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Damage Spectra: Characteristics and Applicationsto Seismic Risk Reduction
Yousef Bozorgnia, F.ASCE,1 and Vitelmo V. Bertero, F.ASCE2
e damageegree-of-
pected, andreducedndreds ofspectra inorthridge
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Abstract: Improved damage spectra are proposed to quantify the damage potential of recorded earthquake ground motion. Thspectra are based on a combination of normalized hysteretic energy and deformation ductility of a series of inelastic single-dfreedom systems. The damage spectra proposed will be zero if the structure remains elastic, i.e., no significant damage is exwill be unity if there is a potential of collapse. By varying a coefficient in their formulations, improved damage spectra can beto commonly used normalized hysteretic energy or displacement ductility spectra. The damage spectra are computed for huhorizontal ground motions recorded during the Landers and Northridge earthquakes. Source-to-site attenuation of the damagethe Northridge earthquake is examined. Calibration of the damage spectra for an instrumented building damaged during the Nearthquake is also carried out. The improved damage spectra are promising for assessment of the performance-based seismicof existing structures. For example, following an earthquake, near real-time contour maps of damage spectral ordinates at selecprovide useful information on the spatial distribution of the damage potential of recorded ground motion for specific types of stThe concept of damage spectra is also promising for carrying out performance-based design of new structures.
DOI: 10.1061/~ASCE!0733-9445~2003!129:10~1330!
CE Database subject headings: Seismic effects; Earthquake damage; Inelastic action; Seismic design; Ground motion; Perfoevaluation; Hysteretic systems.
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Introduction
Quantification of the potential for damage of earthquake gromotion is one of the fundamental issues in earthquake engiing. A reliable measure of the damage potential of ground shahas a wide range of applications for analysis and design ofstructures as well as for seismic evaluation of existing facilitOne important application of this measure is rapid pearthquake mapping of the spatial distribution of the damagetential of recorded ground motion. The maps can be usedexample, for rapid performance-based damage assessment ocific types of structures. Currently, immediately followingearthquake, spatial distributions of selected peak ground mand elastic response spectral ordinates are mapped and posthe Internet~Wald et al. 1999; Lin et al. 2002!. These parameteralthough important, by themselves are not sufficiently reliablquantify the damage potential of ground motion. For examthey do not include important features known to be associwith structural damage, such as inelastic structural responsemulative effects of repeated cycles of inelastic structural defortion, and the duration of strong motion. For the same reascumulative damage due to the main shock followed by se
1Principal, Applied Technology & Science~ATS!, 5 Third St., Suite622, San Francisco, CA 94103. E-mail: [email protected]
2Dept. of Civil and Environmental Engineering, Univ. of CalifornBerkeley, CA 94720.
Note. Associate Editor: Takeru Igusa. Discussion open until Marc2004. Separate discussions must be submitted for individual papeextend the closing date by one month, a written request must be filedthe ASCE Managing Editor. The manuscript for this paper was submfor review and possible publication on February 13, 2002; approveNovember 4, 2002. This paper is part of theJournal of Structural En-gineering, Vol. 129, No. 10, October 1, 2003. ©ASCE, ISSN 0733-942003/10-1330–1340/$18.00.
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J. Struct. Eng. 200
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aftershocks is not accounted for. Additionally, from a practicpoint of view, it is convenient to use a normalized measuredamage, e.g., a measure that will be zero when the structuremains elastic, that will become one, when there is potentialcollapse.
The objective of this study was to develop improved damaparameters to quantify the damage potential of recorded groshaking. To do this, improved damage spectra are proposedexamined. Details of the definitions, development, and characistics of the improved damage spectra are presented here.damage spectra are computed for 220 horizontal ground motirecorded during the Northridge earthquake and 176 recorground motions of the Landers earthquake. A correlation betwthe proposed damage spectra and a widely used damage iintroduced by Park and Ang~1985! is carried out. Effects of theduration of strong motion on the damage spectra are examinedanalysis of the ground motion recorded in the 1999 Kocaeli aDuzce earthquakes in Turkey. Source-to-site attenuation ofdamage spectra of the Northridge earthquake is also examineaddition, spatial distributions of the damage spectra are presefor the Northridge and Landers earthquakes. Finally, the damspectra are evaluated for a specific case of an instrumented sestory reinforced concrete frame building severely damaged durthe 1994 Northridge earthquake.
Damage Spectra
Structural performance and damage limit states can be quantby damage indices. A well-defined damage index is a normalizquantity that will be zero if the structure remains elastic~i.e., nosignificant damage is expected!, and will be one if there is apotential of structural collapse. Other structural performanstates~such as operational, life safe, near collapse, etc.! corre-
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spond to damage index values between zero and one. ‘‘Damspectrum’’ represents the variation of the damage index versusstructural period for a series of single-degree-of-freedom~SDF!systems subjected to a ground motion record.
