and hence the seismic design level) and the structural systemsignificantly affect the vulnerability of the structures (Figures 11 and 12). The URMbuildings are the most vulnerable (statistical cost: €208/m2), while for the R/C buildingsage is the most crucial parameter (buildings designed according to modern seismiccodes are only slightly damaged). Once again the stochastic input motions give satisfac-tory estimations for all building typologies, while the recorded motions underestimatesignificantly the economic loss, and it is interesting to note that the latter is more thecase for R/C rather than for URM.

CONCLUSIONS

Regarding the verification of the vulnerability and direct loss–assessment models,the key finding of the present study was arguably that the main factor contributing to thediscrepancies between statistical and analytically predicted cost of damage was the set ofground motions used. It was found that the prediction was very good overall when the

Table 3. Cost prediction for each zone (in €1,000); EGF and FSM-DSM series are not includedfor the calculation of mean values

Zones “Statistical”PSMseries

FSMseries

FSM-DSMseries E.G.F.

Mean value ofstochasticmotion set

Mean value ofrecorded

motion setMean value,

all sets

(1) (2) (3) (4) (5) �2�+ �3� (6) �2�+ �3�+ �6�B 1,189 1,829 2,592 169 — 2,211 299 1,332C 9,839 6,643 5,139 786 — 5,891 836 3,067D1 428 680 647 39 — 664 77 327D2 4,851 6,470 9,277 422 683 7,873 428 3,468ALL 16,307 15,622 17,656 1,416 — 16,639 1,639 8,195

352 A. KAPPOS ET AL.

stochastic motion sets were used for the vulnerability analysis (discrepancies did exist insome of the zones in the area studied), whereas results based on motions derived on thebasis of the actual records in the far field significantly underestimated damage and loss.It should be noted that the presented results are based on analytical assessment of theeconomic loss, through use of typical 2-D building models, and therefore their validityis restricted by the inherent limitations of the approach used. The quality of informationused for estimating the statistical cost of earthquake damage should also be borne inmind when comparing with theoretically predicted values.

In light of the above, it was clear that there was no real point in trying to calibrate thevulnerability and loss-assessment models on the basis of the obtained results. Thisclearly hints at the importance of accurately knowing the ground motion in areas struckby earthquakes that cause damage to the building stock.

ACKNOWLEDGMENTS

Most of the work presented herein was carried out within the framework of the re-search program “The Athens earthquake of 7-9-99: Vulnerability assessment of struc-

Figure 11. Statistical and estimated economic loss in the study area (EGF and FSM-DSM se-ries are not included).

ESTIMATION OF ECONOMIC LOSS FOR BUILDINGS STRUCK BY THE 1999 ATHENS EARTHQUAKE 353

tures in the earthquake–struck area and comparison with the actual damage distributiondue to the earthquake,” funded by the Earthquake Planning and Protection Organization(EPPO) of Greece. The contribution of Dr. Z. Roumelioti to the seismological part of thestudy is gratefully acknowledged.

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(Received 17 January 2006; accepted 21 December 2006