A brief overview of the most commonly used damage indicis provided here, followed by definitions and characteristicstwo improved damage indices and their corresponding damspectra.
Overview of Most Commonly Used Damage Indices
A damage index~DI! is based on a set of structural responparameters such as force, deformation, and dissipation of eneThere are numerous DIs available~see, for example, Park andAng 1985; Meyer et al. 1988; Powell and Allahabadi 1988; Fajf1992; Cosenza et al. 1993; Williams and Sexsmith 1995; Kratand Meskouris 1997; Ghobarah et al. 1999; Rodriguez and Atizabal 1999; Mehanny and Deierlein 2000!. Herein, an overviewof the most commonly used DIs is presented.
One method of computing DI is to estimate the earthqua‘‘demands’’ associated with the response parameters and comthem with the structural ‘‘capacities’’~Powell and Allahabadi1988!. Traditionally, the capacities are quantified in terms of themaximum values under monotonically increasing deformatioFor example, in seismic design, the maximum deformation capity of a system during an earthquake is taken to be a portion ofdeformation capacity of the system under monotonically increing lateral deformation (umon).
A damage index may be based on plastic deformation~e.g.,Powell and Allahabadi 1988; Cosenza et al. 1993!,
DIm5~umax2uy!/~umon2uy!5~m21!/~mmon21! (1)
where umax and uy5maximum and yield deformation, respectively, and umon5maximum deformation capacity of the systemunder monotonically increasing lateral deformation. In Eq.~1!m5umax/uy is the displacement ductility demanded by earthquaground motion, andmmon5umon/uy is the monotonic ductilitycapacity.
Maximum displacement ductility alone does not necessarreveal information on the cumulative effects of number of cyclof inelastic deformation and dissipation of total energy demandby the earthquake~Mahin and Bertero 1981!. Also, Kratzig andMeskouris~1997! have indicated that maximum deformation ductility is not a suitable measure for a description of damage. Henother structural response parameters such as the cumulativetility and hysteretic energy dissipation have also been used. Smic input energy to a structural system (EI) is balanced by~Uangand Bertero 1990; Bertero and Uang 1992!
EI5EH1EK1ES1Ej (2)
whereEH , EK , ES andEj5nonrecoverable dissipated hysteretenergy, kinetic energy, recoverable elastic strain energy, andsipated viscous damping energy, respectively. Hysteretic ene(EH) includes cumulative effects of repeated cycles of inelasresponse and is usually associated with structural damage. Ifresponse of the structure remains elastic,EH will be zero by defi-nition. For SDF systems, Mahin and Bertero~1976, 1981! definednormalized hysteretic energyEH /(Fyuy) and its correspondingnormalized hysteretic energy ductility as
mH5@EH /~Fyuy!#11 (3)
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where Fy and uy5yield strength and yield deformation of thsystem, respectively. NumericallymH is equal to the displacemenductility of a monotonically deformed equivalent elastic-perfecplastic ~EPP! system that dissipates the same hysteretic eneand has the same yield strength and initial stiffness as the acsystem.
A damage index can be based on hysteretic energy. Forample, for EPP systems, Cosenza et al.~1993! and Fajfar~1992!used
DIH5@EH /~Fyuy!#/~mmon21!5~mH21!/~mmon21! (4a)
For a general force-deformation relationship, the DI above canrewritten ~Cosenza et al. 1993! as
DIH5EH /EHmon (4b)
where EHmon5hysteretic energy capacity of the system undmonotonically increasing deformation. It should be noted thDIH does not account for the effect of the sequence, and therethe history, of different types of hysteretic loops, as discussedKratzig and Meskouris~1997! and by Mehanny and Deierlein~2000!.
A linear combination of maximum deformation response ahysteretic energy dissipation was proposed by Park and Ang~PA!~1985! as
DIPA5~umax/umon!1bEH /~Fyumon! (5)
whereb>0 is a constant, which depends on structural characistics and history of inelastic response. DIPA has been calibratedagainst numerous experimental results and field observationearthquakes~e.g., Park et al. 1987; Ang and de Leon 1994!. DIPA
less than 0.4–0.5 has been reported as the limit of damagecan be repaired~Ang and de Leon 1994!. Cosenza et al.~1993!reported that experimentally based values ofb have a median of0.15 and for this value DIPA correlates well with the results oother damage models proposed by Banon and Veneziano~1982!and Krawinkler and Zohrei~1983!.
Besides the drawbacks of DIPA discussed by Mehanny anDeierlein ~2000! and by Williams and Sexsmith~1995!, the fol-lowing two drawbacks are mentioned here. First, for elasticsponse, whenEH50 and the damage index is supposed tozero, the value of DIPA will be greater than zero@see Eq.~5!#. Thesecond disadvantage of DIPA is that it does not give the correcresult when the system is under monotonic deformation. Unsuch deformation, if the maximum deformation capacity (umon) isreached, the value of the damage index is supposed to bewhich is an indication of potential failure. However, as is evidefrom Eq. ~5!, the DIPA results in a value greater than 1.0. Chet al. ~1995! proposed modification of DIPA to correct the seconddrawback of DIPA mentioned above, however, the first drawbaof the DIPA was not corrected. Despite its drawbacks, the DIPA hasbeen extensively used for different applications. This is, in padue to its simplicity and its extensive calibration against expementally observed seismic structural damage, especially for rforced concrete members.
Improved Damage Indices
Bozorgnia and Bertero~2001a,b! introduced two improved dam-age indices for a generic inelastic SDF system. These damindices are as follows:
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DI15@~12a1!~m2me!/~mmon21!#1a1~EH /EHmon! (6)
DI25@~12a2!~m2me!/~mmon21!#1a2~EH /EHmon!1/2 (7)
where
m5umax/uy5displacement ductility (8a)
me5uelastic/uy5maximum elastic portion of deformation/uy(8b)
me51 for inelastic behavior andme5m if the response remainselastic~m<1!.
mmon5monotonic displacement ductility capacity;EH5hystereticenergy demanded by earthquake ground motion;EHmon5the hys-teretic energy capacity under monotonically increasing lateralformation; 0<a1<1 and 0<a2<15constant coefficients. Usingthe definition of hysteretic ductilitymH ~Mahin and Bertero 1976,1981! given in Eq.~3! for both earthquake and monotonic exctations, the improved damage indices can be rewritten as
DI15@~12a1!~m2me!/~mmon21!#1a1~mH21!/~mHmon21!(9)
DI25@~12a2!~m2me!/~mmon21!#
1a2@~mH21!/~mHmon21!#1/2 (10)
For the special case of EPP systems,
EHmon5Fy~umon2uy! and mHmon5mmon (11)
DI15@~12a1!~m2me!/~mmon21!#1a1~EH /Fyuy!/~mmon21!(12)
DI25@~12a2!~m2me!/~mmon21!#
1a2@~EH /Fyuy!/~mmon21!#1/2 (13)
A few characteristics of the improved damage indices arefollowing.1. If the response remains elastic, i.e., when there is no sig
cant damage, thenme5m<1 andEH50, and consequentlyboth DI1 and DI2 will become zero. This is characteristic oa well-defined damage index.
2. Under monotonically increasing lateral deformation if thdemand on displacementumax reaches the displacement capacity umon, i.e., an indication of failure, both damage indces DI1 and DI2 will be unity. This is true for any force-deformation relationship.
3. If a150 anda250, damage indices DI1 and DI2 @Eqs. ~6!and~7!# will be reduced to the special form given in Eq.~1!.In this special case, the damage index is assumed to onlrelated to the maximumplastic deformation.
4. If a151 anda251, damage indices DI1 and DI2 will onlybe related to the hysteretic energy dissipationEH . In thiscase, damage index DI1 will be reduced to the special formgiven in Eq.~4b!. If additionally the force-deformation relationship is EPP, damage index DI1 given in Eq.~12! will bereduced to the special form given in Eq.~4a!.
5. Equivalent hysteretic velocityVH ~Akiyama 1985; Uang andBertero 1988! is defined as VH5(2EH /M )1/2, whereM5mass of the system. It is evident from the definitionDI2 given in Eq. ~7! that DI2 is related to the normalizedequivalent hysteretic velocity. If aVH spectrum is available,DI2 can be easily generated by properly combining it wthe ductility spectrum.
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Development of Damage Spectra
As mentioned earlier, the damage spectrum of recorded gromotion represents variation of a damage index versus strucperiod for a series of SDF systems. Once a damage index, suDI1 or DI2 , is defined, the damage spectrum can be construcThe steps involved in developing damage spectra for exisstructures are summarized in Fig. 1 for ground motion recordeChalon Road~S20E! in the Northridge earthquake. Fig. 2 showother examples of damage spectra for the 1940 Imperial Vaearthquake recorded at El Centro, and for the Northridge eaquake recorded at Canoga Park. In Figs. 1 and 2, the followcharacteristics for existing structures are used: viscous damj55%; EPP force-displacement relationship; yield strength baon the elastic spectrum of the Uniform Building Code~UBC1997! ~without near-source factors! reduced byRd53.4. This isthe ductility reduction factor suggested by the Structural Enneers Association of California~SEAOC 1999! for special mo-ment frames and it corresponds to an overstrength factor ofAlso, for Fig. 1mmon58, a150.29, anda250.33 and for Fig. 2mmon510, a150.27, anda250.30 are used. These values fora1
and a2 are based on an analysis of the Northridge earthqurecords, as explained in ‘‘Correlation Between New Damagedices and the Park and Ang Damage Index.’’ Computer progNonspec~Mahin and Lin 1983! is employed to compute the basresponse parameters such as displacement ductility and hystenergy demands. DI1 and DI2 are then computed accordingEqs.~12! and ~13!.
Figs. 1 and 2 show the case of a period-independent ostrength factor, reduction factor Rd , andmmon. For short periodstructures~e.g., low rise buildings! generally a larger overstrengtfactor may be used. Using an average period-independentstrength factor may result in unrealistically high DIs at very shperiods. To demonstrate this concept, a hypothetical spectruthe overstrength factor~given constant modification factor,R!,along with the corresponding damage spectra of the El CentroCanoga Park records are shown in Fig. 3. The effect of the pedependent overstrength factor, especially for short period stures, is evident by comparing the damage spectra plotted in2 and 3.
Correlation Between Improved Damage Indices andPark and Ang Damage Index
As mentioned previously, the widely used DIPA @Eq. ~5!# has beencalibrated against numerous experimental and field observatHowever, because of its drawbacks, it is less reliable at itsand high values than intermediate range. Thus, in the intermerange of damage index, a comparison between values of DI1 withthose of DIPA can result in an estimate for coefficienta1 in Eq.~6!. In other words, while the DIs proposed clearly have improvcharacteristics over DIPA, they also take advantage of previocalibrations. Specifically, the following procedure is used to ematea1 : ~1! Ductility and hysteretic energy spectra and DIPA arecomputed for a series of 5% damped inelastic SDF systemshave the same force-deformation relationship as used in FiTwenty structural periods ranging from 0.1 to 4.0 s are specifiand 220 horizontal ground acceleration records of the Northrearthquake are used as earthquake excitation.~2! Coefficienta1 isdetermined through regression analyses, i.e., by comparing vof DI1 with those of DIPA ~for 0.2,DIPA,0.8). A similar processis repeated to estimate coefficienta2 in DI2 @Eq. ~7!#. The sameprocedure is also carried out using 176 horizontal accelerarecords of the 1992 Landers, California, earthquake. The c
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Fig. 1. Summary of steps involved in developing damage spectra
puted values of thea1 anda2 coefficients using the ground mo-tion records of the Northridge and Landers earthquakes are listedin Table 1. Subsets of the results of the regression analyses arealso graphically presented in Fig. 4 for the Northridge earthquake.
Effects of the Duration of Strong Motion
Experimental studies have demonstrated that failure of structuralmembers and systems is influenced by the number of inelasticcycles of response~see e.g., Bertero et al. 1977!. In other words,structural systems generally become more vulnerable if they gothrough repeated cycles of inelastic deformation. This generallyoccurs when the structure is subjected to strong ground motion oflong duration. Hence, in quantifying the damage potential of re-
Table 1. Estimated Values fora1 and a2 Based on RegressionAnalyses
b mmon
a1
Northridgeearthquake
a2
Northridgeearthquake
a1
Landersearthquake
a2
Landersearthquake
0.10 8 0.206 0.273 0.238 0.2800.15 8 0.286 0.332 0.316 0.3310.20 8 0.364 0.385 0.378 0.3800.10 10 0.185 0.243 0.231 0.2450.15 10 0.269 0.302 0.296 0.2970.20 10 0.350 0.354 0.357 0.344
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Fig. 2. Examples of damage spectra, withj55%, mmon510, andEPP behavior, using a period-independent overstrength factor
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Fig. 3. Example of effects of period-dependent overstrength faon damage spectra, withj55%, mmon510, and EPP behavior1334 / JOURNAL OF STRUCTURAL ENGINEERING © ASCE / OCTOBE
J. Struct. Eng. 200
corded ground motion it is important to include the effects of tduration of strong ground shaking.
Hysteretic energyEH by definition ~see, e.g., Uang and Bertero 1990! is a cumulative quantity. More cycles of inelastic deformation correspond to a larger value for the hysteretic enedissipation. Thus, the effects of repeated cycles of inelasticsponse and the duration of strong motion are reflected inEH .Hence, the damage indices that include hysteretic energy teare also influenced by the effects of repeated cycles of ineladeformations and strong motion duration. Herein, an examplethe effects of duration of strong motion onEH and the damagespectrum is presented.
In 1999 two major earthquakes occurred in Turkey:~1! theKocaeli earthquake of magnitudeMw57.4 on August 17, 1999;and~2! the Duzce earthquake of magnitudeMw57.1 on Novem-ber 12, 1999. The Du¨zce event was likely caused by increasestress in local faults as a result of the August 17 earthquake~EERI2000!. The city of Duzce experienced damage due to both evenbut the damage was more widespread and substantial duringNovember 12, 1999 earthquake~EERI 2000!. For both events,ground accelerations were recorded at the Du¨zce recording sta-tion. Fig. 5 shows the east–west ground accelerations recorduring these two events, with 10 s of zero ground acceleratadded in between. Time variations of the displacement respoand hysteretic energy demand at selected periods are also ploin Fig. 5 which is based on the same basic system parameterthose used in Fig. 2~except the near-source factors are also icluded in estimating the design yield strength!. As expected, timevariation of the hysteretic energy clearly shows thatEH includesthe cumulative effects of the duration of strong motion. It is alnoted that the maximum deformation at periodT51.75 s is lessthan that at 2.5 s; however, an opposite trend is observed forhysteretic energy demand.
Fig. 6 shows displacement ductility spectra and the damaspectra of first and second ground motion separately, as welthose for combination of the ground motions. The results shoin Fig. 6 are also based on the same basic parameters as thoFig. 2 ~except thatmmon58, a150.29, anda250.33 and near-source factors are included in the design strength!. The spectra areplotted for periods.0.5 s, because shorter period structures posibly have a larger overstrength factor andmmon. Because theEH
spectrum includes cumulative effects of repeated cycles of inetic deformation~see Fig. 5!, and the damage spectra include thEH spectrum~see Fig. 1!, the damage spectra are also influencby these cumulative effects.
or
Fig. 4. Example of correlation between damage indices (DI1 ,DI2)and DIPA: Northridge earthquake records withb50.15, a150.29,a250.33,mmon58, andj55%
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Fig. 5. East–west ground acceleration recorded at Du¨zce ~Turkey!;displacement response and hysteretic energy demand historiesT51.75 and 2.5 s
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Fig. 6. Displacement ductility and damage spectra for EW gromotions recorded at Du¨zce ~Turkey!; mmon58, a150.29 anda2
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These results indicate that for assessment of the vulnerabof existing structures as well as for the design of new structurthe possibility of damage due to foreshocks, the main shock,severe aftershocks~or possibly multiple events!, should be con-sidered. The cumulative damage is due to the total hystereticergy dissipation demanded by ground motions and a posschange in the maximum displacement ductility due to permanresidual deformation after each event.
It should be noted that the effects of the sequence, and thfore the history, of different types of hysteretic loops~Kratzig andMeskouris 1997; Mehanny and Deierlein 2000! are not consid-ered in the damage spectra proposed here. Although such efare important, quantification of them is difficult due to the lackreliable experimental information. Also, for practical applicatioaccounting for such effects may be difficult to implement. Hencsimpler damage spectra, such as those proposed here, whichplicitly and in a collective sense include these effects throuempirical coefficients~such asa1 and a2) are appealing, andfurther research studies on the effects of different types of hysetic loops are recommended.
Attenuation of Damage Spectra
Once damage spectral ordinates for a set of ground motrecords are computed, it is possible to estimate the variationdamage spectra with source-to-site distance. To demonstrateconcept, attenuation of the damage spectral ordinates for
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Northridge earthquake is modeled. First, damage spectra forhorizontal accelerations recorded at alluvial sites during tNorthridge earthquake are calculated for the same set of pareters as those in Fig. 2. Then, regression analyses are perforto compute the coefficients of the following attenuation relatioship:
ln~DI1!5a1d ln~R21c2!1/21« (14)
whereR5closest distance from the site to surface projectionthe fault rupture plane;«5random error; anda, c, and d areregression parameters that must be computed. Site soil conditat the recording stations and source-to-site distances are tafrom a comprehensive ground motion database compiledCampbell and Bozorgnia~2000! and by Bozorgnia et al.~1999!.The results of the regression analyses for the damage speordinates atT50.5, 1.0 and 2.0 s are shown in Fig. 7. Mediadamage spectra for distances 3, 10, 20, and 40 km from the fare plotted in Fig. 8. It should be noted that the damage speshown in Fig. 8 are based on the assumption that the structoverstrength factor andmmon are constant over the entire periodFor constructed facilities, these factors are possibly highershort periods than those at long periods. Fig. 8 also revealscontrast between the damage spectra at different distancesthe seismic source, and shows the importance of considering nfault effects in a vulnerability assessment of existing structureswell as in the design of new structures.
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Fig. 7. Attenuation of damage spectral ordinates with source-to-distance for Northridge earthquake at alluvial sites, for structuperiodT50.5, 1.0 and 2.0 s
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Examples of Spatial Distributions of DamageSpectra
For any given type of existing structure with specified structurcharacteristics and using ground motion at various recording stions, it is possible to rapidly generate damage spectra and ptheir spatial distribution at selected periods. As an example, ctours of damage spectral ordinates based on 220 horizoground accelerations recorded during the Northridge earthqu
Fig. 8. Damage spectra for Northridge earthquake at alluvial sites,10, 20 and 40 km from surface projection of the fault rupture plan
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are plotted in Fig. 9 for periods of 1.0 and 3.0 s. The damagspectra are computed for the same set of parameters as thoseFig. 2, exceptmmon512. At each recording station, the local soilcondition is used to adjustFy /W of the SDF system~see Fig. 1!.The soil conditions at the recording stations are taken fromcomprehensive strong-motion database compiled by Campbeand Bozorgnia~2000! and by Bozorgnia et al.~1999!. At eachrecording station, the damage spectra are computed for both hozontal components, and Fig. 9 presents the maximum of the twdamage spectra. The bidirectional effects of the two horizontacomponents are not included in the results presented here. Tepicenter of the earthquake and surface projection of the faurupture plane are also indicated. Contour plots for DI2 ~not shownhere! are very comparable to those plotted in Fig. 9.
Each contour map in Fig. 9 is for the same structural characteristics of a SDF system in the area, except for adjustment oFy /W for local soil conditions. The spatial distribution of thedamage spectral ordinates can be modified to incorporate dafrom an inventory of existing structures in the area. For examplefor buildings, data on the structural material, structural systemnumber of stories, age of the structure, etc. can be approximatetranslated into the basic structural data needed to generate damaspectra. A relatively accurate estimate of the spatial distribution othe basic structural characteristics results in more realistic contomaps of damage spectral ordinates. Plotted in Fig. 10 are thdistributions of displacement ductility atT51.0 and 3.0 s de-manded by the ground motion recorded in the Northridge earthquake. Fig. 10 is based on the same basic parameters as thosethe damage spectral ordinates.
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Fig. 9. Distribution of damage spectral ordinate for ground motionsrecorded during the Northridge earthquake,mmon512, T51.0 and3.0 s
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Fig. 10. Distribution of displacement ductility demanded by groumotions recorded during Northridge earthquake,T51.0 and 3.0 s
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The damage spectra are also computed for 176 horizoground motions recorded during the 1992 Landers, Californearthquake. Selected results for the Landers earthquake are sin Figs. 11 and 12. Fig. 11 shows the spatial distribution of daage spectral ordinates DI1 at T51.0 and 3.0 s. For computation othe damage spectra, the same SDF characteristics as those in2 are used, except thatmmon512 anda150.32. Again, for eachcontour map in Fig. 11 a uniform distribution of basic structurcharacteristics in the area is used. The fault trace and the epiceof the earthquake are also mapped. Spatial distributions of
Fig. 11. Distribution of damage spectral ordinates; Landeearthquake,mmon512, T51.0 and 3.0 s
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displacement ductility demanded by ground motion recorded ding the Landers earthquake are plotted in Fig. 12 forT51.0 and3.0 s.
The contour plots in Figs. 9–12 reveal some information abothe severity of the ground motion recorded at different locationCompare the contour plots of the damage spectral ordinates~Fig.9! with the displacement ductility demands~Fig. 10!. In order tocompare them, the ranges of the values of ductility need tocorrelated to various descriptions of structural performance. Sua tentative correlation was given by SEAOC~1999!, in AppendixI, Part B. For example, a near-collapse damage state for a spemoment resisting frame approximately corresponds to displament ductility of 8.0. Considering these tentative relations prvided by the SEAOC~1999!, the contour plots of the damagespectra and displacement ductility are generally consistent.similar manner, for the Landers earthquake, the damage specordinate and displacement ductility forT51.0 s are generally con-sistent~Figs. 11 and 12!. However, atT53.0 s, the results basedon displacement ductility are somewhat less conservative ththose based on the damage spectrum. One practical advantagthe contours of the damage spectra is that they conveniently rresent normalized values. Additionally, as mentioned before, tdamage spectra in their general form include more features ofinelastic response, such as cumulative damage due to repecycles of inelastic deformation and total hysteretic energy dispation demand than the other traditional response parameterscluding the displacement ductility.
Evaluation of Damage Spectra for Van NuysBuilding
Damage spectra as well as various ground shaking and damparameters are computed for specific structures affected by1994 Northridge earthquake~Bozorgnia and Bertero 2001b!. Thepurpose is to evaluate the correlation between the computed dage spectra and overall damage to the structural system. A specase of interest is an instrumented seven-story hotel locatedVan Nuys, California, which experienced major structural damaduring the Northridge earthquake so the building was ‘‘retagged’’ @California Seismic Safety Commission 1996; AppliedTechnology Council~ATC! 1996; Moehle et al. 1997#. The struc-ture is a seven-story reinforced concrete frame building costructed in 1966. Structural damage was primarily in the longitdinal perimeter frames~oriented in the east–west direction!, andthe damage included shear failure of the columns. Motion in th
s
Fig. 12. Distribution of displacement ductility demand; Landerearthquake,T51.0 and 3.0 s
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Table 2. Van Nuys Building; Data Based on Motion RecordedNorthridge Earthquake
Peakacc.~g!a
Elasticspectrum
~g!a atT51.5 s,
5%damping
Relative roofdisplacement
over bldg.heightb~%!
Driftbetween3rd and
2nd floorsb
~%!
Approximateinterstory
drift ratioa,c
~%!
Driftat
T51.5 sd
~%!
0.45 0.46 1.2 1.9 1.3 1.3aUsing the recorded acceleration at ground level of the building~EW!.bBased on recorded building motion.cComputed using the inelastic SDF response and approximate proceof the SEAOC~1999!, Appendix I, Part B. The approximate value can bfurther improved by using empirical factors to account for the concention of inelastic deformation at a specific story.dAt lowest level, for 5% damping, computed using the Iwan~1997!procedure.
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building was recorded during the 1994 Northridge earthqua@California Strong Motion Instrumentation Program~CSMIP!1994#.
For general information, selected data based on recordedtion of the Van Nuys building are listed in Table 2. To compudamage spectra, the basic structural characteristics were tfrom previous detailed structural analyses. For example, usingearly part of the recorded east–west~EW! structural motion in theNorthridge earthquake, a structural period of 1.5 s was identiin the report by the California Seismic Safety Commissi~1996!. Also, the base shear strength was taken from a previpushover analysis of the structure~California Seismic SafetyCommission 1996; ATC 1996; Moehle et al. 1997!. In this paper,given the period, yield strength, recorded acceleration at grolevel ~EW!, and an assumed 5% viscous damping, the damspectral ordinate is computed for an equivalent EPP systemvarious values of monotonic ductility capacity,mmon. The resultsare presented in Fig. 13 which shows the computed damage s
Fig. 13. Variation of damage spectral ordinate for Van Nuys sevestory building, based on ground floor~EW! acceleration recordedduring Northridge earthquake
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tral ordinates DI1 and DI2 versusmmon for different values ofcoefficientsa1 anda2 @in Eqs.~12! and ~13!#.
Fig. 13 can be used in two different ways:~1! given mmon,e.g., based on results of a pushover analysis up to the failuredamage spectral ordinate can be estimated.~2! Conversely, for agiven value of the damage index~DI!, a range ofmmon can beestimated using Fig. 13. For case~2!, an approximate value of Dcan be determined based on description of the observed struperformance in the earthquake. For example, the report byCalifornia Seismic Safety Commission~1996! indicated that forthe Van Nuys building ‘‘the observed damage can be classifiebetween ‘structural stability’ and ‘potential collapse’.’’ Assumithat DI50.8 approximately corresponds to a ‘‘near collapse’’ cdition, Fig. 13 results inmmon in a range of 4.2~based on DI2) to5.6 ~based on DI1). Considering previous structural analysesthe building, this estimated range ofmmon seems a reasonabrange. For example, using the results of ATC-40~1996!, mmon canbe approximately estimated to be in the range of 4.0–4.6.
This example demonstrates that if the basic structural chateristics are estimated within reasonable accuracy, the compdamage spectrum can be in reasonably good agreement wioverall observed performance of the structural system. Thisture of damage spectra is promising for performance-basesessment of existing structures based on recorded ground mFor the purpose of calibrating against the observed damage,are clear advantages in using damage spectra than other gshaking and response parameters such as the peak grounderation and velocity, elastic response spectra, spectrum inte~Housner 1952!, and drift spectrum~Iwan 1997!. The damagespectra include, in a simple way, basic structural characterirelated to the strength, deformation, and energy dissipationpacities, which are important in controlling damage.
Concluding Remarks
The ground shaking and response parameters which havecommonly used to quantify the damage potential of recorearthquake ground motion can be classified into the followcategories.• Parameters that are purely measures of free-field ground
tion. These include peak ground acceleration and velowhich are amongst the most widely used parameters tosure the severity of ground shaking. However, they are inpendent of any data about the behavior and response of stural systems. Therefore, besides their other limitations, tparametersalonehave limited capability in reliably identifyingeither the degree of damage or damaged areas followinearthquake.
• Parameters that are related to elastic response of SDFcontinuous shear-beam models. These include elastic responspectra, the spectrum intensity, and the drift spectrum.though these are also important measures of the damagtential of ground motion and their applications have beentensive, besides their other limitations, they do not incleffects of amplitude and number of cycles of inelastic strtural deformation, which are generally associated with dage.
• Inelastic response spectra in the form of maximum defortion ductility, the inelastic interstory drift ratio, and inelastdesign strength spectra. These spectra reveal some fundamtal features of inelastic response and structural damage;ever, amongst their other limitations, the cumulative effectthe number of cycles of inelastic response are not include
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• Spectrum of hysteretic energy dissipation due to plastic demation and its associated equivalent hysteretic velocity sptrum. These parameters include some fundamental featureinelastic response as well as the cumulative effects of repecycles of inelastic deformation and the duration of stroground motion. However, in order to use these parameterpractice they need to be normalized with respect to a meaof the energy dissipation capacity of the structure.
• Damage spectrum. This represents the variation of a damaindex versus the structural period for a series of inelastic Ssystems. In this study improved damage spectra were induced, examined, and computed for hundreds of horizoground motions recorded during the Landers and Northriearthquakes. The proposed damage spectra explicitly satwo important conditions:~1! They will be zero if the responseremains elastic, i.e., no significant damage is expected; and~2!they will be unity when the maximum deformation capacityreached under monotonically increasing deformation, iwhen there is potential for failure. Another characteristic of tproposed damage spectra is that by varying a coefficienta1
in DI1 or a2 in DI2) the damage spectra can be reduced tocommonly used normalized hysteretic energy or displacemductility spectra. Also, the damage spectra, in their geneform, are influenced by the cumulative effects of repeacycles of inelastic deformation and the duration of strong mtion.The improved damage indices were also correlated with
proposed by Park and Ang (DIPA) in the reliable intermediaterange of DIPA. Hence, while the proposed DIs have improvcharacteristics over DIPA, they also take advantage of previouexperimental and field calibrations of DIPA. A common attractivefeature of the improved DIs and of the original DIPA is that theyoffer simple mathematical expressions between the groundtion demands and the structural capacities of two basic pareters: deformation ductility and toughness~represented by inelastic hysteretic energy dissipation!. It is clear from the expressionfor the damage indices that the larger the supplied deformaductility ~represented bymmon) and toughness~represented byEHmon), the smaller will be the damage spectra. On the othand, the larger the demanded plastic deformation~m-1! andtoughness (EH), the larger will be the damage spectra. Thisconsistent with the conceptual seismic design guideline that wthe structure must be designed to have maximum ductilitytoughness capacities that are economically feasible, theseductility and toughness capacities should not be misused tostantially reduce the design strength. Such misuse may clarge inelastic demands, and consequently large damage dearthquake ground motion.
Although the proposed damage spectra may be furtherproved to include other features of inelastic response, such aeffects of the sequence of different types of hysteretic loopsthe present they are more reliable than other commonly used
There is a need to carry out integrated analytical and expmental investigations to further improve the reliability of empical coefficientsa1 and a2 in the proposed damage spectra, aalso to include the effects of sequence or time history of differtypes of hysteretic loops. Such integrated analytical and expmental investigations can also verify a reliable applicable rangthe other currently available DIs which include the sequencedifferent types of hysteretic loops~Kratzig and Meskouris 1997Mehanny and Deierlein 2000!. It is also suggested to investigavariations with structural period~i.e., spectra! of the overstrengthfactor, and deformation and hysteretic energy capacities un
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different types of lateral deformation. Such an investigationneeded to improve the reliability of various measures of damincluding the damage spectra proposed.
The proposed damage spectra can be used to quantify theage potential of any given recorded ground motion and relateseismic structural performance categories~e.g., operational, lifesafe, near collapse, etc.!. This makes them promising foperformance-based seismic vulnerability assessment of existructures. For example, following an earthquake, rapidly geated contour maps of damage spectral ordinates at selectedods provide useful information on the spatial distribution of daage potential of recorded ground motions for specific typesstructures. Utilization of an up-to-date inventory of existing strtures enhances the reliability of the spatial distribution ofdamage spectra to identify damaged areas. The concept oproposed damage spectra is also promising for carryingperformance-based design of new structures.
Acknowledgments
This study was supported by the California Geological SurvStrong Motion Instrumentation Program, Contract No. 1099-7The support is gratefully acknowledged. The writers also wishthank Professor Mustafa Erdik for supplying the ground motrecords for the Du¨zce, Turkey, earthquake.
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